STRUCTURAL STUDIES OF GRAPHITE INTERCALATION COMPOUNDS AND
ION IMPLANTED GRAPHITE
by
LOURDES G. SALAMANCA-RIBA
B.S., Universidad Aut6noma Metropolitana, Mexico City
(1978)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
July, 1985
@Massachusetts Institute of Technology
Signature redacted
Signature of Author
Department of Physics, July, 1985
Signature redacted
Certified by
Mildred S. Dresselhaus, Thesis Supervisor
/Th
Signature redacted
Accepted by
Chairman, Department Committee on Graduate Students
SSACPEP
I,
ST1
19
OF- TEC11,%!0KGY
SEP 111985
1
Akrehives
STRUCTURAL STUDIES OF GRAPHITE INTERCALATION COMPOUNDS AND
ION IMPLANTED GRAPHITE
by
Lourdes G. Salamanca-Riba
Submitted to the Department of Physics on July 27, 1985, in
partial fulfillment of the requirements for the degree of
Doctor of Philosophy
ABSTRACT
Transmission electron microscopy is used to study the structure of graphite intercalation
compounds and ion implanted graphite at a microscopic level. Inhomogeneities in the
intercalate layer are observed for several acceptor compounds. The intercalation process
of KH.-GICs is studied for several intercalation temperatures and times. For the KH.GIC system, we have observed that the first step of intercalation is a stage n potassiumGIC and the final compound is a stage n KH,-GIC. We have observed regions at the
boundary between pure potassium regions and regions with high hydrogen content that
correspond to an intermediate phase in the intercalation process. The structure of the
commensurate (-f x V7)R19.1* phase of stage 2 SbCl 5-GICs is studied in detail using
computer image simulation and high resolution transmission electron microscopy. We
have found that the best fit to the experimental images is obtained for mixtures of
either SbCl- and SbCl 3 or SbCl6 and SbCl 5 molecular species in the commensurate
(v x f7)R19.1* phase. We have also studied the electron beam induced commensurate
to glass phase transition observed on SbCl 5-GICs and obtained activation energies for
the radiolysis process and the two recombination processes that oppose the radiolysis
process. A model for the commensurate to glass phase change is suggested assuming
that the (V7 x V7)R19.1* phase is formed by a mixture of SbCl6 and SbCl 3 molecular
species. We have obtained the contribution to the c-axis thermal expansion coefficient
associated with each distinct layer of the unit cell in the SbCl 5-GICs and have related
the charge transfer to the ratio of the thermal expansion of the pristine material to that
of the intercalate. The damage to the graphite lattice produced by ion implantation has
been studied as a function of ion mass and dose. The recrystallization process for postimplantation annealed graphite gives values for the activation energies for the regrowth
process. The defects produced by ion implantation have been characterized using the
transmission electron microscope and a model for the recrystallization process has been
suggested in terms of atomic diffurion and climb of dislocations.
Thesis Supervisor:
Title:
Mildred S. Dresselhaus
Abby Rockefeller Mauze Professor of Electrical Engineering
and Physics
2
Acknowledgements
I would like to acknowledge and express my gratitude to my thesis supervisor Professor Mildred S. Dresselhaus and to Dr. Gene Dresselhaus. Their guidance and support
was always there when needed.
I also would like to acknowledge Professor Robert Birgeneau and Dr. Murray Gibson
for their collaboration in many of the topics discussed in this work and careful reading of
this manuscript. I particularly would like to thank Professor Birgeneau for suggesting a
careful study on the influence of the electron beam on the observed glass phase. Special
thanks are in order for Dr. J.M. Gibson for his collaboration on most of the projects
involving electron microscopy presented in this manuscript and especially for allowing
me to use his electron microscope and laboratory facilities at AT&T Bell Laboratories.
His expertise and knowledge of electron microscopy greatly enhanced the outcome of my
work.
I would like to acknowledge Conacyt for the monetary support they gave during my
first years at MIT.
I wish to express my thanks to the people from the Department of Physics of Interfaces at AT&T Bell Laboratories for their hospitality especially, Dr. John Poate, Mr.
Michael McDonald and Ms. Henrietta Weston. Mike McDonald took especial care to
insure that all the equipment in the laboratory was working well and that the necessary
supplies were there. His help in setting up the different stages for the microscope is very
much appreciated.
I wish to express my gratitude to Professors M. Endo and L. Hobbs for useful discussions on electron inicroscopy. Professor Endo not only collaborated on the projects
related to Endo fibers but he also provided the fibers used in this work. I enjoyed greatly
working with Professor Endo during his visits to MIT and appreciated his invitation to
visit his laboratory in Shinshu University. I want to thank Professor Linn Hobbs for
helpful discussions on several topics such as radiation damage in electron microscopy.
I want to acknowledge Paul, Eliot and Carl Dresselhaus for their help in using the
computer. I specially recognize Eliot for writing the program used to print the TEM
simulated images.
I want to thank John Mara for interesting conversations and for his artistic and
professional drawings that were used in this manuscript.
I enjoyed working with former and present members of the Dresselhaus group. It
was gratifying to work late and long hours with Greg Timp (using the microscope)
and Mansour Shayegan (at the National Magnet Lab.). I enjoyed the discussions and
friendship of Boris Elman, Radi Al-Jishi, Bernard Wasserman, Estelle Kunoff and Alla
Antonius. The insight that Estelle and Alla gave me is greately appreciated.
I benefitted from collaborations with Nai-Chang Yeh and Dr. Toshiaki Enoki and
consultations with Shyng-Tsong Chen, Hiroshi (and Mika) Menjo and Phyllis Cormier.
There are other former and present members of the group that need to be acknowledged for their useful suggestions and discussions on different topics. Among them are:
Trieu Chieu, Claudio Nicolini, Gabriel Braunstein, Alison Chaiken, John Steinbeck, Jim
Speck, Ko Sugihara and Masanori Sakamoto.
My late (very) night sessions at MIT would not have been possible without the aid
3
of the MIT campus police who provided safe passage for me between the lab and Tang
Hall.
I would like to acknowledge my very special friend Carl Young (Carlinsky) for his
constant understanding and caring. His good sense of humor and optimism were the
'salt and pepper' of my last years at MIT. I would like to acknowledge Carl's family also
for their support and friendship.
Most important of all, I would like to thank my family for the encouragement and
advice they have always given me for which distance does not matter. The support they
gave me during my studies at MIT was invaluable.
4
Contents
13
1 INTRODUCTION
2
18
....
References (chapter 1) .........................
SYNTHESIS AND CHARACTERIZATION OF GICs
22
22
...................................
2.1
Introduction.
2.2
Sample Preparation. ...............................
24
2.3
Sample Characterization .
27
2.4
Stoichiometry Determination Using Rutherford Backscattering Spectrometry . ...
56
. . . ...................... ........
......
68
References (chapter 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
.
Conclusions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
2.5
...........................
3
HIGH RESOLUTION TRANSMISSION ELECTRON MICROSCOPY
72
ON KH-GICs
4
72
...................................
3.1
Introduction.
3.2
Experimental Details .
3.3
Results and Discussion .
3.4
Intercalation by the Chemical Absorption of Hydrogen into C 8 K ......
106
References (chapter 3) .............................
[10
.............................
.....
............................
.....
COMPUTER IMAGE SIMULATION OF SbCl 5-GICs
...................................
..
4.1
Introduction. .....
4.2
Computer Image Simulation.
4.3
Experimental Details .
4.4
Molecular Models for the (71/ 2X7 1/ 2 )R19.1' Phase. ................
.........................
.............................
......
5
86
87
113
113
115
119
121
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.5
Results and Discussion.
4.6
Conclusions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
References (.hapter 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5 NOVEL LOW TEMPERATURE CRYSTALLINE TO GLASS PHASE
154
CHANGE
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.2
Experimental Details ..............................
156
5.3
X-Ray Results. .........................................
156
5.4
TEM Results. ..........................................
158
5.5
Model for The Radiolysis Process .
5.6
Suggestions for Future Work. ......
168
......................
.....
170
..........................
171
References (chapter 5) .............................
6
173
THERMAL EXPANSION COEFFICIENT OF SbCl 5-GICs
....
..
...
...
........
..
..
...
..
...
. . 173
6.1
Introduction.
6.2
Experimental Details. .
6.3
Results. .......
6.4
Thermal Expansion Coefficient.........................
182
References (chapter 6) .............................
188
174
..............................
175
.......................................
190
7 ION IMPLANTED GRAPHITE
. ..
...
..
. ..
. ..
. . . . . . . . . . . . ..
. 190
7.1
Introduction... ...
7.2
Ion Implantation Conditions ..........................
193
7.3
TEM Observation of Ion Implanted Graphite ....................
194
7.4
Damage of Ion Implanted Graphite . . . . . . . . . . . . . . . . . . . . . . 198
7.5
Recrystallization Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.6
Characterization of Defects. . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7.7
Suggestions for Future Work.
. . . . . . . . . . . . . . . . . . . . . . . . . 226
References (chapter 7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
8
233
SUMMARY
References (chapter 8) ..
. . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6
.. ... 54
List of Figures
Schematic representations of the apparatus used to synthesize a) SbCl 5
-
2.1
GICs and b) FeC! 3 - and CuCI2 -GICs. . . . . . . . . . . . . . . . . . . . .
2.2
(00t) x-ray diffractograms from a) n=1, b) n=2, c) n=3, d) n=4 and e)
n=6 SbCl 5-GICs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
High resolution c-axis lattice image of an SbC15-HOPG sample showing
a single stage region (n=2). . . . . . . . . . . . . . . . . . . . . . . . . . .
40
. . . .
43
2.7
(hko) electron diffraction patterns of a stage 2 SbCl 5-GIC sample.
2.8
Dark field and in-plane lattice images of SbCl 5-GIC samples showing
2.9
31
Fourier synthesis along the c-axis obtained from (00t) integrated intensities for stages 1, 2, 4 and 6 SbCl 5-GICs. . . . . . . . . . . . . ... . . . . . .
2.6
30
c-axis lattice images of BDGF intercalated with CuCl 2 and SbC 5 showing
stage infidelities.
2.5
29
(00t) x-ray diffractograms of a) a stage 2 FeCl 3-GIC sample and b) a
stage 2 CuCl 2-GIC sample. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4
25
inhomogeneities in the structure of the intercalate layer. . . . . . . . . . .
46
. . . . . . . . . . . . . .
48
. . . . . . .
51
(hko) electron diffraction pattern of FeCl 3-GICs.
2.10 Bright and dark field images of a stage 2 FeCl 3-GIC sample.
2.11 (hk0) diffraction patterns and dark field image of a stage 2 CuCl 2-GIC
sample.
. . . . . . . . . . . . . . . . . . . . . . . . . . ..
. .
2.12 Typical RBS spectrum of a cleaved stage 3 SbCl 5-GIC sample. The inset
. . . . . . . . . . . . . . . . . . . . . .
58
2.13 Cl to Sb ratio vs. intercalation time from RBS results. . . . . . . . . . . .
62
. . . . . . . . . . . . . . .
63
shows the experimental geometry.
2.14 RBS spectra of a stage 3 KHg-GIC sample. .*.
7
2.15 Typical RBS spectra of stage 2 FeCl 3- and CuCl 2-GIC samples.
. . . . .
65
2.16 Examples of abnormal RBS spectra from as-prepared SbCl 5-GIC samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
67
Schematic representation of a ray diagram for a transmission electron
microscope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.2
Out of focus image Ti(x, y) of an object with transfer function T(x,y). . .
77
3.3
Transfer function for a 100 kV electron microscope. . . . . . . . . . . . . .
79
3.4
Imaging methods for simple lattice fringes . . . . . . . . . . . . . . . . . .
81
3.5
Impulse response function for a 100 kV electron microscope. . . . . . . . .
84
3.6
(00t) x-ray diffractograms of a sample intercalated with KH at 200*C
. . . . . . . . . . . . . . . . . . . . . .
showing the intercalation process.
3.7
c-axis lattice image of a stage 1 KH-GIC sample intercalated into HOPG
c-axis lattice image of a stage 2 (C 2 4 K)(CsKH) sample prepared by direct
intercalation with KH at 210 0 C.
3.9
90
....................................
at 430*C. ..............
3.8
89
. . . . . . . . . . . . . . . . . . . . . . .
93
c-axis lattice image of a stage 1 sample of (CsK)(C 4 KH) prepared by the
direct intercalation of KH at 2900C.
. . . . . . . . . . . . . . . . . . . . .
95
3.10 (hk0) electron diffraction patterns of HOPG intercalated with KH at: a)
.............................
290*C, and b) 4300C. ...........
.. 98
3.11 Dark field images of the same region of a sample intercalated with KH at
4300C using the direct intercalation process. . . . . . . . . . . . . . . . . . 101
3.12 In-plane lattice image of a stage 1 KD-GIC sample showing the (2 x 2)RO*
commensurate phase.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.13 Model for the atomic arrangement of C8 KH 2/ 3 based on neutron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.14 c-axis lattice fringes of a stage 2 intercalated fiber prepared by chemical
absorption of hydrogen into a stage 1 C 8 K.
4.1
. . . . . . . . . . . . . . . . . 107
Schematic representation of the slicing of the specimen for the image simulation computing method.
. . . . . . . . . . . . . . . . . . . . . . . . . . 117
8
Schematic representation of the slicing of the unit cell of a stage 2 SbCl 5
-
4.2
GIC sample using the multi-slice method. . . . . . . . . . . . . . . . . . . 120
4.3
Model 1 for the SbCl6 molecular species in the commensurate (71/ 2 X71/ 2 )R19.1*
phase.
.........
122
.....................................
4.4
Model 2 for the SbCl- molecular species in the (7 1/ 2 X7 1/ 2 )R19.1* phase. . 122
4.5
Model 1 for a mixture of SbCl6 and .SbCl 3 molecular species in the
(7 1/ 2 X7 1/ 2 )R19.1* phase.
4.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Model 2 for a mixture of SbCl6 and SbCI 3 molecules in the (7 1/ 2 X7 1/ 2 )R19.10
phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.7
Model for the SbCl 3 molecular species at the (71/ 2 X71/ 2 )R19.10 lattice.
4.8
High resolution lattice image of a stage 2 SbCl 5-GIC sample showing the
(71/2X7 1/ 2 )R19.10 in-plane structure.
4.9
.
126
. . . . . . . . . . . . . . . . . . . . 127
In-plane simulated images for the mixture of SbCl6 and SbCl 3 molecules
and experimental TEM images. . . . . . . . . . . . . . . . . . . . . . . . .. 129
4.10 In-plane simulated images for SbCl 5 and a mixture of SbCl 5 and SbCl6
molecular species and experimental TEM images . .
.
. . . . . . . . . . . 131
4.11 In-plane simulated images for SbCl6 and experimental TEM images.
. .
.
136
4.12 In-plane lattice images from the same region but different electron beam
doses.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.13 In-plane fringes of a stage 2 SbCl 5 -GIC sample showing a periodicity of
twice that of the (7 1/ 2 X7 1/ 2)R19.1* phase. . . . . . . . . . . . . . . . . . . 142
4.14 Projected potential along the (100) direction for the model consisting of
a mixture of SbCl6 and SbCl 5 molecular species. . . . . . . . . . . . . . . 145
4.15 (00t) simulated and experimental lattice images.
. . . . . . . . . . . . . . 146
4.16 Depth dependence of the intensity and phase for several (00t) beams.
5.1
..................................
148
157
Room temperature electron diffraction patterns of SbCl 5-GICs showing
the (7 1/ 2 X7 1 /2 )R19.1* phase only.
5.3
.
X-ray spectra of SbC1 5-intercalated vermicular graphite obtained at 295
K and at 16 K........
5.2
.
. . . . . . . . . . . . . . . . . . . . . . 159
(hk0) electron diffraction patterns of a mixed stage (2 and 3) vermicular
9
graphite sample intercalated with SbCI 5
5.4
Normalized dependence of R on electron beam dose for several temperatures, for 80 and 200 keV electrons.
5.5
. . . . . . . . . . . . . . . . . . . 161
. . . . . . . . . . . . . . . . . . . . . 164
Temperature dependence of the critical electron dose (0,) for the C-G
transition in SbCl 5-GIC for 200 and 80 keV electrons.
. . . . . . . . . . 166
5.6
Model for the radiolysis mechanism in SbCl 5-GICs . . . . . . . . . . . . . 169
6.1
(00f) x-ray diffractograms of stage 1 graphite-SbCl 5 at 295 K and at 20 K.176
6.2
a) Temperature dependence of the c-axis repeat distance Ic and b)
for a stage 1 SbCl 5 sample.
6.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Charge density along the c-axis for a stage 1 SbCl 5-GIC sample taken at
20 K .
6.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Temperature dependence of the Bragg angles 2E3 and 2e9 for a stage 2
graphite-SbCl 5 sample.
6.5
. . . . . . . . . . . . . . . . . . . . . . . . . . 177
Temperature dependence of the Bragg angles 28 7 and 288 for a stage 1
graphite-SbCl5 sample.
6.4
AIc/Ic vs. AT
. . .. . . ...
. . . ...
. . . . .
. . . . . . . . . . . . ..
. . . . . . . 180
Temperature dependence of the interplanar spacings dsb-cl and dcl-cb
for a stage 1 graphite-SbCl 5 sample. . . . . . . . . . . . . . . . . . . . . . 181
6.7
Schematic representation of the positions of the Sb and Cl ions in the
graphite ir orbitals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.1
Schematic representation of the ion beam for ion implantation and the
electron beam for TEM observation. . . . . . . . . . . . . . . . . . . . . . 194
7.2
Schematic representation of the electron beam direction and TEM observations for fibers and HOPG. . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.3
Schematic for the projection of defects in two-dimensions and the geometry used to investigate the method used to correct for projection effect. . 197
7.4
(002) bright field images of an unimplanted fiber and fibers implanted to
several doses. ..........
7.5
Dark field images of an unimplanted fiber and implanted fibers with
and
20 9
Bi ion species.
199
..................................
75
As
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10
7.6
(002) lattice image of an implanted graphite fiber and (hko) electron
diffraction patterns of an HOPG implanted and an unimplanted samples.
7.7
204
Dependence of the in-plane crystallite size La (measured from (002) lattice
images) on ion mass for several fluences shown on a log-log plot. . . . . . 206
7.8
Bright field (002) lattice image of a fiber post-implantation annealed at
1500 0 C. ........
7.9
209
.....................................
Arrhenius plot of in-plane (La) and c-axis (L,) crystallite sizes of postimplantation annealed fibers.
. . . . . . . . . . . . . . . . . . . . . . . . . 212
7.10 Lattice image and (hk0) electron diffraction pattern of an HOPG sample
annealed at 1500 0 C for 20 min after implantation.
. . . . . . . . . . . . . 213
7.11 Lattice image of an HOPG sample annealed at 2300 0 C for 20 min after
implantation with
20 9
Bi to 1 x 10 5 ions/cm 2 . . . . . . . . . . . . . . . . . 216
7.12 (hk0) electron diffraction patterns of as-implanted and post-implantation
annealed HOPG samples.
. . . . . . . . . . . . . . . . . . . . . . . . . . . 218
7.13 Arrhenius plot of in-plane (La) and c-axis (Lcr) crystallite sizes for postimplantation annealed HOPG samples . . . . . . . . . . . . . . . . . . . . 220
7.14 In-plane (La) and c-axis (Lc) crystallite sizes vs. annealing time ta for
post-implantation. annealed HOPG samples.
. . . . . . . . . . . . . . . . 221
7.15 (100) dark field image of an HOPG sample post-implantation annealed
at 2700'C for 20 min. showing stacking faults and dislocations. . . . . . . 227
11
List of Tables
2.1
Sample preparation conditions and c-axis repeat distances I, for stages
1-4 and 6 SbCl 5-GICs.
2.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample preparation conditions and c-axis repeat distances I, used to synthesize FeCl 3 - and CuCl 2-GICs.
2.3
. . . . . . . . . . . . . . . . . . . . . . .
. . . .
. . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . 186
Ion penetration depth RP and ion spread ARP calculated from the LSS
T heory.
7.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Thermal expansion coefficients for the different layers for several stages of
SbCl 5-GICs.
7.1
. . . . . . . . . . . . . . . . . . . . . . 133
Thermal expansion coefficients and charge transfer estimates for several
metallic graphitides.
6.2
37
Stacking sequences for the (7 1/ 2 X7 1/ 2 )R19.1* phase in stage 2 SbCl 5 -GICs
used in the multi-slice calculation.
6.1
37
Summary of the measured stoichiometries for GICs obtained from analysis
of the (00e) x-ray diffractograms and of the RBS spectra . . . . . . . . ...
4.1
27
Interplanar spacings for several stages of SbCl5 -GICs obtained from analysis of the (00t) x-ray diffractograms using the RFINE4 program.
2.4
26
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Interplanar distance c/2 vs. ion mass obtained from optical diffractograms
taken from the negatives of the (002) lattice images of ion implanted
BD G F .
7.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Dark field conditions for the observation of dislocation and stacking fault
contrast for graphite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
12
Chapter 1
INTRODUCTION
The study of the structure of a material provides unique information for the understanding and hence the control of its physical properties. Several experimental techniques
can be used to study the structure of materials, such as x-ray diffraction, Raman scattering, neutron diffraction and electron microscopy. In particular, transmission electron
microscopy TEM is a very powerful tool for obtaining information about the structure at
a microscopic level which cannot be obtained by other techniques. The TEM technique
is particularly powerful if this technique is applied in combination with one or more
techniques that provide information about the structure of the bulk.
Graphite is a highly anisotropic material with a hexagonal layered structure. This
anisotropy is reflected in its physical properties. Intercalation [1] and ion implantation
[2] are means for modifying the structure and properties of graphite.
Both processes
yield anisotropic materials with a large variety of interesting physical properties.
Graphite intercalation compounds (GICs) are formed by the insertion of layers of
foreign species between the graphite layers. In these compounds two neighboring intercalate layers are separated by n graphite layers where n is called the stage index. Along
the c-axis, both the intercalate and the graphite can have different stacking sequences.
The properties of the intercalated compound depend on the nature of the intercalant
and in some cases on the stage.[1] GICs are divided into two groups: donors and
ac-
ceptors depending on whether the intercalate layer donates or accepts charge from the
graphite layers. Both donor and acceptor intercalants can form in-plane superlattices
that often are commensurate with the graphite lattice. Many of these intercalants are of
13
interest because their corresponding GICs undergo unusual structural phase transitions
such as commensurate-incommensurate and -melting phase transitions.[1] In this work,
an unusual commensurate-glass phase change induced on SbCl 5 -GICs by electron beam
irradiation is studied using the TEM. The glass phase is the result of damage to the intercalate layers induced by electron beam irradiation. In this process, the graphite layers
remain crystalline. Damage to the graphite lattice can be produced by ion implantation.
Ion implantation is the insertion of foreign species into a material by the bombardment of ions of a certain mass and energy.[2] The advantage of ion implantation over
intercalation is that almost any element of the periodic table can be ion implanted into
graphite and further, the concentration and penetration of the ions can be controlled
independently. Ion implantation has extensively been used for doping semiconductors. [2]
There has been also a very extensive study of the structural [3,4,5,6,7] and electronic
[8] properties of ion implanted graphite.[9,10] In the ion implantation process, the ions
undergo elastic as well as inelastic collisions with the atoms of the substrate. As they
travel through the specimen, they lose kinetic energy and finally come to rest at a certain
depth which depends on their mass, initial energy and mass of the target. The Lindhard,
Scharff and Schiott (LSS) theory, predicts a Gaussian distribution of the implanted ions
with depth.[11] Thus, ion implantation introduces damage to the graphite lattice which
depends on the ion mass and dose. Therefore ion implantation introduces a controllable
amount of damage. In the study of defects induced by ion implantation, the TEM technique is particularly useful since only a small fraction of the sample close to the surface
is modified by ion implantation.
Therefore, techniques used to study the bulk of the
sample often are not sensitive to the effects of ion implantation.
In this work, we applied the techniques of x-ray diffraction and high resolution transmission electron microscopy and electron diffraction to study the structure and structural
changes of several acceptor compounds such as SbCl 5-,
FeCl 3- and CuCl 2-GICs, and
of the donor [12], KHx-GIC. The intercalants SbCl 5 and KHx form commensurate superlattices whereas FeCl 3 and CuCl 2 form incommensurate structures.
The method
used to synthesize the compound depends on both the intercalant and the host material.[1,13,14,15,16,17] The host materials most commonly used are highly oriented pyrolytic graphite (HOPG), kish and natural Ticonderoga single crystals and graphite
14
fibers. Among the fibers, those with the highest degree of structural order are the benzene derived graphite fibers (BDGF).[18,19,20,21,22]
In this work we used HOPG, kish
single crystal graphite and BDGF as host materials for both the intercalation and ion implantation studies. The methods used to synthesize the intercalation compounds studied
in this work as well as the techniques used to characterize them are presented in chapter 2. Several techniques were used to characterize the intercalated compounds. (00t)
x-ray diffraction was used to characterize the bulk samples for stage index and stage
fidelity, while TEM was used to study the in-plane structure and c-axis structure at a
microscopic level and Rutherford backscattering spectrometry was used to obtain the
stoichiometry of the compounds. The values for the stoichiometry of the GICs obtained
from analysis of the RBS spectra are compared with those obtained from analysis of the
(00f) x-ray diffractograms.
Special attention was given to study the structure of the two commensurate intercalants SbCl 5 and KH. The two most commonly observed commensurate phases in
the SbCl 5 -GICs are the (v
phase.[23,24,25,26,27,28,29]
x vf)R19.1* and the (V3 x V/3)R16.1* commensurate
KH, on the other hand, forms a (2 x 2)RO* [30,31] and a
(v'3 x V/3-)R30* [30] commensurate in-plane phases. Using the TEM a single phase can
be studied in these intercalated compounds. In this work, the structure of KH.-GICs
was studied as a function of intercalation temperature and time. The TEM results on
this system gave information about the intercalation process which was found to start
with the intercalation of stage n potassium to achieve a final compound of a stage n
KH.-GIC.[32] The results of this study are presented in chapter 3.
In the study of the structure of crystalline materials using the TEM, it is necessary to
perform a computational analysis of the images obtained experimentally. In this work,
the in-plane and c-axis structures of the (vF x Vr)R19.1* phase in stage 2 SbCl 5 -GICs
were studied by directly imaging the lattice using the TEM and by computer image
simulation.[33] The image simulation was carried out for several models consisting of
diffrrent molecular species in the commensurate
(vf
x v/f)R19.1* phase and for several
stacking sequences of both the graphite and the intercalate. The computed images were
obtained using the multi-slice method.[33] This method was applied by dividing the superlattice unit cell into several slices and using a Fast Fourier Transform algorithm.[34]
15
The simulated images were then compared with the TEM images obtained experimen1
tally. The results from this study suggest two possible models for the (v/ x \/7)R19.1*
phase. These models consist of a mixture of either SbCl6 and SbCl 3 or SbCl6 and SbCl 5
molecular species. The results for the analysis of the simulated images obtained for these
and other models are presented in chapter 4.
During the TEM observation, electron beam induced damage to the intercalate layers
is observed for the SbCl 5 -GICs.
while the commensurate
(-V
In this process the graphite layers remain crystalline
x V'-)R19.1* phase undergoes a change to a glass phase.
This effect is studied as a function of electron dose and sample temperature for different electron beam energies. The results are presented in chapter 5, showing that the
commensurate-to-glass phase change is due to atomic displacements induced by the
electron beam via the creation of an excited state.[26] In this process called radiolysis,
the energy of the excited state is transformed into kinetic energy which can be sufficient
to overcome the binding energy of the atom (molecule).[351
Several phase transitions have been observed in SbCl 5-GICs using different experimental techniques, such as transmission electron microscopy [23,24,261, x-ray diffraction
[27,28,29], specific heat [36] and ultra sound measurements
[37].
The structural phase
transitions observed in the SbCl 5-GIC system, [23,24,26,27,28,291 correspond to a change
of the in-plane structure. The linear thermal expansion coefficient measures the change
of one of the crystal dimensions with temperature, and therefore is a measure of structural phase transitions. In chapter 6 we present studies of the c-axis thermal expansion
coefficient of the SbCl 5-GIC system at low temperatures.
Our results for the c-axis
thermal expansion coefficient of SbCl 5-GICs do not show any indication of a phase transition along the c-axis at low temperatures.
We infer from the total c-axis thermal
expansion coefficient that of every distinct layer in the intercalate sandwich. Our results
show a change in the thermal expansion coefficient of the intercalate with respect to that
of pristine SbCl 5 . This change is associated with the charge transfer from the graphite
layers. Thus, from our
experimental results for the thermal expansion coefficient along
the c-axis, a value for the charge transfer in SbCI 5-GICs is inferred.
Ion implantation produces damage to the graphite lattice.
This lattice damage is
greater for heavy ions and high'doses than for light ions and low doses. The dependence
16
of the lattice damage induced by ion implantation on ion mass and dose is studied using
the TEM and the results are presented in chapter 7. This chapter also presents results
for recrystallization studies as a function of annealing temperature and time, from which
activation energies for the regrowth process are obtained. The defects produced by ion
implantation are characterized using the TEM and a model for the recrystallization
process is suggested based on this study.
Chapter 8 presents the summary and conclusions of this work.
17
References
[1] For an extensive review see M.S. Dresselhaus and G. Dresselhaus, Adv. in Physics
,
30, 139 (1981).
[2] J.W. Mayer, L. Eriksson and J. Davies, Ion Implantation in Semiconductors, Academic Press, NY, 1970.
[3] B.S. Elman, G. Braunstein, M.S. Dresselhaus, G.Dresselhaus, T. Venkatesan and
J.M. Gibson, Phys. Rev. B29, 4703 (1984).
[4] G. Braunstein, B.S. Elman, M.S. Dresselhaus, G.Dresselhaus and T. Venkatesan,
MRS Symposium on Ion Implantation and Ion Beam Processing of Materials, ed.
G.K. Hubler, O.W. Holland, C.R. Clayton, and C.W. White, Boston, Nov.. 1983
(Elsevier, North Holland, NY, 1984), vol. 27, p. 475.
[5] T.C. Chieu, B.S. Elman, L. Salamanca-Riba, M. Endo and G. Dresselhaus, MRS
Symposium on Ion Implantation and Ion Beam Processing of Materials, edited by
G.K. Hubler, O.W. Holland, C.R. Clayton and C.W. White Boston, Nov.
1983
(Elsevier, North Holland, New York, 1984), Vol. 27, p. 487.
[6] M. Endo, L. Salamanca-Riba, G. Dresselhaus and J.M. Gibson, Journal de Chimie
Physique 81, 804 (1984).
[7] L. Salamanca-Riba, G. Braunstein, M.S. Dresselhaus, J.M. Gibson and M. Endo,
Nuclear Instruments and Methods in Physics Research B7/8, 487 (1985).
[8] L.E. McNeil, B.S. Elman, M.S. Dresselhaus, G. Dresselhaus and T. Venkatesan,
MRS Symposium on Ion Implanatation and Ion Beam Processing of Materials, ed.
18
G.K. Hubler, O.W. Holland, C.R. Clayton, and C.W. White, Boston, Nov. 1983
(Elsevier, North Holland, NY, 1984), vol. 27, p. 493.
[9] B.S. Elman, Ph.D. Thesis, Massachusetts Institute of Technology, 1983.
[10] B.S. Elman, M. Shayegan, M.S. Dresselhaus, H. Mazurek and G. Dresselhaus, Phys.
Rev. B25, 4142 (1982).
[11] J. Lindhard, M. Scharff and H.E. Schiott, Dan. Vidensk. Selsk., Mat. Fys. Medd.
3,
14 (1963).
[12] N.-C. Yeh, T. Enoki, L.E. McNeil, G. Roth, L. Salamanca-Riba, M. Endo and
G. Dresselhaus, (MRS Extended Abstracts, Graphite Intercalation Compounds , ed.
P.C Eklund, M.S. Dresselhaus and G. Dresselhaus, Boston 1984), p. 246.
[13] A. Herold, Phys. and Chem. of Materials with Layered Structures, 6, ed. F. Levy,
(Reidel, Dordrecht, Holland, 1979), 323.
[14] M. Colin and A. H6rold, Bull. Soc. Chim. Fr. 1971 (1982).
[15] V.R. Murthy, D.S. Smith and P.C. Eklund, Mat. Sci. Eng. 45, 77 (1980).
[16] J. Melin, Sc.D. Thesis, Universit6 de Nancy I, France (1976).
[17] M. El Makrini, P. Lagrange, D. Guerard and A. Herold, Carbon 18, 211 (1980).
[18] T. Koyama, Carbon 10, 757 (1972).
[19] T. Koyama, M. Endo and Y. Onuma, Jpn. J. Appl. Phys. 11, 445 (1972).
[20] M. Endo, A. Oberlin and T. Koyama, Jpn. J. Appl. Phys. 16, 1519 (1977).
[21] M. Endo, K. Komaki and T. Koyama, Int. Symp. on Carbon, (Toyohashi, 1982),
p. 515.
[22] M. Endo, T.C. Chieu, G. Timp, M.S. Dresselhaus and B.S. Elman, Phys. Rev.
B28, 6982 (1983).
[23] G. Timp, M.S. Dresselhaus, L. Salamanca-Riba, A. Erbil, L.W. Hobbs, G. Dresselhaus, P.C. Eklund and Y. Iye, Phys. Rev. B26, 2323 (1982).
19
[24] M. Suzuki, R. Inada, H. Ikeda, S. Tanuma, K. Suzuki and M. Ichihara, Graphite Intercalation Compounds, edited by Sei-ichi Tanuma and Hiroshi Kamimura, (1984),
p. 57.
[25] L. Salamanca-Riba, G. Timp, L.W. Hobbs, and M.S. Dresselhaus, Mat. Res. Soc.
Symp. Proc. 20, 9 (1983).
[26] L. Salamanca-Riba, G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus and R.J.
Birgeneau, to be published.
[27] R. Clarke and H. Homma, Mat. Res. Soc. Symp. Proc. 20, 3 (1983).
[28] R. Clarke, M. Elzinga, J.N. Gray, H. Homma, D.T. Morelli, M.J. Winokur and C.
Uher, Phys. Rev. B26, 5250 (1982).
[29] H. Homma and R. Clarke, Phys. Rev. B31, 5865 (1985).
[30] L. Salamanca-Riba, N.-C. Yeh, T. Enoki, M.S. Dresselhaus and M. Endo, (MRS
Extended Abstracts, Graphite Intercalation Compounds , ed.
P.C Eklund, M.S.
Dresselhaus and G. Dresselhaus, Boston 1984), p. 249.
[31] T. Trewern, R.K. Thomas and J.W. White, J. Chem. Soc., Faraday Trans. I., 78,
2399 (1982).
[32] N.-C. Yeh, T. Enoki, L. Salamanca-Riba and G. Dresselhaus, Proc. of the
1 7 th
Biennial Conf. on Carbon, Lexington, June 1985, p. 194.
[33] J.M. Cowley and A.F. Moodie, Acta Cryst. 10, 609 (1957); J.M. Cowley and A.F.
Moodie, Proc. Roy. Soc., 71, (London), 533 (1958); J.M. Cowley and A.F. Moodie,
Acta Cryst.
12, 353 (1959); J.M. Cowley and A.F. Moodie, Acta Cryst. 12, 360
(1959).
[34] J.W. Cooley and J.W. Tukey, Math Compt. 19, 297 (1965).
[35] L.W. Hobbs, Quantitative Electron Microscopy, Proc. of the
2 5 th
Scottish Univer-
sity Summer School in Physics, Glasgow Aug. 1983, ed. J.N. Chapman, and A.J.
Craven, SUSSP Publications, Edinburg, (1983), p. 399, and references therein.
20
[361 D.N. Bittner and M. Bretz, Phys. Rev. B31, 1060 (1985).
[37] D.M. Hwang and G. Nicolaides, Solid State Comm. 49, 483 (1984).
21
Chapter 2
SYNTHESIS AND
CHARACTERIZATION OF
GICs
In this chapter we report the methods used to synthesize the GIC samples studied
in this thesis. Section 2.1 contains the introduction to the chapter. Sections 2.2 and 2.3
present a discussion of the sample preparation and characterization, respectively. The
stoichiometry determination using Rutherford backscattering spectrometry is given.in
section 2.4 and the conclusions to the chapter are given in section 2.5.
2.1
Introduction.
More than 100 chemical species can be intercalated into graphite. There are monoatomic
intercalants, such as the alkali-metals (Li, K, Rb, and Cs), and molecular intercalants
such as the metal chlorides (CoCl 2 , CuCl 2 , FeCl 3 and SbCl 5 ) and potassium alloys (KH,
KD and KHg).
The properties of the intercalated compound depend on those of the
parent intercalant.[1] Therefore, intercalation provides a controlled means of changing
the physical and chemical properties of graphite over a wide range.
The method used to synthesize the compound depends on the nature of the intercalant. Parameters such as the temperature of both the intercalant and the graphite,
the pressure, the graphite sample size and the kind of host material are critical for determining the reaction rate and the stage index n (number of graphite planes between two
adjacent intercalate layers). In this chapter we report the methods used to intercalate
22
and characterize several graphite intercalation compounds.
In the study of the properties of GICs it is very important to know the crystal structure and the stoichiometry. The techniques most commonly used to characterize GICs
are: x-ray diffraction, electron diffraction, weight uptake, Raman scattering and chemical analysis. In this chapter we report the use of Rutherford backscattering spectrometry
as a complementary non-destructive technique for the characterization of GICs.
After intercalation, all the samples based on HOPG and kish single crystal graphite
were characterized for stage index using (00f) x-ray diffraction.
Some of the interca-
lated HOPG and intercalated kish single crystal graphite samples were characterized
for both stage index and in-plane structure using a high resolution transmission electron microscope (TEM). The fiber host samples were characterized for stage index using
the TEM. The air stable samples were also characterized by weight uptake. An extensive study of the in-plane structures of SbCl 5 - and KH.-GICs was carried out using
(hk0) electron diffraction patterns and high resolution transmission electron microscopy
(TEM). The results of this study are described in more detail in chapters 3 and 4 of
this thesis. Whereas x-ray diffraction gives information about the structure of the bulk,
TEM provides information about the structure at a microscopic level
(<
100 - 1000
A).
Consequently, both techniques provide complementary information about the structure
of materials.
RBS is a very useful non-destructive technique for studying the stoichiometry of
multi-elemental and layered compounds.[2] Intercalant stoichiometry is a key issue for
the determination of the structural phases and phase transitions of importance for
GICs. The RBS technique yields information averaged over an area corresponding to
the ~ 1 mm diameter of the 4 He ion beam. Analysis of the energy distribution of the
backscattered ions provides information about the stoichiometric dependence on depth
from the near-surface region
(~
1 ym) of the sample; this information is not yet available
using other non-destructive techniques. In this chapter, we compare on the same samples the results obtained from RBS with those obtained from analysis of the (00t) x-ray
diffraction peaks to determine the stoichiometry of GICs. We used the RBS technique to
study the lateral and depth homogeneity of the stoichiometry of GICs. The application
of the RBS technique was made to acceptor and donor intercalants, commensurate and
23
incommensurate compounds, and stable and non air-stable samples.
2.2
Sample Preparation.
In this work we used highly oriented pyrolytic graphite (HOPG), kish single crystal
graphite and benzene derived graphite fibers (BDGF) as host materials. The intercalation conditions are sometimes different for the different host materials.
Generally,
higher temperatures or smaller temperature gradients and longer times are required to
intercalate the fiber host.
The graphite fibers used for this study were derived by pyrolyzing a mixture of
benzene and hydrogen at a temperature of 1100*C.[3,4,5,6] The fibers were subsequently
heat treated in a constant flow of argon gas to either 2900'C for 1 hr or 3500*C for 30
min.
Samples of various stages (n=2, 3, 4 and 6) of SbCl 5-GICs were prepared using the
two zone method previously described [7]. The stage 1 samples and some of the stage
2 and stage 3 samples were prepared by placing the graphite in direct contact with the
SbCl 5 liquid.
Figure 2.1a) shows the schematic of the preparation chamber used for
the intercalation of SbCl 5 . The liquid SbCl 5 was transferred from the bottle inside a
glove box into a sealed glass tube through a teflon valve.
The valve was then closed
and the glass tube containing the SbCl 5 liquid (A in Fig. 2.1a)) was brought to the
preparation chamber. When the two zone method was used, the graphite was placed at
the top end of the long tube (B in Fig. 2.1a)). This tube had a neck that prevented
the graphite sample from falling to the bottom of the tube. When the direct contact
method was used, the graphite samples were placed at the bottom of the long tube (C
in Fig. 2.1a)). In either case, prior to the distillation of the SbCl 5 liquid, the graphite
was heat treated under vacuum (valve D in Fig. 2.1a) open) to ~ 400'C for 4 hr. to
remove surface impurities such as water vapor. Then the valve to the pump was closed
and some SbCl 5 liquid was distilled twice by placing liquid nitrogen first around the
tube-labeled E, and then around the tube labeled C in Fig. 2.la). Finally, the ampoule
was sealed at point F under vacuum, and was placed in a two zone furnace at different
temperatures depending on the desired stage. Table 2.1 summarizes the conditions used
24
to obtain the different stages. Stages 2 and 3 were obtained for the fiber host using the
same intercalation temperatures as for HOPG but longer intercalation times. For the
SbC
5
samples, the intercalation time was varied from 25 hrs. to 340 hrs for the HOPG
and kish single crystal host materials and from 192 hrs. to 300 hrs. for the fiber host.
Bil
te flon
valves
to L-N 2
trapped
forepump
0.8 cm I.D.+
35 cm
D
F
0-ring
E
seals
teflon
A
valve
C
a)
-
I
P SbCl 5
intercalant
graphite
E-
to L-N 2
trapped
forepump
C2 2 gas
dehumidifier-+
sulfuric
acid
b)
Figure 2.1: Schematic representations of the apparatus used to synthesize a) SbCl 5 -GICs
and b) FeCI3- and CuCl 2-GICs.
With regard to the samples prepared by the two-zone method, these samples were
25
removed from the furnace very slowly, keeping the intercalated graphite sample at a
sufficiently high temperature to prevent condensation of liquid SbCl 5 on the sample
surface. The samples which were prepared by direct contact with the liquid were also
cooled very slowly when they were removed from the furnace. All ampoules were opened
in a glove bag containing an argon atmosphere where the sample surfaces were cleaned
with a dry Q-tip.
The acceptor compounds with intercalants FeCl 3 and CuCl 2 were prepared by the'
two zone method, by placing the intercalant (~
1.5 mg) at one end of the tube and the
graphite at the other end under a partial pressure (- 300 Torr) of C1 2 gas.[8} Figure 2.1b)
shows a schematic of the apparatus used to synthesize the FeCI 3- and CuCl 2-GICs. The
FeCl 3 intercalant was prepared in-situ from the reaction of a Fe wire with C1 2 gas at
a temperature of ~ 60*C. The different stages were obtained by keeping the graphite
temperature Tg constant and varying the intercalant temperature T1 (see Table 2.2).
The intercalation times for the FeCl 3 and CuCl 2 samples were usually 8 days for the
HOPG host and 15-20 days for the fiber host.
Table 2.1: Sample preparation conditions and c-axis repeat distances I, for stages 1-4
and 6 SbCl 5-GICs.
Ic (A)
TSbC1s ( 0 C)
Tg (*C)
9.46 0.03
90 - 1o0a)
90 - 100a)
12.78 0 .0 3
120
170
2
16.16
100
170
3
0 .0 3
0.03
19.51
95
180
4
100
200
0.03
27.10
80
200
6
a) The stage 1 samples were synthesized by immersing
the graphite in the SbCl 5 liquid.
b) Some stage 2 and 3 samples were synthesized by
immersing the graphite in the SbCl 5 liquid, in
which case the temperature of the graphite was the
same as that of the SbCl 5 liquid.
)
)
stage (n)
1
The samples intercalated with KH and KD used in the TEM study described in chapter 3 of this thesis were prepared by Ms. Nai-Chang Yeh and Dr. Toshiaki Enoki.[9,10]
The KHg-GIC samples used in the RBS experiment described in section 2.4 of this chap-
26
ter were prepared by Dr. Gregory Timp.[11,12] Hence, the synthesis methods for these
three compounds are not described here.
Table 2.2: Sample preparation conditions and c-axis repeat distances I, used to synthe-
size FeCl 3 - and CuCl2-GICs.
Intercalant
FeCI 3
CuCl 2
stage (n)
2
1 , 2 b)
T a) ( C)
490
495-500
Tg (*C)
500
500
2
1,2b)
480
495-500
500
500
Ic (A)
12.78
0.02
9.40 + 0.02 (n =
12.78 0.02 (n =
0.02
12.79
9.40 0.02 (n =
0.02 (n =
12.79
1)
2)
1)
2)
')T 1 is the temperature of the intercalant (FeCl 3 or CuCl 2 ).
b) Mixed stages (1 and 2) were obtained for the fiber host.
2.3
Sample Characterization.
All the HOPG and kish based samples were characterized for stage index and stage
fidelity using (00t) x-ray diffraction.
The fiber samples and some of the HOPG and
kish samples were characterized for stage using the high resolution transmission electron
microscope (TEM) by observation of c-axis lattice fringes and electron diffraction. The
c-axis repeat distances obtained by all of these methods were in agreement with those
previously reported.[7,8,9,10,12,13,14,15,16]
Characterization by X-Ray Diffraction.
The
(00f) x-ray diffractograms were taken on a General Electric powder diffractome-
ter. Diffraction data were obtained in the
(A = 0.71073
A)
E - 2E mode using either Mo K, radiation
or Cu Ka radiation (A = 1.542
A)
and an energy discriminating Si/Li
detector. A single channel analyzer was used to separate the Ka radiation from the continuum. The stage infidelity for the intercalated HOPG and kish single crystal graphite
samples was always less than 5% for all the samples used in any experiment
reported in
this thesis. On the other hand, single staged samples are very difficult to obtain when
BDGF are used as host material, as is shown below; however, regions with high stage
fidelity could readily be obtained.
27
The Ic repeat distances were obtained from analysis of the (00t) x-ray diffractograms
using a chi-square, .2 minimization of
A(28e,e,) = 2(Ee - et,), the angular difference
between each pair of (00t) and (00e') diffraction lines.[17]
-
Figure 2.2 shows typical (00t) x-ray diffraction patterns for stages 1-4 and 6 SbCl 5
This figure shows that the SbCl 5 compounds studied in this work were single
GICs.
staged compounds. It is important to note that it is very unusual to obtain single stage
1 samples. In this work we were able to prepare stage 1 compounds with admixtures of
< 10 %.
The diffractogram shown in Fig. 2.2a) was taken at room temperature using
a cold stage. The cold stage was used because other diffractograms were obtained from
this sample at lower temperatures for the experiment described in chapter 5. The peaks
marked with * in this figure, correspond to contribution from the sample holder, as was
corroborated by separate x-ray scans obtained without any sample.
Figs. 2.3a) and
2.3b) show (00t) x-ray diffractograms of stages 2 FeCl3 -GIC and CuCl 2 -GIC (HOPG
host) samples, respectively. These figures also show single staged samples.
Single staged samples are more difficult to obtain from intercalated BDGF. Figure
2.4a) shows a region of a fiber that is mostly stage 2 with a small admixture of stage 1
and stage 3 CuCl 2-GIC. The single staged region extends for ~ 1000 A in the plane and
~ 110
A
along the c-axis. Each of the stage 1 and 3 regions shown in this figure extends
only for one period. Regions with high stage infidelity can be observed in the c-axis
lattice images of intercalated BDGF. Figure 2.4b) for example, shows a c-axis lattice
image of a fiber that contains a mixture of stages 2 and 3 SbCl 5 -GIC. It is interesting
to note the difference in texture between the intercalated CuCl 2 and SbCl 5 intercalated
fibers shown in Figs. 2.4a) and 2.4b). The texture is governed more by the intercalant
than the host material, since the former is usually a stronger scatterer than the later.
A difference in texture was also observed for fibers intercalated with KH and K, as
discussed in chapter 3. A more detailed explanation of how the c-axis lattice images
were obtained is given below. Regions showing stage infidelity can also be observed in
some areas of the intercalated HOPG samples using the TEM. Some examples of stage
infidelity are given in chapter 3 for KH-intercalated graphite.
The stoichiometry of GICs can be obtained from analysis of the x-ray diffractograms
using the (00t) integrated intensities.[17] We describe the method here by applying it to
28
STAGE
1
(002)
Ic
(0031
(a)
(001)
A
(9.46 -0.08)
(006)
L
(004),
15
10
5
(00
35
30
25
20
STAGE 2
3)
(C
(08
(007) ,
(00t)
(b)
(002)
15
10
5
z
(009)
(C06)(007)
(001)
(005)
30
25
20
STAGE 3
Cc)
J
(004)
ooN0)
'=02)
5
z
Ic
A
(0010)
2,.08)
= (6.20
(009)
(0)
1(007)
20
10
(CCS)
15
(CC5)
Ic =
30
25
STAGE
4
LU
(d)
0
(002)
5
(C07)(00 )
30
STAGE 6
(CC16)
25
20
15
10
0.08)A
(0012)
(0011)
(004)
003)
LL
19.50
(008)
(CCT)
(e)
]
=(29Z6
:0.08) A
(CC3) (OC5)
(0015)
(C011)
(CCE,
(C
C) i
C
,
5
10
OIFFRACT:CN
15
C012)
20
ANGL E 29
'
CC18)
25
30
CE5REES)
Figure 2.2: (001) x-ray diffractograms from a) n=1, b) n=2, c) n=3, d) n=4 and e)
The diffractogram for the stage 1 sample was obtained at room
n=6 SbCl 5 -GICs.
temperature using a cold stage. The peaks marked * correspond to contribution from
the sample holder.
29
the SbCl 5 system. The integrated intensities under the
(Oe) peaks were obtained using
a single channel analyzer. These intensities were corrected for background and were used
to compute the dependence of the layer charge density on distance perpendicular to the
layer planes (p(z)) from the structure factors by a Fourier synthesis calculation.[17]
(004)
0)
(003)
(002)
(001)
(005)
C
0
5
10
15
20
25
30
35
(003)
C
b)
..
C
(004)
"
(002)
(008)
(002)
(005)
I
0
5
(006)
(009)
I
I
I
I
I
10
15
20
25
30
2e (degrees)
Figure 2.3: (00e) x-ray diffractograms of a) a stage 2 FeCl 3-GIC sample and b) a stage
2 CuCl 2-GIC sample.
30
Figure 2.4: c-axis lattice images of BDGF intercalated with a) CuCl 2 and b) SbCl 5
showing regions with stage infidelity (marked by arrows). The insets are optical diffractograms taken from the negatives of the figures.
31
d IN-
1
-
-
M
W
-40k
--
*~~~do.
wr
-
-
----
'
-
-
-- 0&;;
-,
-~.0"
-
I
J. 4~
fof--**
-
.
4 o,
-*
IMA=7
~
32
Here p(z) is given by
p(z) =
Foot e-
Ct=-0
2
(2.1)
"t
where
Foot = Zfje(2rNzj)
(2.2)
is the structure factor of the (00t) Bragg reflection and fj, zj are, respectively, the scat-
j
within the unit cell. fj can be expressed in terms
of the mean squared thermal displacement < Z
f e8 <Z? >sin29/A)(2
-7r
fi = fjoe(-82
where fj* is the scattering factor of layer
> of layer
j by
)
tering factor and coordinate of layer
?>.3)
j at
rest and A is the x-ray wavelength.
The structure factors Foot are obtained from the experimental integrated intensities
loot (after correction for background) from the relation
loot = SCLCaFoot1 2
where S is a scale factor, CL
=
(2.4)
(1 + cos 2 2)/sin2O is the Lorentz and polarization cor-
rection factor, Ca = exp(-2t/sin) is the absorption correction factor and u and t are
the linear absorption factor and sample thickness, respectively.
Figure 2.5 shows the charge density along the z-axis obtained from Fourier synthesis
of the (00t) integrated intensities in stages 1, 2, 4 and 6 SbCl 5 -GIC samples. For these
calculations we modeled the intercalate sandwich as a layer of Sb atoms between two
layers of Cl atoms, one above and one below the Sb layer.[13,18,19] The identification of
the peaks in Fig. 2.5 is made by considering the relative areas under the peaks in the
charge distribution. [17] From the analysis of the x-ray data, we can obtain the number
of C atoms per Sb atom
n where n is the stage index, and the number of Cl atoms per
Sb atom m in CenSbClm from the areas under the peaks in the charge distribution since
these are proportional to the number of electrons in the planes. From these figures the
positions of the planes along the c-axis can also be obtained by directly measuring the
distances between the peaks. More accurate values for
n and m and for the distances
between the planes were obtained using a least squares fit to the integrated intensities
by means of the structure refinement (RFINE4) program.[20]
33
Figure 2.5: Fourier synthesis along the c-axis obtained from (00t) integrated intensities
for stages 1, 2, 4 and 6 SbCl 5-GICs.
34
n =
C
C
Ci s
b C
I
I
0
j
I C/2
n=2
~
c
sb
c2
c
-C20
IC/2
C/2
0
1 C/2
0
C
C
n=6
C
C
C
2 sb r
C/2
0
35
I
C/2
The values for the interplanar spacings obtained from analysis of the x-ray data are
given in Table 2.3 in terms of dsb-cl, dcl-Cb and dCb-Ci for the distances between the Sb
and Cl layers, between the Cl and C bounding and between C bounding and C interior
(for n> 3) layers, respectively. These values for the interplanar distances for stages 1-3,
were used in the analysis of the (00t) x-ray diffractograms as a function of temperature
to compute the value of the c-axis thermal expansion coefficient of SbCl 5-GICs reported
in chapter 6. The interplanar distances for stage 2 SbCl 5-GIC were also used for the
atomic positions along the c-axis used. to compute the images using the multi-slice
method described in chapter 4. The average values for
analysis are C = 12.921
and m obtained from x-ray
0.30, respectively. C had been previously
0.70 and m = 4.89
reported to be 14 (for n=1-3) and 12 (for n=2); these values have been obtained from
x-ray analysis [181 and from chemical analysis [141, respectively. It is interesting to note,
that for the (A7 x v')R19.1* phase (see chapter 4 of this thesis) observed in the SbCl 5
system a value of
the (Vr
( =
14 is expected. Since in the SbCl 5 system, other phases such as
x v'9)R19.1* and the (14 x 14)RO* as well as a disordered phase have also
been observed [15,191, our results iidicate that in average the intercalate is more dense
in these other phases than in the ("f7
x vf)R19.1* phase. The small but significant
deviation from m=5 is in agreement with the M6ssbauer results [211 on SbCl 5-GICs
which have shown that there is a disproportionation of sites (SbCls, SbCl-, SbCl 3 and
SbCl-) in this system [22].
In the next section, we compare the values of C and m obtained from analysis of
the
(00t) x-ray diffractograms with those obtained from RBS on the same samples.
This study was done as a function of intercalation time, and for cleaved and uncleaved
samples. The results for C and m obtained from both experiments are summarized in
Table 2.4.
Similar analyses were carried out for stages 2 FeCl3- and CuCl2 -GIC samples. The
results in terms of C and m are C = 5.9
2.2
0.8 and 6.5
0.4, for CgnFeClm and Cgn CuClm, respectively.
Table 2.4 along with the values for
0.8, and m = 2.6
0.5 and
The results are summarized in
and m obtained from analysis of the RBS spectra
obtained from the same samples and with values reported in the literature. As discussed
below, the deviation from m=3 for the FeCl 3 system is in agreement with the M6ssbauer
36
Table 2.3: Interplanar spacings for several stages of SbCl 5 -GICs obtained from analysis
of the (00f) x-ray diffractograms using the RFINE4 program.
stage (n)
1
2
3
4
6
a) tma
dSb-CI (A)
0.05 A
1.392
1.435
dCb-ci (A)
dcl-cb (A)
0.05 A
3.340
3.264
ref. [18]
1.405
1.400
1.410
ref. [18]
3.295
3.254
3.260
0.05
A
4ax
ref. [18]
8
15
3.31
3.379
1.470
3.188
1 3.148
1 3.411 1
1.494
is the maximum value of t used in the Fourier expansion.
18
17
Table 2.4: Summary of the measured stoichiometries for GICs obtained from analysis
of the (00f) x-ray diffractograms and of the RBS spectra. The parameters are for the
compound CenMNm. The experimental weight uptake (Wu(exp)) is also reported.
3.5
3.3
4a)
2
3
-
-
0.7
-
-
-
0.6
-
SbCI 5
FeCl 3
2-4,6
-
1 4 d)
4
.4)
-
5
13.5c)
12.9
12c)
4.6c)
2
7.3
5.9
8
.5f)
2.4
1 4 .1
)
1
CuC1 2
2
4.6
6.5
1
0.05
0.75
1a)
d)
0.3
5)
2.6 0.5
3f)
47.6
4.9
9.0g)
39)
6.2f)
31)
6 .09)
4_.9h)
2.0
_
-
1
ref.
-
KHg
Wu(exp)
RBS
( 0.2)
0.7
(
ref.
m
x-ray
%
RBS
0.7)
3.0
C
x-ray
( 0.8)
4.6
-
stage
n
-
Intei-calant
MN
2.2
0.4
29)
57.74
2 h)
') From Ref. [23]. 0) From uncleaved samples. ') rom cleaved samples. ) From ref.
[18] using x-ray analysis. e) From ref. [14] using chemi cal analysis. f) From ref. [24]
from weight uptake. -) From ref. [25]. h) From ref. [8].
37
experiment on FeCl 3-GICs [26} and our TEM observation that some FeCl 2 is present in
the samples. The value of m=2.6 obtained for FeCl3 -GICs from analysis of the x-ray
data given in Table 2.4 suggests a mixture of 60
% of FeCl 3 and 40 % of
FeCl 2 in the
intercalate layer. This large concentration of FeCl 2 in the intercalate layer could be the
result of either intercalation of some FeCI 2 that was formed in the glass ampoule when
the FeCl3 was prepared in situ prior to intercalation, or from oxidation of FeCl 3 into
FeCl2 and C12 during the intercalation process.
Both pristine FeCl 3 and FeCl 2 form hexagonal lattices with lattice constants of 5.25
and 3.10
A,
of 9.10
respectively. These values for the lattice constants give values for
and 3.18 for FeCl 3 and FeCl 2 , respectively.
Thus, a value of
=
A
6.73 is expected for
a mixture consisting of 60 % FeCl 3 and 40 % FeCl 2 . Our values for
obtained from
analysis of both the (00e) x-ray diffractograms and the RBS spectra (explained in section
2.4) for the FeCI 3 system (see Table 2.4) are in agreement with the value of
(
= 6.73
within experimental error.
Table 2.4 also contains the results obtained from analysis of x-ray diffraction and
RBS on stages 1-3 KHg-GICs. A discussion of the results obtained for the KHg-GIC
system is given in section 2.4.
Characterization by TEM.
In this section we present the use of TEM as a tool for stage characterization, stage
homogeneity and in-plane structure analysis of GICs at a microscopic level. Detailed
analyses of the structures of KH- and SbCl5-GICs are presented in chapters 3 and 4 of
this thesis, respectively.
The in-plane and c-axis structure of GICs was studied using two JEOL 200 CX
transmission electron microscopes with high resolution pole pieces (C. = 1.2 and 2.8
mm) and LaB 6 filaments. The distances observed in the images were above the point to
point resolution of both microscopes ~ 2.3
A and
2.9
A.
Accelerating voltages of 200 keV
and 100 keV were selected. The typical exposure time for recording the high resolution
images was < 4 seconds at magnifications of 500,000 X. The images were recorded on
Kodak SO-163 electron microscope film.
The in-plane structure was studied from both (hko) electron diffraction patterns and
38
high resolution lattice images obtained from the intercalated HOPG and intercalated kish
single crystal samples. The structure along the c-axis was obtained from (OUe) electron
diffraction patterns and high resolution lattice images obtained from the intercalated
fibers. The homogeneity of the intercalate layer was studied from lattice images and from
a comparison of dark field images of the same region, obtained using several diffracted
beams.
The dark field images were obtained by placing an aperture at the back focal plane
of the objective lens of the microscope that encompassed only the desired reflection after
this reflected beam had been brought to the optic axis of the microscope by tilting the
incident beam.
The lattice images were obtained under axial illumination by placing an aperture that
enclosed the desired reflected beams and the transmitted beam. Occasionally, the HOPG
and kish single crystal samples showed regions that were bent so that the c-axis was
perpendicular to the electron beam direction. This made it possible to obtain both (00t)
electron diffraction patterns and high resolution lattice images of these regions for the
HOPG and kish-samples. The repeat distances were obtained from optical diffractograms
taken from the negatives of the high resolution lattice images.[27]
The HOPG samples were prepared for TEM observation by repeated cleavage of
the bulk sample. The air stable samples (SbCl 5 , FeCl 3 and CuCl 2 ) were first cleaved
with a razor blade and glued to a microscope slide using wax, with the cleaved surface
side facing the microscope slide. The sample was then cleaved with adhesive tape until
only a thin film was left on the slide. The wax was dissolved in acetone and the thin
sample was recovered with a copper 400 mesh electron microscope grid. The fibers, on
the other hand, were mounted directly between copper grids using no special thinning
technique.
The air sensitive samples (KH and KD) were prepared for TEM inside a
glove bag under an argon atmosphere. The ampoule containing the intercalated sample
was opened inside the glove bag and the sample was repeatedly cleaved until a sample
containing thin (
300
A)
regions along the edges was obtained. The thin sample was
then placed between two 400 mesh electron microscope grids.
In contrast to Figs. 2.4a) and 2.4b), Fig. 2.6 shows a c-axis lattice image of a single
staged (n= 2) HOPG sample intercalated with SbCl 5 . The in-plane (La) and c-axis
39
Figure 2.6: High resolution c-axis lattice image of an SbCl 5 -HOPG sample showing a
single stage region (n=2). The inset is an optical diffractogram taken from the negative
of the figure.
40
41
(Lc) distances for stage fidelity in the negative of Fig.
than the area included in the negative) and Le = 120
been previously reported to extend for La ~ 2000
A for
2.6 are: La > 1000
A.
A
(larger
Single staged regions have
a stage 2 SbCl 5 intercalated kish
single crystals. [281 Regions showing mixed stages are also observed in some regions of the
intercalated HOPG samples, even when the (00t) x-ray diffractograms indicate that the
sample is single staged. Stage 2 samples show admixtures of stage 3 of < 5% (only a few
periods in a distance of ~ 200
A along the c-axis)
and stage 1 samples show admixtures of
stage 2 ; 10%. This is in agreement with previously reported results on stage infidelities
on SbCl 5 -GICs.[12] The c-axis repeat distance measured from the optical diffractogram
taken from the negative of Fig. 2.6 (see inset to Fig. 2.6) is in agreement with that
obtained from
(00t)
x-ray diffractograms taken from the same samples.
(hko) electron diffraction patterns [11] as well as high resolution TEM [29] show
that several in-plane structures coexist in the SbCl 5 -GICs. The in-plane phases most
commonly observed are the (Vfx Vf)R19.1* and the (V/51x V3-9)R16.1* phases that are
commensurate with the graphite lattice. Room temperature electron diffraction patterns
of SbCl 5 -intercalated graphite showing the (v7 x V7)R19.1* phase only and the mixture
of (v7 x Vr)R19.1* and (V3-9 x V3 )R16.1* phases are presented in Figs. 2.7a) and
2.7b), respectively. These two in-plane phases were observed for all stages (1-6) at room
temperature. In Fig. 2.7a) the (100) graphite spot ((100)G) at ~ 2.95
A-1
is indicated
and the (V7x v'7)R19.10* commensurate phase is identified by the spots at ~ 1.11
1.92
A-1
and 3.34
A-1.
Figure 2.7c) shows a schematic representation of Fig. 2.7a). In
this figure the graphite (100)G at ~ 2.95
A.-
indicated in this figure by (100)V, (110)V
1.92
A-1
and 3.34
A-1,
A-1,
is indicated. The superlattice spots are also
and (300) ,-, corresponding to ~ 1.11
A-1,
respectively. The extra spots shown in Fig. 2.7b) compared to
Fig. 2.7a) correspond to the (V39 x V/*3)R16.1* phase. The (V7 x vr)R19.10* phase is
studied in more detail in chapters 4 and 5. The
all the samples. The
(\/39
x
fV/-)R16.10
(Nf7
x V7)R19.1* phase is observed in
phase, on the other hand, is observed in some
areas of most of the samples. We have been able to obtain some samples that show the
(v/
x vf)R19.1* phase only (see Fig.2.7a)), although, usually both phases are present.
42
Figure 2.7: (hkO) electron diffraction pattern of a stage 2 SbCl 5 -GIC sample showing
a) the (V7 x V/7)R19.1o phase only
b) a mixture of the (V7- x v/7)R19.1* phase and the (v39 x V/39)R16.1* commensurate
phases most commonly observed in this system and
c) a schematic of the (v/7 x V/7)R19.1* phase.
43
0
0
o
El
0
0
El
*
0
.0
0
o0
El
*
0
0
.
.0
l.
0
w
-0
0
0
0
.0
0
0
.
w
-
( ( 10
0
0 El-
c
)
v
0
)G
(1O)7
0
-l
(300);
o (11O)f
0
0
Figure 2.8a) shows a dark field image of the (100) (v/fxV7)R19.1* reflection obtained
from a stage 3 SbCl 5-GIC sample. This figure shows islands of the (vfx V7)R19.1' phase
that are surrounded by other phases. We have observed islands of the
phase of 150 - 1000
A
(ii
x V')R19.10
in diameter. Figure 2.8b) shows an in-plane lattice image of a
stage 2 SbCl 5 -GIC sample. This figure shows in-plane fringes of the (-'F x VF/)R19.1*
phase, as well as a circular region of low contrast and an amorphous background. The
low contrast of the circular region indicates that it corresponds to either a light element
such as C1 2 or to a void. These circular regions have the appearance of 'bubbles' and
are very mobile under electron beam irradiation. Under electron beam irradiation the
'bubbles' move around the
(v/
x -V)R19.1* island, but do not penetrate it. The mobil-
ity of the 'bubbles' increases with increasing electron beam intensity. The background
probably corresponds to other ordered phases such as the
(V/5
x V'5)R16.1* phase or
to a disordered phase since in the electron diffraction patterns a diffuse halo close to the
(000) is always observed. Dark field images similar to the one shown in Fig. 2.8a) have
been previously oberved using a scanning transmission electron microscope (STEM).[30]
In the work by Hwang et al. ([30]), (V7- x v/)R19.1* spots along with other spots (not
identified by the authors) where observed in the diffraction. patterns obtained from the
background regions. The islands on the other hand, were identified with the disordered
phase. The discrepancy in the identification of the islands in the dark field images is
probably due to the fact that when using the STEM or the ion microscope, very high
electron or ion doses which are above the threshold for the commensurate to glass phase
change (see chapter 5) are required. Thus, when the beam is converged on the islands
to obtain the data the glass phase is obtained. Dark field and high resolution lattice images as well as x-ray diffraction studies on SbCl5 -GICs (see chapter 5) gave an average
domain size for the (V7- x fi)R19.1* phase of ~ 650 A.[29]
Inhomogeneities in the intercalate layer are also observed in the FeCl3-GIC system.
Figure 2.9a) shows an (hk0) electron diffraction pattern of an FeCl 3 -GIC sample. In this
figure the graphite (100) reflection is indicated by a G. The reciprocal lattice vectors
spots such as those labeled 1 and 2 in Fig.
of
2.9a), are in agreement with the (100)
and (300) reciprocal lattice vectors of pristine FeCl 3 (a, = 5.25
A), respectively. The
reciprocal lattice vectors of spots such as those labeled 3, 4 and 5 in this figure are in
45
Figure 2.8: a) Dark field image of a stage 3 SbCl 5-GIC sample obtained with the (100)
(VI x v7)R19.1* reflection and b) in-plane lattice image of a stage 2 SbCl 5 -GIC sample
showing inhomogeneities in the structure of the intercalate layer.
46
il-
A
P z
.1
Figure 2.9: (hkO) electron diffraction pattern of FeCl 3-GICs from a) a region containing
reciprocal lattice vectors for a mixture of FeCl 3 and FeC 2 intercalate species, b) a
region containing reciprocal lattice vectors corresponding to pristine FeCl 3 and weak
spots corresponding to FeCl 2 and c) schematic of a).
48
19
0
0
0
(D
0
0,0
0D
0
-0
0
0
0
E0
C)
0
* (100)G
o(I00)FCeC
* (300)FeCI33
49
(IOO)F9C2
0 (IIO)F.C
200
| (
)FeC1
0 (11O)G
2
2
agreement with the (100), (110) and (200) reciprocal lattice vectors of pristine FeCl 2
(ao = 3.10
A),
respectively. On the other hand, Fig. 2.9b) shows an electron diffraction
pattern taken from another region of the sample showing spts corresponding to FeCl3
and weak spots (compared to those in Fig. 2.9a)) corresponding to FeCl 2 close to the
(100) reciprocal lattice spots of graphite. Fig. 2.9c) is a schematic of the different spots
in the electron diffraction patterns shown in Figs. 2.9a) and 2.9b). This result suggests
a mixture of FeCl 3 and FeCl 2 in some regions of the intercalate layer. It is interesting
to note the presence of three sets of spots at 1.20
A-1 and 3.60 A-1 (labeled 1 and 2,
respectively) corresponding to FeCl 3 in Fig. 2.9a) with orientations with respect to the
graphite (100) reciprocal lattice vector of 18*, 260 and 330 for the three sets of spots.
On the other hand, Fig. 2.9b) shows a broader angular range of spots at these same
reciprocal lattice vectors. This results suggests that there is more preferred orientation
of the FeCl 3 with respect to the graphite layer in the neighborhood of an FeCl 2 region,
.
than in the regions where there is mostly FeCl3
To further confirm the coexistence of both intercalate species, we obtained dark field
images of the region where the diffraction pattern shown in Fig. 2.9a) was obtained.
Figure 2.10a) shows a bright field image of this region. Two dark field images using
spots labeled 2 and 3 in Fig. 2.9a) were obtained from the region shown in Fig. 2.10a).
The dark circular region in Fig. 2.10a) became very bright only for the dark field image
obtained from spot 3 in Fig. 2.9a) (see Fig. 2.10b)). When spots labeled 2 in Fig. 2.9a)
were chosen, the circular region became dark and the background was bright.
The results presented above for the FeCl 3 system indicate that some regions of the
samples are homogeneous and show continuous regions of intercalated FeCl 3 . There are
other regions where the homogeneous intercalate layer is interrupted by large islands
(~
2000
A
diameter) (see Figs. 2.10a) and 2.10b)) that scatter electrons strongly and
give rise to very intense spots in the diffraction pattern that show hexagonal symmetry
(spots 3, 4 and 5 in Fig. 2.9a)). The measured wave numbers for these bright spots are
in agreement with reported interplanar spacings for pristine FeCl 2 . The TEM results
thus suggest the coexistence of FeCl 2 with FeCl 3 in the intercalate layer, consistent with
M6ssbauer results previously published.[26]
50
Figure 2.10: a) Bright field image obtained by placing an aperture that encompassed the
(000) beam only, and b) dark field image from the same region obtained using the (100)
FeCl 2 spot.
51
Ara
-*
C14
In)
It is interesting to note that the (100) reflections of both FeC1 3 and FeCl 2 are not
allowed in the pristine materials.
The fact that these reflections are observed in the
intercalated compounds indicates that there is no correlation between intercalate layers
and, further that the (100) reflections are rods in reciprocal space.
This result is in
agreement with TEM studies on the FeCl 3 system previously reported.[31,32]
In contrast to the SbCl 5 - and FeCl 3-GICs results, CuCl2-GICs showed the same(hk0)
electron diffraction patterns in all areas of the sample (see Fig. 2.11a)). No reciprocal
lattice vectors in agreement with those of pristine CuCl were obtained, in agreement
with the value of m ~ 2 obtained from analysis of both (00t) x-ray diffractograms
and RBS spectra (discussed in section 2.4). This result indicates that the intercalate
layer is more homogeneous for the CuCl 2 system than for the FeC1 3 and SbCl 5 systems.
The reciprocal lattice vectors in the electron diffraction pattern shown in Fig. 2.11a),
-
correspond to several sets of planes of a slightly distorted unit cell of pristine CuCl 2
Pristine CuCl 2 forms a monoclinic unit cell with parameters a. = 6.70
and c. = 6.85
A, and
#
=
A,
A
b. = 3.30
121* (,3 is the angle between a0 and c.). The distortion in the
,
crystal that gives rise to the electron diffraction pattern observed in Fig. 2.11a) is that
is changed from 1210.to 900. That is, the diffraction pattern in Fig. 2.11a) corresponds
to that of a polycrystal with an orthorhombic unit cell with the same lattice constants
ao, b. and co as pristine CuCl 2 but, with
P
= 90*. Figure 2.11b) is a schematic of the
electron diffraction pattern shown in Fig. 2.11a). This figure shows the different planes
of the distorted CuCl 2 unit cell. Two (010) and several (111) reciprocal lattice planes
are indicated.
Figure 2.11c) shows a dark field image of the region where Fig. 2.11a) was taken.
This figure shows a more homogeneous region than those shown in Figs.
2.8a) and
2.10b) indicating that CuCl 2-GICs are more homogeneous than FeCl 3- and SbCI5-GICs.
Occasionally, in the CuCl 2-GIC sample some bright regions of 300 - 1000
A
such as the
one shown at the upper part of Fig. 2.11c) were observed. The diffraction patterns from
these regions were the same as in other regions. This result suggests that these regions
are brighter because they correspond to one of the several orientations of the intercalate
that are included in the aperture and therefore are contributing to the dark field image.
A way to ascertain that this is the case is to take two or more dark fi.eld images from
53
Figure 2.11: a) (hkO) electron diffraction pattern of a stage 2 CuCl2-GIC sample, b)
schematic representation of a) showing several reciprocal lattice planes and c) Dark field
image obtained from the same region where a) was taken using an aperture as shown in
b) that enclosed reflections originating from several crystallites.
54
9
m
00 0
*
N
4
N
0 5 oU
U
0
0
0
N
00
Ni
-U
~G
-
0
0 000
/
N
0
o
55
G
0
the same area but using different sets of spots in the diffraction pattern. Then, different
areas would get brighter for the different sets of spots allowing for the identification
of the areas that give rise to the different spots. Unfortunately, this procedure was not
carried out at the time when the pictures were taken. The fringes observed in Fig. 2.11c)
correspond to interference between the spots that were included in the aperture (even
when the smallest aperture was used, several beams were included in the aperture to
form the image) and indicate that there is superposition of the two different orientations
of the intercalate along the c-axis.
The electron diffraction patterns for the FeCl 3 and CuCl 2 systems are typical of
incommensurate intercalated compounds. Incommensurability is the absence of registry
of the intercalate layer with respect to the graphite lattice. In this case, the intercalate
layer retains the structure of its pristine form.
2.4
Stoichiometry Determination Using Rutherford Backscattering Spectrometry.
RBS spectra were obtained by Dr. Boris S. Elman from the same sariples used to
obtain the stoichiometry data from analysis of the (00t) x-ray diffractograms presented
in section 2.3. The analysis of the RBS spectra as well as the sample preparation and
characterization for stage index were carried out by the author, who acknowledges Boris'
help in taking the spectra and explaining how to use the computer programs employed
in the analysis for the stoichiometry determination. The RBS data were obtained using
a beam of 2 MeV
4
He+ ions from a Van de Graaff generator. A typical current of 20 nA
through a 1 mm diameter aperture was used. The backscattered particles were detected
at scattering angles of ~ 1750 by a surface-barrier detector (see inset to Fig. 2.12) with
energy resolution of < 20 keV (FWHM) for 2 MeV
4
He+ ions. The energy analysis
was performed using a computer based data acquisition system. To carry out the RBS
measurements on the air sensitive KHg-GIC samples, a glove bag was placed around the
sample holder of the RBS set-up with a constant flow of N 2 gas. The glass ampoules
containing the samples were opened inside the glove bag and the samples were mounted
on the sample holder with vacuum grease.
RBS spectra of SbCl 5 -,
FeCl 3 -,
CuCl 2 -
56
and KHg- GICs were taken for several
stages.[33] In this section we report the results obtained for the stoichiometry of these
compounds, from analysis of the RBS spectra. An extensive study was carried out for
the SbCl 5 system.[34] Therefore, this system is used here to describe the application of
the technique.
4
The essence of the RBS technique is in the analysis of the energy spectrum of the He+
particles backscattered from the atoms of the substrate. Simply considering a process of
hard sphere collisions, it is clearly understood that the heavier the atom of the substrate
from which the incoming particle is backscattered, the less energy will be transferred to
this atom during the collision process. Thus, the higher energies of backscattered helium
ions correspond to heavier masses present in the substrate. Moreover, for each particular
atomic mass in the substrate Mi, one expects to see a step in the energy spectrum at
a characteristic energy Ei, corresponding to the scattering from these atoms of mass
Mi located at the surface of the substrate (see Fig. 2.12). At lower energies than Ei
we expect to have a continuous spectrum corresponding to the in-depth distribution of
species i.
RBS spectra of some of the samples were taken both before and after cleaving. Figure
2.12 shows a typical RBS spectrum for a cleaved stage 3 SbCl 5-GIC sample. The results
are presented in terms of counts vs. energy for the backscattered ions. The experimental
geometry is represented in the inset to Fig. 2.12. In this spectrum, contributions from
specific atomic species can be easily identified, as indicated on the figure. Specifically,
the three sharp steps at energies 1.755 MeV, 1.274 MeV and 0.502 MeV correspond,
respectively, to the energies of backscattered ions from
122 Sb,
36
C1 and 12C atoms on
the surface of the sample when the energy of the primary 4 He+ beam is 2 MeV and the
analyzing angle is ~ 1750. The typical number of incoming ions was preset at ~ 1 MC
of charge.
The RBS spectrum of Fig. 2.12 corresponds to a well-staged layered material, but
because of the very small thickness of the unit cell (e.g., for the SbCl 5 -GIC samples of
this work, 12.7
A
< I, < 27.5
for the case of carbon
A)
for 2 < n < 6 and because of the poor depth resolution
(~ 450 A), the beam of 4He+ particles in the RBS experiment
cannot resolve the differences in chemical species associated with individual layers of
graphite intercalation compounds. The spectrum of Fig. 2.12 is thus indistinguishable
57
from a homogeneous multi-elemental sample with a simple mixture of the three elements
according to the stoichiometry C 43 SbCL4.6 . By taking spectra on samples that were
cleaved, we have shown that all three elements are homogeneously distributed in depth,
all the way from the surface of the sample to a depth on the order of several microns.
Figure 2.12 also shows that no other elements (at least no other elements heavier than
carbon) are present in the sample in detectable amounts.
12000
SAMPLE
F-
OHeBEAM
APERTURE
SAMPLEHOLDER
I-Z 8000
D
0
SOLID
STAT
DETE CTOR
-
sb
4000
0
0.5
I
1.0
I
1.5
I
2.0
ENERGY-(Mev)
Figure 2.12: Typical RBS spectrum of a cleaved stage 3 SbCl 5 -GIC sample. The inset
shows the experimental geometry.
We should emphazise that essentially identical spectra were obtained for freshly
cleaved samples and for samples that had previously been cleaved (up to 6 months)
for other experiments. This implies that no detectable contamination or redistribution
takes place within
1pum of the surface for these compounds under ambient conditions.
As discussed below, we believe that the intercalate inhomogeneity observed as a function
of depth for uncleaved samples arises from the sample preparation procedure.
In order to relate the stoichiometry quantitatively to the heights of the steps in the
RBS spectrum (see Fig. 2.12), it is necessary to perform an analysis of the raw data
58
based on an iteration of the RBS yield equations
[35], as discussed below.
The relative atomic concentrations Ci/Cj for each of the elements are obtained from
the RBS spectrum from the measured relative heights Hi/Hj of the RBS signal at the
surface edge according to the relation [2]
Ci = Hi X - X [e]
[4ij
oi
Hj
Cj
(2.5)
where ai is the differential scattering cross section and [E]i is the stopping cross section
factor of element i given by: [2]
[E]i = Ki(E)E(Eo) + E(K(8)E)
cos(r - 8)
where E(E) is the total stopping cross section of a mixture of atoms
(2.6)
j
of concentrations Cj
which is written in accordance with the principle of additivity of stopping cross sections
as
E(E) = E CiqI(E)
(2.7)
and the stopping cross section Ei(E) for each atomic species is tabulated.[2] The coefficient
Ki(e) in Eq.
(2.6) is the kinematic factor defined as Ki(E) = Ei/Eo where Ei is the
energy of the particle scattered from the surface by a particle of mass Mi at an angle e,
and Eo is the energy of the projectile before the collision. In general the expression for
the kinematic factor Ki(E) is given as:[2]
K (9)
=((1
- (Mi/Mi)2sin'e)1/2 + (Mi/Mi)cose) 2
1 + M1/Mi
(2.8)
where M 1 is the mass of the projectile and Mi is the mass of the target atom. A relation
between [E]i and the concentrations Ci is given by Eqs. (2.6) and (2.7), allowing us to
perform an iteration procedure. To initiate the iteration procedure, the ratio [e];/[E]j in
Eq.
(2.5) is taken as unity. Solution to Eqs.
(2.6-2.8) then yields a better estimate
of the ratio [E]i/[E]j, which is then used to yield a better approximation to the ratio of
concentrations (Ci/Cj). The results are iterated until changes in Ci/Cj of less than 0.1%
are obtained.
In the actual RBS experiment, the measured height Hi in Eq. (2.5) is determined
not only by the concentration Ci of element i, but also by several parameters which are
59
the same for all the elements, such as the total number of incident
4
He+ ions, the solid
acceptance angle of the detector, the energy width of a channel in the detector, etc. For
this reason, it is desirable to deal with normalized concentrations C% defined by
Ci = C/
With this definition, we have (Cf/Cj)
=
Cj.
(2.9)
(Ci/Cj), so that the RBS spectra can be inter-
preted directly in terms of normalized parameters, as is done in Eq. (2.5).
The analysis of the RBS spectra was carried out for different commensurate and
incommensurate GICs.
2.4 in terms of
c
The results from this RBS analysis are summarized in Table
and m. Table 2.4 also contains the values for
and m obtained from
analysis of the integrated intensities under the (00f) x-ray diffraction peaks presented
in section 2.3, and the values are listed under the columns labeled x-ray. The table also
includes under the columns labeled ref. the values of
references.
and m reported in the designated
A discussion of the results for each system studied in this work is given
below. No dependence on host material (HOPG vs. kish single crystal) was found in the
stoichiometry for SbCI5-, FeCl 3-, CuCl 2 - and KHg-GICs.
An analysis of the RBS spectra for fourteen SbCl 5 -GIC samples was carried out in
accordance with the procedure discussed above.
Emphasis was given to as-prepared
samples, freshly cleaved samples and samples that had been previously (for times up to
6 months) cleaved for other experiments.
The results of this analysis for the value of m, the relative Cl:Sb concentration, are
shown in Fig. 2.13 for a range of intercalation times 25 hrs. < t < 340 hrs. Fig. 2.13
presents results for m both for uncleaved samples (Fig. 2.13a)) and for cleaved samples
(Fig. 2.13b)) for stages 2, 3, 4 and 6 SbCl 5-GICs. Fig. 2.13b) shows that the values of m
obtained from analysis of the RBS spectra for the cleaved samples are in agreement with
those obtained from analysis of the (OOU) x-ray diffractograms (reported in section 2.3
of this chapter) on the same samples. The RBS results show that within experimental
error, m has no dependence on intercalation time t for 25 hrs. < t < 340 hrs. This is
consistent with previous reports that four days of intercalation time was probably more
than enough to achieve equilibrium in the intercalation process [7]. By measurement of
RBS spectra as a function of lateral distance, the spatial homogeneity of the intercalant
60
was established, consistent with the completion of intercalation on this time scale.
For the SbCl 5 system, the average value of m obtained from analysis of the RBS
spectra is 4.35
0.20 for uncleaved samples (Fig. 2.13a)) and 4.62
0.20 for the cleaved
samples (Fig. 2.13b)). We believe that in both cases there is a statistically significant
difference between the measured m values from 5 and between m values for the cleaved
and uncleaved samples. The deviation from m=5 is in agreement with the M6ssbauer
results on SbCl 5 -GICs.[21]
To verify that the intercalant atoms are not driven away during the RBS experiment,
we have examined the same area of the sample at different numbers of incoming 4 He+
particles by varying the preset from ~ 0.5 pC to ~ 5 4C in steps of 0.5 jC. Analysis of
the data after each step showed no difference in stoichiometry.
We have also determined the number of C atoms per Sb atom in CCnSbClm in terms
of n, where n is the stage index. The results obtained from analysis of the RBS spectra
also show differences in
between cleaved and uncleaved samples. The average value of
C for the uncleaved samples is 14.13
We note that
0.70 and for the cleaved samples is 13.53
0.70.
has been previously reported to be 14 (for n=1, 2 and 3) and 12 (for
n=2); these values have been obtained from x-ray analysis [18] and chemical analysis
[14], respectively.
value of
The value of for the cleaved samples is in agreement with the average
obtained from x-ray analysis on the same samples, reported in section 2.3 of
this chapter.
The KHg-GIC system has been found to form several phases that are commensurate
with the graphite lattice: a (2 x 2)RO* [11,12,23,36,37], a (2 x v 3_)R(0, 30*) and a
(V3-
x V3)R30* [11,12,36] superlattices. These three commensurate phases have been
found to coexist in the same sample with relative concentrations depending on sample
preparation conditions.[11,12,36] For the (2 x 2)RO* and (2 x V3)R(0*, 300) superlattices,
the expected stoichiometry is C4 .KHg where n denotes the stage index, and for the
(%/3
x v/)R30* superlattice it is C 3,KHg.
Our RBS results on the KHg-GIC system
show a ratio of Hg to K atoms m < 1 in all the samples we have studied (see Table
2.4, and Figs. 2.14a) and 2.14b)). This mercury deficiency is possibly associated with
deintercalation of the mercury occurring during the process of mounting the samples for
the RBS experiment. This is consistent with the temperature dependent in-situ x-ray
61
STAGE INDEX n
2
3
(a)
SYMBOL
0
A
0
4
0
6
5
X-RAY ANALYSIS DATAe,A,0
0
0
E
0
0
0
0
4
H-
.I
( b)
EXPERIMENTAL
ERROR
0
5
0
-
C
9
0
-
-cp
a
(-;-
A
0
0
4
100
200
300
INTERCALATION TIME ( hrs)
Figure 2.13: Cl to Sb ratio vs. intercalation time from RBS results for a) uncleaved and
b) cleaved samples. The solid symbols show the results obtained from x-ray analysis
described in section 2.3 of this chapter.
62
16000
C
12000
K
C
Hg
0
U 8000
cn
4000-
(a)
0
0.5
2.0
1.5
1.0
E (MeV)
16000
12000--
K
C
Hg
0
U8000
4000-
0.5
1.0
1.5
2.0
E ( MeV)
Figure 2.14: RBS spectra of a stage 3 KHg-GIC sample from a) the edge of the sample
and b) from the center of the ~ 1.5 x 1.5 mm 2 sample.
63
experiment [12,36] performed on a stage 1 KHg-GIC sample for 300 K < T < 500 K,
where it was shown that the mercury leaves the graphite host at a temperature lower than
that where potassium leaves. The results for
and m reported here for the KHg-GIC
system were obtained from analysis of one RBS spectrum for every stage and therefore a
sample dependence could produce a scatter from these reported values. The RBS results
for the KHg-GIC system for stage 1 are consistent with the results obtained from an
analysis of the integrated intensities of the (00t) x-ray diffractograms taken from the
same samples (see Table 2.4).
Contrary to the SbCl 5 system, the lateral distribution of the intercalant of a stage
3 KHg sample showed a very interesting depth dependence of the stoichiometry.
The
regions at the edges of the sample showed an equilibrium value of m = 0.62 for the ratio
of Hg to K atoms with a uniform depth distribution for m (see Fig. 2.14a)). In contrast,
the central region of the sample shows a decrease of Hg and K with depth (see Fig.
2.14b)). The analysis of the spectrum in Fig. 2.14b) gave
= 4.76 and m = 0.79. This
is in agreement with the proposed mechanism for intercalation whereby intercalation
starts from the a-face edges and from the sample surface planes. It is interesting to note
that for the preparation of stage 3 KHg-GICs the intercalant has a Hg to K ratio.of 2.5
prior to intercalation.[12]
The results obtained from analysis of the RBS spectra from several cleaved stage
2 FeCl 3-GIC samples are summarized in Table 2.4. A typical RBS spectrum for this
system is shown in Fig. 2.15a). Based on the measured lattice constants, the theoretical
values for
and m, for the FeCl 3-GIC system are
= 9.11 and m = 3. Our results
show a statistically significant deviation from m = 3 in this system. Electron diffraction
patterns and bright and dark field studies from these samples using the TEM (see section
2.3 of this chapter) have shown that on a microscopic scale these compounds are not
completely homogeneous but show regions with an admixture of FeCl3 and FeCl 2 . This
result suggests a value for m < 3. The value of m=2.4 obtained from analysis of the
RBS spectra indicates a 60% concentration of FeCl 2 and 40% of FeCl 3 in agreement with
the results obtained from analysis of the (00e) integrated intensities reported in section
2.3.
Our results do not agree with the stoichiometry C+CP-FeCl 2 3(FeCl 3 ) suggested
by Dzurus and Hennig.[38] From the stoichiometry obtained from analysis of the RBS
64
1400
1200
C
1000C800
')
600-
Fe
400200
01
0.5
1.5
1.0
E ( MeV)
1600
C
1200
C1
0
U 800
400(b)
0
0.5
1.0
1.5
2.0
E (MeV)
Figure 2.15: Typical RBS spectra of a) a stage 2 FeCl 3-GIC sample and b) a stage 2
CuCl 2-GIC sample.
65
spectra for this system we have calculated the percent weight uptake (Wu(RBS)) for
the samples used in this experiment. Our calculated values for Wu(RBS) agree with the
experimental weight uptake values Wu(exp) to within 7% for all the samples we have
studied (see Table 2.4).
RBS spectra from the CuCl 2 system were obtained from three stage 2 samples. The
results from the analysis of the RBS spectra are summarized in Table 2.4. Figure 2.15b)
shows a typical RBS spectrum for this system.
Contrary to the case of FeCl 3-GIC
and SbCl 5-GIC, we found a ratio of Cl to Cu atoms of m- 2, suggesting that there is
no disproportionation of sites in this system. Our results for
analysis of the RBS spectra and from analysis of the
(00t)
and m, obtained from
x-ray diffractograms, agree
with reported stoichiometric values (see Table 2.4). The calculated Wu(RBS) for this
system are in agreement with the experimental values of Wu(exp) to within 5%.
Several of the uncleaved SbCl 5 -GIC samples showed abnormal RBS spectra as shown
for example in Figs. 2.16a) and 2.16b). The spectrum in Fig. 2.16a) was taken from an
uncleaved stage 3 graphite-SbCl 5 sample, and shows an abnormally large concentration
of Sb near the surface of the sample. The spectrum also shows evidence for the presence
of oxygen in the surface region.
It is not clear as to the exact form of the oxygen
compound, though one could suspect the presence of some antimony oxide.
In contrast, the spectrum of Fig. 2.16b) was taken from an uncleaved stage 4 sample
and shows a deficiency of Sb near the sample surface. Both spectra in Fig. 2.16 thus
show deviations in the Sb concentration on freshly prepared (uncleaved) samples within
approximately the same distance in depth (~
500
A).
We should also emphasize that
we have never seen abnormal RBS spectra from cleaved samples.
The significance of this result on uncleaved samples is the observation that the deviation in stoichiometry occurs near the surface layer of freshly prepared samples. Thus,
one must exercise care in the interpretation of any experimental results when the applied technique is sensitive only to a small distance from the sample surface. The spectral
edge heights and lineshapes for carbon and chlorine were observed to vary little between
freshly prepared samples of similar stage.
66
14000-
-
12000
C
-
10000
8000-
Z
CL
sb
6000-
-
4000
2000a)
0.5
1.0
1.5
2.0
ENERGY (MeV)
16000-
12000
C,)
-
14000-
10000-
z
D
CD
2
S8000
sb
o
6000-
4000
-
2000
b)
0.5
1.0
1.5
ENERGY (MeV)
2.0
Figure 2.16: Examples of abnormal RBS spectra from as-prepared, uncleaved a) stage
3 and b) stage 4 SbCL5-GICs.
67
2.5
Conclusions.
Transmission electron microscopy is a very useful tool for studying GICs at a microscopic level. SbCl 5- and FeCl 3 -GICs are inhomogeneous in the sense that there is a
disproportionation of sites in the intercalate layer. On the other hand, no sign of disproportionation of sites was observed in the CuCl 2-GIC system. We have found a slight
deviation of the in-plane reciprocal lattice vectors of the intercalate from the pristine
reciprocal lattice vectors of CuCl 2 , eventhough CuCI2 -GICs are incommensurate with
the graphite lattice.
Rutherford backscattering spectrometry (RBS) is a very useful non-destructive technique to obtain the stoichiometry of GICs. The values of C and m for the stoichiometry
of GICs obtained from the RBS spectra are in agreement with those obtained from
analysis of the (00t) x-ray diffractograms of the same samples. The depth and lateral
dependence of the stoichiometry obtained from analysis of the RBS spectra provide information about the homogeneity of the compounds. KHg-GICs are inhomogeneous in
both the lateral direction and in-depth (for the central region of the sample). A deviation from the theoretical values of m=5 for SbCl5 -GICs, m=3 for FeCl3 -GICs and m=1
for KHg-GICs is observed from analysis of both (00t) x-ray diffractograms and RBS
spectra. A difference in the value of m for cleaved and uncleaved samples is obtained for
the SbCI 5 system.
68
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69
[13] J. Melin, Sc.D. Thesis, Universit6 de Nancy I, France (1976).
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(Springer, Berlin, 1981), p. 168.
[19] H. Homma and R. Clarke Phys. Rev. B31, 5865 (1985).
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70
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71
Chapter 3
HIGH RESOLUTION
TRANSMISSION ELECTRON
MICROSCOPY ON KH-GICs
In this chapter we study the intercalation process and the in-plane and c-axis structure of KH- (KD)-GICs using high resolution transmission electron microscopy. The
introduction to the chapter is given in section 3.1, including some background on image
formation and electron diffraction using the high resolution electron microscope.
Sec-
tion 3.2 contains the experimental details and sample preparation for TEM observation.
Section 3.3 shows the dependence of the in-plane and c-axis structure on intercalation
temperature and time. A comparison of the structure for the two methods of intercalation of KH (KD) is given in section 3.4.
3.1
Introduction.
High resolution transmission electron microscopy (TEM) provides information about
the structure of materials at a microscopic level that cannot be obtained by other methods such as x-ray diffraction, Raman scattering spectroscopy, neutron scattering, etc.
On the other hand, particular care must be taken when interpreting the images obtained
using the TEM, since the TEM observation can introduce artifacts net directly related to
the structure of the original samples. For example, the interaction between the beam and
the specimen under investigation may produce changes in the structure such as the desorption of KH (KD) that takes place during the TEM observation on KH- (KD)-GICs.
72
In chapter 5 of this thesis we show that SbCl 5-GICs undergo a commensurate-glass
phase change under electron beam irradiation. These are two examples where the observations show 'effects' resulting from the damage produced by electron beam irradiation.
There are other 'artifact' effects that may produce an image that does not represent directly the real structure of the material being studied. Therefore, in order to determine
the atomic structure of a material using the TEM, it is necessary to obtain images using
computational methods, that reproduce images obtained under a variety of experimental
conditions. On the other hand, features separated by a distance greater than the resolution of the microscope can be reliably examined without the need of computational
methods.
High resolution lattice images are phase contrast images obtained from coherent interference between the unscattered beam and the diffracted beams. For the interpretation
of lattice images, it is convenient to divide the problem into two parts: the interaction
between the electrons and the potential field of the atoms in the specimen and the subsequent interaction of the electron beam with the electron microscope lenses. Figure 3.1
shows a schematic representation of a ray diagram in a transmission electron microscope
with 2 condenser lenses and 4 imaging lenses. The interaction of the electrons with the
potential field of the atoms in the specimen produces a phase shift in the amplitude of
the electron wave function. The effect of the interaction with the microscope lenses is
to produce an additional phase shift in the electron wave function which depends on
parameters such as defocusing and spherical aberration of the microscope lenses. Therefore, coherence of the electron beam and defocusing are parameters that should be well
controlled for high resolution electron microscopy.[1]
Effect of The Specimen on The Electron Wave Function.
In the scattering of electrons by a specimen, it is the atomic potential field that the
electrons feel as they travel through the crystal. The relativistic Schr6dinger equation
for an electron propagating through a region of potential Vspec(r) is
V2(r) + 2me Wo 1 + eW,
h we2mc2
49(r)
where Wo is the accelerating potential
+ 2
(Vpe
1-
«
2-1/2
Ci
Vspec(r)T(r) = 0
(3.1)
(Vspec << Wo), v is the relativistic electron
73
I
-
Dl
A, C1
DI
D21
C2 CA2
D3
Specimen
LI
-OA
-
D4
P
-
1
S
L2
D5
L3
D6
L4
D7
Figure 3.1: Schematic representation of a ray diagram for a transmission electron microscope with two condenser lenses C1 and C2 and four imaging lenses L1-L4.11]
velocity, m and e are the electron rest mass and charge, respectively, c is the speed of
light in vacuum and h is Planck's constant. For a perfect crystal
Vspec(r) = ZVj(r) = ZVj(r) * 8(r -rj)
j
= Vge 2xIg-r
(3.2)
(3.3)
9
where * denotes convolution, Vj(r) and rj are the potential and fractional coordinate of
atom
j,
Yg = 2-rhiFg
(3.4)
meVe
is the gth Fourier component of the potential in terms of the structure factor of the gth
Bragg reflection
Fg =
5 ff (sg)e(~Bjs )e(27i(g-rj)),
(3.5)
fj and Bj are the electron scattering factor and Debye-Waller factor for atom j, sg is the
excitation error and V, is the volume of the unit cell.
74
For an incident wave of the form T,'(r) = 4 0 e2,ik*r, the diffracted amplitude at the
exit face of a perfect crystal Te(r') can be obtained using the relativistic correction to
Born approximation
27ri
WO + moc 2
ArWo
WO + 2mOc2 )
funit cell
e2ikIrr'I Vspec(r)e27ikrdr
Ir - r'I
(3.6)
where A,. is the relativistic wavelength of the electron and mo the electron rest mass.
If k' defines the direction of the diffracted beam with k' = 1/A where A is the electron
wavelength, then, for r' >> r
Ik,(r) =
27ri
ArWo
W + mo c 2
e2rikr'
r'
Wo + 2moc2)
0
f Vpec (r)e 2ri(k-k')rdr
(3.7)
is the amplitude for Fraunhofer diffraction.
The Born approximation, as described in Eqs. (3.6) and (3.7), is called in electron
microscopy theory the kinematic theory of electron diffraction.[1,2,3,4] This theory provides very useful qualitative information but is only valid when the amplitudes of the
diffracted waves are small compared to the incident wave. This condition is satisfied for
either very thin crystals or for very light atoms. From the kinematic theory the thickness
along the electron beam direction over which the diffracted amplitude builds up to unit
amplitude is
7rVecosO
2AFr
where
= Eg/2
(3.8)
g = VccosO/AFr is the extinction distance for beam g, 0 is the corresponding
Bragg angle and Fr is the relativistically corrected structure factor.[2] Therefore, the
kinematic theory of diffraction is valid only for t < Cg/10 where t is the thickness along
the electron beam direction. The kinematic theory assumes that the unscattered beam
is much stronger than the scattered beams. The validity of this theory as well as the
dynamical theory which accounts for multiple scattering within the specimen is discussed
in some detail below. A more detailed treatment of these two theories can be found in
several references such as [2,3,4].
Effect of The Lenses on The Electron Wave Function.
The optimum contrast condition in high resolution lattice images is obtained at an
out of focus condition. The wave amplitude 'IPAf(r) at a defocus distance Af (see Fig.
75
3.2) obtained using Huygen's principle is
iAC-2ridf /k
Af(r) =
Te
(r')e
_22ELr
dr'
i
(3.9)
r
Ae-2iAf/A
f i
=
q e(r')e[-AW-r'Pdr'
2
iAe- riAf/A
Te(r) * P(r)
=
where %Ie(r')is the amplitude of the electron wave function at the exit face of the
specimen, P(r) = exp[-27ilr 2/AAf] is called the Fresnel propagator and the integration
is carried out over the unit cell volume.
T Af (r) in Eq. (3.9) is the electron wave amplitude at the entrance surface of a lens
with a defocusing value of Af. The effect of the lens on the electron wave function is
=
to introduce a focusing phase shift
A
2x+y2.
2f
For a diverging spherical wave in
y) = Aexp(-ixr(x 2 + y 2 )/AU) where A is a constant and U is the
two dimensions %P(x,
distance between the lens center and the diverging point (see Fig. 3.2), the effect of the
lens is
T (x, y) = Ael~
i_(x2+y2)
AU -el
wx2+y2)
A)
ix2+Y2)
= AeliwV
I
(3.10)
-where = .- - (see Fig. 3.2). The image amplitude at a distance d beyond the back
focal plane (BFP) of the lens when an objective aperture is placed at the BFP of the
lens is [1]
'I(x',y') = AP(x,y)e
=
A'
f
/
i(x2+y2)
Ad
*el-
i~r(X2
2)
Ad
P(x, y)e2ri(x'x+Y'Y)/Addx
(3.11)
where A' is phase factor containing quadratic terms and the objective aperture pupil
function P(x,y) =1 within the aperture, and 0 elsewhere.
The amplitude of the diffraction pattern at the BFP,
'D.P.(uh,uk) (where (uh,uk)
are the reciprocal space coordinates at the back focal plane of the lens) for a perfect lens
is given by [1]
'D.P.(uh,
uk)
e
i
+ul)
-
Jff
T(x',
e[2i
)x'+()Y'dx'dy'
(3.12)
76
@(X.Y
P
P
wP xur>
T(X,Y)
P
"XY
ae)
Figure 3.2: Out of focus image xWi(xy) of an object with transfer function T(x,y).[1]
where T(x', y') is the specimen transmission function (T(x',y') = _
for the kinematical approximation).
Ze Vj(r)*S(r
- rj)
y) = cDT(x', y') is the amplitude of the wave
'e(x,
function at the exit.face of the microscope. Eq. (3.12) takes account of the effect on
the electron wave function produced by the specimen and the objective lens. For U ~
Eq.
f,
(3.12) is essentially the Fourier transform of the specimen exit wave amplitude
F(u,v) = F.T.{xP!e(x,y)} for u=uh/Af and v = uk/Af.
The effect of the lenses on the image at a distance z from the back focal plane of the
objective lens for a lens with aberrations is given by
'i(x, y) = -(WO.p.(u,
z
v)P(u, v)eiuiv))
*
P,(u, v) = -F.T.{(TD.p.(u, v)P(u, v)ei"(U')}
z
(3.13)
where P(u, v) is the objective aperture pupil function, P,(u, v) is the Fresnel propagator
for the distance z between the back focal plane and the image plane,
-(u, v) = 2{AfA2(u2 + v 2 )/2 + CA 4 (u 2 + v 2 ) 2 /4},
A is the electron wavelength,
(3.14)
Af the defocusing value, u 2 = h 2 /a 2 and v 2 = k 2 /b 2 the
squares of the reciprocal lattice vectors for the Bragg beams g=(h,k) and C, is the
spherical aberration of the microscope. Equation (3.14) incorporates the phase shift introduced by both spherical aberration and defocusing. The effect of spherical aberration
is to defract the beams leaving an axial object at a large angle
e,
more strongly than
those leaving the object at a small angle. The result is that the more strongly scattered
beam crosses the microscope axis before the Gaussian image plane. The distance in the
77
image plane ri corresponding to a distance r. in the object, is proportional to
e3,
so that
ri = roM = C.ME3i where M is the magnification.
Substituting for
'D.P.
using Eq. (3.12) in terms of F(u,v), the image amplitude for
magnification M (z=Mf) is [1]
Ti(x, y) =
1
-iel-i;r(Y
2+ 2,
) Iif
002io
f F(u, v)P(u, v)eiE(uv)e2i[u
+v-]dudv.
(3.15)
The product P(u,v) exp[i7(u,v)] in Eq. (3.15) is the microscope transfer function
Tm(u,v) (see Fig. 3.3),
Tm(u, v) = P(u, v)exp[i=(u, v)].
(3.16).
Thus, the image wave amplitude in Eq. (3.15) is essentially the Fourier transform of the
product F(u, v)Tm(u, v). Instabilities in the lens excitation current and fluctuations in
the accelerating voltage are taken into account by multiplying Tm(u, v) by a damping
envelope of the form exp(-
r 2A 2e /A 2 ) [1] where
A =
cC
(3.17)
I2)
W)
Cc is the chromatic aberration and a(Wo) and u(I) are the standard deviations for the
distributions of accelerating voltage and current, respectively. The chromatic aberration
is a constant that relates the fluctuatons in the accelerating voltage (AWo) and lens
current (AI) to the change in focus (Af) that these fluctuations produce.
The result
of chromatic aberration of the lenses is to defract less strongly waves with high energy.
Thus, chromatic aberration produces a change in the focus value Af so that if Aro is a
distance in the object then Aro = E)Af where 80 is again the angle between the ray
leaving the object and the microscope axis. Substituting for Af [1,4] from
Af
AVo
2AI
f
VO
I
(3.18)
we get
Aro = OGCc
AVo
VO
2A
I
.
(3.19)
The effect of chromatic aberration can be reduced when a LaB6 filament is used,
since, this filament emits electrons with a smaller energy spread than pointed tungsten filaments.
The microscope transfer function defines the resolution limit of the
78
+r-
(a)
(111) Si
tj
12
4
IK I nm-i
Max. gun-bias
Min. gun bias
-1
+Ir-
(b)
(111) Si
3
V2V
-,
4
IKI nm~I
Passband
- 1
Figure 3.3: Transfer function for a 100 kV electron microscope with C, = 2.2 mm. a)
for n=0 Scherzer focus (Af = -110.4 nm) and b) n=3 (Af = -331.5 nm).[11
79
microscope.
There are essentially two resolution limits: the point resolution which is
given by the first zero of the transfer function (Fig. 3.3) at the Scherzer focus (n=0 in
Afn = [CA(8n+3)/2]1/ 2 ). The Scherzer focus defines the zeroth pass band in the transfer
function and the optimum focus condition for straight forward interpretation of images
of defects.[1] For the JEOL 200 CX, the Scherzer focus is ~ -657.0
A
(C
and the point-to-point resolution for the top entry and side entry microscopes is
(C, = 1.21 mm) and 2.9
A
(C. = 2.8 mm), respectively.
A)
2.3 A
= 1.21
The second resolution limit
is defined by the electronic instabilities and is given by d ~ [-A&]1/2.
This resolution
limit is called the information resolution limit. This limit establishes the highest detail
in resolution that can be extracted from a micrograph using image processing methods.
For the JEOL 200 CX, this limit is ~ 1.4
A.
A good approximation for the optimum
resolution which takes account of both spherical aberration and diffraction aberration
(introduced by the size of the objective aperture) is given by d = 0.66C. 1 4 A/4.[1,5]
For a perfect crystal, the image amplitude Qi(r) can be written in terms of the
amplitude of the diffraction pattern 'PD.P.(g) at the back focal plane of the objective
lens as
Ti(r) =
Z '.p.(g)exp{-27ri
(g - r)}exp[iE(g)]
(3.20)
g
where the summation is over the diffracted beams at the back focal plane that are
included in the objective aperture and are given by Eq. (3.12).
It is clear from Eqs. (3.14) and (3.20) that the effect of the lenses is to introduce an
extra phase factor to the image wave function which depends on defocusing, spherical
aberration of the microscope lenses, stability of the microscope high voltage and lens
current.
There are several methods used to obtain lattice images: (1) axial illumination with
a displaced aperture (see Fig. 3.4a)), (2) tilted illumination (see Fig.
3.4b)) and (3)
axial illumination and aperture centered (see Fig. 3.4c)). Structural information can
be extracted more acturately when method 3 is used since for the first method, the
image resolution is limited by fluctuations in the objective lens current or high voltage,
which may produce fringe displacements during an exposure. When the second method
is used, it is very difficult to extract structural information even though the highest line
80
a
0
a
lactice Cringes
Ewald sphere
aperture
g
(b)
OxO
0
g
0o
(c)
a~
a
a
0og
-Aj
-g
a
__
/a
g
x Optic axis
o
Bragg beams
a
Figure 3.4: Imaging methods for simple lattice fringes: a) untilted illumination, and
displaced aperture b) tilted illumination and c) three beam fringes.[1]
resolution two beam lattice fringes are obtained with this method.LI Thus, method (3)
is the most common method used for studying the structure of materials using the TEM.
For axial illumination using the method shown in Fig. 3.4c), from Eq. (3.20) the
image amplitude for a perfect crystal is given by
Pi(r) = 'P 0 exp(27rik - r) + E
1P (g)exp(2-ri(k + g + sg) - r)exp(iE(g))
(3.21)
= ()
where the summation is carried out over all the beams included in the aperture, %P,
is the amplitude-of the incident wave, IP(-) = Dge 'i
Bragg beams and
are the complex amplitudes of the
eg is the scattering phase of beam g. The image intensity is calculated
81
from
I(x) = Ti(r)T!(r)
=
02,+
'2' +29 E'Po4gcos(27rg - r)cos(.(g) + eg) +E Pg'Pgcos(27r(g
g
g
- g') -r).
g,g'
(3.22)
In the case of three beam fringes (see Fig. 3.4c)),
fringes are observed for
n=0, i1,
2, ...
'(uh)
= '-h
= nir or from Eq. (3.14), for
and E = -r/2, half spacing
Af = nA/02
-
C094/2, for
and where 0, is twice the Bragg angle. From Eqs. (3.14) and (3.22) we
.
can see that the image intensity is periodic in both zf and C5
The diffracted amplitudes
%PD.P.(g)in
Eq. (3.20) express the total scattering by the
crystal in a particular direction. In order to calculate 'QD.P.(g) using Eq. (3.12), the
specimen transmission function T(x', y') must be obtained. There are several theories
in electron diffraction that are used to calculate T(x', y'): (1) the kinematic theory of
diffraction which gives qualitatively useful results and provides quantitative information
for very thin specimens (several nm) of light atomic numbers, (2) the dynamical theory
which takes account of multiple scattering within the specimen, (3) the weak phase
object which assumes kinematic scattering within the specimen, (4) the strong phase
object which takes the Ewald sphere to be a plane normal to the incident beam direction
and (5) the thick phase grating approximation which takes account of multiple scattering
and, to some extent, the curvature of the Ewald sphere. The first two of these theories
are explained in more detail below.
The Kinematic Theory of Electron Diffraction.
In the kinematic theory [2,3,4], it is assumed that the undiffracted beam is very much
stronger than any of the diffracted beams. The solution to Schr6dinger equation (Eq.
3.1) at the exit face of a specimen of thickness t can be written as
' (r) =
4'
e2'i{[1+v(r)/wo]-1/2-1}t/Ao
P iae-iav(r)t
e (x, y) = 4o exp(- iop(x, y))
82
(3.23)
for V(r) << Wo (weak phase approximation), and where
0 is the incident wave am-
plitude, o = meA/(2rh 2) is a constant, m and e are the electron relativistic mass and
charge, respectively, h = h/27r, h is Planck's constant and Op =
f/
2
V(x, y, z)dz is the
projected potential of the specimen of thickness t along the electron beam direction.
It is important to understand how the image intensity depends on sample thickness
and orientation.
From the kinematic theory, using an extension of the weak-phase
approximation to include the effect of Fresnel diffraction (focus variation through the
thickness of the specimen) we obtain [3]
W
= -iaVgt
(s
t)
exp(-i7rsgt)
(3.24)
where Vg is the Fourier coefficient of the potential and the excitation error sg defines the
orientation of the crystal with respect to the incident electron beam direction.
The diffracted intensity for unit incident amplitude is
I(g) =
-
sin
Ig
(Ztsg) 2
tg
(3.25)
The intensity I(g) in Eq. (3.25) oscillates with thickness and has maximum values of
1/ 2s2 . For sg = 0, I(g) = i'rt
be applied for t <
2
/g increases as
t 2 and the kinematical theory can only
g/10.
From Eq. (3.15), for a centered objective aperture the image wave amplitude is [1]
%Pi(x,y)= 1 - ioOp(-x, -y) * F.T.{P(u,v)exp[iE(u,v)]}
(3.26)
for unit magnification and the image intensity is
I(x,y) = ki(xy)T (xy)
; 1 + 2aop(-x, -y) * F.T.{sinE(u, v)P(u, v)}
(3.27)
where the function F.T. {sinE(u, v)P(u, v)} is the impulse response of the microscope
(see Fig. 3.5).
From Eq. (3.27) we see that the image contrast is proportional to the
specimen projected potential convoluted with the impulse response of the microscope.
The impulse response function specifies the instrumental parameters and aberrations.
Dynamical Theory of Electron Diffraction.
83
,
I
0.3
)
-0.2
-0.1
S
I
I
/T
l
I
I
0.0
I
I
).2
0.1
I
0.3
U
L
0.4
n
6
Figure 3.5: Impulse response for a 100 kV electron microscope with C, = 0.7 mm and
Lf = -61 nm.[1]
If the diffracted amplitudes %I(g)become very large, it is possible that the diffracted
wave is itself scattered by the atoms, in which case the dynamical theory of electron
diffraction [1,2,4] must be applied. The larger the number of beams used to form the
image, the smaller the value of t over which the kinematical theory applies.
In the
dynamical theory
P(r) = P0 (z)exp(27rik - r) + E
g(z)exp(2irik' - r)
(3.28)
g
where k' = k + g +
sg and (, and
4
'g
vary with z as a result of multiple scattering
within the specimen.
There are two formulations for the dynamical theory of electron diffraction: (1) as
a system of differential equations and (2) as an eigenvalue problem. The formulation
as a system of differential equations was applied for electron diffraction [6] using the
dynamical theory of x-ray diffraction [7,81. For two beams, an incident wave of amplitude
Wo and a scattered wave xIg passing through a specimen of thickness dz, the differential
equations relating these two wave functions are
dgig = {
qo(z)exp(-27i(k - k') - r)}dz
qlg(z) +
O
Cg
84
(3.29)
mc22r62
)M
C2
and
O(z) + S 'g(z)exp(27ri(k
dQO = {
- k') - r)}dz
(3.30)
or, since sg is along the z axis
d *- =
-'(z)
+ -
(z)exp(27risg z)
(3.31)
o(z)exp(-2risgz)
(3.32)
Pg
and
(
dP
d-E- = 7ri-Wg(z) + ridz
CO
where g = 7VccosO/AFg and A and Fg are the relativistically corrected wavelength and
structure factor. These equations have solutions of the form
(3.33)
TO) = A()exp(27riy(0)z)
where the AW) are constants and
0) =
(s
-
s2 + 1/
(-1)
(3.34)
.
The same procedure can be extended to the n-beam case. The set of differential
equations for the n-beam case is solved using computational methods.[9,10,11]
In the second formulation, the problem consists on solving Schr6dinger equation (Eq.
(3.1)) for the periodic potential of the specimen. The solutions are Bloch waves of the
form
TM)(r) = b()(k,r) = EC )exp[27ri(k) + g) - r].
(3.35)
g
Substituting T(r) into Eq. (3.1) we obtain a set of equations for the coefficients Cg
(K 2
-
(k + g) 2 )Cg(k) +
me h
VgCg
(k) = 0
(3.36)
1+ W)
(3.37)
where
K2
me
2
WO 1+ W
)
+ Vspec(r)
is the wave vector ir-side the crystal. From Eq. (3.36) the dispersion curves for the wave
vector k are obtained.[2,4]
In the following sections, we present the results obtained from electron diffraction
patterns, dark field images and high resolution lattice images on KH- and KD-GICs.
85
We compare the results for the two different intercalant species and for the two different
intercalation processes.
Synthesis of the KH.- (KDy)-GIC's can be achieved by direct intercalation of KH
(KD) [12] or by chemical absorption of hydrogen (deuterium) into potassium-GIC [13].
However, stage 1 KH,- (KDy)-GICs can only be obtained by the direct intercalation of
KH (KD). The stoichiometry of the compound depends on the intercalation process, with
a higher hydrogen (deuterium) uptake for the direct intercalation of KH (KD) (x ~ 0.8)
[12] than for the chemical absorption of hydrogen into potassium-GIC (x ~ 0.66)
[14]. In
this work, we used high resolution transmission electron microscopy (TEM) to study and
compare the structure of KH, (KDy)-GIC obtained by the two intercalation methods.
We have used both highly oriented pyrolytic graphite (HOPG) and benzene-derived
graphite fibers (BDGF) as host materials. The HOPG based samples give information
about the in-plane structure, whereas the fiber host provides information about the caxis structure. In this chapter we present studies on the structure of these compounds
as well as the stage dependence and intercalation process as a function of intercalation
temperature and time. During the TEM observation, electron beam induced desorption
of the hydrogen takes place, thereby allowing detailed examination of the desorption
process.
3.2
Experimental Details.
The samples used in this experiment were intercalated by Ms. Nai-Chang Yeh and
Dr. Toshiaki Enoki, using either the direct intercalation method [15] or the chemical absorption method [13]. A higher hydrogen (deuterium) uptake for the direct intercalation
of KH (KD) (x ~ 0.8) [12] than for the chemical absorption of hydrogen into potassiumGIC (x ~ 0.66) [14] has been reported. In this work, the TEM observation was done
using two transmission electron microscopes. A JEOL 200 CX (C, = 2.8 mm) with a
LaB 6 filament was used to obtain the high resolution images and a JEM 100 CX with a
pointed tungsten filament was used for the low magnification studies. After completion
of the intercalation process, the samples were characterized for stage by Ms. Nai-Chang
Yeh using (00t) x-ray diffraction through a glass ampoule containing a partial pr'essure of
86
hydrogen gas and some intercalant powder. The samples were then prepared for electron
microscopy inside a glove bag under an argon atmosphere. The HOPG based samples
were prepared by repeated cleavage until a sample with thin regions ( ; 300
A)
along the
edges was obtained. The thin sample was placed between Cu 400 mesh electron microscope grids. The intercalated fibers, on the other hand, were directly placed between the
Cu grids with no special thinning technique. The grids containing the samples were put
in the sample holder which was then taken out of the glove bag and quickly introduced
.
into the microscope column, to minimize the exposure to air
In studying the structure of KH- (KD-)GICs using the TEM, we have obtained
information from (hko) and (hki) electron diffraction patterns, dark field images and
high resolution lattice images. The dark field images were obtained by tilting the beam
until the desired reflection was on the optic axis of the microscope. An objective aperture
was then placed at the BFP including only the desired reflection. The in-plane high
resolution lattice images were obtained under axial illumination by placing an objective
aperture that encompassed the unscattered beam and reflections up to 1.70 A- 1 . The
c-axis lattice images were also obtained under axial illumination, by placing an aperture
that enclosed reflections up to 1.88
A-'.
The interplanar spacings were obtained from
optical diffractograms obtained from the negatives of the images.[1]
3.3
Results and Discussion.
Pristine KH and KD have very similar structures.
tices with a lattice parameter of 5.70
A.
Both compounds form fcc lat-
Therefore, similar structures are expected for
both intercalated compounds. We have studied the structure at a microscopic level for
both intercalant species using the TEM and have found the same structure for both
compounds.
The intercalation process of KH (KD) into graphite has been studied using (00e)
x-ray diffraction on HOPG samples intercalated at several temperatures T: and for
various times ti.[161 The x-ray diffraction study showed that for 350*C < Ti < 430*C,
the first step of intercalation (after a few hours) was a stage 1 potassium-GIC (repeat
distance Ic = 5.35
0.03
A).
After a few days, peaks -in the (00t) x-ray diffractograms
87
corresponding to a mixture of stage 1 potassium-GIC and stage 1 KH-GIC (IC = 8.55
0.03
A)
were obtained with a small admixture of stage 2 KH-GIC. Finally, after 10 days
of intercalation, only peaks corresponding to stage 1 KH and the small admixture of stage
2 KH-GIC were observed. This intercalation process was also observed by Guerard et
al.[17] Similarly, stage 2 KH compounds were obtained for 2000 C < T < 210'C. For the
stage 2 compounds (see Fig. 3.6), the first step of intercalation was stage 2 potassiumGIC (IC = 8.75
0.03
A),
and the final compound (after ~ 10 days) that was observed
was a stage 2 KH-GIC (I = 12.08
0.03
A).
For 2100 C < Tj < 350"C, mixed stages
(potassium-GIC and KH-GIC) were obtained. The repeat distance of 12.08
A
obtained
for stage 2 KH-GIC is larger than that obtained by P. Eklund et al [18] (11.90
A repeat distance of 11.93
A
A).
has been obtained using x-ray diffraction from samples
that had been intercalated a year before.[19] It is interesting to note that essentially
the same Shubnikov de Haas frequencies were obtained from the samples with a smaller
repeat distance of 11.93 A than for those with a larger repeat distance of 12.08
A.[19]
It is
possible that the two different repeat distances correspond to a different hydrogen content
in the intercalate layer with a slightly smaller hydrogen content for the smaller repeat
distance than for the larger one (the difference in hydrogen content is not large enough
to produce a change in the Shubnikov de Haas frequencies). There is also the possibility
(as explained below) that some KH (in its pristine form) is contained as inclusions in
the intercalate layer of the samples with larger repeat distance as was found for the case
of NaH-GICs.[17]
The process of intercalation described above is different from that observed for the
chemical absorption of hydrogen into stage 1 potassium.[14] In the chemical absorption
method, the first step of intercalation is stage 1 potassium-GIC (obtained by intercalation of potassium only), and the final step (after the absorption of hydrogen) is a stage
2 KH-GIC.[14] Some of the samples used in the x-ray diffraction experiment, were used
to prepare samples for the TEM experiment. The TEM results were consistent with the
x-ray diffraction results [16], as explained below.
The c-axis repeat distance I, was deduced using the TEM from (00i) lattice fringes
obtained either from regions of the intercalated HOPG samples that were bent in such a
way that the
(00e) planes were parallel to the electron beam direction or from the edges
88
(004)
C 8 KH x+C 24 K (200'C)
(003)
[002]l
(
(af ter 4 days)
[0031
( ):C 8 KHx
C24K
01001)(002)
(005)[004)
(I)
(008)
(007)
(004)
C8KHx +C 24 K (200'C)
Stage 2 (after 7 days)
(003)
C
(001)
003
(1
002]
(007)
(005)[()(4]
A
(0 )(09
C3Kr~rx ( 200 C)
(N03)
(00)"Stage
(001)
2(of ter 10days)
(002)
(005)
(j
SI
3
I
I
I
(009) (0010)(01
L(00)
I
I
I
9
15
21
27
Diffraction angle 20 (degrees)
33
Figure 3.6: (00t) x-ray diffractograms of a sample intercalated with KH at 200'C showing
the intercalation process (obtained by Nai-Chang Yeh).
of the intercalated BDGF. Figure 3.7 shows a c-axis lattice image of an HOPG sample
intercalated at 430*C. This figure shows a single staged sample with Ic = 8.53
The same repeat distance (within experimental error) of 8.55
A was
0.08
A.
obtained from (00t)
x-ray diffraction from the same sample. This repeat distance is in agreement with the
model suggested by Gudrard [14], and schematically represented in the inset to Fig. 3.7.
In this model, the intercalate layer forms a three layer sandwich along the c-axis with
two layers of K atoms, one above and one below a layer of H atoms. This structure is
89
Figure 3.7: c-axis lattice image of a stage 1 KH-GIC sample intercalated into HOPG
at 430*C. The insets are a schematic of the structure along the c-axis and an optical
diffractogram taken from the negative of the figure.
90
91
91l
K
.4
io
I
$i~
f
x
C)
similar to that of KHg-GICs [20,21,22] where the intercalate layer forms a three layer
sandwich with the Hg layer sandwiched between the two layers of K atoms. It has been
suggested that the layer of Hg atoms consists of two layers of Hg, with the Hg atoms
A
staggered from each other by ~ 0.254
[21,22]. It is shown below that the in-plane
structure of KH-GICs is also similar to that of KHg-GICs.
KH-GIC samples intercalated at lower temperatures showed several repeat distances.
Figure 3.8 shows c-axis lattice image of a sample intercalated with KH at 2100C for
11.90
0.08
This figure shows three repeat distances 8.80
8 days.
A.
0.08
The values of 8.80
A and
11.90
A correspond
and a stage 2 KH-GIC, respectively. The value of 10.62
A,
10.62
0.08
A
and
to a stage 2 potassium-GIC
A can
be explained as the repeat
distance of a stage 2 hydrogen deficient region which separates a region of a pure stage 2
potassium-GIC and a region of a stage 2 KH-GIC with normal hydrogen concentration.
The three regions are presented schematically in the figure. This result is in agreement
with the x-ray diffraction result, where it was found that for ti < 10 days, a mixture of
0
0
stage 2 potassium-GIC and stage 2 KH-GIC was obtained for 200 C < Tj < 230 C.
Figure 3.9 shows a c-axis lattice image of an HOPG sample intercalated with KH
at 2900C. Analysis of the (00f) x-ray diffractograms obtained from this sample showed
two repeat distances of 5.35
0.03
A
0.03
and 8.55
A
suggesting an admixture of a
stage 1 potassium-GIC and a stage 1 KH-GIC. The c-axis lattice image in Fig. 3.9,
shows two repeat distances of 5.38
0.08
A
and 14.06
0.08
A.
The I, of 5.38
A
corresponds to a stage 1 potassium-GIC. Similar values for the repeat distance were
obtained from (00t) lattice fringe images of benzene-derived graphite fibers intercalated
with KH at 3200C. The repeat distance of 14.06
A
can also be related to a region in
the boundary between a stage 1 potassium-GIC region and a stage 1 KH-GIC region.
The hydrogen deficient region in the boundary, can be interpreted as being formed by
a periodic mixture of alternating layers of stage one potassium-GIC and stage 1 KHGIC as shown schematically in the inset to Fig. 3.9. The fact that the repeat distance
of 14.06
A
corresponds to boundary regions, was corroborated by c-axis lattice images
obtained from other regions of this sample which showed two repeat distances of 14.06
and 8.55
A.
A
This result is also in agreement with the x-ray diffraction result [16] where
0
0
a mixture of stage 1 potassium and stage 1 KH was obtained for 290 C < T < 350 C.
92
Figure 3.8: c-axis lattice image of a stage 2 (C 2 4K)(CsKH) sample prepared by direct
intercalation with KH at 210*C.
93
e
e
Sv
0
9
K
0
8.77A
/4v
C24 K
c
K
0
10. 657-A
C
C K HX
X < /2
3,
X"O QA/mK-x~xx
C8 K H
H
H
K
c
c
x X ~0.8
0
I I.90 A
Figure 3.9: c-axis lattice image of a stage 1 sample of (C 8 K)(C 4 KH) prepared by the
direct intercalation of KH at 290'C.
95
C
K
0
8.55A
H H
K
I
C4K H X
-
46'-
HH
___
__ ___ __
K
13.91 A
C
____
(C
4
K
KHX)(C 8 K)
K
C8K
5.35A
A repeat distance of 13.80
A
has been observed on samples intercalated with KH by the
chemical absorption of hydrogen into stage one potassium-GIC that were encapsoulated
with K metal and heated to a temperature just above the melting point of the potassium
metal.[14] The repeat distance of 13.80
A in
[14] was also interpreted as a periodic mixture
of a stage 1 KH-GIC and a stage 1 potassium-GIC. The smaller repeat distance of
13.80
A
compared to 14.06
A
is probably due to the fact that the hydrogen content in
a KH-GIC is lower when the chemical absorption method is used than when the direct
intercalation method is used.
The repeat distances of 14.06
A
(n=1) and 10.62
A
(n=2) at the boundary between
a pure potassium-GIC region and a hydrogen saturated region are observed in small
regions (- 100
A
thick). Consequently, they cannot be observed using x-ray diffrac-
tion, since x-ray diffraction is a bulk probe. Thus, the TEM results support the x-ray
diffraction results for the process of intercalation of KH into graphite and give additional
information about the intercalation process. The TEM results suggest that the intermediate phase between a potassium-GIC and a KH-GIC is that observed at the 'boundary'
regions, and further, that as the intercalation proceeds, the boundary moves toward the
pure potassium-GIC region. The net effect is that the hydrogen saturated regions grow
at the expense of the pure potassium regions within the intercalation compound.
Other values for repeat distances were obtained in other regions of the stage 1 samples
using the TEM: 8.07
0.08
A
and 9.36
0.08
A.
Some of these I, values are perhaps
related to desorbed regions, where hydrogen deficient phases might exist.
We have also studied the in-plane structure of KH-GICs using the TEM for several
intercalation temperatures and times. Two commensurate in-plane phases were found
to coexist in samples intercalated with KH and KD for stages 1 and 2 and intercalation
temperatures between 200'C and 430*C: a (2 x 2)RO* phase and a (V'_ x
(see Fig. 3.10a)).[23] The set of spots at 2.21
A~1
and 3.11
A~1
y'3)R30'
phase
seen in Fig. 3.10a),
correspond to an incommensurate phase with reciprocal lattice vectors in agreement
with the (200) and (220) reciprocal lattice vectors for pristine KH. During the TEM
observation, several changes in the diffraction pattern take place; the commensurate
phases disappear and the set of spots at 2.21 A- 1 and 3.11 A' become sharp rings. To
minimize the effect of the electron beam, an accelerating voltage of 100 KV was used,
97
Figure 3.10: (hkO) electron diffraction patterns of HOPG intercalated with KH at: a)
290 0 C, and b) 430*C.
98
99
and even with this lower voltage the spots at 2.21
to pristine KH were observed.
A
and 3.11
A
corresponding
It is possible that these broad incommensurate spots
correspond to small crystallites of KH sitting on the surface of the sample that desorbed
primarily during the TEM observation. The elongated (200) and (220) spot patterns at
q=2.21
A-' and 3.11 A-1, respectively, are identified with an orientational alignment
of the unit vectors of the KH crystallites with those of the graphite substrate due to
It has been reported [17] that for NaH-
the epitaxial growth of the KH crystallites.
GICs some of the intercalate retains its pristine hydride form and is probably sitting
Thus, we believe that for KH-GICs, it is
as inclusions between the graphite layers.
also possible that some small KH crystallites are in the intercalate layer.
The TEM-
induced desorption occurs since an accelerating voltage of 100 KV gives the electrons
a kinetic energy above the threshold energy to produce atom displacements in knock-
A-' and
on collisions with the hydrogen atoms.[24] We believe that the rings at 2.21
A-1
3.11
observed in the electron diffraction patterns after electron beam irradiation
correspond to speckles of desorbed KH on the surface of the sample.
Figure 3.10b) shows an electron diffraction pattern of a stage 1 sample intercalated
with KH at 430*C. This figure shows only the (2 x 2)RO* commensurate in-plane structure and very weak spots at the 2.21
A-1 and 3.11 A-1 reciprocal lattice vectors. Some
electron diffraction patterns obtained from other regions of the same sample showed
weak
(v3
x V'-)R30* spots indicating a small admixture of the two phases. This result
indicates that the higher intercalation temperature of 430*C favors the formation of the
less dense (2 x 2)RO* in-plane phase.
Figure 3.11 shows dark field images using the (2 x 2)RO* (Fig. 3.11a)) and (v"3 x
V'3)R30* (Fig. 3.11b)) spots taken from a region of the sample intercalated at 430*C
where the two in-plane phases coexisted. These dark field images show small
islands of the (-
(- 250 A)
3.11b)) separated by a large (- 1000
x V3)R30* phase (Fig.
A)
background of the (2 x 2)RO* phase (Fig. 3.11a)). This figure indicates that the two
commensurate in-plane structures form separate phases.
Dark field images obtained from the (V/- x ,F3)R300 and the (2 x 2)RO
a sample intercalated at 320'C showed islands of dimension of ~ 300
A
spots of
for the (v"_ x
v/3)R300 phase and ~ 600A for the (2 x 2)RO* phase. Analysis of dark field images from
100
Figure 3.11: Dark field images of a sample intercalated with KH at 430*C using the
direct intercalation process. The images were obtained using a) the (2 x 2)RO and b)
the (v'3 x V3)R30* spots. The images in a) and b) were obtained from the same region
of the sample.
101
102
the two in-plane phases for samples intercalated at different temperatures showed that
the relative concentration of the two phases depends on intercalation temperature. Our
results indicate that the (2 x 2)RO phase is dominant for high intercalation temperatures
whereas the
(A3
x V3)R30' phase is dominant for low intercalation temperatures. It is
interesting to note that these two in-plane phases have also been observed in KHg-GICs
[20,21]. In the KHg-GIC system a (2 x V3-)R(OO, 300) commensurate phase has also been
observed using the TEM.[20] This phase has not been observed in the KH-GIC system.
Similar (hk0) electron diffraction patterns and c-axis repeat distances were obtained
for the KD-GIC samples. This indicates that both intercalants form the same structure
upon intercalation, as was expected from their structure in the pristine form. Figure
3.12 shows an in-plane lattice image of a stage 1 KD-GIC sample showing a periodicity
of 4.26
0.08 A. This periodicity corresponds to the (2 x 2)RO* commensurate phase.
A possible arrangement for the K and H atoms in the
(v'3
x V1)R30* phase and
the (2 x 2)RO* phase, is that the K atoms sit at either the (Vf x V3)R30* or at the
(2 x 2)RO* sites in either an a a or
a 8 stacking within the intercalate layer. That is,
the two K atoms in the intercalate sandwich, can sit on top of each other (a a stacking),
or in equivalent but distinct positions (a g stacking) and the hydrogen atoms are at
the positions that are not occupied by the K atoms. A possible structure for the KH-
GIC system has been suggested based on neutron scattering experiments from C8 KH2 /3
samples.[25] The model proposed [25] consists of two (2 x 2)ROO layers of K atoms placed
face to face and shifted by ao (the graphite lattice constant) with respect to one another
(see Fig. 3.13). In this model the hydrogen atoms take the unoccupied sites. Thus, for a
small value of x ~ 0.66 not all the hydrogen sites are occupied and the unit cell is larger
than the (2 x 2)R30' unit cell. An orthorhombic unit cell with parameters a = 8.56 A,
b = 12.39 A and c = 21 = 17.06 A has been suggested for the KH-GIC system.[12]
Up to now, we have no evidence for this large space periodicity, probably because the
TEM is more sensitive to the K atoms than to the hydrogen atoms and from ref [25], it
is the hydrogen atoms that define the larger unit cell. Quasielastic neutron scattering
experiments on stage 2 KH- (KD-)GIC samples prepared by the chemical absorption
method, showed no evidence for hydrogen (deuterium) motion for momentum transfers
up to 2.5 A-1 (resolution ~ 100 peV at 295 K and ~ 1 peV at 453 K).[26]
103
Figure 3.12: In-plane lattice image of a stage 1 KD-GIC sample showing the (2 x 2)RO0
commensurate phase. The sample was prepared by direct intercalation of KD into
graphite at 410*C.
104
-
;
-
4,
pa
74.
.
jot
v4
w
A
x
@
H
H
153.
3-31
Figure 3.13: Model for the atomic arrangement of C8K12/3 based on neutron diffraction
patterns.[25]
3.4
Intercalation by the Chemical Absorption of Hydrogen into C8K.
Figure 3.14 shows c-axis fringes of a stage 2 KH, intercalated fiber prepared by
chemical absorption of hydrogen into a stage 1 potassium intercalated fiber. This figure
shows two different repeat distances in two separate regions of the fiber. In one of these
regions a repeat distance of ~ 11.76
0.08A was observed corresponding to the stage
2 KHz in agreement with the value of 11.88
region, fringes with spacing ~ 3.4
with spacings ~ 8.4
A
A
A
reported by Gudrard et al.[14] In this
periodically stacked between layered structures
are clearly observed, demonstrating the structure of the stage 2
KJ1--GIC with Ic = 11.8
A.
Also in this figure, a repeat distance of ~ 8.7
A
can be
observed in a different region of the sample. This repeat distance is in agreement with
the value reported for stage 2 potassium-GIC
[27]
and corresponds to a desorbed region
of the sample. It is important to note that the texture observed in the desorbed region
is different from that of potassium compounds that have been directly synthesized
106
Figure 3.14: Bright field c-axis lattice fringes of a stage 2 intercalated fiber prepared by
chemical absorption of hydrogen into a stage 1 C 8 K intercalated fiber. The figure shows
a CsKHx region and a C 24 K (desorbed) region. The inset is an optical diffractogram
taken from the negative of the photograph.
107
t.'
-
0A
00
.in.-Alp
IL.f
-4*.
using BDGF as host material.[28] The smaller repeat distance (11.76
A)
observed for
the samples synthesized using the chemical absorption method than that obtained from
samples synthesized by the direct intercalation method
(~
12.08
A), is consistent with a
smaller hydrogen content (x ~ 0.66 [14]) for samples prepared by the chemical absorption
method than for the direct intercalation method (x ~ 0.8 [12]).
The high degree of in-plane structural order observed in these KH.-GICs ranks them
among the best ordered intercalation compounds that can be synthesized. In addition
to this high degree of structural order, the ionic nature of KH creates high interest in
the charge transfer associated with these compounds.[15,29}
109
References
[1] J.C.H. Spence, Experimental High Resolution Electron Microscopy, (Clarendon
Press, Oxford, 1981).
[2] P. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron
Microscopy of Thin Crystals, (Robert E. Krieger Publishing.
Co. Inc., 1977), p.
100.
[3] A. Howie, The Theory of Electron Diffraction Image Contrast in Electron Microscopy in Materials Science (eds. U. Valdre and A. Zichichi, Academic Press,
New York, 1971).
[4] L. Reimer, Transmission Electron Microscopy, (Springer Verlag, Berlin, New York
and Tokyo, 1984).
[5] 0. Scherzer, J. Appl. Phys. 20, 20 (1949).
[6] A. Howie, M.J. Whelan, Proc. Roy. Soc. A263, 217 (1961); A267, 206 (1962).
[7] C.G. Darwin, Phil. Mag. 27, 315 and 675 (1914).
[8] Z.G. Pinsker, Dynamical Scattering of X-Rays in Crystals, Springer Series, Solid
State Sci., 3, (Springer, Berlin, Heidelberg, New York, 1978).
[9] J.M. Cowley and A.F. Moodie, Acta Cryst. 10, 609 (1957).
[10] D.F. Lynch, Acta Cryst. A27, 399 (1971).
[11] P. Goodman and A.F. Moodie, Acta Cryst. A30, 280 (1974).
[12] D. Gu6rard, C. Takoudjou and F. Rousseaux, Synthetic Metals 7, 43 (1983).
110
[13] M. Colin and A. H6rold, Bull. Soc. Chim. Fr. 1971 (1982).
[14] D. Guerard, P. Lagrange and A. H6rold, Materials Science and Engineering 31, 29
(1977).
[15] N.-C. Yeh, T. Enoki, L.E. McNeil, G. Roth, L. Salamanca-Riba, M. Endo and
G. Dresselhaus, MRS Extended Abstracts, Graphite Intercalation Compounds , (ed.
P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus, Boston 1984), p. 246.
[16] N.-C. Yeh, T. Enoki, L. Salamanca-Riba and G. Dresselhaus, Proc. of the
1 7 th
Biennial Conf. on Carbon, Lexington, June 1985, p. 194.
[17] D. Guerard, Proc. of the Symposium on Graphite Intercalation Compounds, Tsukuba,
May 1985.
[18] P.C. Eklund, private communication.
[19] T. Enoki, N.-C. Yeh, S.T. Chen and M.S. Dresselhaus, to be published.
[20] G. Timp', MIT PhD. Thesis, 1983.
[21] M. El Makrini, P. Lagrange, D. Guerard and A. Herold, Carbon 18, 211 (1980).
[22] P. Lagrange, M. El Makrini, and A. H6rold, Revue de Chimie Minirale 20, 229
(1983).
[23] L. Salamanca-Riba, N.-C. Yeh, T. Enoki, M.S. Dresselhaus and M. Endo, (MRS
Extended Abstracts, Graphite Intercalation Compounds , ed.
P.C Eklund, M.S.
Dresselhaus and G. Dresselhaus, Boston 1984), p. 249.
[24] L.W. Hobbs, Quantitative Electron Microscopy, Proc. of the
2 5 th
Scottish Univer-
sity Summer School in Physics, Glasgow Aug. 1983, ed. J.N. Chapman, and A.J.
Craven, SUSSP Publications, Edinburg, (1983), p. 399,
[25] T. Trewern, R.K. Thomas, G. Naylor and J.W. White, J. Chem. Soc., Faraday
Trans. I, 78, 2369 (1982).
[26] T. Trewern, R.K. Thomas and J.W. White, J. Chem. Soc., Faraday Trans. I., 78,
2399 (1982).
111
[27] M.S. Dresselhaus and G. Dresselhaus, Advances in Physics 30, 139 (1981).
[28] M. Endo, T. C. Chieu, G. Timp, M.S. Dresselhaus and B.S. Elman, Phys. Rev.
B28, 6982 (1983).
[29] T. Enoki, H. Inokuchi and M. Sano, MRS Extended Abstracts, Graphite Intercalation Compounds , (ed. P.C Eklund, M.S. Dresselhaus and G. Dresselhaus, Boston
1984), p. 243.
112
Chapter 4
COMPUTER IMAGE
SIMULATION OF SbC1 5 -GICs
In this chapter we compare high resolution lattice images of the (v'7x V/\)R19.1o commensurate phase obtained on stage 2 SbCl 5-GICs using the TEM with images obtained
using computer image simulation. Section 4.1 contains the introduction to the chapter.
The computational methods most commonly used for image simulation are described in
section 4.2. Sections 4.3 and 4.4 present the experimental details and the models used
in the multi-slice method, respectively.
The comparison of the simulated images and
the TEM images is presented in section 4.5. Section 4.6 presents the conclusions to the
chapter.
4.1
Introduction.
In the following section we present the development of the different computational
methods used to obtain structural information from TEM micrographs. We concentrate
on the multi-slice method [1,2] since this was the method that was used in this work. In
this chapter, we apply the technique to the study of the (V/7 x vf)R19.1* in-plane phase
observed in SbCl 5-GICs [3,4,5,6,7,8], as well as to the structure of this system along the
c-axis.
Both electron [3,5,6] (see chapter 2) and x-ray [7,8] diffraction studies have shcwn
that SbCl5 forms several in-plane structures such as the
(V7
x V7_)R19.1* and
(v/39 x
V3)R16.1* structures that are commensurate with the graphite lattice and often coexist in the same sample. There are also disordered regions that give rise to halos in
.113
the diffraction patterns. It was already mentioned in chapter 2 that, along the c-axis
direction, the SbCls intercalate forms a three layered sandwich with two layers of Clions, one above and one below each layer of Sb ions.[4,9] M6ssbauer experiments have
shown that there is a disproportionation of sites into SbCl5 , SbCl~, SbCl 3 and SbClmolecular species in SbCls-GICs.[101 Several models for the molecular arrangements of
these species in the commensurate phases have been suggested.[7, 11]
In its pristine form SbCl 5 retains its molecular bonding in both the liquid and solid
phases. In the isolated molecule, the Sb atom is at the center of a trigonal bipyramid that
has the five C1 atoms at its vertices, such that dsb-3cI = 2.29
A
and dsb-2cI = 2.34
A.
Solid SbCl 5 forms a hexagonal lattice (space group P63/mmc) with two molecules per
unit cell, and having the following parameters: a = 7.49
A
and c = 8.01 A.[12] These
lattice parameters for SbCl 5 suggest that SbCl 5 intercalated into graphite would form
a (3 x 3)R30* commensurate superlattice. Solid SbCl 3 forms an orthorhombic crystal
structure (space group Pbnm) with a tetramolecular cell of dimensions a,
bo = 8.12
A and c.
= 9.47
A.
= 7.37
A,
The SbCl 3 molecules are trigonal pyramids having Cl atoms
at the apices.[12] In contrast to the SbCl 5 lattice constants, the value of 7.37
A suggests
that the SbCl 3 intercalated into graphite would form a (V7- x Vf)R19.1* commensurate
superlattice. It is interesting to note that, to our knowledge, SbCl 3 does not by itself
intercalate into graphite. In section 4.4 we show that simulated images obtained for the
(v7
x \/i)R19.1* structure consisting of either SbCl5 or SbCl 3 molecules, do not agree
with the experimental TEM images.
In this chapter, models for the (Vi x x/7)R19.1* structure are suggested based on
high resolution transmission electron microscopy (TEM) and computer image simulation.
We compare the TEM images obtained for different focus conditions with those obtained
from computer simulation. During the TEM observation the
(-v
x V7-)R19.1' structure
undergoes a change to a glass phase. This phase change is induced by electron beam
irradiation and is described in detail in chapter 5 of this thesis. In this chapter, we also
present high resolution lattice images obtained for different electron beam doses.
114
4.2
Computer Image Simulation.
The problem of electron diffraction in electron microscopy can be divided in two
parts: (1) the effect of the specimen potential on the electron wave function and (2)
the subsequent action of the electron microscope lenses on the diffracted beams. These
two interactions were already described in chapter 3 and are discussed in several references.[13,14,15,16
There are two groups of techniques available for computation of
electron scattering by crystalline materials. Both groups use the dynamical theory of
electron diffraction described in section 3.1.[14,161 One group of computational methods
involves matrix operations and consists of both the Bloch wave formulation [2,171 and the
scattering matrix method [18,19,201. The second group involves a mathematical slicing
of the crystal along the beam direction. There are two methods that involve slicing of
the crystal, the multi-slice method [1,21] and the real space physical optics formulation
[22,231. In this work the multi-slice method was used for the computation of the images
and therefore, this is the method that will be described here.
The multi-slice programs used in this work were obtained from Arizona State University and were written by Dr. M.A. O'Keefe and Dr. A. Skarnulis in the period from
1970-1980. They were later modified for IBM software by Drs. D. Kuhl, J.C.H. Spence
and M.A. O'Keefe.
These programs are based in the use of a 128 x 128 Fast Fourier
Transform, and are limited to ~ 16000 beams. The programs are divided into two sets:
1 the ZOLZ program which takes into account zero order Laue zone effects only, and 2
the 3DPROG which takes into account the effect of higher order Laue zones. The ZOLZ
program approximates the crystal potential by its two dimensional projection through
one unit cell in the electron beam direction. The 3DPROG is used for structures with
large periodicity along the electron beam direction and for non-periodic specimens. In
this work, we used the 3DPROG for the computation of both in-plane and c-axis lattice
images.
The ZOLZ program consists of three programs. The first program FC0128 calculates
the Fourier coefficients of the crystal potential for the zero order Laue zone. The second
program DEFRACT128 performs the multiple electron scattering calculations, and the
third one
IM128 synthesizes the beams in a Fourier series to form the electron lattice
115
image. The 3DPROG uses two programs between FC0128 and IM128. The first one,
PG128 calculates the phase grating coefficients and the second one, MS128 performs the
multi-slice approximation, as explained below.
When the electrons are scattered by the atoms in the crystal they may encounter
elastic as well as inelastic collisions. If the probability density for inelastic collisions is
pi(r) then if 0,, is the incident wave function, the scattered wave function 0,(r) can be
written using the weak phase approximation (V(r) << Wo) (Eq. 3.23) as
V),(r) = 4'oexp[-api(r)H + iVpec(r)H
(4.1)
where H is the thickness of the specimen, Vspec(r) is the specimen potential defined in
Eq. (3.2), o = (meA/2rh 2)(1+eW./emc 2 ) and a are constants, m and e are the electron
rest mass and charge, respectively, A is the electron wavelength, WO. is the accelerating
potential and c is the speed of light in vacuum. Using the thin slice approximation,
(r)
01 - api(r)AZ + iaV(r)AZ]
4i
(4.2)
where AZ < 10 A is the thickness of the specimen along the electron beam direction. The
effect of this approximation on the electron wave function is to introduce a perturbation
in both the amplitude and the phase. Defining the transmission function q(x,y) for a
slice of thickness AZ as
q(x, y) = 1 - api(r)AZ + iuV(r)AZ,
(4.3)
we can write
(r) = q(x, y) Oo.
(4.4)
In order to apply the thin slice approximation to thicker specimens, the crystal
is divided into N slices of thickness AZ so that NAZ = H (see Fig.
4.1), and the
approximation is applied for every slice. The effect of the n th slice is then obtained by
multiplying the wave function on a plane at the center of the slice (see Fig. 4.1) by the
transmission function of the nth slice q(x, y). The source in Fig. 4.1 is defined by q,
and the distance between the planes is R,. The contribution from the nth slice to the
wave function at a distance R from the specimen is given by the Huygen's principle
n(r) = [n-i(r) * pn(r)] - qn(r)
116
(4.5)
q2 q 3
S~)q,
q,.,qN
X
Figure 4.1: Schematic representation of the slicing of the specimen for the image simulation computing method.
where * denotes convolution,
pn (r)
2
2
= p(x, y, zn) = eikn(x +y )/2R
is the propagation function for the distance between the (n -
qn(x,y) = 1 - ap(x, y,zn)AZ
2
(4.6)
1)th and nth slices and
+ iOVspec(x,y,zn)AZ
(4.7)
is the transmission function of the nth slice. The total wave function at R is given by
iterating Eq. (4.5) N times. For an incident wave function 0. the iteration is initiated
by setting 4'(r) = 4ipqi(r).
The effect of the term ap(x, y, z)AZ in Eq. (4.7) corresponding to inelastic scattering
can be identified with absorption of electrons and may be completely removed from the
Then, qn(xy) = exp(iogp(x,y,zI)AZ) is taken as a phase grating where
calculation.
Op(x, y, zn) is the specimen projected potential at z = zn, and is given by
Op(x, y, Zn) = E V(h, k,O)exp{27ri[(hx/a) + (ky/b)]}
(4.8)
h,k
for slices of thickness AZ > c (where c is the lattice parameter along the electron beam
direction), or
Op(x,y,zn)
=
5
h,k,e
V(h,k,t)sin(rfAZ/c)
vk,kte (7r AZ/c) e[2 "t/ce
2;i[(hx/a)+(ky/b)ll
(4.9)
for a slice of thickness AZ < c centered at z. and where a, b and c are the lattice
constants along x, y and z, respectively.
Equation (4.9) takes account of the scattering
117
to diffraction points out of the zeroth Laue zone.[24] Thus, the structure factors and
Fourier coefficients of the potential V(h,k,e) are calculated using the FC0128 program
and the phase gratings q(x,y) (Eq. (4.7)) are calculated using the PG128 program.
It was shown in chapter 3 (Eq. (3.12)) that the amplitude distribution of the diffraction pattern observed at the back focal plane of a perfect objective lens is essentially the
Fourier transform of the wave function at the exit face of the specimen. Using this result
and Eq. (4.4), the contribution of the nth slice to the diffraction pattern is given by [1,2]
'I'(u) = ['I'_i(u) - Pn(u)] * Qn(u)
(4.10)
'I'(u) = F.T.{F.T.-'{%ni(u) - Pn(u)} - F.T.~1{Qn(u)}}
(4.11)
or
where Tn(u), Pa(u) and Qa(u) are the Fourier transforms (F.T.) of tln(r), pn(r) and
qn(r),
respectively. Here F.T. denotes the Fourier transform from real to reciprocal space
and F.T.-' is the inverse Fourier transform.
In the multi-slice method, the iteration is usually performed in reciprocal space since
for a perfect crystal the wave function is finite only at discrete points of the reciprocal
lattice.
The- Fourier transforms are calculated using the fast Fourier transform FFT
algorithm [25], since for a large number of beams, the calculation of TI,(u) from Eq.
(4.11) is faster using the FFT algorithm, than performing the convolution in Eq. (4.10).
The Tn(u) wave functions are calculated in the MS128 program from Eq.
(4.11) by
iterating N times where N is the total number of slices. The image is then computed in
the IM128 program, where parameters such as defocusing, spherical aberration, beam
divergence, vibration, etc. are taken into account as described in chapter 3 (Eq. (3.13)).
The defocusing value is the distance of the exit face of the specimen from the focal plane
of the objective lens. By convention, a negative value of defocusing corresponds to an
underfocused image, and a positive value of defocusing corresponds to an overfocused
image. In these programs, absorption effects are not taken into consideration.
In the multi-slice method, several tests are necessary to guarantee the validity 3f the
method. These tests are also used to choose the number of beams and the slice thickness
used in the calculation. The unitary test is used to check that the number of beams and
slice thickness are adequate.
In terms of the transmission function, this test requires
118
that
y)
=q(x,
= 1
(4.12)
or in reciprocal space
Q(h, k) * Q*(-h, -k) = E Q(h', k') - Q*(h + h', k + k') = 8h,O8,O
(4.13)
h',k'
where
8h,k
is the Kronecker delta function. In this work lq(x, y)12 was always greater
than 0.999987.
The second test is to calculate the total intensity of the beams used for the iteration.
The total intensity should be unity after the first slice and then should slowly decrease,
but the total intensity I should not decrease below 0.9. If I should fall below 0.9, more
beams are required in the iteration.
If the intensity rises above 1 then thinner slices
and probably more beams are required since I > 1 is not physically possible. In this
work, the intensity I of the beams after a thickness of ~ 190
and
-
150
A
A
(for the in-plane images)
(for the c-axis images) was always in the ranges 0.96 < I < 1.0 and
0.94 < I < 1.0, respectively.
In the computation of the in-plane structure of stage 2 SbCl 5-GICs, the unit cell was
divided into 5 slices of equal thickness, each slice containing one atomic layer as shown
in Fig. 4.2, so that higher order Laue zone effects were taken into consideration. We
considered several intercalate stacking sequences along the c-axis and several molecular
arrangements for the in-plane
4.3
(V/
x \f7)R19.1' structure.
Experimental Details.
Stage 2 SbCl 5-GIC samples were prepared using the two-zone method[26] and characterized for stage using (00t) x-ray diffraction techniques as described in chapter 2 of
this thesis. The samples for electron microscopy were prepared by repeated cleavage of
the SbCl 5-GIC samples as described in chapter 2. The TEM observation was carried
out using a JEOL 200CX top entry transmission electron microscope (C. = 1.2 mm)
and a LaB 6 filament. The in-plane high resolution images were taken under axial illumination by placing an objective aperture that encompassed reflections up to the (100)
(q = 1.108
A- 1) (V7-
x V7)R19.1* superlattice reflections. The c-axis high resolution
119
~
x(
A
;4
x
X4
1 2.75 A
X
0
o-
----
x
x
C
C
CI
CI
Sb
Sb
C I
CI
x
C
-o--o-
o---C
-----
c
oo
x(
A(~
2.5A
~
(>
2. 5 A
2.5
x
x
x
x
x x
A
2.5A
| 2. 5 A
Figure 4.2: Schematic representation of the slicing of the unit cell of a stage 2 SbCl,-GIC
sample using the multi-slice simulation when the electron beam is parallel to the c-axis.
lattice images were also obtained under axial illumination by placing an- aperture that
enclosed reflections up to the (004) (q = 1.971
A- 1)
reflection. Images from the same
region were obtained under different focus conditions. The lattice images were obtained
by finding first the in-focus condition and then taking an under focus series of pictures
in steps of -280
A.
The interplanar spacings were obtained from optical diffractograms
taken from the negatives of the lattice images as explained in chapter 2.[13]
During the TEM observation, an electron beam induced commensurate to glass phase
change is observed. This phase change is described in detail in chapter 5. In order to
minimize the effect of the electron beam, a relatively low magnification of 190,000 X was
selected so that low beam intensities could be used to record the images, and further,
that several images could be obtained from the same area before appreciable damage
was observed. The images were recorded on Kodak SO-163 film, with exposure times of
2 secs.
The image simulation was carried out using the multi-slice method [1,2] described in
section 4.2 for several molecular structures, each consistent with the (-/7 x /7f)R19.1*
superlattice of the SbClr system. The in-plane (electron beam parallel to the c-axis)
simulated images were obtained by dividing the unit cell along the c-axis into five slices
120
of equal thickness (2.55
A),
each slice containing one atomic species (see Fig.
4.2).
Simulated images of the (OUe) planes were obtained for some models that had a unit cell
four times larger than the
(V7
x \/7)R19.1* unit cell (see section 4.4). These simulated
images were obtained by dividing the unit cell along the (100) direction (taken as the
electron beam direction) into two slices of thickness 6.498
A.
The calculations were
carried out for several graphite and intercalate stacking sequences.
4.4
Molecular Models for the
(%/F x
V7-)R19.1* Phase.
Several models were used in the multi-slice simulation for different molecular arrangements in the
(V7
x V7_)R19.10 lattice. These models depend on the kind of molecular
species and therefore the placement of the atoms assumed to form the
(v
x V7)R19.1*
structure. A model consisting of SbCl- molecular species forming the
(V7
x V7)R19.1*
structure has been suggested based on x-ray diffraction experiments.[8] If the SbClmolecular species is considered to. be the only species forming the
(v/-
x -,F)R19.10
phase, there are two possible arrangements of the ions at the lattice sites. In the first
+
5
model (sketched in Fig. 4.3), we consider that in projection along the c-axis, the Sb
ions of the SbC16 molecule sit above a graphite hexagon and the Cl- ions of the lower
layer say, sit on every other hexagon of the six neighboring hexagons to the one where
the Sb 5 + ion sits.
The three Cl- ions of the upper layer sit on the remaining three
graphite hexagons (see Fig. 4.3). This model allows an AA stacking of the graphite
bounding layers. The second model (suggested in reference
[8]) is sketched in Fig. 4.4.
In this model the SbS+ ion of the SbCl6 molecule sits above a carbon atom (at a vertex
of a hexagon) and the Cl- ions of the lower Cl layer sit on the three hexagons that share
the vertex where the Sb 5+ ion sits. The three Cl- ions of the upper Cl layer sit (in
projection) at the vertices shared by only two hexagons where Cl- ions from the lower
Cl layer sit. In this case, only an AB stacking of the carbon bounding layers is possible.
The b and c intercalate stackings correspond to the other two equivalent positions of the
molecules in the intercalate layer and are essentially obtained from the a stacking by a
translation of (2/3,1/3,0) (for the b stacking) and of (1/3,-1/3,0) (for the c stacking).
121
C)
C
GCI c-axis
OSb
I
OCI
cc
0
Figure 4.3: Model for the SbCl6 molecular species in the (v'7 x V7-)R19.1* structure
used in the multi-slice computation. AA stacking of the graphite bounding layers is
possible with this model.
Qc'i
Figure 4.4: Model for the SbCI6 molecular species in the (Vy7 x V7-)R19.1* phase where
only AB stacking of the graphite bounding layers is possible.
122
Care must be taken in calculating the coordinates of the Cl- ions for the different
graphite stackings.
In order to satisfy the disproportionation of sites in the intercalate layer obtained from
M6ssbauer experiments, and because of charge considerations (transport measurements
do not show any sign of islands where the charge is localized as would be the case for
(W7 x V7)R19.1*
(N/
islands of SbCl6 molecules), we also considered other models for the
x V7-)R19.1' structure consisting of mixtures of either SbClg and SbCl 3 or SbClg
and SbCl 5 . The model consisting of a mixture of SbCl6 and SbCl 5 was suggested by
Hwang et al.
[27]
based on energy disperssive x-ray studies on stage 4 SbCl 5 -GICs. In
this model ([27]), it is assumed that the ( fix Vf)R19.10 phase is formed by a mixture of
SbCl6 and SbCl 5 and the disordered phase is formed by a mixture of SbCl3 and SbCl.
Two models were used for the mixture of SbCl6 and SbCl 3 molecular species in
the (V'7 x v1)R19.1* superlattice.
In order to satisfy the disproportionation of sites
(ratio of SbCl6 to SbCl 3 = 2) obtained from M6ssbauer experiments, and to have a
homogeneously distributed charge in the intercalate layer, we assumed a ratio of SbCl6
to SbCl 3 of 1 in the
(v
x VY)R19.1o structure and the disordered phase and the other
ordered phases to be formed by mixtures of SbCl6, SbCl 5 and probably some SbCl4
We have inferred a ratio of SbCl 5 :SbClI :SbCl 3 of 7:2:1 in SbCl 5
-
molecular species.
GICs, from the measurement of the c-axis thermal expansion coefficient (see chapter 6).
For this model, the area of the unit cell is four times that of the
(V7
x V/F)R19.1* unit
cell, the larger unit cell, containing two molecules of SbCl6 and two of SbCl 3 . In order
to get the same number of Cl- ions in the upper and lower Cl layers, one of the SbCl 3
molecules was considered to have two Cl- ions in the upper layer and one in the lower
one while the other SbCl 3 molecule had one Cl- ion in the upper C1 layer and two in the
lower one. Another possibility would be to have an SbCl 3 molecule with all the three
Cl- ions in the upper layer, and the other SbCl 3 molecule with all the Cl- ions in the
lower layer.
Two possible arrangements of the molecules similar to those for the SbCl6 model
were considered. One where the AA stacking of the carbon bounding layers is possible
For the
(see Fig. 4.5), and one where only the AB stacking is possible (see Fig. 4.6).
mixture of SbCl6 and SbCl 3 molecular species.in the (\7 x \/1)R19.1* lattice, there are
123
G
0
0
0
(2)
Fiur 45:Mo el iia o ha show 10
0
(of b1 Gn (9
@
~sit
~ ~~ ~ ~ 5 aaeuvln iFg.43btfamxue
VfxV)1o
latie ies Th arao9 h ntcl ssonadi
G0
isfurtme
ht
fth
V~
~)1o
9
uni ell.
Figure 4.5: Model similar to that shown in Fig. 4.3 but for a mixture of SbC6 and
SbC 3 molecular species in the (V7 x v/7)R19.1* phase. The SbC16 and SbC13 molecules
sit at equivalent (V7- x v/7)Rlg.l'o lattice sites. The area of the unit cell is shown and it
is four times that of the (V7- x V7)R19.1* unit cell.
Figure 4.6: Model similar to that shown in Fig.
SbC13 molecules in the (v/f x --F)R19.1' phase.
124
4.4 but for a mixture of
SbC16 and
six possible stackings of the intercalate a, b,
c, d, e and f. Stackings a, b and c are
equivalent to the a, b and c stackings of SbCl6 described above and shown in Figs. 4.3
and 4.4 but now with a mixture of the two molecular species (SbCl- and SbCl 3 ). Stacking
a is shown in Figs. 4.5 and 4.6 for the two models and stackings b and c are obtained
from a by a translation of (1/6,1/3,0) and (-1/6,1/6,0), respectively. Stackings d, e and f
are obtained from a, b and c, respectively, by a translation of (1/2,0,0). A translation by
(0,1/2,0) produces different atomic configurations but, in projection, they are equivalent
to d, e and f. In this work we only considered translations by (1/2,0,0) except for the
simulated images obtained for the adg stacking of the intercalate (described in section
4.5) where the g stacking was obtained from the a stacking by a translation by (0,1/2,0).
The a stacking for the SbCl 5 molecular species in the (v7 x v7)R19.1* lattice, is
obtained from that for the SbCl- by removing one C1~ ion from every molecule. The
number of Cl- ions in both Cl layers is maintained the same by removing one Cl- ion
from the upper layer for one molecule and one from the lower layer of the neighboring
molecule. Thus, for this model the area of the unit cell is again four times larger than the
area of the (V7- x V/)R19.1* unit cell, and the structure can be pictured as containing
four SbCl6 molecules per unit cell, each missing one Cl- ion; two.SbClg molecules that
are missing a Cl- ion from the upper Cl
layer and two that are missing a Cl- ion from
the lower layer.
The model used for the mixture of SbCl 5 and SbCl6 molecular species in the commensurate
(V7- x ,f7)R19.1' phase was also considered to have a unit cell four times
larger than the
(V7
x V7)R19.1* unit cell, with two molecules of SbCl6 and two of
SbCl 5 . One of the SbCl 5 molecules had three Cl- ions in the upper layer and two in
the lower layer, whereas the other SbCl 5 molecule had the opposite, two in the upper
layer and three in the lower layer. This model was similar to that for the mixture of
SbCl6 and SbCl 3 shown in Fig. 4.6. The coordinates of the atoms- for this model can be
obtained from those for the mixture of SbCl6 and SbCl 3 by adding two Cl- ions to each
SbCl 3 molecule. For this mixture there are also several possible stacking sequences for
both the graphite layers and the intercalate layers. In this work only the AB stacking of
the graphite bounding layers and the aaa and abc stackings of the intercalate layer were
.
considered for the mixture of SbClg and SbCl 5
125
The model used for the SbCl
molecular species as the only component of the
(V7
x
V"_)R19.1* phase is shown in Fig. 4.7. This model is similar that presented in Fig. 4.5
for a mixture of SbC1- and SbCI 3 molecular species but with SbCl molecules replacing
3
the SbCl6 molecules.
Figure 4.7: Model used in the multi-slice simulation for the SbCl molecular species at
3
the (V7- x \F/)R19.1* lattice sites. This model is equivalent to the one shown in Fig. 4.5
but with only SbCl 3 molecules.
4.5
Results and Discussion.
Figure 4.8 shows an in-plane lattice image for the (V7- x v/_)R19.1* structure of
a stage 2 SbCl 5 -GIC sample obtained using the TEM. Several images of the (Vr x
V7)R19.1* structure were obtained from the same area of the sample, but for different
focus conditions; three typical examples of these images are shown in the central column
of Fig. 4.9 and are also repeated in the central column of Fig. 4.10 for three different focus
conditions. Simulated images were obtained for the (V7 x V7)R19.1* phase for several
stacking sequences of both the intercalate and the graphite layers. Table 4.1 summarizes
the stacking sequences used in the simulation for several graphite stacking sequences and
for a variety of molecular species in the intercalate layer in the
126
(V7
x V/_)R19.1O
Figure 4.8: High resolution lattice image of a stage 2 SbCl 5-GIC sample showing the
(V'7 x V7)R19.1* in-plane structure.
127
4)4s
A
Pp
4!' -
Figure 4.9: Multi-slice simulation of the
(V7
x v\/)R19.1' structure for the mixture of
SbCl- and SbCl 3 molecules for ABaCAbBCcABdCAeBCfABa...
ABgABa.. (right) and experimental (center) for a) -510
focus conditions.
129
(left) and ABaABd-
A, b) -790 A and c) -1070 A
-IPA
V
SbC1 6 +SbC
*
*
*
*
.0
S
0.
6
0 0 0 0 a 0 a 0 0 a a 9
*
0
'
'
0 '
'
5 0
a
'
''
''
*
0
0
0
*
6
*
0
so
*
*.eeee.O..o
- 4
'
5
0
a)
*
*
'
0 ,o0
00
*
*
0 00 00
ooooooOS
00
,oooooeoe@@oC
*
'
*
'
0
00
C
*
*
*
*
*
3
**
e0
* ***********e
e
Af =-510 A
.
.
.
.
.
.
.
.
.
.
.
.
.
0
0 .
.
.
.
0
0
..
.
.
.
.
0
.
0
.
.
.
0Q0QOQ0Q0000
oo@@0o.*@Q
.
.
.
.
.
.
.
.
.
.
..
QO@@@O@@QO@Q
..
.
.
.
.
.
0
.
.
.
,
~0
0
o~o~o~o@@.o@
At =-790 A
)
C.
At =-107o
abcdef
A B/C A/B C
A
adg
A B/A B
Figure 4.10: Experimental (center) and simulated images for SbCl5 (left), and a mixture of SbCl 5 and SbCl- (right) molecular species in the (N/7 x V/7)R19.1* structure.
Both simulated images were obtained for an aaa stacking of the intercalate. The focus
conditions for the TEM images are a) -510. A, b) -790.0 A and c) -1070 A.
131
aV SV
eee
VOLOtI
i
IV
21
T05
0-
't's.
By/By
eee
V06L-:IV
e 0aa0
ia
44
(n
0000000
0
v
vOoaeaaooo
40 ot
dtD@@@@@@@d
t
VOLS - :-I
q
aO0OaGOOG 00 a0
lips
( 1(I (- 1
1'
111
~
It It b a tS t; ecr
lDqS
a
structure. In this table the lower-case letters denote the intercalate stacking, the capital
letters denote the graphite stacking and
/
denotes the intercalate layer position.
A
more detailed explanation for the models is given below. For those models consisting of
mixtures of either SbCl- and SbCl 3 , or SbCl~ and SbCl 5 , and also for the SbCl 5 and
SbCl 3 molecular species, the area of the unit cell is four times that of the (V7x V')R19.1*
lattice. All the models presented in Table 4.1 preserve the three layer structure of the
intercalate described in chapter 2.
In the multi-slice calculation reported in this work, ionic scattering form factors were
used to calculate the structure factors employed in the multi-slice programs. Since the
charge transfer for SbCl 5-GICs is 0.2-0.4 (see chapter 6), the intercalate remains almost
completely ionic and it is therefore reasonable to use the ionic form factors instead of
the atomic ones. A higher value for the charge transfer would bring the effective form
factors closer to the atomic form factors.
We have found a strong dependence of the
computed image on whether the ionic or atomic form factors were used, as shown below.
Table 4.1: Stacking sequences for the (V1 x v'7)R19.1* phase in stage 2 SbCl 5 -GICs
used in- the multi-slice calculation.
SbClabP
A/AB/BA
ab4
SbCl- and SbCl 3
.
abcdef4
SbCl 5
abde4
ab4
3
2
SbCl 5 and SbCl-
4-
aaa
adg'
aaa
abde
ab 4
3
4
abc 4
abcdef
abc
AB/CA/BC
1 Very good agreement with the TEM images.
2 Good agreement with the TEM images.
' Not good agreement with the TEM images.
4 No agreement with the TEM images.
AB/AB
BA/CA/BA
SbCl 3
-
-
C layers
A/AB/BC/CA
aaal
--
abc 3
The defocus value was estimated from optical diffractograms taken from the disordered background contained in some areas of the negatives of the TEM micrographs.
These amorphous regions give rise to bright and dark rings in the optical diffractogram
with a radial intensity that follows a sin2 (0) dependence [13] where '(0)
Eq.
is given by
(3.14), written in terms of the electron scattering angle 0. The electron scatter-
ing angle 0, that gives rise to ring rn in the optical diffractogram, is related to r, by
133
On
= AMrn/Aefm where M is the electron microscope magnification, At is the wavelength
of the laser used to take the optical diffractogram (632.8 nm for the helium-neon laser)
and f and m are the focal length of the Fourier transforming lens and the magnification
of the magnifying lens in the optical bench, respectively.[13] If some lattice fringes are
included in the optical diffractogram, then On = 2r,,OB/rB where rB is the radial distance
of the Bragg spot in the optical diffractogram and OB is the corresponding Bragg angle.
The values of defocusing (Af) and spherical aberration (C.) were estimated from a linear
regression best fit for n/9i
cal diffractograms.[13
vs. n2 obtained from the rn distances measured from the opti-
Cs and Af are obtained from the slope and ordinate for . = zero,
respectively. Unfortunately, only two broad rings of high intensity were obtained in the
optical diffractograms taken from the amorphous regions of the negatives obtained at a
large underfocus condition even though more rings should be seen for a high underfocus
value [13]. This is because the objective aperture used to take the pictures, cut the frequency components higher than 2.51
A-'.
Only for the smallest underfocus condition,
the rings in the optical diffractogram were clear and sharp (compared to those for larger
underfocus value). Consequently, the estimated values of Af at large underfocus are not
very accurate. Since the micrographs were taken at defocus values in steps of -280
A,
we used the value of Af obtained for the smallest underfocus condition to correct for the
larger underfocus values.
In order to match the simulated images with the TEM lattice images we obtained
simulated images for several sample thicknesses and for a range of underfocus values
including the experimental, calculated (from the fit to n/02 vs.O2) and corrected (as
explained above) underfocus conditions (Af = -100, -280, -300, -500, -510, -560, -657,
-790, -840, -1070, -1275, -1400 and -2416
A).
The conditions used to decide if the
computed images obtained for a particular model and stacking sequence matched the
TEM series of micrographs were: (1) that the images in the focal series showed the
right symmetry (hexagonal), (2) the right trend in contrast with increasing underfocus
since there is a contrast reversal with increasing underfocus from -790
A
to -1070
A
as explained below and (3) the images that satisfied (1) and (2) had to differ in focus
condition by ~ -280
A.
The analysis of the simulated images obtained for the different
models presented in Table 4.1 is given in detail below.
134
Figures 4.9-4.11 show in-plane TEM (experimental) images and simulated images
obtained for some of the models presented in Table 4.1 for several values of Af. All the
simulated images shown in Figs. 4.9-4.11 were obtained including 725 beams (Fourier
components) in the calculation and for a thickness of 153
A.
This thickness corresponds
to 60 slices of 2.55 A/slice or 12 unit cells of 12.75 A/unit cell. The thickness of the
sample was not measured since graphite cleaves easily along the c-planes without forming
a wedge edge.
Consequently, the usual methods used to measure specimen thickness
from thickness fringes such as variations in the fringe spacing from a wedge shaped
specimen (maxima in intensity occur at thicknesses equal to integer multiples of the
extinction distance)
[13]
cannot be applied to GICs. We have estimated the thickness
of the samples from pendoll6sung plots obtained for several (00t) beams (as explained
A. It is shown
the c-axis for thicknesses > 140 A agree with the
that the sample was thicker than 140 A, as was
below) and have found a change in contrast for a thickness of
below that our simulated images along
experimental TEM images, indicating
140
-
estimated. Because of the uncertainty in the sample thickness, simulated images of the
in-plane structure were obtained for thicknesses in the range 12.75
of 12.75
A
A
to 191.30
A in steps
(one unit cell) for several focus conditions. In general, the simulated images
depended very strongly on thickness for very small thicknesses t, but for t > 6 unit
cells (76.5
A)
the images did not change dramatically with thickness. Other microscope
parameters used in the computation of the images were radius of the objective aperture
r = 0.5
A-1,
spherical aberration C. = 1.21 mm, semi angle of illumination div=1.0
mrad, half width of Gaussian spread of vibration vib = 0.0
spread of defocus del = 50
A and
half width of Gaussian
A.
In the following, we will discuss the agreement or disagreement between the TEM
images and the images obtained using the multi-slice method for every model presented
in Table 4.1. First, we want to note that there is a change in contrast with increasing
underfocus from Af = -790
A
to Af = -1070
A
in the TEM micrographs shown in
Figs. 4.9-4.11. Also during the TEM observation, the intensity of the high resolution
(A7
x V7)R19.1* image changes (giving the appearance of sample bending) (see Fig.
4.12). Therefore, the intensity of the TEM images shown in Figs. 4.9-4.11 corresponds
to the average intensity over the period of time during which the pictures were taken
135
Figure 4.11: Experimental (second column from left to right), and simulated images for
the model consisting of SbCl~ molecular species forming the (,f x \/7)R19.1' structure. The simulated images were obtained from left to right, for AaABbBCcCAa...,
AaBAaBAa... and AaBAbCAa... stacking sequences. The defocus condition is indicated
in the TEM micrographs.
136
U
.0
C,,
I
0
0 0
0 0
o
......
If
b
V
.
m4
to 4
.4
w
W
.0.0.4
004
137
4
n
U
0
.aaaAaa
aa***a.
*~*8**~
.*aaaaa
a aa a a a a
aaaaaaa
aaaaaaa
aaaaaaa
'3
4
4
U
C-,
n
C-)
4
4
II
Figure 4.12: a)-c) In-plane lattice images obtained from the same region and under the
same conditions but for different electron beam doses.
138
-
S-
A'
\1%\
)Fresmuum
139
(~
2 sec). Consequently, some of the fine detail of the (N7 x
/7)R19.1' structure may
be lost in the experimental images in Figs. 4.9-4.11.
Simulated images obtained for the (V'-x V7)R19.1* phase formed by the SbCl 3 molecular species only did not show agreement with the experimental TEM images shown in
the central panel. of Figs. 4.9-4.11. This poor agreement is attributed to the lack of homogeneity in the distribution of the Cl- ions in the intercalate layer. This distribution
of Cl~ has in projection a threefold symmetry which is reflected in the simulated images.
On the other hand, two of the models consisting of a mixture of SbCl~ and SbCl 3 molecular species (see Fig. 4.9) showed better agreement with the TEM images. The images
obtained for the ABaABdABgABa.. stacking (right column in Fig. 4.9) show very good
agreement with the experimental TEM images (central column in Fig. 4.9) for the three
focus conditions shown. The images obtained for the ABaCAbBCcABdCAeBCfABa..
stacking for defocus values of -510
A and
-790
A
show fair agreement with the respec-
tive TEM images. On the other hand, no agreement was found for the image with a
defocus value of -1070
A.
left column for Af = -1070
This can be seen in the simulated image presented in the
A,
which shows bright spots in a mostly bright background,
whereas the corresponding TEM image shows bright spots in a dark background. Thus,
a comparison of these two sets of figures with the experimental TEM images shown in
the central column of Fig. 4.9, suggests that the simulated images obtained for the adg
stacking of the intercalate reproduce better the experimental images. No good agreement
was obtained for any of the other stacking sequences listed in Table 4.1 for this mixture
of molecular species in the
(vr
x vf)R19.1* structure. The simulated images obtained
with the other models, showed either a symmetry other than hexagonal (AaABbBCc-
CAdABeBCfCAa..) or a different defocus dependence (BAaCAbBAdCAeBAa...). Fair
agreement with the experimental TEM images was found for this mixture of molecular
species in an AaABbBCcCAdABeBCfCAa.. stacking when the atomic form factors were
used in the calculation, but no agreement was found for the same stacking sequence when
the ionic form factors were used in the computation.[28]
Figure 4.10 shows experimental TEM images (central column) and simulated images
for the models consisting of SbCl5 in the AaBAaBAaB.. stacking (left column of Fig.
4.10) and a mixture of SbCl6 and SbCl 5 also in the AaBAaBAaB...
140
stacking (right
column of Fig. 4.10). For the SbCl 5 model, no simulated image similar to the TEM image
shown in Fig. 4.10c) was obtained for several values of Af = -840,
-1070,
-1275
and
-1400 A. On the other hand, the images obtained for a mixture of SbCl6 and SbCl 5 show
very good agreement with the experimental TEM images shown in the central column of
Fig. 4.10. Based on x-ray fluorescence results using the scanning transmission electron
microscope, it had been suggested that the (vl x vT)R19.1* phase in SbCl 5 -GICs was
formed by a mixture of SbCl6 and SbCl 5 molecular species.[27]
Figure 4.11 shows simulated images for the model consisting of the SbCl6 molecular
species in the intercalate layer for an AaBAaBAaBA.., AaBAbCAaBAb.. and AaABbBCcCAaA.. stacking sequences. The simulated images for the AaBAaB.. and AaABbBCcCAa.. stackings show poor agreement with the TEM images. This can be seen in
the following way: the image obtained for the AaABbBCcCAa.. stacking sequence for
the largest defocusing value shows dark spots in a bright background while the experimental TEM image shows bright spots in a dark background. The image obtained for
the AaBAa.. stacking sequence for the largest defocusing value, shows bright spots at
half the (Vf x vT)R19.1* lattice constant, which are not observed in the experimentally
obtained TEM image. The simulated images obtained for the AaBAbCAaBAb .. stacking do not reproduce any of the experimental TEM images. This model for an abab..
stacking of the intercalate was proposed based on x-ray diffraction measurements on
(V' x
SbCls-GICs.[8] An average
V")R19.1* intercalate domain size of ~ 650
A
was
obtained from x-ray diffraction and dark field and high resolution electron microscopy
(see chapter 5) experiments on SbCl 5-GICs.[29]
This suggests that islands of interca-
molecular species are not likely to exist, since this would
late containing only SbCl
imply that the charge is concentrated in these islands, rather than being homogeneously
distributed in the intercalate layer.
The periodic arrangement of Sb 5+ and Sb 3 + ions for a mixture of SbCl6 and SbCl 3
species, requires spots in the (hk0) electron diffraction pattern at ~ 0.55
not observed experimentally.
lattice fringes (11.62
Fig. 4.13).
0.08
A-'
which are
We also have evidence for this structure from in-plane
A spacing)
observed in small regions of the SbCl 5-GICs (see
On the other hand, a non periodic arrangement of the SbCl6 and SbCl 3
molecular species at the
(V/7
x x/)R19.1* sites would not require the extra spots at
141
Figure 4.13: In-plane fringes of a stage 2 SbCl 5-GIC sample showing a periodicity of
twice that of the (V'7 x V/7)R19.1' phase.
142
titt
-vi
143
0.55
A'-
in the electron diffraction pattern.
Simulated images of the (00t) planes were obtained for the models consisting of
mixtures of either SbCl- and SbCl 3 or SbCl6 and SbCl 5 for the stacking sequences
that fitted best the in-plane TEM lattice images and are shown in the right columns of
Figs. 4.9 and 4.10. The simulated images were obtained by assuming the electron beam
direction to be along the (100) direction and by dividing the unit cell along this axis
into two slices, each slice of thickness 6.498
A.
Figure 4.14 shows the projected potential
along the (100) direction for the two slices used in the calculation of the (00f) lattice
images for the mixture of SbCl6 and SbCl 5 molecular species in an AaBAaBAaBAa...
stacking sequence in the
(Vt x
ft)R19.1* structure.
In the same way, projected potentials were obtained for the mixture of SbCl6 and
SbCl 3 molecular species in the AaBAdBAgBAaBA..
this case the unit cell along the c-axis was 3 x 12.75
used to calculate the images of the
stacking sequence except that in
A.
These projected potentials were
(00f) planes using the multi-slice method described
in section 4.2.
Figure 4.15 shows the experimental TEM (central column) and the simulated (left
and right columns) images of the (00t) planes for the SbCl- and SbCl 3 (left column) and
for the SbCl6 and SbCl 5 (right column). This figure shows that the simulated images
obtained for both models are in very good agreement with the TEM images. The model
of the mixture of SbCl6 and SbCl 3 molecular species in the
(v7 x
V7)R19.1' structure,
explains the commensurate-to-glass phase change observed during the electron beam
irradiation (see chapter 5).
On the other hand, the model consisting of a mixture of
SbCl- and SbCl 5 molecular species, agrees with the x-ray fluorescence results.[27]
Pendoll6sung plots
[131 were obtained for several of the (00t) beams that were in-
cluded in the objective aperture for the simulated images. Figure 4.16 shows the beam
intensities and phases (with respect to the (000) beam) for several beams (000), (001),
(003) and (004) (Figs.
4.16a) 4.16b), 4.16c) and 4.16d), respectively) for the model
consisting of a mixture of SbCl- and SbCl 5 molecular species in the
(ft
x ft)R19.1
structure. It can be seen from these figures that the intensities of the (003) (Fig. 4.16c))
and (004) (Fig. 4.16d)) beams have a maximum at t- 145
A. This is the same thickness
at which the intensity of the (000) beam in Fig. 4.16a) has a minimum. This thickness
144
ll
l
III
16
IN
a-i
W
1A. M
41 1 -V +I --
r
a
~wa
16
ow ova SmN
no1
-011
WN
N
*--1
&4
---
r *Y
ilia
we
aw
hb
RA
'N
+
U in
1
U
-- P W--0 91--9
m
=
III
0
Mi
M
W-
-
60
r
Al-ha
.il
Pa
m oP 3
weo
.. 1h
11
' V-I
Id'N
P Om N
14
IN #01 Ow"4
AN
M
od
4sI
4m
-
qu
4in
d
U
9
11-Ill
fm
A *4 MO
in -n N
I"
.0
1
.-
a-no
U
U-U - + W -v UW-U 9*-M +
1
s.4-m-.-+
A
a
N
H
--I
54-
M WSWM
-r MMW S o ws1
111
ri
Q1
*0 '1
Ilk
"A'
kk
1-0
Figure 4.14: Projected potential along the (100) direction for the two slices used to
compute the (00i) lattice images for the model consisting of a mixture of SbCl~ and
SbCls molecular species in the (v/'7 x v/7)R19.1* structure.
145
Figure 4.15: (00t) lattice images obtained experimentally (central column) and using
the multi-slice method for a mixture of SbCl~ and SbCl 3 (left column) and SbCl~ and
SbCl 5 (right column) molecular species in the (V7- x v/7)R19.1* structure.
146
,.
~~p~,*aj~a* hiJ*~~~dWI*9I~y .tv
1
4~~I~
~
t.
_____________________
-is
SbCI6 & SbCI 3
SbC15 & SbC16
SbI&SCI
Figure 4.16: Depth dependence of the intensity of a) the transmitted beam and the
diffracted beams b) (001), c) (003) and d) (004) and phase (with respect to the (000)
beam) dependence on depth for the e) (001), f) (003) and g) (004) diffracted beams.
148
(uuu)
(UU 1)
c)
s~e-
1)
e
)
,
luu
f "f
7
0
99.99..699.
DepIh W
(UUJ)
999.1
96.9
e
IJ._sJ j
.J..a
*
~
Devlh W$
DUpIh W
d
)U 0 1)
-
Ii,
999
)
99n
99.*I-.
Uevil, -A
Ile. I
149
M .11
996.
Irv.#
of ~ 145
A
is half the extinction distance of the (000) beam (1/2
o). Figures 4.16e)-
4.16g) show the phase dependence on thickness for the (001) (003) and (004) beams,
respectively.
It can be seen from these figures that there is a dramatic change in the
phase of the diffracted beams with respect to the transmitted beam for t- 145 A. This
indicates that there is a change in image contrast at this thickness. The (00f) simulated
images obtained for a thickness of 104
A
and those for a thickness of 156
A
showed
opposite contrast, in agreement with the phase dependence on thickness. The contrast
in the TEM images shown in Fig. 4.15 (central column) agrees with that of the simulated
images obtained for a thickness of 156 A indicating that the sample was thicker than
145 A, as was expected.
4.6
Conclusions.
Based on the results for the in-plane and c-axis simulated images, we consider the
(v/7x V7-)R19.1* islands more likely to be formed by a mixture of either SbCl6 and SbCl 3
molecules with no Sb 5 + to SbS+ long range order, or by SbCl6 and SbCl 5 molecules containing only the Sb5 + species. The model of a mixture of SbCl6 and SbCl 3 molecular
species in the
(V
x
v/7)R19.1* phase can be used to explain the commensurate to
glass phase change observed during electron beam irradiation (see chapter 5).[29] Images obtained with higher resolution such as that obtained with the atomic resolution
microscope (ARM) are needed to absolutely decide which is the correct model for this
structure.
150
References
[1] J.M. Cowley and A.F. Moodie, Acta Cryst. 1_0, 609 (1957); J.M. Cowley and A.F.
Moodie, Proc. Roy. Soc., 71, (London), 533 (1958); J.M. Cowley and A.F. Moodie,
Acta Cryst.
12, 353 (1959); J.M. Cowley and A.F. Moodie, Acta Cryst. 12, 360
(1959).
[2] P.G. Self, M.A. O'Keefe, P.R. Buseck and A.E.C. Spargo, Ultramicroscopy 11, 35
(1983).
[3] G. Timp, M.S. Dresselhaus, L. Salamanca-Riba, A. Erbil, L.W. Hobbs, G. Dresselhaus, P.C. Eklund and Y. Iye, Phys. Rev. B26, 2323 (1982).
[4] L. Salamanca-Riba, G. Timp, L.W. Hobbs, and M.S. Dresselhaus, Mat. Res. Soc.
Symp. Proc. 20, 9 (1983).
[5] M. Suzuki, R. Inada, H. Ikeda, S. Tanuma, K. Suzuki and M. Ichihara, Graphite Intercalation Compounds, (edited by Sei-ichi Tanuma and Hiroshi Kamimura, 1984),
p. 57.
[6] Y. Yosida, N. Tanuma, S. Tagaki and K. Sato, Extended Abstracts, Graphite Intercalation Compounds, (ed. P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus,
Mat. Res. Soc., 1984), p. 51.
[7] J. Melin, Doctor of Physical Sciences Thesis, Universite de Nancy, 1976 (unpub-
lished).
[8] H. Homma and R. Clarke, Phys. Rev. B31, 5865 (1985).
151
[9] P.C. Eklund, J. Giergel and P. Boolchand,
Physics of Intercalation Compounds,
(ed. L. Pietronero and E. Tosatti, Springer-Verlag Berlin Heidelberg, NY, 1981),
p. 168.
[10] P. Boolchand, W.J. Bresser, D. McDaniel and K. Sisson, Solid State Commun. 40,
1049 (1981).
[11] R. Clarke, Extended Abstracts, Graphite Intercalation Compounds, (ed. P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus, Mat. Res. Soc., 1984), p. 152.
[12] R.W.G. Wyckoff, Crystal Structure (ed. Interscience Publisher, N.Y., 1964).
[13] J.C.H. Spence, Experimental High Resolution Electron Microscopy, (Clarendon
Press, Oxford, 1981).
[14] P. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron
Microscopy of Thin Crystals, (Robert E. Krieger Publishing. Co. Inc., 1977).
[15] A. Howie, The Theory of Electron Diffraction Image Contrast in Electron Microscopy in Materials Science (eds. U. Valdre and A. Zichichi, Academic Press,
New York, 1971).
[16] L. Reimer, Transmission Electron Microscopy, (Springer Verlag, Berlin, New York
and Tokyo, 1984).
[17] M.A. Bethe, Ann. Physik (Leipzig) 87, 55 (1928).
[18] L. Sturkey, Acta Cryst. 10, 858 (1957).
[19] L. Sturkey, J. Phys. Soc. Japan 11, Suppl. BII, 92, (1962).
[20] J.M. Cowley, Diffraction Physics, (North-Holland, Amsterdam, 1981).
[21] P. Goodman and A.F. Moodie, Acta Cryst. A30, 280 (1974).
[22] D. Van Dyck, J. Microscopy 119, 141 (1980).
[23] P.G. Self, J. Microscopy 127, 293 (1982).
152
[24] D.F. Lynch, Acta Cryst. A27, 399 (1971).
[25] J.W. Cooley and J.W. TPukey, Math Compt. 19, 297 (1965).
[26] V.R. Murthy, D.S. Smith and P.C. Eklund, Mat. Sci. Eng. 45, 77 (1980).
[27] D.M. Hwang, X.W. Qian and S.A. Solin, Extended Abstracts, Graphite Intercalation
Compounds, (ed. P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus, Mat. Res.
Soc., 1984), p. 155.
[28] L. Salamanca-Riba, J.M. Gibson and G. Dresselhaus, Abstract for the Intl. Conf.
on Carbon, Lexington, July 1985.
[29] L. Salamanca-Riba, G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus and R.J.
Birgeneau (to be published).
153
Chapter 5
NOVEL LOW TEMPERATURE
CRYSTALLINE TO GLASS
PHASE CHANGE
In this chapter we report the electron beam-induced commensurate-glass phase
change observed on SbCl 5 -CICs using the transmission electron microscope.
The in-
troduction to the chapter is given in section 5.1. Section 5.2 contains the experimental
details.
Sections 5.3 and 5.4 present the x-ray and electron microscopy results. The
model for the phase change is given in section 5.5, and some suggestions for future work
are given in section 5.6.
5.1
Introduction
There are three possible radiation effects that are usually encountered in TEM: specimen heating, electron-nucleus interaction (knock-on) and electron-atomic electron interaction (radiolysis).
The last two processes may produce atomic displacements by
direct momentum transfer in the knock-on process or by the creation of an excited state
in the radiolysis process.
Electron beam induced damage has been observed to occur in alkali-halides, organic
solids and silicates during transmission electron microscopy- (TEM) observation.[1,2] The
damage is the result of atomic displacements produced by electron beam irradiation
through the creation of an excited state. The energy of the excited state is transformed
into kinetic energy of the atom by an energy-momentum conversion mechanism. This
154
kinetic energy is larger than the atomic binding energy. In this chapter we report atomic
displacements induced by electron beam irradiation in a layered material formed by two
kinds of species: SbCI 5 and graphite. Only the SbCl 5 layers undergo the transition to a
glass phase, while the graphite layers remain crystalline.[3] Thus, this system provides
a model two-dimensional glass phase with a controllable amount of disorder. Further,
the glass phase is stable provided that the temperature is not increased, so that many
different measurements on this novel system should be possible.
It was already discussed in chapter 3 that SbCl 5-GICs often show the coexistence
of several commensurate in-plane phases, such as the
(v7 x V'7)R19.10* and (V'e x
V39)R16.10* structures, whose relative concentrations depend on sample preparation
conditions.[4,5,6,7] Several phase transitions have been inferred in SbCl 5-GICs using a
variety of experimental techniques. [4,5,6,7,8,9,10,11,12,13]
In this chapter we study the unusual commensurate
change
(C-G)
(V7 x Vr)R19.10*
to glass phase
in the intercalate layer that takes place on cooling below ~ 180 K using
TEM, where the low temperature phase is the glass phase.[4,5,8,13] The C-G phase
change is not observed in x-ray diffraction experiments. It was first suggested [13] that
the C-G phase change occurred only in dilute samples, and that further the intercalate
layer was dilute in the thin samples needed for TEM, but not in the thick samples used
in x-ray diffraction. In order to determine whether the discrepancy between the high
resolution x-ray and TEM results was due to differences in sample composition or to
differences in the experimental techniques, we performed x-ray diffraction and electron
microscopy studies at low temperatures using stage 2 SbCl 5-GIC samples of common
origin for both types of experiments. We investigated the dependence of the C-G phase
change on host material, host crystallite size and experimental technique.
We have
found from electron and x-ray diffraction experiments performed on stage 2 SbCl 5 -GIC
samples that the crystalline to glass phase change results from electron beam damage.
The induced phase change was studied as a function of electron dose and energy. In this
chapter we report a controlled means of producing a quasi-two dimensional glass phase.
Two competing annealing processes are observed with two different activation energies.
This crystalline-glass phase change is attributed to atomic displacements induced by
electron beam irradiation.[31 In this chapter we suggest a model for the mechanism that
155
induces the C-G phase change.
Experimental Details
5.2
The SbCl 5-GIC samples used in this investigation were prepared with the two zone
method and characterized for stage as described in chapter 2, using as host materials
highly oriented pyrolytic graphite (HOPG), kish single crystal graphite, and vermicular
graphite. The vermicular graphite is an exfoliated graphite with a particle size of ~ 330 A
in the c-direction and ~ 850 A in-plane.[14] In order to purify the vermicular graphite,
it was heat treated at 1200*C before intercalation. The x-ray spectrum taken after this
heat treatment showed only graphite reflections. The x-ray experiments were carried out
by Dr. G. Roth and Dr. A.R. Kortan on a triple-axis x-ray spectrometer using Cu Ka
(A = 1.5418 A) and Mo K. (A = 0.7107 A) radiation from a Rigaku 12kW rotating anode
x-ray source.[15] The spectrometer was equipped with a Displex 4 He-Cryostat, allowing
a variation in sample temperature between 16 K and room temperature.
Samples for
electron microscopy were prepared by repeated cleavage of the SbCl 5-GIC samples. Some
of the stage 2 samples used in the TEM experiment were prepared from the samples used
in the x-ray diffraction experiment. The electron microscopy observation was carried out
using a JEOL 200CX top entry transmission electron microscope (TEM) with a liquid He
cooled specimen stage allowing temperatures > 35 K.[16] Electron diffraction patterns
were taken from the SbCl 5 samples at different temperatures for different electron beam
intensities and doses and for several electron beam energies.
5.3
X-Ray Results.
X-ray studies were performed on high quality SbCl 5-intercalated Kish graphite single
crystals. The inset to Fig. 5.1 shows transverse scans through the first order intercalate
V
peak at room temperature and at 18 K, normalized to the intensity of the graphite
(10) peak. As can be seen, no change in intensity or line-shape is observed for the -/F
peaks, therefore demonstrating that no C-G phase change has taken place. The room
temperature in-plane diffraction pattern was determined to contain only intercalate V7_
peaks up to third order. A Lorentzian line was fitted to the -\,
156
peaks of higher order.
0.75
KISH-SbCI
5
5
(004)
-a 0.25-
(004)
003
1002)
(
STAGE 2
0D0.50
(00341
V
I
0
-
I
[- \95
18 K
..
0
_:
I
*
20
(002)
21
3
22 23
S(Degrees)
24
)
(00
I
-
(009)
(005)
/
-I
(004)
16 K
I
(008)
|
.
,(005
20
10
(10
-006)
......
295 K~
40
30
29 (de grees)
50
Figure 5.1: X-ray spectra of SbCI5-intercalated vermicular graphite obtained at 295 K
and at 16 K. The inset shows the first order (fix Vi)R19.100 hr-x-ray diffraction peaks
of SbCl 5-intercalated kish graphite (stage 2) at 295 K and at 18 K, normalized to the
intensity of the graphite (100) peak.
An upper limit of 650
1.1 x 10~2
A
was calculated for the average intercalate domain size from the
A-' linewidth (instrumental resolution = 5.8 x
obtained from transverse scans through high order
V7
10-3
A-'
at q = 2.964
A-'),
peaks. The limit is comparable
with the average in-plane size of vermicular graphite particles (850
A).[141
Therefore, it
can be assumed, that for the SbCI5-GIC samples the limited particle size of vermicular
graphite puts no additional constraints on the typical intercalate domain size. Similar
domain sizes in the range 300
A
to 1000
A were
obtained using both dark field and high
resolution imaging techniques with the TEM.
Figure 5.1 shows high resolution x-ray spectra obtained from SbCl 5 intercalated
vermicular graphite at room temperature (upper curve) and at 16 K (lower curve).
Besides the strong (00e) reflections, which are indexed by assuming a mixture of stages
157
2 and 3 SbCl 5-GIC, the graphite (100) and the intercalate (100) (15.80) and (300)
(48.40) (V7 x -/7)R19.10* superlattice reflections are observed.
At 16 K, the (00t)
peaks shift to higher scattering angles, due to the thermal contraction along the c-axis
that will be discussed in chapter 6.
On the other hand, the positions of the
\/7)R19.100 peaks are essentially the same (AE
(V7
x
; 0.1*) at both temperatures, since the
in-plane contraction of the graphite is very small, and the intercalate remains locked
to the graphite lattice. The fact, that the first and third order superlattice peaks have
approximately the same intensity at both temperatures, indicates that there is no major
change in the
(-f
x v/7)R19.10 structure, in agreement with the result obtained for the
kish graphite samples. Therefore, even in microscopically thin samples such as vermicular
graphite, no C-G phase change is observed using x-ray diffraction.
5.4
TEM Results.
. Figure 5.2 shows an (hk0) electron diffraction pattern of a stage 2 HOPG sample
intercalated with SbCl 5 . This figure shows only the (V/- x %F7)R19.1*phase described in
detail in chapter 2. In contrast to the x-ray results, presented in the previous section,
electron diffraction patterns obtained from SbCl 5-GICs show the commensurate phase
at room temperature and the glassy phase at low temperatures for all graphite host
materials and for all stages (1-4) studied. Figures 5.3a) and 5.3b) show typical electron diffraction patterns obtained from SbCl 5-intercalated vermicular graphite at room
temperature and at ~ 50 K, showing the commensurate and glassy phases, respectively.
Figure 5.3b) shows that at low temperatures the graphite remains crystalline but the
(v/
x V7_)R19.100 spots have disappeared and instead rings with maximum intensity
at ~ 1.20
A-1
and 1.97
A-1
identified with the glass phase are observed. For the glass
phase seen in the TEM, long range order is lost and especially the third order satellite
is not observed. The difference between the x-ray and TEM results indicates that the
occurrence of the C-G phase change is not dependent on differences in the samples used,
but rather on differences in experimental techniques.
To study the influence of the electron beam, samples were first cooled to ~ 50 K
without the presence of the electron beam. Then diffraction patterns were taken with
158
Figure 5.2: Room temperature electron diffraction patterns of SbCl 5-GICs showing the
(-f x v'-)R19.1* phase only.
159
160
Figure 5.3: (hkO) electron diffraction patterns of a mixed stage (2 and 3) vermicular
graphite sample intercalated with SbC1 5 for a) T=295 K, and b) T=50 K.
161
162
a low beam intensity (I. ~ 1.6 e/A 2 -s) and a relatively small electron irradiation dose
(0 ~ 80 e/A 2 ).
The diffraction patterns indeed showed very sharp (,/7 x V/7)R19.10*
spots, (similar to Fig.
5.2) even at a temperature of
50 K. As 0 was increased to
-
0 ~ 540 e/A 2 at ~ 50 K, the glassy phase was observed, demonstrating that the C-G
phase change is induced by electron beam irradiation at low threshold doses.
The three possible 'radiation effects' usually encountered in TEM are: (1) specimen
heating, (2) electron-nucleus interaction (knock-on) and (3) electron-atomic electron
interaction (radiolysis).
We show below that the mechanism responsible for the glass
phase is radiolysis.
We have calculated the rise in specimen temperature
AZTma by solving the radial
form of the differential equation for heat conduction
1
where
+ j(d
(r d)
(5.1)
/e=0
R is the thermal conductivity of the sample, j the current density, and d U/d z
the electron energy loss per unit length along the beam direction. For the appropriate
boundary conditions we obtain:
A Tm, =
-
(d U/d z)/e
1
-+b2j
+ In s_
(5.2)
where s is the radius of the film thermally anchored at the periphery and b is the radius of
the irradiated area. From our experimental conditions and using the reported values for
R[17] at T = 50 K, we calculate a local maximum increase in the specimen temperature
ATma. < 5 K for I,
10 e/A 2 -s, which is not enough to produce the observed phase
change. The C-G phase change can also be produced at higher temperatures, but as we
shall discuss below, a much higher electron dose is required.
The critical dose 0,, necessary to produce the C-G phase change, was arbitrarily
defined as the electron dose such that R = 0.15 where R = (I, - Ir)/I, and I., Ir are
the intensities of the electron diffraction patterns at
-
1.10
A-'
along the superlattice
(100) direction (spot) and along the graphite (100) direction (ring), respectively. Our
measurements of activation energies and the dependence on electron beam energy, discussed below, are independent of the value of R chosen to characterize 0,. Figure 5.4
shows the normalized dependence of R on electron dose for several temperatures
163
0.9
I
0.7
IL
0.6
I
R =1.15e-1.76k/(c
"
.6-
I
o 20OK(200keV)
A
54K(200keV)
w 295K (80keV)
~A
0.8
I
I
C
- R=1.47e
0.4
-P/
R47
0-
0.3
U-
0.2
0.1
0
I
0
I
I
I
II
0.8
kc
0.4
II
1.2
I
1.6
Figure 5.4: Normalized dependence of R on electron beam dose for several temperatures,
for 80 and 200 keV electrons.
164
and electron beam energies.
It is important to note that R vs. 0/0, is independent
76
of temperature but strongly dependent on electron beam energy (R = 1.15 e-1. 0/Oc
and R = 1.47 e-2.270/0. for 80 and 200 keV electrons, respectively).[3] The exponential
factors in Fig. 5.4 scale approximately with the electronic stopping powers (Eq. (5.3))
[18] for the two energies, indicating that radiolysis is the mechanism that induces the
C-G transition.[1,21 The electronic stopping power is given by
dE
dx
-
47rZ 2 e4N
-1In
mv2 l
2mv2\
-(5.3)
I
where I ~ Z x 10 eV is the electronic binding energy, Z is the atomic number of the
target, N is the atomic density, v the electron velocity, m the relativistic mass of the
electron and e the electron charge.
Radiolysis may produce atomic displacements by the creation of an electronic excited
state.[1,2] We have evidence for the displacement of Cl- ions from previous work on x-ray
fluorescence studies on SbCl 5-GICs using the scanning transmission electron microscope
(STEM) at room temperature. Our STEM results show that the counts for the Cl Ka
radiation increase by ~ 10.6% during the electron beam irradiation process, whereas the
counts for the Sb L1 radiation remain approximately constant (decrease by
; 2.8%).
c for both the 80 and 200 keV electrons
Figure 5.5 shows that the critical fluence
follows approximately the same Arrhenius plot at high temperatures. The critical dose
0, shown in this figure can be expressed as a sum of two exponential functions with
activation energies (Ea) of - 0.11
0.01 eV and ~ 0.012
0.005 eV. The rate of damage
can be expressed in terms of the order parameter S in the following manner
dS = -S-e fff
where
j
is the current density,
(5.4)
e
dt
eff is the effective ionization cross-section and f is the
fraction of ionization events which result in permanent damage.
Solving Eq. (5.4) we get:
--
S = exp
where 0 is the electron dose. The critical dose
0C=
U'q f
4, can
- In
165
(5.5)
ef f
be expressed from Eq. (5.5) as:
-(5.6)
\1C)
- 200keV
*100 keV
80 keV
1050
Ea~O.11eV
C\j-
O 0<0
Q)104-
-
E~O.012eV
7
A
A
1021
o
0.5
1.0
1.5
2.0
2.5
3.0
100/T(K-1)
Figure 5.5: Temperature dependence of the critical electron dose
sition in SbCl 5 -GIC for 200 and 80 keV electrons.
166
(0,)
for the C-G tran-
where Sc is the critical order parameter. If an activated step is involved in the forward
radiolysis process so that
f = be-ER/kT
where b is a constant, then:
e
=
boef
ln
SC
exp(ER/kT).
(5.7)
On the other hand, for two activated annealing mechanisms opposing the damage
process,
be-ER/kT
f
be-ER/kT + die-El/kT + d 2 e-Er2/kT
where di are constants and Eri and ER are the activation energies for the annealing
mechanisms and the damage process, respectively. Then,
4=
-
n
-
1 + -exp[-(E,1 - ER)/kT] + -exp[-(E,
A exp[-(Er, - ER)/kT] + B exp[-(E,
2
2
- ER)/kT]
- ER)/kT]
(5.9)
where A and B are constants. Our experimental results give numerical values for the
coefficients in Eq. (5.9)
2
3
0C = 128.9 x 10 5 exp[0.11 eV/kT] + 5.63 x 10 exp[0.012eV/kT] e/A
and suggest that there is a competition between two annealing mechanisms, as discussed
below.
We have found no dependence of the damage process on either electron beam intensity
or sample thickness in the ranges (1.0 e/k 2 -s to 3 x 10 3 e/A 2 - s) and (100
A
to 500
A),
respectively. In contrast to the results of the ultrasound measurements on SbCl 5-GICs
[11], our experiments seem to be independent of cooling rate.
SbCl 5-GICs have been inferred at
-
Phase transitions in
200 K from ultrasound measurements [11], electrical
resistivity [7,9] and x-ray diffraction [6,10] and at ~ 150 K and ~ 220 K from specific
heat measurements.[12] The results how' ver [12] are found to be sample dependent. The
anomaly in the specific heat observed at
-
150 K [12] was related to rotational motion of
the SbCl 5 molecules above this temperature. A similar effect has been observed in NMR
studies on SbF 5-GICs [19] where upon cooling, the motion of the fluorine ions stops
167
suddenly at ~ 150 K. In this context we suggest that diffusion or free motion of the
Cl- ions gives rise to a annealing mechanism which is dominant at high temperatures.
Assuming an activation energy for diffusion of the Cl- ions Eri ~ 0.13 eV (same as
obtained in NMR experiments on SbF 5
ER = 0.02
0.01 eV and Er 2 = 0.03
[19]), we obtain from our experimental results
0.01 eV.[3] The second annealing mechanism will
be discussed in the following section.
5.5
Model for The Radiolysis Process.
In the electron irradiation process, intercalate atoms acquire enough kinetic energy to
surmount the potential barrier which locks them to the graphite. There are many possible
mechanisms for the C-G transition. Here we discuss one possible scenario based on an
analogous observation in electron irradiated NaCl.[20] We first suggest that the
(V7
x
V7)R19.10* structure is formed by a mixture of the SbCl6 and SbCl 3 molecular species
(more about this model was discussed in chapter 4) observed in Mdssbauer experiments
on SbCl 5 -GICs.[21] Under electron beam irradiation, a Cl- ion of the SbCl6 molecule is
excited (probably ionized), leaving a hole behind. This hole becomes localized between
two Cl- ions of the SbCl- molecule (see Figs. 5.6a) and 5.6b)) and a Cl
molecule is
formed at a single lattice site. The latter is unstable and produces a displacement of one
of the Cl- ions (leaving behind an SbCl 5 molecule) to a site next to an SbCl 3 molecule,
and an SbCl4 molecule is formed (see Fig. 5.6c)). The consequent mixture therefore
yields a glass phase. On the other hand, a second annealing process would be obtained
if the Cl~ ion of the Cl
molecule either goes back to its original position or to another
SbCl 5 molecule; for both cases no effective damage is produced.[3] At low temperatures
OC is small since a few interstitial atoms are enough to induce a crystalline-glass phase
change [22] and the recombination mechanism is slow at low temperatures.
The above model, of course, is quite speculative. There is some possibility that the
low temperature glass phase involves the pinned dislocation model of D.R. Nelson [22
who predicted that a two-dimensional solid with quenched impurities would exhibit a
re-entrant melting to a glass phase at low temperatures. This would require that the
commensurability energy be small, as indeed seems to be the case in SbCl 5-GICs.
168
In
r e
Sb
Sb C1 3
C)-
C
SbCI6
(b)
SbCl 5
(c)
SbCI3
SbCl~
Figure 5.6: a)-c) show the model for the radiolysis mechanism in SbCL5-GICs.
169
any case, further work on this 2D system will undoubtedly advance our understanding
of glasses.
Conclusions.
We have found that the commensurate-glass phase change observed in SbCl5 -GICs
is induced by electron beam irradiation. Radiolysis is the mechanism that induces the
phase change.
Our results indicate the presence of two annealing mechanisms that
oppose the radiolysis process and occur concurrently. The mixture of SbCl- and SbCl 3
molecular species in the (/7 x /7')R19.10* phase can be used to explain the radiolysis
process and the annealing mechanisms.
5.6
Suggestions for Future Work.
Another interesting study on this material would be the dependence of the annealing
temperature on electron dose. Spectroscopic studies of SbCl 5 -GICs in the glass phase to
determine the chemical nature of the constituents would be invaluable. Thermodynamic
and transport measurements on this novel quasi-two dimensional glass could also yield
interesting results. The study of the glass phase in bulk samples is possible since any
ionizing radiation should induce the C-G phase change.
A detailed study of
4,
vs.
T such as the one reported in this chapter for other
stages will give information about differences in behaviour of an approximately threedimensional glass (stage 1) and a two-dimensional glass (stages
> 2).
The study of other intercalation compounds where there is disproportionation of sites
(SbF 5-GICs) and other metal chloride-GICs where there is no disproportionation of sites
(CuCl 2 - and CoCl 2-GICs)
under electron beam irradiation at different temperatures
would give more information about the radiolysis mechanism responsible for the phase
change.
170
References
[1] L.W. Hobbs, Quantitative Electron Microscopy, Proc. of the
25
th
Scottish Univer-
sity Summer School in Physics, Glasgow Aug. 1983, ed. J.N. Chapman, and A.J.
Craven, SUSSP Publications, Edinburg, (1983), p. 399, and references therein.
-
[2] E. Zeitler, ed., Cryomicroscopy and Radiation Damage, North Holland Amsterdam,
(1982).
[31 L. Salamanca-Riba, G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus and R.J.
Birgeneau (to be published).
[4] G. Timp, M.S. Dresselhaus, L. Salamanca-Riba, A. Erbil, L.W. Hobbs, G. Dresselhaus, P.C. Eklund and Y. Iye, Phys. Rev. B26, 2323 (1982).
[5] M. Suzuki, R. Inada, H. Ikeda, S. Tanuma, K. Suzuki and M. Ichihara, Graphite Intercalation Compounds, edited by Sei-ichi Tanuma and Hiroshi Kamimura, (1984),
p. 57.
[6] R. Clarke and H. Homma, Mat. Res. Soc. Symp. Proc. 20., (1983).
[7] R. Clarke, M. Elzinga, J.N. Gray, H. Homma, D.T. Morelli, M.J. Winokur and C.
Uher, Phys. Rev. B26, 5250.(1982).
[8] L. Salamanca-Riba, G. Timp, L.W. Hobbs, and M.S. Dresselhaus, Mat. Res. Soc.
Symp. Proc. 20, 9 (1983).
[9] H. Fuzellier, J. Melin and A. H6rold, Carbon 15, 45 (1977).
[10] H. Homma and R. Clarke, Phys. Rev. B31, 5865 (1985).
171
[11] D.M. Hwang and G. Nicolaides, Solid State Comm. 49, 483 (1984).
[12] D.N. Bittner and M. Bretz, Phys. Rev. B31 1060 (1985).
[13] W. Jones, P. Korgul, R. Schl6gl and J.M. Thomas, J. Chem. Soc., Chem Commun.
468 (1983).
[14] R.J. Birgeneau, P.A. Heiney and J.P. Pelz, Physica 109 & 11OB, 1785 (1982).
[15] A. Erbil, A.R. Kortan, R.J. Birgeneau, M.S. Dresselhaus, Phys. Rev. B28, 6329
(1983).
[16] J.M. Gibson and M.L. McDonald, Ultramicroscopy 12, 219 (1984).
[171 M. Elzinga, D.T. Morelli and C. Uher, Phys. Rev. B26, 3312 (1982).
[18] H.A. Bethe, Ann. Phys. 5, 325 (1930); F. Bloch, Ann. Phys. 16, 285 (1933); Z.
Phys. 81, 363 (1933).
[19] I. Stang, G. Roth, K. Liiders, H.-J. Giintherodt, GraphiteInterealation Compounds,
Extended Abstracts, ed. by P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus,
1984, p. 171.
[20] M.N. Kabler and R.T. Williams, Phys. Rev. B18, 1948 (1978).
[21] P. Boolchand, W.J. Bresser, D. McDaniel and K. Sisson, Solid State Commun. 40,
1049 (1981).
[22] D.R. Nelson, Phys. Rev. B27, 2902 (1983).
172
Chapter 6
THERMAL EXPANSION
COEFFICIENT -OF SbC1 5 -GICs
In this chapter we discuss the thermal expansion coefficient of SbCl 5-GICs obtained
from analysis of (00t) x-ray diffractograms. Section 6.1 contains the introduction to the
chapter. Section 6.2 shows the experimental details. The results and the calculation of
the thermal expansion coefficients for the different intercalate layers are given in sections
6.3 and 6.4, respectively.
6.1
Introduction.
The thermal expansion coefficient
y of a crystal is a measure of the change in crystal
volume V with temperature T (-y =
). The linear thermal expansion coefficient
(a) is a measure of the change of one of the crystal dimensions with temperature. Consequently, structural phase transitions such as order-disorder phase transitions can be
studied by measuring a as a function of temperature. X-ray diffraction is a very sensitive
method for measuring
a for crystalline materials since it provides a means of calculating
interplanar spacings very accurately.
The anisotropy of graphite is manifested in many of its physical properties as well as
in its thermal expansion. The temperature dependence of the c-axis lattice constant of
graphite is large compared to that of the in-plane lattice constant.[1,2] The c-axis linear
expansion coefficient of graphite intercalation compounds is a measure of the change in
the repeat distance Ic with temperature.
It was already shown in chapter 5 using both (hkO) electron and x-ray diffraction
173
techniques that the positions of the in-plane
(V1'
x V7)R19.1* reflections do not change
(within experimental error) on cooling from 300 K to 16 K (see chapter 5).[3] These
results indicate that the in-plane thermal expansion coefficient of SbCl 5 intercalated
graphite is very small. In this chapter we show that the temperature dependence of the
c-axis lattice constant for graphite intercalated with SbCl 5 is larger than that for the inplane lattice constant, reflecting the anisotropy of the thermal expansion of intercalated
graphite. The value of a is obtained from analysis of (00i) x-ray. diffractograms taken
at several temperatures for stages 1-3 SbCl 5 -GIC. We also obtained the temperature
dependence of the interplanar spacings between the layers that form the intercalate
sandwich and inferred the thermal expansion coefficient of every one of these layers.
The interplanar spacings between the layers are obtained from Fourier synthesis of the
(00t) integrated intensities.
Several phase transitions have been inferred for SbCl 5-GICs at low temperatures using a variety of experimental techniques.[4, 5,6,7,8,9,10,11,12] Some of these phase transitions involve in-plane structural changes of the intercalate.[6,7] Therefore, anomalies in
the c-axis thermal expansion coefficient of SbCl 5 -GIC.s at low temperatures would be expected to give information about structural changes along the c-axis in the temperature
range where phase transitions have been observed.
6.2
Experimental Details.
The stage 1-3 samples used in this experiment were prepared and characterized
for stage index, as explained in chapter 2. The repeat distances
I, obtained at room
temperature were in agreement with those previously reported.. [13,14]
The (00t) x-ray diffraction study was carried out on a General Electric powder
diffractometer equipped with a liquid 4He cold stage. Diffraction data were obtained in
the
E - 28 mode using Mo K, radiation (A = 0.71073 A) and an energy discriminating
Si/Li detector.
A single channel analyzer was used to separate the Mo K" radiation
from the continuum. (00f) x-ray diffractograms were taken for stages 1-3 SbCl 5 -GICs
in the temperature range 10 K
< T <
300 K. The samples prepared for the x-ray
experiment were obtained by cleaving the as grown samples to get a sample of ~ 0.08 mm
174
4
in thickness. Such a thin sample was required by the liquid He stage in order to have
the incident x-ray beam tangent to the sample surface at 28 = 0.
6.3
Results.
Figure 6.1 shows
295 K (Fig.
(00e)
x-ray diffractograms of a stage 1 SbCl 5 sample taken at
6.1a)) and at 20 K (Fig.
6.1b)).
The shift of the (00t) peaks in Fig.
6.1b) to higher angles is due to the thermal contraction along the c-axis. The peaks
indicated with * in these figures correspond to contribution from the sample holder, as
was corroborated by separate scans obtained without any sample. To study the thermal
contraction we have obtained the temperature dependence of the c-axis repeat distance
L on cooling and on heating. The I values were obtained from analysis of the (00t) x-ray
diffractograms taken at several temper-atures and using a chi-square, E minimization
of A(28e,e') = 2(Ee - Ee'), the angular difference between each pair of (00t) and (QOL')
diffraction lines. [151 The results are shown in Figure 6.2a) for a stage 1 sample. We have
fitted the data shown in this figure with straight lines, and inferred a value for the total
c-axis thermal expansion coefficient
a(1) = 3.27
0.1 x 10-5 K-1 at room temperature
from the average of the slopes of the two lines and the value of I
temperature (a = A).
= 9.46
A
at room
We have also calculated a from the slope of the AIc/Ic vs.
curve shown in Fig. 6.2b) and obtained a(1) = 3.91
AT
0.3 x 10-' K-'.
The value of a can also be obtained from the temperature dependence of the high
order Bragg angles 2et. From Bragg's law
2-csin8t = fA
where A is the x-ray wavelength. Then
a=
a can be written in terms of et as:
-
cosee AE(
s.e
AT
sin8t LL
(6.1)
Figure 6.3 shows the temperature dependence (on both cooling and heating) of the
diffraction angles 2Ee for t = 7, 8 for 10 K < T < 300 K for a stage 1 SbCl 5 sample.
Figure 6.3 shows no difference in the temperature dependence of 287 and 288 on cooling
and on heating within experimental error. The temperature dependence of the diffraction
angles 28t for graphite-SbCl 5 shown in Fig. 6.3 is similar to that observed for stage 1
175
(002)
295 K
(003)
(a)
(006)
'E
(004)
(005)
(007)
(008)
(002)
C
(003)
C:-
(001)
(004)
I
5
I
10
(006)
9f v
(b)
15
(005)
I
I
20
25
(007)
(008)
30
35
I
Di ffraction angle degrees (29)
Figure 6.1: (00e) x-ray diffractograms of stage 1 graphite-SbC1 5 at a) 295 K and b) 20
K.
176
9.50 9.50
I
'
a)
I
j
II
I
i
a= 3.28 x 10-5 K-1
(COOLING)
9.45
a=3.25x10- 5 K-1
(rErATING)
0<
9.40
Error bar
9.35
200
100
0
300
Temperature ( K)
0.004
b)
0.003
U
a~' 3.9jx0-5 K~
0.002
0
-
0.001
0
20
40
60
80
100
AT(K)
Figure 6.2: a) Temperature dependence of the c-axis repeat distance I
AIc/Ie vs. AT for a stage 1 SbCIs sample.
177
and b)
35.8
1
o Cooling
35.6-~*
Heating
35.40
0
35.2t 35.031.231.0
30.8-
0
30.630.41
0
300
200
100
0
Temperature (K)
Figure 6.3: Temperature dependence of the Bragg angles 2E7 and 288 for a stage 1
graplite-SbCI 5 sample.
graphite-FeC
3
[16] in the same temperature range. From a least square fit to the data
shown in Fig. 6.3 and using Eq. (6.1) we obtain a(1)
=
3.85
0.2 x 10~' K-'. From
the results for a shown above we take the value of a(1)
=
3.63
0.3 x 10-' K-' for the
total linear thermal expansion coeflicient for stage 1 along the c-axis.
We have also obtained (00t) x-ray diffractograms at different temperatures for stages
2 and 3. A value for the thermal expansion coefficient for a stage 2 SbCl 5 -GIC sample
was obtained from the temperature dependence of the Bragg angles 2E8 and 2E9g (shown
in Fig. 6.4). From the slopes of the curves fitted to the data and using equation (1)
we obtained
16.16
A
a(2) = 3.38
to 16.06
A
0.3 x 10-' K-1. For a stage 3 sample, a change in I from
was obtained from (00t) x-ray diffractograms taken at 295 K and at
178
29.80,
1980 -1 -
1
5
0334xU
o
0
29.68-.
K
0
9
29.56-
(I)
(T26.40
* Cooling
-
-o
o Heatilly
.
2 29.44
0
G"
(NJ
a=3.42x 10 5
26.35-
0
.
26.30-
=8
.o
26.25-
0
0 0
26.20-
0
.
100
200
o
300
Temperature (K)
Figure 6.4: Temperature dependence of the Bragg angles 288 and 289 for a stage 2
graphite-SbCl 5 sample.
20 K, respectively. From this change in Ic we estimate
a(3) = 3.09
0.3 x 10-5 K-1.
The stage dependence of a is discussed in more detail in section 6.4 of this chapter.
The thermal expansion coefficients between the layers in the intercalated compound
were also obtained from analysis of the (00t) x-ray diffractograms taken at different
temperatures from a stage 1 SbCl 5-GIC. It was previously described in chapter 2 that
upon intercalation, SbCl 5 forms a three layered intercalate structure along the c-axis
with two layers of C1 ions, one above and one below a layer of Sb ions. The interlayer
distances dsb-cl, dCo-Cb and dcl-ci between Sb and Cl layers and between Cl and
C bounding (Cb) and C interior (Ci) layers were obtained by carrying out a Fourier
synthesis of the (00f) integrated intensities [15] as explained in chapter 2. Specific results
were obtained for stage 1 SbCI 5-GICs for temperatures in the range 10 K < T < 300 K.
Figure 6.5 shows an example of the charge density along the c-axis for a stage 1
SbCl5 sample, obtained from analysis of the (00f) x-ray diffractograms taken at 20 K.
The peaks are identified by considering the relative heights of the peaks in the charge
179
C
C
Sb
C I
CI
0
_IC
IC
2
2
z
Figure 6.5: Charge density along the c-axis from a Fourier synthesis of the (00t) integrated intensities for 8 lines in a stage 1 SbCl5 -GIC sample taken at 20 K.
distribution since the heights are related to the total number of electrons in every layer
[151. Once the peaks are identified, the interplanar distances dSb-CI, dcI-cb and dcl-ci
(dci-ci only for n> 2) are directly obtained by measuring the distances between the
peaks in the charge distribution figure. Figure 6.6 shows the temperature dependence of
the interplanar distances dsb-cI and dcl-Cb obtained for a stage 1 sample.
The thermal expansion coefficients for the Sb and Cl layers (asb-cl) and the Cl and
Cb layers (acI-cb) were calculated from the slopes of the curves dsb-cI vs. T and,
dc-cb vs. T and Adcj-Cb/dcj-Cb vs. AT, respectively. The values thus obtained were
- 7.34
aSb-C
0.3.X 10-5 K-1 and aCi-cb ~ 1.75
0.2 x 10-' K-1. The value of
7.34 x 10-5 K-1 for asb-Cl is larger than -/3 = 6.66 x 10-5 K-' for pristine SbCl 3 [17],
where
a or
-1
-y
is the volumetric thermal expansion coefficient. To our knowledge no value for
for pristine SbCl 5 has been reported in the literature. On the other hand, the
value of 1.75 x 10-5 K-1 obtained for aCI-Cb is smaller than acI-Cb = 2.56 x 10- 5 K-1
measured in stage 1 graphite-FeC
3
.[16] The intercalate layer in the FeCl 3 system is also
formed by three atomic layers, with two layers of Cl- ions, one above and one below a
layer of Fe 3+ ions.
The values of asb-cl and
acI-Cb were used to estimate the total thermal expansion
180
3.340
i
1
dcI Cb
3.3301
j=1.75 x 10-5 K
0
a
0
S<
* Cooling.
3.3201-
o Heating
1.390
-
dSb-CI
1.380
0
1.370 1.360
1.350
0
g
0
~0.0
i
III
I
5 K-l
c=7.34x10t
i
100
III
200
I
I
300
Temperature ( K)
Figure 6.6: Temperature dependence of the interplanar spacings dsb-cI and dcl-cb for
a stage 1 graphite-SbC 5 sample.
181
coefficient for stage n (ci(n)) SbCl 5-GICs and for every layer x (c4 ) in the intercalation
compound. The specific results of this calculation are presented in section 6.4 of this
chapter.
Thermal Expansion Coefficient.
6.4
From the calculated values for the thermal expansion coefficients presented in section
6.3 of this chapter we have inferred the thermal expansion coefficient of each layer in
the intercalate sandwhich as well as the stage dependence of the total thermal expansion
To obtain the thermal expansion coefficient of every layer in the
coefficient (oi(n)).
intercalated compound, we extended the model for the thermal expansion coefficient in
metallic graphitides suggested by Lelaurain et al. [18] to compounds with a three layered
intercalate sandwich.
Figure 6.7 shows a schematic representation for the Sb and Cl positions in the
graphite -x orbitals.
This model is based on that for metallic graphitides suggested
by Guerard et al.[19] In the Gudrard et al. model, the graphite 7r orbitals are considered
to be formed by two cones, each one of them being surrounded by a spherical part with
radius x/2 = 0.71
A
(x=1.42
A
is the C-C in-plane distance).
From Fig. 6.7 and using the Lelaurain et al. model [18] we can express the interlayer
thermal expansion coefficients acIc1b and asb-cl in the following manner:
aCiC-Cb =
aSb-ClI
=
rCl
rci + rSbUI+
%i
+dSb-l. USb
/s-i
USb
dsb-.C1
where uc, = ((rc, + x/2) 2
and
(rci + x/2
rci
Cac + d
dcl-Cb
dcl-Cb
UCI
y
-
rSb
i
cI>
(rci + rSb)
s
(6.2)
i(6.3)
x2)1/2 = dcl-cb - y, USb = ((rci + rSb) 2 - a.2)1/2 = dsb-cl,
ac, aciI and iiS are the thermal expansion coefficients for the C layer and the Cl
and Sb layers in the intercalated compound, respectively; x = 1.42
distance , a. = 2.46
0.965
A
A
where c = 3.35
A is the
C-C in-plane
is the graphite in-plane lattice constant and y = (c - x)/2 =
A is
the graphite-graphite interplanar distarce.
From the expressions for uci and USb and the values for dSb-cl and dcl-Cb obtained
from our analysis of the
rci = 2.06
A
(00t) x-ray diffractograms at room temperature, we obtain
and rsb = 0.77 A.
The value of 2.06 A is larger than the radius of
182
yx
x/2
uC
USb
rSb
IC
ao
T
Figure 6.7: Schematic representation of the positions of the Sb and Cl ions in the graphite
7r orbitals.
(= 1.81
(= 0.76
A).
A)
and the value of 0.77
A is approximately equal to the radius of.Sb 3
+
Cl
These values obtained for the ionic radii rsb and rol are the maximum
possible values since the expressions for uci and usb in terms of rol and rsb were obtained
by assuming that the ions are hard spheres that are in contact. Substituting these radii
in equations (2) and (3) we obtain ac = 1.34 x 10-5 K~
1
and asb = 2.95 x 10-' K-'.
Following a similar calculation we obtain the thermal expansion coefficient of the
SbCl5 sandwich in the intercalated compound (aibc ) in terms of the total thermal
expansion coefficient a(1)
IC
}I,: - y
aSbCl = (
(2(rci +rsb)) rci+ rSb+ X/2
a(1) -
2
-'ac C
IC
(6.4)
Substituting our experimental result for a(1) and the calculated values for rci and
in Eq. (6.4) we obtain a bCi1 = 5.48 x i0-
K
1
rsb
0.82jysbC1 3 . It was found by Lelaurain
et al [18] that the ratio of the thermal expansion coefficient of a metallic intercalate
(a' ) to that of the free metal (am) was larger, the smaller the charge transferred to
the graphite atoms 8 (see Table 6.1). Assuming that the same result applies to acceptor
compounds, we obtain for the SbCl 5 system a charge transfer per intercalate molecule
183
Table 6.1: Thermal expansion coefficients and charge transfer estimates for several metallic graphitides. Obtained from [18].
Compound
of
a
al
am
al ,/aM
5
0.353
0.60
C 6 Li
x10- 5 K~1
31
18
51
C8 K
C 8 Rb
39
33
40
33
84
86.2
0.476
0.383
0.68
0.78
C 8 Cs
19
14.4
90.3
0.159
0.92
C6 Ba
C 6 Eu
10
12
1.5
2
25
30
0.060
0.067
1.18
1.18
C6 Yb
20
12.5
31
0.403
1.50
8 = 0.15, which is a reasonable value for an acceptor compound.
A value of
8
in the range 0.25-0.44 was derived for stage 2 SbCl 5-GICs from a theoretical fit to
reflectivity measurements using the tight binding method.[20] From the value for the
charge transfer of 8
0.2 we obtain equilibrium values for the relative concentrations of
SbCl5 :SbCl6:SbCl 3 = 7:2:1.
The total thermal expansion coefficient
a(n) for stage n SbCl 5-GIC [5] can be ex-
pressed in terms of ac-c, aSb-cl and acI-cb using the model suggested by Mazurek et
al. [16]
a(n) = (ac-c (n - 1)dc-c + 2asb-cdsb-cI + 2ac-cbdcj-Cb)
.
(6.5)
From the Lelaurain et al. model a(n) can also be expressed in terms of the thermal
expansion coefficients ac, aisb and asci of the individual layers, in the following manner:
a(n) = (2yac + 3.35(n - 1)ac + 2rc
0 Dici I + 2rcID2ai I + 2rsbD2asb)
where Di = (rci + x/2)/uci and D 2 = (rci + rSb)/uSb.
Using either Eq.
(6.6)
(6.5) and
the values of asb-cl and acI-Cb obtained in section 6.3 of this chapter and ac-c =
2.73x10-
K-1 [1,2], or Eq. (6.6) and the ac, asb and asc values for the individual layers,
we calculate for stages 1-4 a(n) = 3.41, 3.25, 3.13 and 3.06 x10-
5
K-1, respectively.
The calculated values of a(n) for n= 1, 2 and 3 are in satisfactory agreement with the
values obtained from our experimental results reported in section 6.3 of this chapter
(a(1) = 3.63
0.3, a(2) = 3.38
0.3 x 10-5 K-1 and a(3) = 3.09
184
0.3 x 10-5 K-1). The
values of
a(n) obtained in this experiment for the SbCl 5 -GIC system, agree with those
calculated using Eq. (6.5) and the values of ac-Cl and aFe-cl reported by Mazurek
et al.[16] for FeCl3 -GICs.
ce(n) = 3.55, 3.34, 3.21 and 3.13 x 10-5 K-1 for n= 1, 2, 3
We should mention that the values of a(n) =2.55, 2.59, 2.62 and
and 4, respectively.
2.64 x 10~5 K-1 reported in [16] for FeCl3 -GIC stages 1, 2, 3 and 4, respectively, do not
agree with the values calculated using the expression for a(n) (Eq. (6.5)) suggested by
the authors.
Table 6.2 summarizes the results for the thermal expansion coefficients for the intercalate layers asb and aci obtained using Eqs. (6.2) and (6.3) and our experimental
results for aSb-c and aICI-Cb for stages 1-3.
The values of asb-cl and
CiCI-Cb were
obtained from the temperature dependence of the respective interplanar spacings. The
table also contains the ratio of acsbcI,/aSbcI, where aSbCI, = 31SbcI3
=
6.66 x 10-
K-
[17] is assumed. Values for the thermal expansion coefficient for the intercalate sandwich
for stage n abI
(n) in Table 6.2 were obtained by generalizing Eq. (6.4) for stage n to
obtain
c1~SbCi
IC
SbCin
2(rCi + rSb)
dsb-CI + dci-c - y)
rc, + rSb + x/2
-
(n -
1)3.35 + 2y e
(6.7)
IC
Using the model suggested by Lelaurain et al. [18] for the relation between the charge
transfer and the ratio of the thermal expansion coefficient of the intercalate to that of
the free material, we infer from our results for asbol 5
/asc1& given in Table 6.2 that the
charge transfer is higher for higher stages than for lower stages and estimate values for 5
of 0.15, 0.17 and 0.28 for stages 1, 2 and 3, respectively. The same stage dependence of
the charge has been observed in donor compounds from Knight shift measurements. [21]
Our experimental results on stages 1, 2 and 3 SbCl 5 -GICs show no evidence for a
structural phase transition along the c-axis for temperatures in the range 10 K < T <
300 K.
Several structural phase transitions have been reported in the SbCl 5 system
in this temperature range. Namely, a two dimensional melting transition was observed
at
~ 230 K from ultrasound measurements on stage 4 SbCl 5 -GIC.[9]
A transition at
~ 230 K has also been observed using x-ray diffraction [7,8] and electrical conductivity
[7,12].
This transition was first identified as a commensurate-incommensurate
phase
transition [7], and later as a result of a dipole-dipole coupling of SbCl 3 molecules in
185
the intercalate layer
[8].
An order-disorder phase transition has been observed in some
SbCl 5 -GIC samples at T ~ 220 K from specific heat measurements.[10]
Table 6.2: Thermal expansion coefficients for the different layers for several stages of
SbCl 5-GICs.
asb-ci
a(n)
stage
n
ac1-o
x10-
exp.
0.3
3.63
3.38
3.09
1
2
3
5
ac-o
dSbI
QXbCls/aSbCl 6
0.2
2.67
0.2
2.95
3.31
3.77
0.2
1.34
1.22
1.17
K-1
calc.
0.3
7.34
7.28
7.55
3.41
3.25
3.13
0.2
1.75
1.81
1.66
0.82
0.80
0.71
Our results show that the thermal expansion coefficient of SbCl 5-GICs along the
c-axis is larger than that in the basal plane. The largest change in interplanar spacing
when T is changed from room temperature to ~ 20 K corresponds to that between the Sb
and Cl layers (~
2.2%). On the other hand, the change in interplanar spacing between
the Cl and C layers is ~ 0.5% for the same temperature differences. Thus, the relative
expansion of
dSb-CI is ~
4.5 times that of dCj-Cb over this temperature range.
We have obtained a decrease in the thermal expansion coefficient of SbCl 5-GICs
with increasing stage index. The same stage dependence was obtained for the thermal
expansion coefficient of alkali metal GICs.[22] For the alkali-metal GICs, the c-axis thermal expansion coefficient was analyzed using a one-dimensional quasiharmonic approximation in which the thermal energy was obtained from the longitudinal
branches.
(00e) phonon
From this result they derived Griineisen parameters which show the same
stage dependence as the thermal expansion coefficient. They attribute the larger value
of the thermal expansion coefficient of low stages to a strong and anharmonic alkalimetal-graphite interaction. This suggests that for SbCl 5-GICs, a similar anharmonic
intercalant-graphite interaction takes place.
Conclusions.
The expression used for
a(n) in terms of the thermal expansion between every layer
in the compound seems to apply to our experimental results for stages 1-3 SbCl 5-GICs.
186
A detailed study of the thermal expansion coefficient for other acceptor compounds is
necessary to relate the charge transfer to the ratio of the thermal expansion coefficients
of the intercalate to that of the parent compound.
187
References
[1] B.T. Kelly, Phys. of Graphite, (Appl. Science Publishers, London, 1981) p. 197.
[2] W.N. Reynolds, Physical Propertiesof Graphite, (Elsevier Press, Amsterdam, 1968),
p. 80.
[3] L. Salamanca-Riba, G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus and R.J.
Birgeneau, to be published.
[4] G. Timp, M.S. Dresselhaus, L. Salamanca-Riba, A. Erbil, L.W. Hobbs, G. Dresselhaus, P.C. Eklund and Y. Iye, Phys. Rev. B26, 2323 (1982).
[5] L. Salamanca-Riba, G. Timp, L.W. Hobbs, and M.S. Dresselhaus, Mat. Res. Soc.
Symp. Proc. 20, 9 (1983).
[6] R. Clarke and H. Homma, Mat. Res. Soc. Symp. Proc. 20, 3 (1983).
[7] R. Clarke, M. Elzinga, J.N. Gray, H. Homma, D.T. Morelli, M.J. Winokur and C.
Uher, Phys. Rev. B26, 5250 (1982).
[8] H. Homma and R. Clarke, Phys. Rev. B31, 5865 (1985).
[9] D.M. Hwang and G. Nicolaides, Solid State Comm. 49, 483 (1984).
[10] D.N. Bittner and M. Bretz, Phys. Rev. B31, 1060 (1985).
[11] W. Jones, P. Korgul, R. Schl6gl and J.M. Thomas, J. Chem. Soc., Chem Commun.
468 (1983).
[12] H. Fuzellier, J. M6lin and A. H6rold, Carbon 15, 45 (1977).
188
[13] V.R. Murthy, D.S. Smith, and P.C. Eklund, Mater. Sci. Eng., 45, 77 (1980).
[14] J. Mdlin and A. H6rold, Carbon 13, 357 (1975).
[15] S.Y. Leung, M.S. Dresselhaus, C. Underhill, T. Krapchev, G. Dresselhaus and B.J.
Wuensch, Phys. Rev. B24, 3505 (1981).
[16] H. Mazurek, G. Ghavamishahidi, G. Dresselhaus and M.S. Dresselhaus, Carbon 20,
415 (1982).
[17] Landolt-B6rnstein, Crystal Structure Data vol. 3, 7a, p 385.
[18] M. Lelaurain, P. Lagrange, D. Gudrard and A. H6rold, Proc. of the International
Conf. on Carbon, Bordeaux 1984, p. 290.
[19] D. Gu6rard and P. Lagrange, Proc. of the InternationalConf. on Carbon, Bordeaux
1984, p. 288.
[201 J. Blinowski, Nguyen Hy Hau, C. Rigaux, J.P. Vieren, R. Le Toullec, G. Furdin,
A. Herold and J. Melin, Journal de Physique 41, 47 (1980).
[21] J. Conard, H. Estrade, P. Lauginie, H. Fuzellier, G. Furdin and R. Vosse, Physica
B99, 521 (1980).
[22] S.E. Hardcastle and H. Zabel, Phys. Rev.
189
B27, 6363 (1982).
Chapter 7
DAMAGE AND
RECRYSTALLIZATION
STUDIES OF ION
IMPLANTED GRAPHITE
In this chapter we discuss the effect of ion implantation on the graphite lattice and
the recrystallization process for post-ion implanted annealed graphite. Section 7.1 contains the introduction to this chapter. The ion implantation conditions and the TEM
observation are given in sections 7.2 and 7.3, respectively. The damage dependence on
dose and ion species is presented in section 7.4. Sections 7.5 and 7.6 contain the regrowth
kinetics and defects characterization, respectively. Some suggestions for future work are
given in section 7.7.
7.1
Introduction
In this chapter we present the study of defects in the graphite lattice produced by
ion implantation and we relate these defects to the implantation conditions.
fects produced by carbon, hydrogen, helium and xenon
The de-
[1], neutron, [2,3] and electron
[4] bombardment of graphite and the subsequent recrystallization process [5] have been
previously studied using the transmission electron microscope (TEM).[6] An extensive
experimental study has been carried out on ion implantation of bulk graphite[7,8
and
implantation-induced modifications of the structural [9,10] and electronic [11] properties of bulk graphite have been reported. Ion implantation affects only the near surface
190
properties of bulk graphite. Because of their small diameters, graphite fibers are much
more sensitive than bulk graphite samples to monitor implantation-induced changes
of the structure and properties of graphite.[12] In addition, the high structural perfection of benzene-derived graphite fibers (BDGF) [13,14,15] allows quantitative study of
implantation-induced modifications to the near surface structure.
Ion implantation is the introduction of foreign species into a material of mass M1,
by the bombardment of ions of mass M 2 and energy E.[16] Ion implantation provides
an alternative method of introducing dopants into a lattice.
In contrast to chemical
doping, almost any element of the periodic table can be ion implanted into a material
with the advantage that dopant concentrations produced by ion implantation do not
depend on diffusion processes. Ion implantation provides a general technique for surface
modification of graphite which is applicable over a wide temperature range. In contrast
to chemical intercalation into graphite fibers, ion implantation provides materials which
are stable to temperatures of ~ 20000 C and higher.
The major factors in the ion implantation technique are the range distribution of
the implanted atoms, the concentration and nature of the defects that are created, the
location of these defects in the unit cell of the host material and the modification of the
physical properties of the implanted material. Some of these factors are related to the.
ion implantation parameters.
The controllable parameters in ion implantation are: ion mass, ion energy, total dose,
dose rate and sample temperature. Thus, ion implantation provides a controlled means
for studying the damage process as well as the recrystallization and regrowth kinetics of
highly damaged materials. In contrast to thermal diffusion, with ion implantation the
profile and the number of implanted ions can be controlled independently. The former
is a function of the accelerating voltage, while the latter can be determined by the
integrated beam current. The main parameters determining the range of an ion are the
ion energy and the atomic numbers of both the implanted ion and the target. In the case
of ion implantation into single crystals, the crientation of the target and the vibrational
frequency of the lattice atoms are also important parameters for determining the ion
range.
In the case of amorphous materials, the range distribution is approximately
Gaussian since the energy lost per collision is not the same for all ions. In this case,
191
the mean range (Rp) and spread (ARp) can be determined from the Lindhard, Scharff
and Schiott (LSS) theory [17] (C(x, E) z
Cmxe-(x-Rp)
2
/(Rp)
2
where C(x,E) is the
distribution of ions at depth x for an implantation energy E, and Cmax is the maximum
value of the distribution of ions) or more sophisticated versions of this theory. It has
been reported that the LSS theory can be applied to ion implanted graphite when the
ion beam direction is parallel to the c-axis.[7]
In order to study the effect of ion implantation on the physical properties of the
implanted material, it is important to know the nature of the defects created by the implanted ions and their relation to the implantation conditions. Defects in materials can
be studied by different methods; such as x-ray diffraction, Raman scattering spectrometry, Rutherford backscattering ion channeling and transmission electron microscopy.
Generally, x-ray diffraction is used to measure the interplanar coherence distances from
the linewidths of the diffracted beams.[18] This technique has been extensively applied
to the study of graphitization. [18] Raman spectroscopy, on the other hand, is especially
sensitive to the lattice disorder.[7,19,20] In particular for graphite, the relative intensity of the disorder-induced line at ~ 1360 cm-
1
to the Raman allowed zone center
(1580 cm-1) E2g2 mode varies as the inverse of the in-plane crystallite size.[21] On the
other hand, high resolution transmission electron microscopy (TEM) provides a unique
technique for the direct visualization of defects with large spatial extent, such as dislocations.[6,22,23] The defects can be observed using the TEM because of the strain
that they introduce into the lattice, and it is this strain field that the electrons feel as
they move through the specimen. High resolution TEM, dark field imaging and electron
diffraction provide sufficient information for the complete characterization of defects in
crystalline materials. [6,22,23]
Experimental results on recrystallization and regrowth kinetics of highly oriented
pyrolytic graphite (HOPG), using a variety of experimental techniques, have been previously reported for several implanted ionic species.[9,24] In this chapter we describe the
damage dependence on dose and ion species in ion implanted BDGF.[25] We also present
results for the recrystallization process and regrowth kinetics of post-implantation annealed HOPG and BDGF as a function of annealing temperature and time using the
TEM.[26] We have used HOPG and BDGF as host materials to obtain complementary
192
information on the damage and recrystallization processes. TEM studies on HOPG provide information on the microstructure in the basal plane. The geometry of the fibers,
on the other hand, allows convenient imaging of the c-axis lattice planes and therefore,
the direct observation of the structural damage along the c-axis associated with ion
implantation.
7.2
Ion Implantation Conditions
The fibers-used for this study were derived by pyrolyzing a mixture of benzene and
hydrogen at a temperature of 1100'C.[27,28,29] These fibers were subsequently heat
treated in a constant flow of argon gas to either 2900'C for 1 hr or 3500*C for 30 min.
The ion implantation was carried out at room temperature with an ion energy of 30
keV. The fibers and HOPG samples were mounted on a metal plate with silver conducting
paint. The ion beam from the ion implanter was directed normal to the fiber axis (see
Fig. 7.1a) and along the c-axis of the HOPG samples. Several ion species were used for
the damage study ( 3 1 P,
75
As,
121
Sb and
20 9
Bi) with fluences in the range 5 x 1012 <
4
1 x 1015 ions/cm 2 . For the recrystallization studies, fibers and HOPG samples were ion
implanted with
20 9
Bi ions with an energy of 30 keV to a dose of 1 x 1015 ions/cm2 . For
this choice of implantation parameters, the lattice damage extends all the way to the
surface of the sample. The low ion energy was chosen to obtain a shallow ion penetration
depth so that the damaged region and the unimplanted substrate could both be observed
at the same time using the TEM. Table 7.1 shows the values of the ion penetration depth
RP and ion spread
ARP calculated from the LSS theory.[17]
Table 7.1: Ion penetration depth Rp and ion spread ARp calculated from the LSS
Theory. [17]
Ion
31P
75
As
22
1 Sb
209
Bi
Rp (A)
284.98
ARp (A)
107.19
169.93
151.37
146.90
47.86
34.46
25.86
193
e- Beam
Ion Beam
)
(\a
Dark Field Image
(b)
Smage
)
(c
Figure 7.1: Schematic representation of a) the ion beam for ion implantation and the
electron beam for TEM observation directions. Schematic representations of the TEM
observation of b) (002) dark field and c) lattice images of the implanted and unimplanted
sides of a fiber.
7.3
TEM Observation of Ion Implanted Graphite
In comparing the structure of ion implanted and unimplanted graphite, bright field,
dark field, selected area electron diffraction and high resolution lattice images were examined using two JEOL 200 CX transmission electron microscopes with high resolution
pole pieces (C. = 1.2 and 2.8 mm) and LaB 6 filaments.
The distances observed in
the images were above the point to point resolution of both microscopes ~ 2.3
2.9
A.
A
and
An accelerating voltage of 200 keV was selected to get higher penetration depth
of the electron beam. The typical exposure time for recording the images was 4 seconds
194
at magnifications of 500,000 X. The images were recorded on Kodak SO-163 electron
microscope film.
The HOPG samples were prepared for TEM observation by repeated cleavage of
the bulk sample. The sample was first glued to a microscope slide using wax, with the
implanted surface side facing the microscope slide. The sample was then cleaved with
adhesive tape until only a thin film was left on the slide.
The wax was dissolved in
acetone and the thin sample was recovered with a copper 400 mesh electron microscope
grid. The fibers, on the other hand, were mounted directly between copper grids using
no special thinning technique.
Measurements of the correlation lengths in the basal plane (La) and along the c-axis
(Lc) were obtained by directly imaging the graphite lattice, taking dark field images
and from the full width at half maximum (B) of the electron diffraction spots using
B = 0.9A/(Lcoseb) where A is the electron beam wavelength, L the particle size and
eb the corresponding Bragg angle.[30 For the implanted fibers, La and L, were obtained
from (002) lattice images by measuring the length of the fringes and the number of
parallel stacked layers, respectively (see Fig. 7.1c)). La and L, were determined from
the (002) dark field images by measuring the lengths of the bright 'spots' along the
directions parallel and perpendicular to the fiber axis, respectively, (see Fig.
7.1b))
and from the full width at half maximum (FWHM) of the (002) spots in the electron
diffraction patterns.
For the HOPG samples, La was measured from the size of the
bright spots in the (100) dark field images and from the FWHM of the (100) ring in the
electron diffraction patterns. The c-axis crystallite size (Lcr) for the random regrowth
(as explained in section 7.5 of this chapter) observed in the post-implantation annealed
HOPG samples was measured from lattice images and dark field images, the same way as
Lc for the implanted fibers. Figure 7.2 shows schematically the electron beam direction
and TEM observation for both HOPG and the graphite fibers.
The values of La, Lc and Lcr obtained by any of these methods were corrected for
the projection effect since the electron microscope provides basically two-dimensional
information. This correction was made by assuming a simple model for a constant density
of linear defects in the sample. The mean separation of defects in three dimensions L is
2
then related to the projected separation of defects R (see Fig. 7.3a)) by L = (tR)'/ where
195
er Beam
e- Beam
0*
C-axis
1000A:'
0
-axis
~500A
HOPG
Objective
lens <
Back foca
40U
BDGF
-e
plane
(hkO) plane
(hk) plane
Dark f ield
image
Bright f ield
image
Image
plane
Figure 7.2: Schematic representation of the electron beam direction and TEM observations for fibers and HOPG.
t is the thickness of the sample along the electron beam direction and t was estimated
to be ~ 500
A
for the fibers and ~ 200
A
for the HOPG samples. We investigated the
validity of this correction using the TEM by tilting a fiber about its local c-axis (see Fig.
7.3b)) so that the thickness of the fiber along the electron beam direction increased to
t' = t/sinE where
E
is the angle between the electron beam direction and the fiber axis,
and t is the thickness of the fiber for
then taken for several angles
E.
E
= 900. Lattice images from the same region were
The projected values of La (Ra) and L, (Re) measured
from the obtained lattice images followed the dependence Li = /Rit/sine (i = a, c).
Suitable regions of the fiber for lattice imaging observations are the areas within a few
hundred angstroms from the fiber edge. In these regions the fiber thickness was usually
~ 500
A.
The graphite planes in these regions were oriented such-that the graphite c-
196
**
I
L
(a)
e- Beam-
SC-Axis
(b)
Figure 7.3: Schematic illustrations of a) linear defects in three-dimensions and their
projection in two-dimensions, and b) the geometry used to investigate the validity of the
model used to correct for the projection effect.
axis was perpendicular to the electron beam direction. The electron diffraction patterns
of these regions always contain the (00f) reciprocal lattice vectors. The lattice images
were obtained by placing a circular aperture at the back focal plane of the objective lens
of the microscope that encompassed at minimum the (000) and (002) reflections. The
interlayer spacing of the lattice fringes was obtained by taking an optical interferogram
of the negative of the electron micrograph, and using the pristine graphite fiber interlayer
spacing of 3.36
A
as a reference.
The dark field images were obtained by placing an aperture that would encompass
only the (002) reflection for the fibers and either one of the (100), (110) and (102) reflections for the HOPG samples after tilting the electron beam until the desired reflected
197
beam was along the axial direction (see Fig. 7.2). The analysis of dislocations in HOPG
was carried out using (10N) for N = 0 and 1 and (11N) for N = 0 and 2 dark field images
after tilting the sample into the appropriate two-beam diffraction conditions.[6,22,23]
7.4
Damage of Ion Implanted Graphite
In order to study the structural effects of ion implantation, lighter ions such as 31P
and heavy ions such as
2 09
Bi were implanted at an energy of 30 keV into graphite fibers
with a variety of ion fluences. The pristine benzene-derived graphite fibers exhibit large
areas of straight and defect-free graphite layers arranged parallel to the fiber axis (see
Fig. 7.4a)), with the graphite layers extending over 1000
A
along both the a-axis and
the c-axis directions.[13,15] The interlayer spacing is determined to be 3.36
optical diffractograms (see inset to Fig.
A
from the
7.4a)) taken from the negatives of the (002)
lattice images and also from the (002) x-ray diffraction line using Cu K, radiation.
These graphite layers show three-dimensional stacking order.
The three-dimensional
order is determined from both the (112) diffraction spots of the selected area elpctron
diffraction patterns (see inset to Fig. 7.5a)) and the (112) x-ray diffraction line.
Figure 7.4 shows (002) lattice images of an unimplanted fiber (Fig. 7.4a)) and ' 22 Sb
ion implanted fibers to various fluences from 5 x
1012 to 1 x 1015
ions/cm 2 (Figs. 7.4b)-
d)). It is clearly observed in the figure that with increasing fluence, there is a decrease in
both the in-plane crystallite diameter (La), and in the thickness of the crystallites (L,).
At the highest fluence of 1 x 1015 ions/cm 2 (Fig. 7.4d)), the fringes corresponding to the
graphite layers have completely disappeared. These changes in the graphite layers are
reflected in the optical diffractograms shown in the insets to the figure. Namely, as the
fluence increases, each spot in the optical diffractogram of the pristine fiber (inset to Fig.
7.4a)) develops into a collection of speckles and extended diffraction in the vicinity of
the (002) spots (insets to Figs. 7.4b)-d)); this indicates that the long range order of the
layers with respect to the fiber axis has been lost. Thus by increasing the fluence, not
only is the crystallite size reduced but also the parallel arrangement of the crystallites
with respect to the fiber axis is destroyed.[25]
The effect of the ion mass on the structure of the implanted fiber is shown in
198
Figure 7.4: (002) bright field images of a) an unimplanted fiber and fibers implanted
with 12 2 Sb ions to doses of b) 5 x 1012, c) 1 x 1014 and d) 1 x 10'" ions/cm 2 at 30 keV.
199
lit:
A
i.
i,
ifit
14k'Il~
I
till
75
As and c) 209 Bi ion
Figure 7.5: Dark field images of a) an unimplanted fiber, and b)
2
implanted fibers to a dose of 1 x 1015 ions/cm at 30 keV. The insets show the respective
electron diffraction patterns.
201
6M'k
I
IAiM
202
L
7.5 as studied by the (002) dark field technique.[25] The corresponding selected
Fig.
area electron diffraction patterns are shown as insets to the figures.
show the results of
20 9
Bi (heavy ion) and
75
In this figure we
As (lighter ion) implantation to a fluence of
1 x 1015 ions/cm 2 in comparison with the (002) dark field image for the pristine fiber.
The pristine graphite fiber exhibits sharp (002) and (112) 3-dimensional diffraction spots
in the diffraction pattern (see inset to Fig. 7.5a)), indicating highly ordered graphite
layers oriented parallel to the fiber axis. The corresponding (002) dark field imnage (Fig.
7.5a)) shows a bright Bragg band indicating large graphite crystallites. Ion implantation
of
209
Bi and
75
As at the same fluence and accelerating voltage reduces the crystallite size
to dimensions as small as 20
A
and 50
A, respectively (after carrying out the correction
for the projection effect explained in section 7.3 of this chapter), as can be seen from the
(002) dark field images (see Figs. 7.5b) and 7.5c)). It is known that heavier ions yield
smaller crystallite diameters after implantation, indicating that the heavier the ion, the
greater the damage to the graphite structure.
Implantation-induced misalignment of
the crystallites with respect to the fiber axis, can be clearly observed from the arced and
diffuse (002) diffraction spots in the insets to Figs. 7.5b) and 7.5c).
2
Figure 7.6 shows the damage produced by a high dose (1 x 1015 ions/cm ) of heavy
20 9
Bi ions. Fig. 7.6a) shows that ion implantation under the conditions specified above
destroys most of the fiber lattice order (for reference see Fig. 7.5a)). The texture of the
fiber shown in Fig. 7.6a) is similar to that of amorphous carbon.[31]
209
The in-plane lattice damage produced by a heavy ion ( Bi) and high dose (1 x
101 5 ions/cm 2 ) can be seen in the (hk0) electron diffraction pattern of the as-implanted
HOPG sample shown in Fig. 7.6b). For comparison, Fig. 7.6c) shows an (hk0) electron
diffraction pattern of a reference unimplanted HOPG sample. The diffraction pattern
presented in Fig. 7.6b) shows diffuse rings with intensity maxima at 2.98
and 5.11
0.03
A-1,
0.03
A-1
as well as sharp (hko) spots superimposed on the diffuse rings. The
diffuse rings indicate disorder in the basal plane of the implanted region whereas the spots
are identified with diffraction from the graphite substrate beneath the amorphous region,
since the sample was thicker than the thickness of the disordered region (~
170
A).
Figure 7.7 shows the dependence of the in-plane (La) crystallite size on ion mass for
several fluences, based on the measurements of the (002) lattice images.[25] The
203
Figure 7.6: a) (002) lattice image of graphite fibers and b) (hko) electron diffraction
pattern of an HOPG sample ion implanted with 2 09 Bi to 1 x 10"5 ions/cm 2 at 30 .keV,
and c) (hk0) electron diffraction pattern of unimplanted HOPG. The insets to a) are an
optical diffractogram taken from the negative of the figure and a schematic representation
of the ion beam direction.
204
04
lk
205
crystallite sizes obtained from the (002) dark field and lattice images were found to
give a similar dependence of the crystallite size upon fluence and ion mass within the
experimental error. As indicated- in Fig. 7.7, the dependence of the crystallite size on
ion mass Mi goes approximately as Mi-1/
2
2
for a fluence of 1 x 1015 ions/cm . A weaker
dependence on the ion mass seems to apply at lower fluences.
102
-
I
o 5x10' 2 cM-2
S1014 cm-2
1015 CM-2
~MI~'
0<
S10'
100L10'
102
103
Mi
Figure 7.7: Dependence of the in-plane crystallite size La (measured from (002) lattice
images) on ion mass for several fluences shown on a log-log plot.
The effect of ion implantation can also be observed in the c-axis interplanar spacings obtained from optical diffractograms taken from the negatives of the lattice image
micrographs.
Our analysis indicates an increase (to as much as 3.9
A)
in the c-axis
interplanar spacing c/2 after implantation. Interplanar distances up to 3.55
A
have been
obtained from measurements of dimensional changes on natural graphite flakes irradiated with neutrons
(0
~ 1020 n/cm 2 ) at high temperatures.[321 The dependence of c/2
on ion mass is shown in Table 7.2 for an ion energy of 30 keV and fluences in the range
5 x 1012 < 0 < 1 x 1015 ions/cm 2 . The increase in interlayer spacing is larger for heavy
ions than for lighter ones, which suggests that in part the ions lie interstitially between
206
the graphite layers. Interplanar spacings as high as 3.44
A
have been calculated from
x-ray diffraction from carbon samples annealed at temperatures (- 16000C) where C
atoms are known to lie interstitially.[33] Interstitial as well as vacancy clusters have been
)
previously observed in natural graphite flakes irradiated with neutrons (0 > 1016 n/cm 2
and C ions (0 > 1016 ions/cm 2 ) at high temperatures.[32] The detailed nature of the
defect sites remains to be elucidated.
There are several possible experiments that would give information about the nature
of the defects produced by ion implantation. For example, it is possible to image sin-
Table 7.2: Interplanar distance c/2 vs. ion mass obtained from optical diffractograms
taken from the negatives of the (002) lattice images of ion implanted BDGF to doses in
1 x 1015 ions/cm 2 with an energy of 30 keV.
the range 5 x 1012 < '
Ion
31P
75
As
22
1 Sb
209
Bi
c/2 (A)
3.53
3.57
3.80
3.91
0.08
0.08
0.08
0.08
gle defects or small clusters of defects using the atomic resolution microscope (ARM).
Therefore, a detailed study of the defects produced by ion implantation as a function
of dose is possible if a thin sample (suitable for TEM) is implanted several times and
analyzed using the ARM after every implantation. Using HOPG and BDGF one can
get complementary information about the damage process. After every implantation the
defects can also be analyzed using the technique described in section 7.6 of this chapter.
The suggested experiment would give information about whether or not there is a critical
size of defect cluster above which the defects are sheared, and below which the defects
are unsheared as has been previously observed in graphite irradiated with neutrons.[6]
Conclusions
Using benzene-derived graphite fibers which have the highest degree of crystallinity
of fibrous graphitic materials, high resolution transmission electron microscopy has been
used to clarify the structural properties of ion implanted graphite. The originally single
207
crystal regions of the BDGF break up into smaller crystallites as a result of ion implantation. With increasing ion mass and fluence, the crystallite dimensions La and L, both
become smaller, and the crystallite misalignment with respect to the fiber axis becomes
larger.
Furthermore, ion implantation produces an increase in the interlayer spacing,
which becomes larger as the ion mass increases. These implantation-induced structural
changes could be used to modify surface properties of carbon fibers such as PAN-based
fibers for application to increase bonding in high quality carbon fiber reinforced composites.
7.5
Recrystallization Studies
This section reports the post-implantation annealing studies in the highly anisotropic
semimetal graphite using high resolution transmission electron microscopy. The defects
produced by ion implantation of highly anisotropic materials and their subsequent annealing differ significantly from the corresponding defects in isotropic semiconductors
and metals. We focus here on this difference in behavior. The recrystallization process
and regrowth kinetics are compared for HOPG and BDGF as host materials.[26]
In the previous section we have shown that ion implantation with
20 9
Bi with an
energy of 30 keV to 1 x 1015 ions/cm2 produces great damage to the graphite lattice (see
Fig. 7.6). These implantation conditions were chosen for the recrystallization studies of
post-implantation annealed graphite to.decide wether or not the regrowth was epitaxial.
The heavily damaged samples were annealed after implantation under a constant flow of
argon gas at several annealing temperatures 1500*C < Ta
range 15 min
ta
<
90 min for the fibers and 5 min
K
<
2800'C and times in the
ta
20 min for the HOPG
samples to study the recrystallization process.
The effect of annealing after implantation with
20 9
Bi with an energy of 30 keV to
1 x 1015 ions/cm 2 on the fiber host can be seen in Fig. 7.8. The onset of some degree
of ordering in the (002) lattice fringes (Fig. 7.8) of fibers annealed at Ta = 1500*C for
1 hr. indicates that some recrystallization occurs for Ta <
1500 0 C (compare Fig. 7.8
with Fig. 7.6a)). The multiple spot pattern found in the optical diffractogram (inset to
Fig. 7.8) confirms that the parallelism with respect to the fiber axis has not been
208
Figure 7.8: Bright field (002) lattice image of a fiber annealed at 1500'C for 1 hr after
implantation with 209 Bi to 1 x 1015 ions/cm 2 at 30 keV.
209
~lit,
~\\~~a/
0It
,i1,t~iUiM11'li~
it
~
t
completely restored at Ta = 15000C. Interplanar spacings c/2 in the range 3.36
0.08
A
< c/2 < 3.85 t 0.08
A were measured
from the optical diffractogram assuming the
opposite (unimplanted) side of the fiber to have c/2 = 3.36
A.
Annealing temperatures of
Ta ~ 2800'C restored the order which was lost by ion implantation, but the interplanar
spacing obtained from the optical diffractograms indicates c/2 values as large as ~ 3.80
0.08
A
even after the high temperature annealing. This result is discussed in more detail
below.
The in-plane (La) and c-axis (L,) correlation lengths were obtained from the (002)
lattice images, from the (002) dark field images and from the full width at half maximum
of the (002) spots of the electron diffraction patterns, as explained in section 7.3 of this
chapter. Figure 7.9 shows Arrhenius plots for the corrected La and Le values as a function
of 1/Ta x 10' K-1 for post-implantation annealed fibers. We derive activation energies
E, ~ 0.66
0.08 eV/atom and E, ~ 0.78
0.08 eV/atom from the La and L, plots for
the in-plane and c-axis grain growth processes, respectively. A similar value for E, was
obtained for the post-implantation annealed HOPG (Ea,
0.67
0.08 eV/atom).[26}
By comparison with the results for the as-implanted sample given in Fig. 7.6b), Fig.
7.10 shows a bright field image and an electron diffraction pattern for an HOPG sample,
post-implantation annealed at Ta = 1500*C for 20 min.
Several rings can be seen
from the electron diffraction pattern shown in Fig. 7.10. The (100) and (110) graphite
rings are sharper than for the as-implanted sample (see Fig.
7.6b)) indicating that
two-dimensional (in-plane) regrowth has started at this annealing temperature.
appearance of a broad ring with maximum intensity at 1.78
0.03
A-1
The
corresponding
to the (002) reciprocal lattice vector of graphite indicates that random recrystallization
takes place together with the 2-D regrowth. This process gives rise to the formation of
small crystallites that have their c-axes randomly oriented.[26] Figure 7.10 shows those
crystallites that have their c-axes lying in the basal plane of the substrate. The random
recrystallization process takes place because the implanted region of the sample was
amorphized to the extent that some of the memory of the crystallinity was lost. Since
in-plane (2-D) regrowth also takes place at this annealing temperature, we conclude
that not all the memory was lost during ion implantation and many of the crystallites
grow from tiny seeds with their c-axes parallel to the c-axis of the substrate.
211
500
1
1
o La from L.I.
e L0 from D.P.
-Ai
A Lc from L.I.
LC from D.P.
200~A
(I)
1000
4--
-j
50-
Ec~0. 6 6 0.08eV/atom
~- 5
LC.
9
20-
0
La
101
2
3
4
5
_ji
6
7
9
)
1/ Ta x104( K- 1
8
Figure 7.9: Arrhenius plot of in-plane (La) and c-axis (L,) crystallite sizes measured from
lattice images (L.I.) and diffraction patterns (D.P.) vs. reciprocal annealing temperature
(1/Ta) for fibers annealed for 1 hr after implantation with 20 9 Bi to 1 x 101 5 ions/cm 2 at
30 keV.
212
.
Figure 7.10: Lattice image and (hk0) electron diffraction pattern of an HOPG sample
2
15
annealed at 1500*C for 20 min after implantation with 20 9 Bi to 1 x i0 ions/cm
213
214
For higher annealing temperatures Ta ~ 2300'C, the randomly oriented crystallites
increase in length forming wavy ribbons (see Fig. 7.11). At both 1500*C and 2300'C, the
2-D and random regrowth processes are competing processes. Figures 7.12b)-d) show
the effect of annealing at several temperatures on the
209
electron diffraction patterns
Bi ions at 30 keV to a dose of 1 x 10" ions/cm 2
.
of HOPG samples implanted with
(hko)
The (hkO) electron diffraction pattern of the as-implanted HOPG sample is shown in
Fig. 7.12a) as reference. The electron diffraction patterns of samples post-implantation
annealed at Ta > 2500*C showed a ring pattern of spots at the graphite (100) and (110)
reciprocal lattice vectors (see Fig. 7.12d)). In addition, the broad ring at 1.78
A-' shown
in Fig. 7.12b) sharpened as Ta was raised from 1500'C to 2300'C (see Fig. 7.12c)). As
Ta is increased from ~ 2500*C to ~ 2700*C, the number of spots in the ring pattern
decreases, so that at the higher annealing temperature only a few spots remain and
these are located close to the graphite spots from the substrate (see Fig. 7.12d)). At the
same time the ring pattern at 1.78
A-'
continues to sharpen and spots begin to appear
superimposed on the sharpened ring; furthermore, diffraction at 1.78
A-1
only is found
for certain regions of the sample, and is absent elsewhere for Ta = 2700*C. These results
indicate that the epitaxial regrowth process takes place along with the 2-D regrowth. By
Ta ~ 2700'C the 2-D and epitaxial processes overtake the random orientation regrowth.
For the HOPG samples, the in-plane crystallite sizes (La) of the 2-D regrown regions
were obtained from dark field images from the (100) ring by measuring the size of the
bright regions.
The c-axis crystallite size (Lr) for random orientation regrowth was
measured from dark field images using the (002) ring and from the lattice images. These
values for La and Lcr were also corrected for the projection effect explained in section 7.3
of this chapter. Arrhenius plots for La and Lr for the post-implantation annealed HOPG
are shown in Fig. 7.13 as a function of 1/Ta x 104 K
for 1500 0 C
and ta = 20 min. From these plots we have obtained Ea ~ 0.67
Ecr ~ 0.47
27000 C
< Ta
0.08 eV/atom and
0.08 eV/atom for the 2-D and random regrowth processes, respectively.
To study the kinetics of the recrystallization process, we measured the same regrowth
90 min. for
parameters as a function of annealing times ta in the range 15 min. < ta
fibers, and 5 min. < ta
20 min. for HOPG samples annealed at Ta
=
1500*C and
2500*C. Two different time dependences were found for the in-plane and c-axis
215
.
Figure 7.11: Lattice image of an HOPG sample annealed at 2300*C for 20 min after
implantation with 20 9 Bi to 1 x 10" ions/cm2
216
Mie~em
sar;-r;-.A
amuVA
20 9
Bi
Figure 7.12: (hkO) electron diffraction patterns of HOPG samples implanted with
2
ions at 30 keV to 1 x 1015 ions/cm for: a) as-implanted, and post-implantation annealed
at b) 1500*C, c) 2300*C and d) 2700*C for 1 hr.
218
219
I
51-
2[-
102
Lc * from D.F.
from D.F.
Ler AA from
L.I.A0
5[-
0
A
e
A
Ea~ 0.6 7'O.08eV/atom
,A Ea~rv0.47 +nlp 3\V/t m
-
-j<
1
1
I
I
I
I
2
3
4.
5
6
)
10 4 / T( K-1
Figure 7.13: Arrhenius plot of in-plane (La) and c-axis (Lcr) crystallite sizes measured
annealing
from diffraction patterns (D.P.) and dark field images (D.F.) vs. reciprocal 20
9
Bi ions
temperature (1/Ta) for HOPG annealed for 20 min. after implantation with
2
to 1 x 1015 ions/cm at 30 keV.
regrowth processes. Though for each process, the ta dependence was the same for these
very different values of Ta. Specifically, we obtained
t/ 2 and ~ ta/ dependences for
the in-plane and c-axis recrystallization processes, respectively, for both host materials;
[261 that is, the La and L, vs. ta curves obtained for the annealed fibers are parallel
to those for the annealed HOPG. Figure 7.14 shows the results for the case of HOPG.
220
The ~
t.
dependence of annealing of IIOPG in this figure corresponds to the random
regrowth process.
STa
=2500 C
0.-
-
100
000*
A To 1500 C
50D000
-
C-
20-
O.2.
0.4
CL
2
I
5
10
20
50
to (minutes)
.
Figure 7.14: In-plane (La) and c-axis (L,) crystallite sizes vs. annealing time ta
for IIOPG samples annealed at 1500*C and 2500*C after implantation with 2 09 Bi to
1 x 1015 ions/cm2
Annealing studies of ion implanted IOPG and BDGF give information about complementary aspects of the recrystallization process of graphite.
process depends strongly on the initial amount of damage.
high doses
(>
1015 ions/cm 2 ) and low ion energies (-
This recrystallization
Heavy ions such as
2 09
Bi,
30 keV) produce a very dis-
ordered layer that shows a regrowth process different than that previously observed
in post-implantation annealed studies of HOPG implanted with
of 1 x 1016 ions/cm
observed.
2
75
As ions to a dose
[9,24] where only the 2-D and epitaxial regrowth processes were
It should be noted that electron diffraction patterns of the as-implanted
samples were qualitatively similar for both ion species.
For
75
As implantation, the
electron diffraction patterns of the annealed samples did not show the diffraction ring
at ~
1.78
A-,
these samples.
indicating that the random regrowth process did not take place for
We attribute this to the fact that implantation of 75As ions to a dose
221
of 1 x 1016 ions/cm 2 did not produce as much damage as
20
9Bi ions to a dose of
1 x 1015 ions/cm 2 . Based on the regrowth behavior, we conclude that the very disordered
layer produced by ion implantation with
duced by
75
209
Bi ions is less anisotropic than the one pro-
As ions. On the other hand, the electron diffraction patterns of pulsed-laser
irradiated graphite with energy densities ~ 3.5 J/cm 2 show a ring at 1.78
A-'.[34] More
work is required to characterize the different kinds of highly disordered structures that
can be produced by ion implantation.
0.08 eV/atom and a time dependence of ~ ta
Activation energies Ea ~ 0.67
were obtained for the in-plane (2-D) grain growth process for both host materials.
From the grain growth studies along the c-axis for the annealed fibers, we obtain E,
0.08 eV/atom and a ta.2 5 0.0
0.78
4
dependence.
If we assume that diffusion limits
grain growth, the time dependence of grain growth is then ~ ta
a diffusion activation energy E =
2
Ea or 2E,
-
~
and we can deduce
1.5 eV which is an intermediate value
between reported activation energies for diffusion of single interstitials in the basal plane
0.4
(Es
0.1 eV) [35] and along the c-axis (E' ~
2.9
0.3 eV).[6] It is clear that the
in-plane grain growth requires diffusion of atoms. The regrowth along the c-axis on the
other hand, is achieved by annealing of the dislocations produced by ion implantation
(see section 7.6 of this chapter).
The annealing of dislocations is required to get the
proper stacking of the graphite layers.
(E
=
I(E + E )
~
This process is a diffusion activated process
1.6 eV) in which three-dimensional diffusion producing climb
of dislocations takes place.[6] This is consistent with the type of dislocations observed
in the HOPG samples. It is suggested that a slower time dependence for the 3-D grain
growth process is observed since some 2-D ordering is necessary before the alignment of
the graphite planes takes place. This is a consequence of the anisotropy of the crystal
structure of graphite.
The interplanar spacings c/2 for the HOPG samples were obtained from optical
diffractograms taken from the negatives of lattice images showing (002) fringes for both
randomly oriented crystallites and bent over regions showing (002) planes. For Ta
23000 C, the measured c/2 values were in the range 3.35
but for 2300 0 C
range 3.35
< Ta
0.1
A
5
0.1
A < c/2 < 3.70
0.2
<
A,
2700*C, the interplanar spacings were found to be in the
< c/2 <
3.50
0.1
222
A,
dramatically smaller than the values
c/2
0.08
~ 3.80
A
obtained for the fibers annealed at Ta ~
2800 0 C. This result
suggests that, for the fiber host, the ions cannot diffuse out of the implanted region even
after annealing to high temperatures ~ 2800'C, as easily as for the HOPG host. This is
because of the different structure between the two host materials.
To ascertain whether ions were present in the annealed samples, we obtained Rutherford backscattering spectroscopy (RBS)' measurements from the near surface region of
-the post-implantation annealed HOPG samples.
The RBS data obtained on HOPG
samples post-implantation annealed to Ta > 1500*C showed no evidence of
present in the samples. Using the RBS technique,
209
209
Bi ions
Bi was detected in the as-implanted
samples, while trace amounts were also present in those annealed at 1500*C. This is
in agreement with previous RBS results for high temperature annealing of HOPG implanted with
75
As to 1 x 10
5
ions/cm 2 [361, showing that the
75
As ions diffuse between
the graphite planes and out of the implanted region of the sample for Ta > 2300 C.
The difference in the interplanar spacings for post-implantation annealed fibers and
HOPG suggests that the
20 9
Bi ions are retained in the annealed fibers and not in the
HOPG samples because of the difference in micro-structure of these two host materials.
On the other hand, x-ray fluorescense studies using the electron microprobe and the
scanning transmission electron microscope (STEM), did not show evidence of
present in any of the annealed fibers.
fibers. It is possible that
making the ratio of
20 9
209
209
209
Bi ions
Bi was hard to detect even in the as-implanted
Bi was not detected because it had diffused within the fiber
Bi counts/background very small. Another factor that makes this
ratio small in the case of the electron microprobe is due to the electron beam penetration
depth of ~ 1 pim being large compared with the
209
Bi ion penetration depth.
Conclusions
The regrowth process of ion implanted graphite appears to be generally similar for
both HOPG and BDGF host materials, and activation energies of ~ 0.7 eV/atom are
observed in both cases.
The different time dependences for the in-plane and c-axis
regrowth processes can be explained by diffusion and the annealing of dislocations. The
anisotropy of the graphite structure gives rise to major differences both in the damage
'The RBS data was obtained by Dr. Gabriel Braunstein.
223
and regrowth processes in-plane and along the c-axis. A significant difference between
ion implantation into graphite and isotropic materials is that the highly disordered state
of graphite is not unique and consequently its regrowth process is also not unique.
7.6
Characterization of Defects.
Defects in crystals produce additional phase shifts to the diffracted beams with respect to that of the perfect crystal. The amplitude of the reflected beam in an imperfect
crystal using the general kinematic theory [22] is given by:
=
ixra
-(r)
exp(-27riK' - r')
(7.1)
where K' = g + s is the wave vector of the diffracted wave, g is the reciprocal lattice
vector and s is the deviation parameter in reciprocal space, rn = r, + R, where r, is
the position of the unit cell in the perfect crystal and R, is the displacement of the unit
cell from its proper position, a is the spacing between the planes parallel to the surface,
and
rVecosG
AFg
where V, is the volume of the unit cell,
e
(7.2)
the Bragg angle for reflection g, Fg the rela-
tivistically corrected structure factor for reflection g, and A the relativistically corrected
electron wavelength.
Neglecting the term in s - R,, in Eq. (7.1), the phase factor becomes
= exp(-27rig - R)exp(-27risz)
(7.3)
where R is the unit cell displacement at depth z in the crystal and the first exponential
factor in Eq. (7.3) is the extra phase factor produced by the imperfect crystal.
Thus, the diffraction contrast observed in the dark field imaging technique is due to
a phase contrast mechanism. Defects are observed in the electron microscope because of
the strain that they produce in the lattice. In particular for the case of dislocations, the
strain field varies continuously around the dislocation. The displacement of a unit cell
around a dislocation is given by the Burgers vector b. The most important results of
the diffraction contrast theory applied to the case of graphite [6] are given in Table 7.3.
224
Table 7.3. Dark field conditions for the observation of dislocation and stacking fault
contrast for graphite for sheared and unsheared dislocation loops.[7.6]
g
_________
Unsheared
k01
(100)
g -b Contrast
loop g - b Contrast
g - b Contrast g -
loop
b= 2 c(001)
0
0
0
(112)
(101)
(110)
Contrast
1/2
0
Stacking
fault and
1
Dislocation
0
1 or 2
0
Dislocation
dislocation
Sheared loop
b = }2 c(001)
+ 3 a(100)
1(661 %)
Stacking
333
or
fault and
1j33j%3 dislocation
)
0(331 %)
0
or
1(66 2 % )Dislocation
!,6
6'
or!6
Stacking
fault and
di~location
___
_____
The characterization of dislocations and stacking faults was carried out using dark
field images for several two-beam diffraction conditions on HOPG samples annealed at
2500 C and 2700*C for 20 min. The dislocations and stacking faults observed in the
dark field images with the appropriate two-beam condition (see Fig.
7.15) for g =
(100), (110) and (112) in the same regions indicate that most of the defects produced
by ion implantation are sheared loops.[6] This implies that g - b :
0 (b is the Burger's
vector of the dislocation) for all the g values used. No appreciable extra dislocations
were observed for g = (112) (reciprocal lattice vector that would satisfy the diffraction
condition for contrast of dislocations of unsheared loops) compared to those observed
for g = (100) and (110).
From this result and the direct observation of interstitial loops using the lattice
imaging technique on annealed fibers we infer that most of the defects produced by ion
implantation are sheared dislocations (see inset to Fig. 7.15) formed by the agglomeration of interstitials with b = .c(001) + la(100) where a and c are the graphite lattice
constants.[6] This is in agreement with previously reported defects found in irradiated
graphite with neutrons to doses >
7.7
1 x
1020
neutrons/cm 2 at low temperatures.[3]
Suggestions for Future Work.
The study and characterization of defects induced by ion implantation as a function of
implantation temperature using the TEM might give different kinds of defects produced
for implantation at high temperatures than for low temperatures. TEM studies on thin
(< 175
A)
samples implanted and annealed under the conditions specified in section
7.5 of this chapter would give information about the regrowth process when there is no
crystalline substrate i.e. no epitaxial regrowth.
226
Figure 7.15: (100) dark field image of an HOPG sample post-implantation anneal-ed at
2700*C for 20 min. showing stacking faults and dislocations. The sample was implanted
with 209 Bi to 1 x 1015 ions/cm 2 . The inset is a schematic representation of a sheared
dislocation loop.
227
-a
- b
-
-a
-
-a -b
-
-a
228
b
b
c
b
c
b
b
a
b
a
.---
bab
-
-b
b
ab
a-
References
[1] D.J. Mazey and R.S. Barnes, Sixth Intl. Congress for Electron Microscopy, Kyoto,
1966, .1, Maruzen, Tokyo, 1966, p. 365.
[2] W. Bollmann, Phil. Mag. 5, 621 (1960).
[3] W.N Reynolds, P.A. Thrower and B.E. Sheldon, Nature 189, 824 (1961).
[4] W.N. Reynolds and P.A. Thrower, J. Nucl. Mater. 10, 209 (1963).
[5] J.A. Turnbull and M.S. Stagg, Phil. Mag. 14, 1049 (1966).
[6] For an extensive review see P.A. Thrower, Chemistry and Physics of Carbon 5,
edited by Philip L. Walker, Jr. (Marcel Dekker, Inc., New York, 1969), p. 217.
[7] B.S. Elman, M. Shayegan, M.S. Dresselhaus, H. Mazurek and G. Dresselhaus, Phys.
Rev. B25, 4142 (1982).
[8] B.S. Elman, Ph.D. Thesis, Massachusetts Institute of Technology, 1983.
[9] B.S. Elman, G. Braunstein, M.S. Dresselhaus, G.Dresselhaus, T. Venkatesan and
J.M. Gibson, Phys. Rev. B29, 4703 (1984).
[10] G. Braunstein, B.S. Elman, M.S. Dresselhaus, G.Dresselhaus and T. Venkatesan,
MRS Symposium on Ion Implantation and Ion Beam Processing of Materials, ed.
G.K. Hubler, O.W. Holland, C.R. Clayton, and C.W. White, Boston, Nov. 1983
(Elsevier, North Holland, NY, 1984), vol. 27, p. 475.
[11] L.E. McNeil, B.S. Elman, M.S. Dresselhaus, G. Dresselhaus and T. Venkatesan,
MRS Symposium on Ion Implanatation and Ion Beam Processing of Materials, ed.
229-
G.K. Hubler, 'O.W. Holland, C.R. Clayton, and C.W. White,Boston, Nov. 1983
(Elsevier, North Holland, NY, 1984), vol. 27, p. 493.
[121 T.C. Chieu, B.S. Elman, L. Salamanca-Riba, M. Endo and G. Dresselhaus, MRS
Symposium on Ion Implantation and Ion Beam Processing of Materials, edited by
G.K. Hubler, O.W. Holland, C.R. Clayton and C.W. White, Boston, Nov. 1983
(Elsevier, North Holland, New York, 1984), Vol. 27, p. 487.
[13] A. Oberlin, M. Endo and T. Koyama, Carbon 14, 133 (1976).
[14] T.C. Chieu, M.S. Dresselhaus and M. Endo, Phys. Rev.
B26, 5867 (1982) and
references therein.
[15] M. Endo, T.C. Chieu, G. Timp, M.S. Dresselhaus and B.S. Elman, Phys. Rev.
B28, 6982 (1983).
[16] J.W. Mayer, L. Eriksson and J. Davies, Ion Implantation in Semiconductors, Academic Press, NY, 1970.
[17] J. Lindhard, M. Scharff and H.E. Schiott, Dan. Vidensk. Selsk., Mat. Fys. Medd.
33 14 (1963).
[18] A. Marchand and A. Pacault, Nouveau Traiti de Chimie Minerale, 8, no. 1, 457
(1968); D. Fishbach, Chem. and Phys. of Carbon 7, ed. P.L. Walker, Jr., (Marcel
Dekker, New York, 1971), p. 1; A. Pacault, Chem. and Phys. of Carbon 7, ed.
P.L. Walker, Jr., (Marcel Dekker, New York, 1971), p. 107.
[19] B.S. Elman, M.S. Dresselhaus, G. Dresselhaus, E.W. Maby and H. Mazurek, Phys.
Rev. B24, 1027 (1981).
[20] R. Lespade, R. Al-Jishi and M.S. Dresselhaus, Carbon 20, 427 (1982): A. Marchand, P. Lespade and M. Covzi, Extended Abstracts of the
1 5 th
Carbon, University of Penn., p. 282 (1981).
[21] F. Tuinstra and J.L. Koenig, J. Chem. Phys. 533, 1126 (1970).
230
Biennial Conf. on
[22] P. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron
Microscopy of Thin Crystals, ed. Robert E. Krieger Publishing Co. Inc., 1977, p.
165.
[23] S. Amelinckx, P. Delavignette and M. Heerschap, Chemistry and Physics of Carbon
1, edited by Philip L. Walker, Jr. (Marcel Dekker, Inc., New York, 1965), p. 1.
[24] T. Venkatesan, B.S. Elman, G. Braunstein, M.S. Dresselhaus and G. Dresselhaus,
J. App. Phys. 56, 3232 (1984).
[25] M. Endo, L. Salamanca-Riba, G.Dresselhaus and J.M. Gibson, Journal de Chimie
Physique 81, 803 (1984).
[26] L. Salamanca-Riba, G. Braunstein, M.S. Dresselhaus, J.M. Gibson and M. Endo,
Nuclear Instruments and Methods in Physics Research, B7/8, 487 (1985).
[27] T. Koyama, Carbon 10, 757 (1972).
[28] T. Koyama, M. Endo and Y. Onuma, Japan J. Appl. Phys. 11, 445 (1972).
[29] M. Endo, K. Komaki and T. Koyama, Int.
Symp.
on Carbon, p.
515 (1982,
Toyohashi).
[30] B.D. Cullity, Elements of z-ray Diffraction, (Addison-Wesley Publishing Co., Inc.,
1978) p. 284.
[31] G.R. Millward and D.A. Jefferson, Chemistry and Physics of Carbon 14, edited by
Philip L. Walker, Jr. and Peter A. Thrower (Marcel Dekker, Inc., New York, 1978),
p. 1.
[32] G.W. Hinman, A. Haubold, J.O. Gardner and J.K. Layton, Carbon 8, 341 (1970).
[33] C. Schiller, J. Mering, P. Cornuault and F. Du Chaffaut, Carbon 5, 385 (1967).
[34] T. Venkatesan, D.C. Jacobson, J.M. Gibson, B.S. Elman, G. Braunstein, M.S.
Dresselhaus and G. Dresselhaus, Phys. Rev. Letters 53, 360 (1984).
[35] W.N. Reynolds, Chemistry and Physics of Carbon 2, edited by Philip L. Walker,
.
Jr. (Marcel Dekker, Inc., New York, 1966), p. 1 2 1
231
[36] B.S. Elman, G. Braunstein, M.S. Dresselhaus and T. Venkatesan, Nuclear Instruments and Methods in Physics Research B7/8, 493 (1985).
232
Chapter 8
SUMMARY
The work reported in this thesis consisted of two parts, (1) the study of the structure
of graphite intercalation compounds and (2) the damage to the graphite structure produced by ion implantation. In the study of GICs several techniques were used to obtain
.complementary information about the structure of these compounds. (00f) x-ray diffraction and electron microscopy (electron diffraction and high resolution lattice imaging),
were used to obtain information about the stage homogeneity. We have found that the
fibers are more inhomogeneous than the HOPG, as had already been observed.[1,2 We
have observed inhomogeneities in the in-plane structure in several acceptor compounds
such as FeCl 3- and SbCl 5 -GICs. In FeCl 3-GICs we have direct evidence for the intercalation of FeCl 2 from (hk0) electron diffraction patterns and bright and dark field images
obtained using the TEM. The FeCl 2 intercalate forms islands of
-
2000
A
in diameter.
This result is in agreement with the value of m < 3 obtained from analysis of the RBS
spectra and the (00t) x-ray diffractograms obtained from the same samples.[3] This result is also consistent with M6ssbauer experiments previously published.[4] On the other
hand, the CuCl 2-GIC system is more homogeneous, and no evidence for another copper
chloride species such as CuCl was found in agreement with the value of m ~ 2 obtained
from analysis of both the (00t) x-ray diffractograms and the RBS spectra obtained from
the same samples. Deviations from the theoretical stoichiornetry were also found in systems that form commensurate in-plane superlattices such as SbCl 5 - and KHg-GICs. In
the SbCl 5-GIC system a value of m < 5 was obtained from analysis of the RBS spectra
obtained from both cleaved and uncleaved samples, with m being lower (m=4.4) for
233
the uncleaved samples than for the cleaved samples (m=4.6). This result is consistent
with the M6ssbauer results [5] obtained on SbCl 5-GICs where a disproportionation of
sites into SbCl 5 , SbCl6, SbCl 3 and SbCl4 is found in the intercalate layer. Besides this
difference between cleaved and uncleaved samples, the stoichiometry of the SbCl 5-GIC
samples was observed to be homogeneous in depth and lateral direction.[6] On the other
hand, KHg-GICs were found to show a decrease in Hg content with depth. The Hg/K
ratio was also smaller at the center of the samples than at the edges. Thus, suggesting
that intercalation had not gone to completion.
The SbCl 5-GIC system is not homogeneous with regard to the in-plane structure
of the intercalate. We have found that the (v/7 x V7)R19.1* phase forms islands of an
average size of 650
A.
Our image simulation studies suggest that these islands are formed
by a mixture of either SbCl6 and SbCl 3 or SbCl6 and SbCl5 molecular species in an
AaBAdBAgBAaBAdBAg.. or AaBAaBAaBAa... stacking, respectively. [7] To absolutely
decide which is the correct model for the (-/ x V7)R19.1* structure, higher resolution is
required. The model consisting of a mixture of SbCl- and SbCl 3 is consistent with the
radiolysis process responsible for the commensurate to glass phase change induced by
electron beam irradiation.[7] In the radiolysis process a Cl- ion of the SbCl6 molecule
is excited by the electron beam producing an electron-hole pair, the hole gets localized
between two Cl- ions of the SbCl6 molecule and a C1 2 molecule is formed at a single
lattice site. This molecule is unstable producing a displacement of one of the Cl- ions to
a neighboring SbCl 3 molecule forming an SbCl4 molecule and leaving behind an SbCl 5
molecule.
The resulting mixture of molecular species has a different arrangement in
the graphite lattice and the glass phase is obtained. Our experimental results for the
temperature dependence of the critical electron dose required to induce the glass phase,
can be explained by assuming two activation recombination or annealing mechanisms
that oppose the radiolysis process and that are dominant in different temperature ranges.
The recombination mechanism that is dominant at high temperatures is identified with
free diffusion of the Cl- ions.
The recombination mechanism which is dominant at
low temperatures is identified with Cl- ions that are displaced back to their original
position in the SbCl- molecule or to an SbCl 5 molecule. From our experimental results
we have obtained activation energies for the radiolysis process (ER = 0.02 eV) and for
234
the recombination mechanisms (Ed = 0.13 eV and E, = 0.03 eV).
We have studied the c-axis thermal expansion coefficient of SbCl 5-GICs in the temperature range 20 K < T < 300 K and have obtained the contribution to the thermal
expansion coefficient of every layer in the intercalation compound. We have found that
the model for the thermal expansion coefficient of stage n a(n) suggested by Mazurek
et al.[8] applies to the SbCl 5-GIC system. Using the model suggested by Gudrard et
al. [9] the contribution from every layer in the intercalate to the thermal expansion coefficient was calculated. A value for the charge transfer of ~ 0.2 is obtained from the ratio
of a'sbci
5/aSbCIs,
and from this value we obtained equilibrium values for the relative
concentrations of SbCl 5 : SbCl- : SbCl = 7: 2 : 1.
In the study of the structure of KH.-GICs, as a function of intercalation temperature and time, we have obtained evidence for the intercalation process starting with
stage n potassium GICs and with a final product of stage n KH-GIC, in agreement with
(00f) x-ray diffraction studies [101. We have observed regions at the boundary between
pure potassium regions and regions with high hydrogen content that are identified as
an intermediate phase in the intercalation process. These regions are poor in hydrogen content and have repeat distances of ~ 14.06
respectively.
A
and ~ 10.62
A for
stages 1 and 2,
Two in-plane commensurate phases have been observed in the KH-GIC
system, a (2 x 2)RO* and a
(VF
x V3)R30* phase. The (2 x 2)RO* commensurate phase
is dominant at high intercalation temperatures, while the (V3- x V3-)R30* phase is dominant at low intercalation temperatures. The c-axis repeat distances for the stage two
compounds synthesized by the chemical absorption of hydrogen into stage 1 potassium
is smaller than that for stage 2 KH-GICs synthesized by the direct intercalation of KH.
This is in agreement with the fact that there is less hydrogen content when the chemical
absorption method is used.[11,121
In the ion implantation process, the crystallite size decreases with increasing ion
mass and fluence.
A dependence of approximately MV" 2 was obtained for the in-
plane crystallite size.
~ 3.9
A
A large increase in the c-axis repeat distance from 3.35
A
to
is obtained from the optical diffractograms taken from the negatives of the
lattice images.[13] The graphite structure is obtained after annealing to 28000 C for 1
hour, but the c-axis repeat distance does not decrease below ~ 3.8
235
A for the
fibers, nor
below ~ 3.5
A
for the HOPG host. This result suggests that probably some of the ions
are retained between the graphite layers of the fibers after annealing at high temperatures
but the ions do not remain in the graphite lattice of the HOPG host after annealing to
temperature above 2000'C, as obtained from RBS experiments.[14] Our analysis of the
defects from the post-ion implanted annealed HOPG samples indicates that the defects
induced by ion implantation are primarily sheared dislocations with Burger's vector along
b=
}c +
!a. The two dimensional regrowth takes place by diffusion of single interstitials
in the plane and the three dimensional regrowth takes place by climb of dislocations.[14]
236
References
[1] M. Endo, T.C. Chieu, G. Timp, M.S. Dresselhaus and B.S. Elman, Phys. Rev.
B28, 6982 (1983).
[2] T.C. Chieu, Ph.D. Thesis 1983.
[3] L. Salamanca-Riba, B.S. Elman, M.S. Dresselhaus and T. Venkatesan, MRS Symposium on Ion Implantation and Ion Beam Processing of Materials, edited by G.K.
Hubler, O.W. Holland, C.R. Clayton and C.W. White, Boston, Nov. 1983 (Elsevier,
North Holland, New York, 1984), Vol. 27.
[4] S.E. Millman, Solid State Commun. 44, 23 (1982).
[5] P. Boolchand, W.J. Bresser, D. McDaniel and K. Sisson, Solid State Commun. 40,
1049 (1981).
[6] B.S. Elman, L. Salamanca-Riba, M.S. Dresselhaus and T. Venkatesan, J. Appl.
Phys. 55, 894 (1984).
[7] L. Salamanca-Riba, G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus and R.J.
Birgeneau, to be published.
[8] H. Mazurek, G. Ghavamishahidi, G. Dresselhaus and M.S. Dresselhaus, Carbon 20,
415 (1982).
[9] D. Gu6rard and P. Lagrange, Proc. of the InternationalConf. on Carbon, Bordeaux
1984, p. 288.
[10] N.-C. Yeh, T. Enoki, L. Salamanca-Riba and G. Dresselhaus, Proc. of the
Biennial Conf. on Carbon, Lexington, June 1985, p. 194
237
1 7 th
[11] D. Gudrard, C. Takoudjou and F. Rousseaux, Synthetic Metals 7, 43 (1983).
[12] D. Guerard, P. Lagrange and A. H6rold, Materials Science and Engineering 31, 29
(1977).
[13] M. Endo, L. Salamanca-Riba, G. Dresselhaus and J.M. Gibson, Journal de Chimie
Physique 81, 804 (1984).
[14] L. Salamanca-Riba, G. Braunstein, M.S. Dresselhaus, J.M. Gibson and M. Endo,
Nuclear Instruments and Methods in Physics Research B7/8, 487 (1985).
238