The Defect Structure and Transport Properties of Some High
Tc Superconductors
By
Ming-Jinn
Tsai
B. S. Mechanical Engineering
National Taiwan University, Taipei, Taiwan, ROC (1980)
M. S., Materials Science
National Sun Yat-Sen University
Kaohsiung, Taiwan, ROC (1985)
Submitted to the Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements of
the Degree of Doctor of Philosophy
at the
Massachusetts Institute of Technology
February, 1991
@ Massachusetts Institute of Technology, 1990.
Signature of Autl
_
Depa men
Materials Science and Engineering
q
(A
January, 11 1990
Certified by
Professor Harry L. Tuller
sis Supervisor
Accepted by
Professor Linn W. Hobbs
Chairman, Departmental Committee on Graduate Students
ARCHIVES
MASSACHUAETTS ;siI iuF
OF TECPo' GY
MAAR 0 8 1991
LIBRAHIES
DEFECT STRUCTURE AND TRANSPORT PROPERTIES OF SOME
HIGH Tc SUPERCONDUCTORS
by
MING-JINN TSAI
submitted to the Department of Materials Science and Engineering on
January 11, 1991 in partial fulfillment of the requirements for the
Degree of Doctor of Philosophy
ABSTRACT
The defect structures and transport properties of La2-.xSrxCuO4.
8, Nd2-xCeXCuO4+a, and YBa 2Cu 3-xTix0 6+a were studied by 4-probe DC
conductivity and thermoelectric power measurements as functions of
The conductivity and
temperature, P0 2 and doping concentration.
thermoelectric power of La 2 CuO 4. 8 both follow a P0 2 1/6 dependence
at high temperatures, consistent with a defect model which involves
equilibration between doubly-ionized oxygen defects and holes. The
insensitivity of both properties to temperature implies that the
enthalpy of the redox reaction is insignificant. Initially, Sr doping of
La2-.xSrxCuO4.8 is compensated by holes which increases the
conductivity, up to a maximum at x ~ 0.3. A transition to oxygen
vacancy compensation at x ~ 0.3 is evidenced by a decrease in
The conductivity
conductivity and an increase in P0 2 dependence.
also undergoes an apparent metal-insulator transition with x at x At large x, a more rapid change of conductivity with
0.9.
temperature at high temperature is attributed to a redox reaction, an
interpretation which is supported by a fixed-composition cooling
In LaSrCuO4-8, a p-n transition emerges at high
experiment.
temperatures and low PO2's.
Nd 2 CuO 4.- is an n-type semiconductor. The electron mobility
was found not to be thermally activated. At high temperatures the
electron density is primarily determined by a reduction reaction.
The Ce donor substitution on Nd sites increases the conductivity up
At high Ce levels, the charge carriers become
to 15% of Ce.
degenerate so that the conductivity and thermoelectric power
become Po 2 and temperature independent.
Above that
YBa2Cu3-xTix06+s is metallic below ~ 400 *C.
temperature the redox reaction dominates carrier generation. At T =
700 *C in 1OOppm 02, it undergoes a p-n transition. The magnitude
of conductivity and its dependence on temperature and P0 2 are
nearly independent of Ti concentration up to x = 0.1 and are very
similar to the undoped YBa 2 Cu 3 0 6+8, suggesting a large oxygen
disorder.
Thesis Advisor: Harry L. Tuller
Title: Professor of Ceramics and Electronic Materials
TABLE OF CONTENTS
TITLE PA GE................................................................................--------------------------...........1
........ -...------------------------.................. 2
AB STRA CT.................................................................
.... 4
TABLE OF CONTENTS...............................................................................
..... 7
LIST OF FIGURES.....................................................................................-. ...... 14
LIST OF TABLES..............................................................................
15
ACKNOWLEDGEMENTS..........................................................................................
16
1. INTRODUCTION...................................................................................................
2. LITERATURE REVIEW.......................................................................................19
19
.
2.1 La 2-xSrxCuO4- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..---2.1.1 Structure, Solid Solution and Stoichiometry............ 20
24
2.1.2 Transport Properties.........................................................
28
2.1.3 Defect Chemistry................................................................
3
2.2 Nd 2-xCexCuO 4+s ...........................................
2.2.1 Structure, Solid Solution and Stoichiometry............ 34
6
2.2.2 Transport Properties.........................................................3
9
2.2.3 Defect Chemistry................................................................3
1
.~~~......4
o
~~~~~~~...
.2.3 YBa 2Cu 3-xTixO 6+......---..-2.3.1 Structure, Solid Solution and Stoichiometry............4 1
2.3.2 Transport Properties...........................6....46
8
2.3.3 Defect Chemistry................................................................4
54
3. T HE O R Y ......................................................................................................................
4
3.1 Electrical Properties.....................................5
54
3.1.1 Electrical Conductivity.....................................................
55
3.1.1.1 M etals.......................................................................
6
3.1.1.2 Semiconductors.....................................................5
3.1.1.3 Conductivity of YBa 2Cu 30 6+8.-------..........---------... 60
1
3.1.2 Thermoelectric Power.......................................................6
. 62
3.1.2.1 M etals......................................................................
62
3.1.2.2 Semiconductors.....................................................
3.1.3 Localization and Metal-Insulator Transitions.........66
66
3.1.3.1 Localization............................................................
3.1.3.2 Metal-Insulator Transitions............................ 68
70
3.2 Defect Chemistry................................................................................
71
3.2.1 La 2-xSrxCuO 4 . .....................................................................
3.2.2 Nd 2.xCexCuO 4+8 ....---....---------------------------. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.3 YBa2Cu3-xTix06+ .....................................................................
80
83
4. EXPERIMENTAL......................................................................................................
83
4.1 Sample Preparations.........................................................................
4.1.1 Citric Solution Method.......................................................
83
84
4.1.2 Oxide-Mixing Method........................................................
1
4.2 Electrical Property Measurements............................................9
93
4.2.1 Conductivity...........................................................................
96
4.2.2 Thermoelectric Power.......................................................
96
4.2.2.1 Heat-Pulse Technique........................................
4.2.2.2 Constant Temperature Gradient Technique.98
4.2.2.3 Thermoelectric Power of Pt............................. 103
104
4.2.3 Measurement Strategy......................................................
4.2.3.1 Isothermal Annealing.........................................104
106
4.2.3.2 Isobaric Cooling.....................................................
4.2.3.3 Fixed-Compositional Cooling............................ 106
4.3 Structural and Phase Characterizations.................................. 107
107
4.3.1 X-Ray Diffraction..................................................................
108
4.3.2 Electron Microscopy............................................................
6
5. RESULTS..................................................................................................................11
6
5.1 La2-xSrxCuO4-8 System..................................................................11
11 6
5.1.1 La2CuO4. ...........................................................................
5.1.2 La2-xSrxCuO4.s (0 < x < 1)...................................................123
5.1.3 LaSrCuO 4 .8............................................ *.. ..... ..... ...... ..... ..... .... . 137
53
5.2 Nd 2-xCexCuO 4+8 System..................................................................1
153
5.2.1 Nd2CeCuO 4+8..........................................................................
169
5.2.2 Nd 2-xCexCuO 4+s (0 < x < 0.2).............................................
187
5.2.3 Nd1 .85Ce 0 .15 CuO 4+ ..........................................................
187
. ------------.................................
- - .
5.3 YBa 2Cu 3 -xTixO&s...
201
6. DISCUSSION...........................................................................................................
201
6.1 La 2 -xSrxCuO 4 -8System......................................................................
6.1.1 Defect Model and Transport of La 2 CuO 4+8 ........ . . .. . .. 201
207
6.1.2 Doping Effects of Sr.............................................................
6.1.3 Defect Model of LaSrCuO4........................................... 215
6.1.4 Oxygen Stoichiometry of LaSrCuO4.......................... 216
6.2 Nd2-xCexCuO4. System......................................................................217
6.2.1 Transport Properties of Nd2CuO 4 .8................. . .. .. . .. .. .. . . 217
6.2.2 Defects of Nd 2CuO4 4. ................................... ... ... .... .... ... .... ... 222
222
6.2.3 Oxygen Stoichiometry........................................................
6.2.4 Doping Effects of Ce.............................................................225
229
6.3 YBa 2Cu 3-xTixO,6 Systsem................................................................
7. CONCLUSION..........................................................................................................232
234
8. FUTURE WORK......................................................................................................
238
REFERENCES .............................................................................
List of Figures
Fig. 2.1.1
Unit cell of La2CuO 4 structure A: La atom, B: Cu atom, and
C: 0 atom [Longo and Raccah, 1973].....................................2 1
Fig. 2.1.2
Hole concentration of La2.SrxCuO4.6 vs. x [Sreedhar and
Ganguly, 1990; the open and circles from Torrance et al.,
1988; and the open squares from Nguyen et al., 1981 ].21
Fig. 2.1.3
Variation of the a (a), c (b), molar volume (c) and a/c (d)
as a function of x in the La2.xSrxCuO4.8 system [Sreedhar
and Ganguly, 1990;
open circles and triangles from
Nguyen etal., 1981].....................................................................
23
Fig. 2.1.4
Resistivity (a) and thermoelectric power (b) of Ln 2 CuO 4
[Ganguly and Rao, 1973]..........................................................
25
Fig. 2.1.5
Variation of conductivity as a function of 1/T of La 2 xSrxCuO4.8 for 0 s x s 0.16 (a) and for 0.25 s x s 1.0 (b)
[N guyen et al., 19831..................................................................
26
Fig. 2.1.6
Schematic density of states vs. energy diagrams for the sbonding 3d electrons of La2CuO 4 (a) [Goodenough, 1973]
9
and (b) [Singh et al., 1984.......................................................2
Fig. 2.1.7
Conductivity (a) and thermoelectric power (b) of La 2 CuO 4
31
vs. log PO2 [Su et al., 1990]........................................................
Fig. 2.2.1
Unit cell of Nd 2 CuO 4 structure [Muller-Buschbaum et al.,
35
1975)........................................
Fig. 2.2.2
Variation of the a and c lattice parameters as a function
of x for Nd2CuO 4 [Wang et al., 1990].............................. 3 5
Fig. 2.2.3
Oxygen nonstoichiometry of Nd 2 CuO 4 (a) and Nd 2 xCexCuO4+8 (b) as a function of oxygen partial pressure
and temperature [Suzuki et al., 19901.................................3 7
Fig. 2.2.4
Log (conductivity) of Nd 2-xCexCu0 4. 8 vs 1000f for (a) x =
0, log(Po 2 ) = 0, (b)x = 0, log(Po 2 ) = -3.5, (c) x = 0.05,
log(PO 2 ) = 0, and (d) x = 0.05, log(PO 2) = -3.9 [Mehta et al.,
1989]..............................................................................................
. . 38
Fig. 2.2.5
Log (conductivity) of Nd 2-xCexCuO 4 .6 vs. log(PO 2) (a) x = 0
and (b) x = 0.05 at various temperatures [Huang et al.,
. .. 4 0
1989]..............................................................................................
Fig. 2.2.6
Schematic Brouwer diagram of defect concentrations vs.
dopant concentrations in Nd2-xCexCu04 or La2.xBaxCuO4
(a) and reduced thermoelectric power(b), and electrical
conductivity (c) vs. dopant concentration of Nd 2 2
xCexCu0 4+s [Pieczulewski et al., 1989].................................4
Fig. 2.3.1
Structure of YBa 2Cu30 6 +....-..------.--...-.----------. . . . . . . . . . . . . . . . . . . . . . . . . . 44
Fig. 2.3.2
Temperature dependence of the normalized resistance of
YBa 2 Cu 3 -xA20 6+s., where A = Cr, Mn, Fe, Co, Ni and Zn
44
[X iao et al, 1987]...........................................................................
Fig. 2.3.3
Log (conductivity) (a) and thermoelectric power (b) vs.
1000/T for YBa 2 C u 30 6+8 measured at a series of
controlled PO2's as indicated [Choi et al.,1989].................47
Fig. 2.3.4
Log (conductivity) (a) and thermoelectric power (b) vs.
log (P0 2 ) for YBa 2 Cu 3 06+8 measured at a series of
controlled temperatures as indicated [Choi et al.,1989]. 4 9
Fig. 2.3.5
Reciprocal of oxygen exponent (na) as a function of
temperature for YBa 2Cu 30 6+8 [Nowotny et al., 1990]....... 5 1
Fig. 2.3.6
Log (conductivity) (a) and thermoelectric power (b) vs.
1000/T for YBa 2 Cu 3 0 6 +8 with fixed values of 8 [Choi et
. . 52
al.,1989]........................................................................................
Fig. 3.1.1
Log (carrier density) vs. l/T of a typical semiconductor.....
.................................................................................................................
57
Fig. 3.2.1
Log (defect concentration) vs. log (PO 2 ) of La2-xSrCuO 4 .3
(after Opila and Tuller [1990])................................................7
3
Fig. 3.2.2
Log (defect concentration) vs. log ([Sr]tot) of La2-xSrxCuO4.8 (after Opila, Tuller, Wuensch and Maier [1990])..........7 5
Fig. 3.2.3
Log (defect concentration) vs. log (P 0 2 ) of Nd2-xCexCuO 4.-8
79
forC e as a donor...........................................................................
Fig. 3.2.4
Log (defect concentration) vs. log (P 0 2 ) of Nd 2 -xCexCuO 4.-8
81
for Ce as an acceptor.......................................................................
Fig. 4.2.1
Typical I-V curve of a 4-probe DC conductivity
94
m easurem ent................................................................................
Fig. 4.2.2
Configuration of the multi-sample holder.........................9
Fig. 4.2.3
Configuration of the sample holder for measuring
conductivity and thermoelectric power..............................9 7
Fig. 4.2.4
Typical AV vs. AT curve by heat-pulse technique for
thermoelectric power measurement....................................99
Fig. 4.2.5
Thermoelectric power of LaSrCuO 4 .3 vs. 1000/T in oxygen
measured by both constant temperature gradient and
10 1
heat-pulse m ethods..................................................................
Fig. 4.2.6
Thermoelectric power vs. temperature gradient of
LaSrCuO4.8 at constant average temperatures in oxygen.....
....................................................................
.........................................
5
10 2
Fig. 4.2.7
Thermoelectric power of Pt vs. temperature..................105
Fig. 4.3.1
X-ray diffraction patterns of LaSrCuO4- (a), and La 2 CuO 4.
.-- 109
8 (b).............................---...--........--
Fig. 4.3.2
X-ray diffraction patterns of Ndi. 8 Ceo. 2 Cu0 4.
N d2CuO4 .8 (b)...............................................................................
Fig. 4.3.3
X-ray diffraction patterns of YBa 2 Cu 2 .9 TiO. 1 06+8 (a) and
YBa 2Cu 306&+ (b)...........................................................................
11.1
Fig. 4.3.4
SEM micrographs of the calcined powders of LaSrCu0 4.3
(a) and Nd 2Cu0 4+4(b)..............................................................11
2
Fig. 4.3.5
TEM images of the as-sintered Lal. 82 Sro. 18 Cu04-8 (a) and
LaSrCuO 4. 8 (b) samples...........................................................11
3
Fig. 4.3.6
TEM images of La 2 CuO 4. 8 taken in-situ at (a) 348 *C, (b)
340 *C,(c) 320 *C,and (d) 300 *C........................................11 4
Fig. 5.1.1
Resistivity of La 2 CuO 4. 8 vs. temperature in various PO 2 's.
(a) and
11 0
...............................................................................................................
117
Fig. 5.1.2
Resistivity of La 2CuO 4. 8 vs. temperature cooled in 1 atm
1 19
02..........................................................................................................
Fig. 5.1.3
Thermoelectric power of La 2 CuO 4. vs. temperature in 1
atm 0 2.................................................................................................
12 1
Fig. 5.1.4
Log (a) and normalized thermoelectric power of La 2CuO 4. 8
vs. log(PO 2) at various temperatures.................................1 22
Fig. 5.1.5
Normalized thermoelectric power of La 2 CuO4.8 vs. log (a)
124
at various tem peratures.............................................................
Fig. 5.1.6
Log (a) of La 2 -xSrxCu0 4 .8 vs. 1000/T in 1 atm 02 for
25
various x's (0.0 5 x s 0.3)........................................................1
Fig. 5.1.7
Log (a) vs. log(Po 2) of La2-x.SrxCu04-8 at 800 *C for various
12 6
x's (0.0 x s 0.3)............................................................................
Fig. 5.1.8
Resistivity
of La 1 . 85 Sro.i 5CuO 4.5 vs. temperature for
various Po2's.................................................................................
10
12 7
Fig. 5.1.9
L og (a ) of La2-x Sr C u O4.8 vs. 1000O/T in 1 atm 02 for
various x's (0.4
x :5 1.0)............................................................129
Fig. 5.1.10
Log (a) of La 2 -xSrCuO4. vs. x at 800 *C in 1 atm 02.....130
Fig. 5.1.11
Log (a) of La 2 -xSrCu0 4 .8 vs. log(Po 2 ) at various
temperatures for (a) x = 0.4, (b) x = 0.5, (c) x = 0.6, (d) x =
13 1
0.8, (e) x = 0.9, and (f) x = 1.0..................................................
Fig. 5.1.12 Log (a) vs. log(PO 2 ) of La 2 .SrxCu0 4 .8 for various x's (0.4 <
x s 1.0) at (a) 700 *C, (b) at 800 *C and (c) 900 *C.......... 138
Fig. 5.1.13
Log (a) of LaSrCuO 4.8 vs. 1000/T in various P0 2's...........142
Fig. 5.1.14
Normalized thermoelectric power of LaSrCu0 4 .3 vs.
1000/T in various PO2's...............................................................144
Fig. 5.1.15
Log (a) and normalized thermoelectric power of
LaSrCu0 4.8 vs. log (PO 2) at various temperatures............146
Fig. 5.1.16 Normalized thermoelectric power vs. log (a) of LaSrCu0 4. 8
at various tem peratures.............................................................
14 7
Fig. 5.1.17 Log (a) vs. time of LaSrCuO 4.- annealed at 950 *C in
various P0 2's.....................................................................................
14 9
Fig. 5.1.18 Log (a) vs. 1000/T of LaSrCu0 4.- cooled in various PO2 's at
constant 5.....................................................................................
. . 15 1
Fig. 5.1.19
Log (a) and normalized thermoelectric power vs. 1000/T
of LaSrCuO 4 .8 in 100ppm 02 at constant 8.......................1 52
Fig. 5.2.1
Log (a) and normalized thermoelectric power vs. 1000/T
54
of Nd 2 Cu04. in I atm 02.........................1
Fig. 5.2.2
Log (a) vs. 1000/T of Nd 2 Cu04.a in various P02's.
Numbers in the parentheses indicate how much the true
magnitudes of conductivity have been shifted on the
6
vertical log scale for clarity....................................................15
Fig. 5.2.3
Normalized thermoelectric power vs. 1000/T of Nd 2 Cu0 4.
15 7
6 in various PO2's............................................................................
Fig. 5.2.4
Log (aT) and normalized thermoelectric power vs. 1000/T
115 8
........-......
of Nd2Cu0 4.5 in 1 atm 02..........
Fig. 5.2.5
Log (a) vs. 1000/T of Nd2CuO 4.- in various P0 2's at
constant 8.....................................................................................
. .1 6 0
Fig. 5.2.6
Normalized thermoelectric power vs. 1000/T of Nd 2CuO4.
16 1
8 in various PO2's at constant 8.............................................
Fig. 5.2.7
Normalized thermoelectric power vs. log (a) of Nd 2 Cu0 4. 8
at constant 8 in (a) 0.1% 02, (b) 350 ppm 02 and (c) 100
ppm 0 2......................... . -------------------------------... ........................ . 16 4
Fig. 5.2.8
Log (T) and normalized thermoelectric power vs. 1000/T
of Nd 2 CuO 4 .8 in 100ppm P0 2 isobarically and at constant
16 7
8.............................................................................................................
Fig. 5.2.9
Log (a) vs. log (P0 2 ) of Nd2 CuO 4. 8 at various temperatures.
..........................................................................................
.............. 16 8
Fig. 5.2.10 Normalized thermoelectric power vs. log (Pa 2 ) of
Nd2CuO 4. at various temperatures..................... 170
Fig. 5.2.11 Normalized thermoelectric power vs. log (a) of Nd 2 Cu0 4 .8
at various temperatures........................... .... 171
Fig. 5.2.12 Log (a) vs. 1000/T of Nd 2 .xCexCuO4.3 cooled in 1 atm 02
for various x's.........................................
Fig. 5.2.13
...........
.----------.----. 17 2
Log (a) vs. x of Nd 2 -xCexCu04.8 in 1 atm 02 at various
. .......-------- 1 7 4
temperatures...........................
annealed at 900 *C in
75
various Po2's.................................................1
Fig. 5.2.14 Log (a) vs. time of Nd 2 -xCexCuO4-
12
Fig. 5.2.15 Log (a) of Nd 2 -x.CexCu0 4.s vs. log (P0 2 ) for various x's at
(a) 800 *C, (b) 850 *C, (c) 900 *C, (d) 950 *C, and (e) 1000
17 6
*C............................................................................................................
Fig. 5.2.16 Log (a) of Nd 2 -xCe CuO 4.8 vs. log (P 0 2 ) at various
temperatures for (a) x = 0.00, (b) x = 0.01, (c) x = 0.05, (d)
x = 0.10, (e) x = 0.15, and (f) x = 0.20................................... 181
Fig. 5.2.17 Log (a) and normalized thermoelectric power vs. 1000/T
of Ndi. 85Ceo. 15Cu0 4 .8 in 1 atm 02....----------................-----------...1
88
Fig. 5.2.18 Log (a) and normalized thermoelectric power vs. log (P 0 2 )
of Nd .85Ceo.15Cu0 4. at 800 *C..............................................1
89
Fig. 5.3.1
Log (a) vs. 1000/T of YBa 2Cu 3-xTix06+8 in (a)1 atm 02, (b)
10% 02, (c) 1.0% 02, (d) 0.1% 02, (e) 100 ppm 02............. 190
Fig. 5.3.2
Log (a) vs. time of YBa 2 Cu 3-xTix0 6 +8 cooled in 100 ppm 02.
...............................................................................................................
19 6
Fig. 5.3.3
Log (a) vs. 1000/T of YBa 2Cu 2 .9Tio.10 6+8 cooled in various
... ..... 19 7
PO2's................................................................................
Fig. 5.3.4
Log (a) vs. log (P0 2 ) at various temperatures of YBa 2 Cu3xTix0 6 +6 for (a) x = 0.005, and (b) x = 0.10......................... 198
Fig. 6.1.1
Kroger-Vink diagram for La 2Cu0 4±3.....................
Fig. 6.1.2
Log (a) vs. log (x) of La 2 -xSrxCuO4-8 (0 < x s 0.3)............. 209
Fig. 6.1.3
Resistivity vs. temperature of La 2 -xSrxCuO4.3 (0.4
0.8) in 1 atm 02............--..---------...................
Fig. 6.1.4
Pseudo-ternary diagram of La 2 0 3-SrO-CuO system....... 218
Fig. 6.2.1
[Log (a) + 2Log (8)] vs. log (P0 2 ) of (a) Nd 2CuO4.O-8 and (b)
. . . . . . . . . . . 224
. . ........
..... ......
Nd 2Cu03.9993---------------------------------------------------
Fig. 8.1.1
Structures of La 2 SrCu 206-8 (a) and LaSrCuO4.- (b)....... 236
13
... . ... .. .. ... .. .
205
x
214
List of Tables
Table 3.2.1
of defect concentrations in Nd 2.system for Ce as a donor.................................7 8
P02 dependence
xCexCuO4.8
Table 4.1.1
Chemicals used for powder preparation by solutions...8 6
Table 4.1.2
Chemicals used for powder preparation by oxides.......8 7
Table 4.1.3
Compositions and processing of the samples made in
89
this research................................................................................
Table 4.1.4
Compositions of La 2 .xSrxCu04.a (x = 0.0 and 0.15)
analyzed by inductively coupled plasma emission
90
spectrom etry..............................................................................
Table 5.1.1
Activation energies (AE) in eV of conductivity and PO2
power law dependence (n) of conductivity of at 800 *C
41
(a Oc(Po2)n) of La2-xSrxCuO4...............................................1
Table 5.2.1
Activation energies (AE) in eV of conductivity (a),
thermoelectric power (Q), and (aT) of Nd 2 CuO4- in
various temperature and P0 2 ranges for both isobaric
162
cooing and fixed composition cooling.............................
Table 6.1.1
Conductivity, hole concentration and mobility of La2...2 11
,SrxCu04.- at 800 *C 1 atm 02....................
14
Acknowledgement
First of all I want to express my gratitude to Professor Harry
Tuller for his enduring support and guidance during these years. His
advices and encouragements are crucial to the completion of this
thesis.
My next thanks go to Gyeong Man Choi, whose experiences and
works prior to this research has greatly lessened the energy required
for the experiments.
I appreciate the inspiring discussion with Elizabeth Opila and
Marlene Spears.
I cherish the friendship of Marlene Spears, Elizabeth Opila,
Steve Kramer, other members of the group, Thao Nguyen, Jenq-Yang
Chang and many other people. They have made my life in MIT and
this country enjoyable
Finally I thank my family for their unselfish and persistent
support.
15
Chapter 1
Introduction
Research on the high Tc superconductors started its history less
than five years ago when Bednorz and Muller reported the 35 *C Tc
superconductivity of Lai. 82 Ba. 18 CuO 4 -8 in 1986 [Bednorz and Muller
1986].
The potential importance of these materials to the under-
standing of the basic science of superconductivity and applications
has made them among the most studied materials in human history.
These high Tc superconductors also exhibit one of the most interesting and complex interplays between chemistry, crystal structure and
physical properties of any ceramic material studied to date.
A num-
ber of compositional systems have since been discovered with a wide
Most of these superconductors are
range of transition temperatures.
complex cuprates with perovskite-related structures containing Cu-O
planes and/or chains.
La 2 -x.(Sr,Ba)xCuO4.8 was the first system of the
high Tc superconductors reported.
The Ln 2-x(Ce,Th)xCuO4+a (Ln = Pr,
Nd, Sm) system was the first cuprate system to exhibit n-type superconductivity.
These two systems are also amongst the simplest in
compositions and structures among the high Tc cuprate superconductors.
YBa 2 Cu 3 0 6+5, on the other hand, being the first superconductor
with Tc higher than the liquid nitrogen temperature and thus exhibiting a potentially greater impact on technology, has received the
lion's share of attention.
In this study we focus on the high tempera-
ture transport properties and defect chemistry of these three compositional systems in light of their relative simplicity (e.g. compared
16
4
to the Tl,Bi/Ba,Sr/Ca,Cu/O systems) and their representativeness of
compositions, structures, and properties of the high Tc superconductors.
temperatures of these materials casts a
The high transition
great challenge on the conventional BCS theory of superconductivity.
In spite of all efforts by theorists, we can say that no one particular
theory so far can explain all the observed phenomena nor can be
generalized to all other materials.
Electrical, magnetic, optical transi-
tions, connected with structural transitions, metal-insulator transitions, and antiferromagnetic transitions have been studied for correlation to the high Tc transitions.
are usually related to one another.
It is known that these properties
But the details of these relation-
ships are still controversial and not well established due to the high
sensitivity of these properties and transitions to the thermal history,
This sensitivity demonstrates the
composition and local structure.
importance of proper and careful processing.
It also serves as a good
example of how we can manipulate these transport properties by
fine adjustment of the preparation parameters if we understand the
relationships well enough.
a relatively large
These compounds can often accommodate
oxygen non-stoichiometry in certain temperature ranges and/or remain stable with high concentration of dopants.
In this research we
study the defect structures and transport properties of these materials by systematically
measuring the electrical
conductivity and
thermoelectric power as functions of dopant concentration, temperature and oxygen partial pressure in order to delineate the individual
effects on the properties.
These data are also correlated where pos17
sible to other literature data connected with the defect structure and
transport properties of these systems.
at temperatures
The measurements are taken
approximating those at which these materials are
processed to insure a rapid approach to equilibrium and to provide
in-situ information relevant for evaluating the defect structures.
The defect chemistry of these high Tc
superconductors
is
somewhat different from traditional ionic compounds in that the CuO bond in the basal plane, which plays a key role in electronic transThe electronic band at the Fermi level is
port, is highly covalent.
highly hybridized due to the proximity in energy between copper 3d
and oxygen 2p states.
The valence state of Cu and its concentration
are thus not so easily defined as in the ionic cases.
However the
chemistry of oxide superconductors cannot be discussed without reference to oxidation states.
The idea of discriminating oxidation state
and real charge of copper and other ions proposed by Sleight [1988]
seems to be a good approach to solve this dilemma and is adopted in
this study.
18
Chapter 2
Literature Review
This chapter is separated into three sections, each of which is
devoted to one compositional system.
of the crystal
description
structure,
Each section begins with a
solubility range
for other
elements and the oxygen stoichiometry.
The electrical transport
Finally
the defect chemistry is
properties
are discussed next.
reviewed.
Because of the vast literature on high Tc superconductors
in recent years it is almost impossible to make a general review
covering all the phenomena in this thesis.
In this chapter only the
high-temperature features of the structures and related transport
It is worth noting that
properties and defects will be reviewed.
some of the data or implications of these reports are obviously in
Specific issues which are still open to
conflict with each other.
controversy will also be addressed.
2.1 La2-xSrxCuO4.8
Before La 2 -. SrxCuO 4 was discovered to be a superconducting
oxide, the structure and transport properties of this compound had
been examined by a number of groups [Foex, 1961, Longo and
Raccah,1973; Ganguly and Rao, 1973; Goodenough, 1973; Nguyen et
al., 1981; Nguyen, Studer and Raveau, 1983; Singh, Ganguly, and
Goodenough,
properties
Low temperature
1984; Michel and Raveau, 1984].
were
examined
but
the
temperatures
enough to induce the superconducting transition.
19
were not low
All of these studies
were focused on the structure and properties of the material in its
normal state.
2.1.1 Structure,
Solution and Stoichiometry
Solid
Undoped La 2 CuO 4.
has the K2NiF 4 structure, which consists of
alternate KF rock salt and KNiF 3 perovskite layers along the c-axis
At room temperature it has a distorted orthorhombic
(Fig. 2.1.1).
structure with a = 5.363
Raccah, 1973].
A,
b = 5.409
A
and c = 13.17
A
[Longo and
In La2CuO4.- the copper atoms are coordinated to six
oxygen atoms, which sit at the corners of an elongated octahedron.
A)
The Cu-O bond length in the equitorial plane (2.4
the c-axis (1.9
A)
is longer than in
in contrast to Nd 2 CuO 4 43 which has two short and
four long Cu-O distances [Longo and Raccah, 1973].
These copper-
oxygen octahedra are joined to one another at the four corner oxygen
atoms closest to the copper so that it allows three dimensional space
to be filled in a highly two-dimensional manner.
This structure
undergoes a transition to a tetragonal phase at = 300 *C.
At low
temperatures several structural transitions have also been reported
[e.g. Skelton et al., 1987].
The orthorhombic-tetragonal transition in
the undoped material tends to occur at lower temperature
or is
completely suppressed when it is doped with a small amount of Sr or
Ba.
This structural transition seems unrelated to superconductivity
since it was found that the structural transition at low temperatures
stops near x = 0.19, whereas Tc disappears near x = 0.25 [Torrance et
al., 1989].
When
xAxCuO
4.8
doped with alkaline
earth
metals
(where A = Ca, Sr or Ba) retain the
20
the oxides
same
La 2 -
K2NiF 4 type
B
A
x
Fig. 2.1.1 Unit cell of La 2CuO 4 structure A: La atom, B: Cu atom, and C:
0 atom [Longo and Raccah, 1973)
I
/ /lOObarO£ 2
£
£
£
+
C
£
£
f
0 3,-
06
02
Sf
Fig. 2.1.2
Content
08
0
a
Hole concentration of La2.xSrxCu04. vs. x [Sreedhar and
Ganguly, 1990; the open and circles from Torrance et al.,
1988; and the open squares from Nguyen et al., 1981 ].
21
Their oxygen content depends on the nature of the A ions
structure.
and on the substitution rate x which can lead to wide homogeneity
ranges:
0.2 for A = Ca and Ba and 0 s x s 4/3 for A = Sr
0 s x
[Michel and Raveau, 1984].
Within the crystal structure, Sr or Ba,
The
which are similar in size of La, occupy the sites of La at random.
phase which
most reduced
exhibits the highest deviation
from
stoichiometry has been synthesized: La2/ 3 Sr 4 /3CuO3.33 [Nguyen et al.,
1981]. For x > 1 superstructures derived from the tetragonal cell (a ~
n*aLasrcuo 4 , with n = 3, 4, 4.5, 5, 6) due to the oxygen vacancies in the
Cu-O plane have been observed by X-ray and electron diffraction
[Nguyen et al., 1981;
Sreedhar and Ganguly, 1990].
The doping of Sr on the La site initially is compensated by the
generation
of holes while the oxygen content remains relatively
Further doping, on the other
constant in the range of ( 0.0 < x < 0.33).
hand, is compensated by the formation of oxygen vacancies.
phenomena
have
been
observed
by
oxygen
These
stoichiometry
measurements by TGA studies [Nguyen, Studer and Raveau, 1983;
Michel and Raveau, 1984; Sreedhar and Ganguly, 1990] and lattice
parameter measurement by XRD [Nguyen et al., 1981; Sreedhar and
Ganguly, 1990].
The evolution of the hole concentration as a function
of x in the La2-xSrxCuO4.8 system is shown in Fig. 2.1.2. [Sreedhar
and Ganguly, 1990].
The transition in the compensation mechanism
can be deferred by annealing the sample in a pressurized oxygen
environment [Torrance et al., 1988].
The lattice parameters, c/a ratio, and the molar volume of the
series La 2 -x.SrxCuO4. (0.1 s x s 1.2) are plotted in Fig. 2.1.3 as
functions of x [Sreedhar and Ganguly, 1990;
22
Nguyen et al., 1981].
In
(c)
(a)
95-
>.
91-
E
37
> 931-
E 92~.
372r
(d)
370-
3 50-
(b)
13 3-
3 40
I
0
I
2
0
0 6
08
10
12
'
025
Fig. 2.1.3
050
075
'
100
t25
Variation of the a (a), c (b), molar volume (c) and a/c (d)
as a function of x in the La 2 .SrxCuO4.3 system [Sreedhar
open circles and triangles from
and Ganguly, 1990;
Nguyen et al., 1981].
23
the range 0.0 < x < 0.33 the c parameter increases gradually while the
The c/a ratio reaches a maximum
a parameter show a decrease.
The
around x = 0.33, up to which there is no oxygen deficiency.
increase in the c/a ratio in this range is dependent on two factors: (i)
the relative size of the substituent ions and (ii) the change in the CuO network in going from Cu2 + ions to low-spin Cu 3 + ions.
The
decrease in the c/a ratio for x > 0.33 is associated with the formation
of oxygen vacancies.
2.1.2
Transport Properties
Most
property
electrical
These
temperatures.
measurements
properties
are
highly
made
at
low
dependent
on
the
are
thermal history and vary from one sample to another.
Only a limited
number of studies have focused on high temperature properties and
defect chemistry.
Ganguly and Rao [1973] first measured the conductivity and
thermoelectric power of La 2 CuO4.- from room temperature to
*K.
Results are shown in Fig.2.1.4.
independent
conduction.
resistivity
The
(-
positive,
independent (~ 250 gV/*K)
conduction by holes.
0.16
high,
-
1000
The low and nearly temperatureohm-cm)
and
also
suggests
near
metal-like
temperature-
thermoelectric power is consistent with
The effect of the oxygen partial pressure on the
properties is not mentioned and the measuring environments were
not specified.
The first systematic high-temperature
measurements
related to the doping effect of impurities on the electrical properties
were performed by Nguyen et al. [1983]
Their data (Fig. 2.1.5) show
that for x s 0.25 the conductivity increases with x but is independent
24
!
1000 1
2.0
1.0
30
2.0-
0e
00.
1*0
20
3 0
6'0
16 C S
1000 1
70
It
0
0
(a)
0-00
0
0
0:
0
0
:
0
.0
0
So
C
0
0
"0
0
t00
.
£0
(a)
-740
Fi
2.. g.
Fig. 2.1.4
eitvt'
00000o
[Ganguly
a
n
an a1973]
hrol
2
ctrcpweOb&f
nC
Resistivity (a) and thermoelectric power (b) of Ln 2 CuO 4
[Ganguly and Rao, 1973]
25
_____________________
L, C.-
X 033
x:0
1
X:02S
o0
r
cmX:066
t aIN
0
2
3
MCAT.
s
5
4
.Vol
6
7
X: 10
(a)
Fig 5
2
3
4
1
6
7
(b)
Fig. 2.1.5
Variation of conductivity as a function of 1/T of La2.
xSrCuO4.8 for 0 s x s 0.16 (a) and for 0.25 s x s 1.0 (b)
[Nguyen et al., 1983].
26
A
of temperature
intermediate
conductivity
-
temperatures
These
again.
below
and
measurements
anomaly
It decreases to a minimum at
300 *K.
observed
increases
then
were
The
air.
.in
performed
at intermediate
temperature
with
temperatures
was
related to oxygen intercalation at that particular temperature [Michel
and Raveau, 1984]. For 0.33 s x s 1.0 the conductivity decreases
with x and the slope changes sign so that conductivity increases with
temperature above x - 0.66. There is also a transition in slope at
Recently Gurvitch and Fiory [1987]
also observed linear p(T) behavior in Lal.8 25 Sr. 1 75 Cu04 from below Tc
to 1100 *K and suggest weak electron-phonon coupling of the
high temperature for x > 0.66.
transport
Sreedhar
phenomenon.
resistivity with x in the 0
et
al.
[1990]
measured
x 5 1.2 at low temperatures.
the
However
the resistivity of LaSrCuO4.6 is unusually small, contradictory to the
The initial increase in conductivity
results by Nguyen et al. [1981].
with x is related to the increase of hole concentration
dopant [Tsai et al., 1988].
with the
The decrease in conductivity at higher
values of x (0.5 < x < 1.2) is related to the disorder-induced
localization due to the creation of oxygen vacancies [Sreedhar and
Ganguly, 1990].
La 2 .xSrxCu04.5
shows apparent
both with temperature and composition.
metal-nonmetal
transitions
For example the undoped
material is metallic [Ganguly and Rao, 1973; Nguyen et al., 1981] at
high temperature and insulating at low temperature [e.g. Guo et al.,
The Ba-, Sr-doped or highly oxidized sample on the other
hand becomes metallic at all temperatures above Tc [e.g. Gurvitch
Most of these transitions from the narrow band
and Fiory, 1987].
1988].
27
with structural
distortions or
case are related
to or associated
antiferromagnetic
ordering to explain the abrupt disappearance of
the band gap.
Although antiferromagnetic
ordering or structural
distortion have been observed they do not always occur at the
metal-nonmetal transition (i.e. from positive temperature coefficient
to negative temperature coefficient of resistivity) temperature and
the correlation and interpretation of these phenomena
composition;
remain controversial.
When heavily doped (x > 0.66) the material
seems to become semiconducting [Nguyen et al., 1983].
This may be
due to Anderson localization connected with superstructure ordering
resulting from the high oxygen vacancy concentrations.
To interpret the transport phenomena, Goodenough, applying
crystal-field theory, proposed a schematic band diagram for La2Cu04
[Goodenough, 1973] and a later refinement [Singh et al., 1984] (Fig.
Goodenough argued that covalent mixing of the 3d orbitals
2.1.6).
with the nearest-neighbor
0 2 --ion 2p orbitals could be neglected
only 3d bands of Cu in the
because it does not change the symmetry;
vicinity of the Fermi level were considered since the 0 2p band
position was viewed as being well below the Fermi energy.
recent calculations
and experimental
results show that the holes
have substantial 0 2p character. [e.g. Mattheiss, 1987;
Dawson, 1987;
But
Takegahara et al., 1987].
Bullett and
Consequently, a simplified
model based only on Cu 3d bands may not be adequate.
2.1.3
Defect
Chemistry
Nguyen et al. [1981] observed some effects of the oxygen
atmosphere
on
the conductivity,
28
implying
that defects
could
be
DENSITY OF STATES
Cr
*2
y2
J2.
I
,
d 22Cui
- - - -
- E
E
U*> W
U-W-
--
Cu::
- -EdI2
z2
C
2 2
N ( E)
X2_ y2
-
(b)
(a)
Fig. 2.1.6 Schematic density of states vs. energy diagrams for the sbonding 3d electrons of La 2 CuO4 (a) [Goodenough, 1973]
and (b) [Singh et al., 1984].
29
electrical
by
studied
measurements.
they
But
provided
no
quantitative description of the relationship between them. Recently
Su et al. [1990] measured the high temperature (650 - 850 *C )
electrical conductivity and Seebeck coefficient as functions of oxygen
partial pressure and temperature in La 2 Cu0
4 46.
They found a 1/6
power dependence of both conductivity and Seebeck coefficient on
P 0 2 (Fig. 2.1.7), which implies the following redox reactions and
electroneutrality
condition:
KOX
1/2 02 (g) = Oi" + 2h';
= [Oi"]p2P 0 2 -1/2
and
p = 2[0;"] = (2Kox)1/3Po21/6.
A hole mobility of 2.07 cm 2 /Vsec (We calculate a value of 0.207
c m 2 /Vsec based on their data) was obtained by them from the
conductivity and reported values of oxygen excess which was
assumed to be in the form of doubly ionized oxygen interstitial (peff =
a/(28e)).
This mobility value precluded the small polaron transport
They
mechanism they previously had suggested [Su et al., 1989].
obtained 8 from the calculation of thermoelectric power which is
based on the following equation:
Q=
where
k/e[ln(Nv/p) + A],
NV is the effective density of valence states and A is a
constant related to the entropy of transport.
However applying this
equation, derived for a case of a non-degenerate semiconductor, to
La 2 Cu0 4 .3, a degenerate semiconductor (or metal), appears to be
questionable.
This argument also applies to their thermoelectric
power calculations for La 2-xBa 1 CuO4- [Su et al., 1988].
30
1.5c
I
2
1.30 -
u0
.
T=850*C
#%1.10-
E
C 0.90Slope= / ^
U 0.70
0.50
0.30
.
-. 0
19V
.
-4.0
-3.0
LOG
-2.0
0
P 2
I
T
-1.0
I
V
T
0.0
I
I
1.0
(ctm)
(a)
-0.80
-
-1.00-
1.20 -
C -1.40 -1.60-
-1.8018
--2.00
- 5.0C)
-3 0
-00
LOG p02 (atm"
Fig. 2.1.7
(b)
Conductivity (a) and thermoelectric power (b) of La 2 CuO4
vs. log P0 2 [Su et al., 1990].
31
Theoretical calculations of the defect reaction energies have
been performed on this system by two groups in England.
Islam et
al. [19881 found by defect simulation that the formation of Cu3 + is
energetically preferred to that of 0- and that there is a large energy
barrier (4.2 eV) to the Cu2 + disproportionation reaction.
the doping of the material and its oxidation
favoured
(-0.29
-0.25
and
eV
However,
are energetically
implying that the
respectively),
formation of holes is favored over that of oxygen vacancies upon
doping.
This is consistent with the experimental data for small x (<
0.3) only, since for large x, oxygen vacancies form.
Allan and
Mackrodt [1988] calculated that VLaf' and holes h* are the majority
defects and that copper and oxygen vacancies VCu" and Vo** serve as
the minority defects.
The formation energy of anti-site pairs, Lacu* +
CuLa', and Frenkel energies are high (> 4 eV).
The calculations also
predict strong electron/hole-lattice coupling.
From the formation
energy of the defects they consider the major redox reaction as:
LaLax + 3/4 02 (g) -+ VLa"' + 3h' + 1/2 La 20 3.
From the mass action and electroneutrality equations,
[VLa"'][h'] = K1 0P0 2 3/4exp(-E1/kBT),
and
3[VLa"'] - [h']
they derived a PO 2 power dependence of 3/16 for [VLa'"] and [h'].
[h'] = (3K
3 16
0 4
1 )1/ Po 2 / exp(-E1/4kBT).
Unfortunately these relationships are not observed by conductivity
or TGA measurements.
neglected the oxygen
oxidizing atmosphere
This may be due to the fact that they
interstitials which have been observed in
[e.g.
Chaillout et al.,
32
1989].
The other
possibility is that the values they obtained are based on calculations
at 0 *K, which might not be good at high temperatures.
The nature of the holes has been the focus of many studies.
[1987] proposed
Emery
a theory based on the antiferromagnetic
ordering of the Cu spins which requires 0 2p band holes in La 2 CuO4.
Allan and Mackrodt [1988] suggested that this may not be the case
and Cu3 + and 0- might both exist in La2CuO4.
There is experimental
evidence both for [e.g. Tranquada et al., 1987] and against [e.g. Alp et
al., 1987] oxygen related holes.
Sleight [1989] pointed out it is not
proper to ask whether the hole is associated with an oxygen or a
copper since there is a high degree of copper-oxygen admixture near
An alternative and perhaps more accurate
the Fermi level.
description of this, which reflects the strong pda
nearest-neighbour
interaction between the Cu 3dx2-y2 and 0 2px.y orbitals, is that the
holes are delocalized over Cu and 0 (covalent rather than ionic)
atoms giving complexes of the type that Shafer et al. [1987] have
designated as (Cu-0)+.
2.2 Nd2.xCexCuO4.
Tokura et al. [Tokura et al, 1989] and Takagi et al. [Takagi et
al.,
1989]
recently
superconducting
Unlike
the
that
discovered
oxide system with
other
two
systems
this is
electrons
in
this
the first
high
Tc
as charge carriers.
study,
it
shows
superconductivity above a critical electron density achieved by Ce
doping with an x value between 0.14 and 0.18 and/or by thermal
treatment under a low partial pressure of 02 at temperatures higher
The structure and properties of
than 1000 *C [Hor et al., 1989].
33
Nd 2 CuO 4 had been studied previous to its discovery as a
undoped
high Tc superconductor, as in the case of La 2.xSrxCuO4.8 system.
2.2.1
Structure,
Solution and Stoichiometry
Solid
In 1973 when Ganguly and Rao [1973] and Goodenough [1973]
studied the electrical
properties
assumed that this material
(K 2 NiF
4
Wollschlager,
1975]
in
1975
mistakenly
[Muller-Buschbaum
and
was it pointed out that it has a different
structure (Nd 2CuO 4 or T' structure) with a = 3.9422
A
they
had the same structure as La 2 CuO4
Only
structure).
of Nd 2 CuO4
as shown in Fig. 2.2.1.
with 14/mmm space group.
A
and c = 12.168
The Nd 2 CuO4-type oxides are tetragonal
Compared to La 2 CuO 4 (Fig. 2.1.1) the
cation positions are exactly the same.
The major difference is that
the apical oxygens of the Cu-0 octahedra are shifted so that it is
composed of sheets of Cu-O squares. The coordination number of Cu
is 6 (octahedra with Jahn-Tellar distortion) in (La, M) 2 CuO 4 while it is
4 (square planar) in Nd 2 -xCexCuO4..8
Nd 2 .xCexCuO4.-
forms solid
solution within the homogeneity region 0 < x < 0.2 even though
sometimes second phase may appear for x < 0.2 [e.g. Markert et al.,
1989].
The oxidation state of Ce is believed to be nearly 4+ based on
iodometry and examination of the unit cell dimensions [e.g. Huang et
al., 1989b].
Variation of the lattice constants has been studied as a function
of dopant [e.g. Huang et al., 1989b;
Wang et al.,1990].
The c axis
decreases and a axis increases with increasing x as shown in Fig.
2.2.2.
The variation of the c axis can be simply understood based on
the ionic radius
of the dopant (Ce4+: 1.11
34
A)
versus the host (Nd 3 +:
0
0
0
.Nd
*CU
00
0
0
0
a
Fig. 2.2.1 Unit cell of Nd 2CuO 4 structure [Muller-Buschbaum, 1975].
0
AM
04
0
0.1
0.2
0.3
x in Nd2 .xCeCuOz
Fig. 2.2.2 Variation of the a and c lattice parameters as a function of x
for Nd 2CuO 4 [Wang et al., 1990].
35
1.25
A).
The increase of the a parameter could be due to the charge
transfer from Ce 3 + to the (Cu-0) so that the bond is lengthened
[Wang et al., 19901.
Nd 2.,CexCuO4.
[Markert et al.,
al., 1990;
is generally accepted to be oxygen deficient
1989; Takayama-Muromachi et al., 1989;
Izumi et al., 1989;
Suzuki et
Williams et al., 1989] for x = 0 to 0.2
although oxygen excess has also been reported [Moran et al., 1989;
Wang et al.,1990].
Partial ordering of these oxygen vacancies have
been observed by neutron diffraction [Izumi et al., 1989] and highresolution TEM [Williams et al., 1989].
These vacancies proved to be
preferentially introduced at site 0(2), but site 0(1) may also become
slightly
deficient
thermal
treatment
under
pressures of 02 [Izumi et al., 1989].
Fig. 2.2.3
show how the oxygen
stoichiometry
upon
changes
as
functions
of temperature
low
partial
and oxygen
partial pressure for x = 0 and 0.15 [Suzuki et al., 1990].
2.2.2
Transport
Ganguly
resistivity
Properties
and Rao
[1973]
and thermoelectric
were
power
the first
the
of undoped Nd 2 CuO 4 and
concluded that it is an n-type semiconductor
*K.
to measure
in the range 120-1000
Mehta, Hong and Smyth [1989] reported that undoped and Ce-
doped Nd 2CuO 4 behave primarily as n-type material and undergo the
"semiconductor-metal
transitions"
at
large
charge
carrier
concentrations by either Ce doping or chemical reduction (Fig. 2.2.4).
When the donor concentration is low ( x = 0, 0.02 and 0.05) the
material shows "semiconducting characteristics" in terms of electrical
conductivity in the
temperature
range 700 - 900 *C.
36
As the donor
4.00
3.99
3.98
3.97
3.96
-4
-3
-1
-2
(a)
log(Po 2 /at@)
Nd1 . 8 5 Ce0.
15 Cu0
4.000
3.998
3.996
3.994
3.992
3.990
-4
-2
-3
Iog(Po 2 /atm)
Fig. 2.2.3
-1
(b)
Oxygen nonstoichiometry of Nd 2CuO4 (a) and Nd 2 xCeCuO4,8 (b) as a function of oxygen partial pressure
and temperature [Suzuki et al., 1990].
37
~-~--
-4.2
0
soU
sec
U
1
so
|
2
4
3
0
I000/()
1(X)0/T (k)
(C)
(a)
'42
Fs
900C
GOO
t
1
2
A
3
1000/7 ()
(d)
(b)
Fig. 2.2.4
30^C
Log (conductivity) of Nd 2 .CexCuO 4 48 vs 1000/T for (a) x
= 0, log(PO 2 ) = 0, (b)x = 0, log(PO 2 ) = -3.5, (c) x = 0.05,
log(PO 2) = 0, and (d) x = 0.05, log(PO 2 ) = -3.9 [Mehta et al.,
1989].
38
concentration increases, the material shows "metallic" behavior. Su,
Elsbernd and Mason [1989] pointed out that at low cerium levels,
electron conduction in Nd 2 -x.CexCuO 4 . is apparently via small polaron
hopping as evidenced
by a difference
in activation
conductivity (0.79 eV) and thermopower (0.45 eV).
energy for
However for the
mobility to be within the small polaron regime (= 0.1 cm 2/Vsec)
oxygen
nonstoichiometry
the
(8) would have to be as high as - 0.1
according to their data, which is unusually high for this material.
Besides, the redox reaction that usually accompanies the isobaric
cooling process was not considered.
This is important especially in
the undoped Nd 2 CuO 4 .6 case where the oxygen stoichiometry is
believed to be a strong function of the oxygen partial pressure and
temperature [e.g. Suzuki et al., 1990].
2.2.3
Defect
Chemistry
Little effort has been applied towards clarifying
temperature
defect structure of this system.
the high
Hong, Mehta, and
Smyth [1989] showed that the electrical conductivity increases with
decreasing oxygen partial pressure (Fig. 2.2.5), presumably due to an
increased electron concentration upon reduction.
Since the PO 2
dependence becomes shallower with increasing donor doping, this
implies that the donors are compensated by electrons.
quantitative
description
on
the
relationship
concentration and oxygen partial pressure.
There was no
between
dopant
Pieczulewski et al. [1989]
measured the conductivity and thermoelectric power of this system
and proposed a defect model involving the following reactions:
anion Frenkel reaction:
39
4.5
a 900 C Undoped
S&00 C Undoped
* 700 C Undoped
40
LOG PO 2 (Pa)
(a)
0
-'
35
-1
0
1
2
3
4
5
LOG Po 2 (PC)
(b)
vs. log(P0 2 ) (a) x = 0
Nd
-x.CexCuO4+8
of
Fig. 2.2.5 Log (conductivity)
2
and (b) x = 0.05 at various temperatures [Huang et al.,
1989].
40
00 -+ Vo** + Oi",
KF = [Vo**][Oi"]
redox reaction:
2e' + 1/202
KO = [Oi"]/n 2p021 /2
Oi",
-+
and electroneutrality
equation:
n + 2[Oi"] = 2[Vo''] + [CeNd]
to generate the Brouwer diagram in Fig. 2.2.6a.
This was to be
compared with the conductivity and thermoelectric power data (Figs.
Again for this comparison to be made they
2.2.6b and 2.2.6c).
assume
that
either
the
mobility
is
independent
of
dopant
concentration or the reduced thermoelectric power is proportional to
log (carrier concentration),
semiconductors only.
which is applicable for nondegenerate
Both assumptions need further justification.
2.3 YBa2Cu3-xTixO6+8
Unlike the other two systems discussed above, YBa 2Cu 30 6+8
was a completely new material at the time it was announced as
being a new high Tc superconductor.
The incentive in investigating
such formulations was to find oxides with more Cu-0 layers in the
unit cell of a layered perovskite structure.
This was based on the
observation that the Cu-0 layer is essential to superconductivity in
La 2.xSrxCu0 4.s.
It was believed that an increase of the Cu-O plane or
chain density might increase Tc.
This proved to be a good approach
although it is difficult to maintain more than three Cu-0 layers due
to phase instability resulting from structural relaxations.
2.3.1
Structure,
Solid Solution and Stoichiometry
41
O 2
---- h
--
-
or
S'or
V0
or
or
e'
.'1
Ce4,
V0,
~72
z-
LOG DOPANT CONCENTRATON
(a)
.eC.0 4 .
E1L
7
WA
-WWm
. 4M
e_.,u
850'C
., 700'C
I
.- a
uAJ
___u__
770'C
800'C
um 800*C
.ULLM 850*C
850'C
so
-
-N
LOG 0OPANT CONCENTRATON
-. 2,
..
-c.Ae
.OG 0CPANT CONCLNTRArwCN
(b)
Fig. 2.2.6
650*C
.. m700'C
770'C
4.&A.
(C)
Schematic Brouwer diagram of defect concentrations vs.
dopant concentrations in Nd 2 .Ce 1 CuO4 or La 2 -xBaCuO 4
(a) and reduced thermoelectric power(b) and electrical
conductivity (c) vs dopant concentration of Nd 2 .
xCexCuO 4 ...6 (Pieczulewski et al., 1989].
42
The so-called 123 compound has a basic structure of a layered
In between the barium and the
perovskite as shown in Fig. 2.3.1.
yttrium
layers,
pyramids(Cu(II)).
atoms
copper
are coordinated
in
oxygen
with
The bases of the copper-oxygen pyramids face
one another across a plane of yttrium atom.
In between
two
consecutive layers of barium, copper atoms are coordinated with
The corners
four oxygen atoms in a flat, diamond-like shape(Cu(I)).
of the diamonds are connected to form a chain of diamonds.
In YBa 2 Cu 3 07 the copper atoms have an average valence of
+2.33 in both the chains and the bases of the pyramids.
When the
oxygen content is reduced from seven to six, the insulator YBa 2 Cu306
is formed.
Oxygen is removed from one crystallographic site only i.e.
the one connecting Cu(I).
As the oxygen content is increased, oxygen
is added to the site next to Cu(I) in such an ordered way to from as
The
many copper-oxygen diamonds as possible [e.g. Cava, 1990].
including
the
critical
is
stoichiometry
oxygen
occurrence
of
to many
important phenomena
superconductivity,
metal-insulator
transition at low temperature, structural transitions and even the pFor example, quenching from a
n transition at high temperature.
higher temperature in which oxygen content is less than a certain
amount destroys the superconductivity, causes removal of the
orthorhombic distortion in the perovskite structure and results in a
metal-insulator transition at low temperatures [Budhani et al., 1987].
Unlike
the other
two systems,
to investigate
the possibility
temperature, or clarifying the
is
The purpose of doping YBCO has
superconducting without doping.
been
(YBCO)
YBa 2 Cu306+8
of enhancing
mechanism of high-Tc
43
the
transition
superconducti-
Fig. 2.3.1 Structure of YBa 2 Cu306+8
7 OO
Fig. 2.3.2
Temperature dependence of the normalized resistance of
YBa 2 Cu3-xAxO6+8., where A = Cr, Mn, Fe, Co, Ni and Zn
[Xiao et al, 1987].
44
vity.
Substitution or doping has been studied on every cation and
anion site
in
For example:
YBCO.
superconductivity
remains
essentially unaffected by the substitution of Y with isoelectronic
rare-earth elements that have a large localized magnetic moment
[Kanbe et al., 1987; Dunlap et al., 1987];
substitution on the Ba site
with La will depress the superconductivity [e.g. Kwok et al., 1988]. In
this study we focus on substitution of atoms on the Cu site where the
superconducting
electron
holes are considered
to move.
Many
elements, mostly the 3d transition metals have been used as dopants
[e.g. Maeno et al., 1987; Kajitani et al., 1988; Xiao et al., 1987]. The
solubility of these dopants are usually high (as high as 20% of the
total Cu in the Fe case [Mazaki et al., 1987] and 33% in the Co case
[Kajitani et al., 1988]) except W and Nb [Kuwabara and Kusaka,
1988].
The solubility of Ti is above 10% of the total Cu [Xiao et al.,
1987].
The effect of most dopants is to induce the tetragonal phase
and to decrease Tc without destroying the superconductivity
(Fig.
2.3.2) [e.g. Xiao et al., 1987].
As mentioned before, there are two Cu sites in the structure
(Cu(I) and Cu(II)).
Since the superconductivity is believed to be
confined in the CuO 2 -Ba-CuO2 layer assembly [Hor et al., 1987], the
Cu site onto which substitution occurs is critical in determining the
This depends on the nature of the dopant. For
role of doping.
example nickel atoms occupy only the Cu(II) sites; zinc atoms occupy
the Cu(I) and Cu(II) sites with occupancies of 0.20 and 0.05; Co atoms
were found at both Cu(I) and Cu(II) sites with occupancies of 0.83
and 0.08 [Kajitani et al., 1988]. However no study reports on the Ti
site occupancy.
45
most
While
study
the
influences
of
groups
the
superconductivity,
effects
the
of
doping
on
dopant
on
oxygen
stoichiometry and the oxidation state of the Cu are not particularly
The oxygen content of Ni- and Zn-doped samples were
emphasized.
by annealing
changed
little
in high-pressure
while the
oxygen,
oxygen content increases to more than 7.0 in Co-doped samples
In Fe-doped samples, the oxygen content
[Shimakawa et al., 1988].
was proved to be constant (6.87 ± 0.05) with dopant concentration
Judging from the aliovalent nature of the Ti 4
(Obara et al., 1988].
+
ion on the Cu 2 + ion site, the charge density and/or the oxygen
content should be altered by either electronic or ionic compensation.
Transport
2.3.2
Studies
of
Properties
the
high-temperature
transport
properties
by
electrical measurements of undoped YBCO have been performed by
several
groups.
The
temperature
and
oxygen
partial
pressure
dependence of the conductivity and thermoelectric power reported
by these groups are in good agreement with one another.
and 2.3.3b.
show the conductivity
Figs. 2.3.3a
power as
and thermoelectric
functions of temperature in various oxygen partial pressures [Choi et
al., 1988].
When temperature is low and oxygen partial pressure is
high, the conductivity is nearly temperature insensitive and of high
magnitude, resembling typical metallic behavior (region I).
region
the
insensitive.
thermoelectric
power
is
positive
and
In this
temperature
However, the conductivity becomes thermally activated,
with negative activation energy, at intermediate temperatures and
The corresponding thermoelectric power
reduced P0 2 (region II).
46
w00
700
600 70
S00o
500
300 'c
400
30*
00
0
60I
Log
0
--
1
-2
-3
.
1.0
I
1.2
1.4
1000/T
800 700
600
1.6
(K- 1
1.8
)
500
300 '
400
300-
Log P02 (atm)
200
100
0-
-10
i
I
j
10
12
14
8
18
000/T (K-')
Fig. 2.3.3
Log (conductivity) (a) and thermoelectric power (b) vs.
1000/T for YBa 2 Cu 3 06. 8 measured at a series of controlled
P0 2 's as indicated [Choi et al.,1989).
47
Further, at
remains positive but increases rapidly with temperature.
high temperature and low oxygen partial pressure, the conductivity
and
reverses
show a thermally
activated
process
with positive
In this region the thermoelectric
activation enthalpy (region III).
power passes through a maximum and reverses sign to n-type at the
temperatures
highest
and
oxygen
lowest
partial
pressures,
suggesting a p-n transition.
Both Choi et al. [1988] and Su et al. [1988] support at least in
the low oxygen content regime that the transport in YBa 2 Cu 3 0 6 +8
occurs by the small polaron mechanism.
Nowotny and Rekas later
[1990] modified this model by an adjustment in the calculation of
conductivity
and
thermoelectric
power,
which
involves
both
electrons and electron holes as carriers.
2.3.3
Defect
P0
2
Chemistry
dependent
electrical
YBa 2 Cu 3 06+8 was examined
measurements
on
undoped
by the same groups [Choi, Tuller and
Tsai, 1989; Su, Dorris and Mason, 1988; Mehta and Smyth, 1989; Yoo,
1989;
Nowotny and Rekas, 1990].
with one another.
Their data are quite consistent
Typical data are shown in Figs. 2.3.4 where the
conductivity and thermoelectric power are measured isothermally as
functions of P 0 2 [Choi et al., 1988]. It is indicated that there is a
gradual change of slope from 1/2 to -1/2 from oxidizing to reducing
conditions in conductivity and the thermoelectric power follows the
In a more detailed study, Nowotny et al. [1990]
express the reciprocal of the slope of thermoelectric power vs P0 2 as
same trends.
48
-4
I
-3
I
I
0
Log P
2
(atm)
(a)
3
YSCO
2
C
1700
16c
0
A
i
-3 -z
ITo
I
-I
Log P0 2 (atm)
(b)
Fig. 2.3.4
Log (conductivity) (a) and' thermoelectric power (b) vs.
log (PO 2 ) for YBa 2 Cu 3 0 6 +8 measured at a series of
controlled temperatures as indicated [Choi et al.,1989]
49
nd(-q a/k)
= [d(In p o 2)T
and plot it as a function of temperature (Fig. 2.3.5).
It is found that
the trends are similar but the slopes in most cases are smaller than
This
1/2 even at low PO 2'S.
relationship
is critical
to
the
identification of the proper defect model [Choi et al., 1988; Su et al.,
1988].
A fixed composition measurement was also carried out by Choi
et al.
[1988]
so the the property change
due to the oxygen
stoichiometry change during cooling could be isolated.
are shown in Fig. 2.3.6
at constant PO2,
The results
In contrast to the results of Fig. 2.3.3
the conductivity
decreasing temperature.
decreases
,
taken
monotonically
with
The temperature dependence, particularly
at the lower temperatures, decreases rapidly with decreasing oxygen
At the highest temperatures, all three curves appear to
content.
The thermoelectric power data, though
approach a common curve.
showing an inconsistency at the starting point of each curve with the
constant
P0
2
stoichiometry
decreases with
cooling curve,
suggesting
the
that
decreasing
corresponding
oxygen
increase
in
conductivity is at least in large part due to an increase in carrier
density.
data
from
These data were correlated to the oxygen stoichiometry
thermogravimetric
analysis
for a defect model
that
involves CuO, Cu+ and Cu 2 + in the materials instead of Cu+, Cu 2 + and
Cu 3+ proposed by others [Su et al., 1988; Nowotny and Rekas, 1990].
It is postulated that the hole concentration will decrease with
donor doping.
The p-n transition observed in the high temperature
regime will occur at lower temperature and
50
in higher oxygen partial
I
TEMPERATURE (*C)
201
10
0
£
3
w
z
LU
zLU
LL
0r
TlK)
Fig. 2.3.5
oxygen exponent (na) as a function
Reciprocal
temperature for YBa 2 Cu 306+8 [Nowotny et al., 1990].
51
1
I I I
.
I
I
1
03
0
-2 I-.
CW
YBCO
3-3
Fixed compoSitIon
-4 1-
I
I
-8.,
I
1.5
1.0
s
I
I
2.0
2.5
3.0
3.5
1000/T (K-C)
(a)
I
I
YBCO
Fixed compostion
0
C2
0.35 a 02
0.1 sO
1 S 0
cr
I
I.,
5
1i0
I
1.5
I
2.0
1000/T
I
2.5
I
3.0
3.5
(K')
(b)
Fig. 2.3.6
Log (conductivity) (a) and thermoelectric power (b) vs.
1000/T for YBa 2 Cu 3 06+6 with fixed values of S [Choi et
al.,1989].
52
pressure
if this
transition
is induced
by carrier
concentration.
However, Huang et al. [1990] reported that the high temperature
electrical properties of YBCO are not much affected by the donor
doping of La on Ba sites in terms of P0
of conductivity.
2
dependence and magnitude
They concluded that the stoichiometric composition
for YBa 2 Cu306 is a highly acceptor-doped material.
On the other
hand, the effect of aliovalent doping on the Cu site has not been
studied and no studies of PO 2 -dependence in Ti-doped YBCO have
been reported.
Judging from the importance of Cu ions in the role of
superconductivity, substitution of Cu by Ti may result in substantial
change in the transport properties.
53
Chapter 3
Theory
In this chapter the theory related to the electrical properties
and defect chemistry of superconducting
oxides will be briefly
Models involving defect formation in these systems will
discussed.
also be presented.
3.1 Electrical
Properties
The electrical properties of materials relate to how the charge
carriers transport under the driving forces of electric fields, thermal
and chemical gradients.
variables
Since they are usually functions of external
such as temperature
and oxygen partial pressure it is
necessary for us to specify these parameters to characterize these
properties.
They may also be strong functions of intentionally or
For this reason the impurity level
unintentionally added impurities.
has to be specified
satisfactorily
predict
too.
A proposed theory or model should
variations
of
the
properties
with
these
parameters.
3.1.1
Electrical
Conductivity
It is convenient to write the electrical conductivity showing the
individual contributions of each charge carrier as:
(3.1)
a = X nIlelpi
where
ni and pi, are the ith charge carrier density and mobility
respectively.
By writing the electrical conductivity as a product of
54
-1
the carrier density and mobility, it becomes convenient to contrast
For
the temperature dependence of a for metals and semiconductors.
metals,
independent
n is essentially
temperature dependent.
of T,
while p. is weakly
In contrast, n for semiconductors is highly
temperature dependent in the intrinsic regime and p. may be more
temperature
strongly
In
dependent.
oxide
the
semiconductors,
charge carrier may be electronic and/or ionic.
3.1.1.1
Metals
Transport in metals can be best described by band theory
which rests on the assumption that each electron belongs collectively
to all the atoms of a periodic array since the charge carriers move
from one atom to the next in a time short compared to the period of
lattice vibrations.
the
impairs
The most important scattering mechanism which
motion
of
the
electrons
for
both
and
metals
semiconductors is electron-phonon scattering (scattering of electrons
by thermal motion of the lattice) except at very low temperatures.
That is why the conductivity of a metal is usually expressed as
a = ne 2 T/m*,
where m* is the effective mass and c is the relaxation time.
For a
metal, r is interpreted as the scattering time of electrons with energy
near the Fermi level and n is the total density of free electrons.
In
this sense the electron mobility of a metal can be written as
=
(3.2)
er/m*
which shows that materials with small effective masses have high
At high temperature, p. is proportional to 1/T due to
mobilities.
electron-phonon scattering.
The number of charge carriers in the
55
conduction band is of the order of the lattice site density and is not a
The conductivity of a metal thus declines
function of temperature.
with increasing temperature.
3.1.1.2
(I)
Semiconductors
Carrier
Density
Compared
metals,
to
the
carrier
concentration
semiconductor usually is a strong function of temperature.
of
a
The
temperature dependence of the carrier density can be divided into
two temperature regimes (Fig. 3.1.1) i.e. the intrinsic regime and the
extrinsic regime.
(i)
Regime
Intrinsic
At high temperatures, electrons and holes are excited across
the band gap between conduction and valence bands respectively
and have the form:
n = p = (NcNv)1/
2
(3.3)
exp (-Eg/2kT),
where Nc and Nv are the effective density of states in the conduction
band and valence band respectively and Eg is the energy gap.
(ii)
Extrinsic
Regime
(a). Saturation or exhaustion regime:
Above some intermediate
temperature, all the shallow dopants or impurities are ionized.
The
carrier concentration is determined by the level of the dopants or
impurities.
Assuming donor-doping
n ~ ND,
where ND is the donor concentration.
56
Intrinsic region
log, n
Slope - E,/2k
Saturation or exhaustion
region
slope - 0,
m
Fig. 3.1.1
-
Nd
Trap ionization region
Slope
-
(Ed - E,)/2k
or (Ed - E,)k
Log (carrier density) vs. l/T of a typical semiconductor.
57
(b). Ionization regime:
At low temperatures where (Eg-ED) >
k3T, not all impurities and defects are ionized.
The electron density
is then given by
(3.4)
n = (NDNC)1/ 2 exp[-(Eg-ED)/2kT],
where ED is the energy level of donor.
(II)
Mobility
the
While
semiconductors
occupied
same
as in metals,
mechanisms
are
present
in
because of the lower numbers of
states in the conduction bands of semiconductors,
temperature dependence
different.
scattering
of the various scattering
the
mechanisms are
For the phonon scattering process, the mobility can either
increase or decrease
with temperature depending on the coupling
mechanisms [Smith, Janek and Adler, 1971].
But in either case the
temperature dependence of the scattering is relatively unimportant
in the contribution
to the conductivity compared
to the carrier
formation process except in the following cases:
(i) Polaron
For many transition-metal and rare earth oxides which have
narrow d or f bands in the vicinity of the Fermi energy, the BlochWilson band theory appears to fail because of the neglect of electronelectron correlations.
Even though the material has an integral
number of electrons per primitive cell, the carriers in these narrow
bands are localized around their ion cores and form polarons (the
combination of an electron and the induced lattice polarization).
58
In
mobility is described
this case electron
by diffusion theory (or
hopping of small polarons):
(3.5)
= (eDO/kT) exp(-EH/kT), and
Do = A(1 -c)ao 2v,
where A(1-c) is a geometric factor times the probability that a nearneighbor is unoccupied;
frequency
and
mechanism
is
crystals.
ao is the lattice parameter; v is the jump
EH is the hopping energy.
common
very
The small polaron
in polar semiconductors
and ionic
The mobilities of polarons are small and generally on the
order of 10-4 to 10-2 cm 2 /V-sec at elevated temperatures.
A "large polaron" theory is applied when the radius of the
localized state is greater than the lattice spacing.
temperatures
above
the Debye temperature
The mobility at
is given by
[Appel,
1968]
p=
0T-/2
and has a value
(ii)
Impurity
1-100 cm2 /V-sec at elevated temperatures.
Conduction
This process, which proceeds by thermally activated hopping
between the impurity or vacancy levels themselves is important in
partially
compensated
semiconductors
at low temperatures.
The
conductivity can be expressed as [Mott, 1987]:
(3.6)
a= A exp {(B/T)n}
with
B = const/N(EF)a 3 ,
59
where a is the distance between nearest neighbors, N(EF) is the
density of states at the Fermi level, and n is a constant ranging from
0.2 to 1 (variable range hopping).
(iii) Ionic Conduction
In this case, electrical conduction can arise through the motion
of lattice ions as they move from one lattice vacancy to another, or
from one interstitial site to another. This conduction is important
especially in ionic crystals, where there are relatively few mobile
electrons or holes even at high temperature. Ionic conductivity takes
the form of diffusion:
= (ao/kBT)exp[-(Ef + Em)/kBT],
=ionic
(3.7)
where Ef is a formation energy and Em is the migration energy of the
defect.
3.1.1.3 Conductivity of YBa 2 Cu306.5
Su et al. [19881 proposed, at least for the low oxygen content
region, that transport in YBa 2 Cu 3 0 6 +8 occurs by the small polaron
hopping mechanism.
Accordingly the electrical conductivity can be
described by the following expression:
2
a = qcp =c(1-c)
gqa o
k
kT
ex
( --Em
-kTj
where c is the carrier concentration,
(3.8)
the mobility of carriers, a the
jump distance, uo the vibrational frequency, Em the hopping energy,
In the p-type region, the charge transfer
3
2
in YBa2Cu 306+8 involves jumps between lattice sites Cu +/Cu + so that
and g the geometric factor.
c = h [Cu 3+] and (1 - c) = [Cu 2 +].
60
Nowotny and Rekas [1990] on the
other hand proposed that both types of electron carrier participate in
the conduction involving quasi-free electron holes and related jumps
between
Cu 2 + and Cu3 + as well as quasi-free electrons transported
according
to
the
hopping
between
mechanism
Cu+ and Cu 2 +.
Therefore the conductivity was modified as
2+
2
+ae(T)n u
a=ah(T) CU
n
p
(3.9)
where
2
g hq a Uo
k T (k
Emh
T}
(3.10)
2
ae(T) = geq a
kT
_e_
U"
~
kT) .(3.11)
Eq. 3.9 seems to agree with experimental data quite well with
reasonable parameters (Fig. 7 in their paper [Nowotny and Rekas,
1990]).
3.1.2
Thermoelectric
Since
Power
the electrical
conductivity
contains
two independent
parameters i.e. n and p, a measurement of conductivity alone does
not
allow
normally
determined.
the
carrier
concentration
or
type
to
be
Additional information is needed to deconvolute the
two components.
The thermoelectric power which is a function of
carrier concentration, is generally combined with conductivity data
for this purpose.
When a temperature gradient occurs along a uniform bar of
material there will be a flow of carriers to the cold end of the bar.
61
lead
temperatures
different
The
to
different
electrochemical
potentials for electrons at the two ends, and charge flows until an
electric field builds up that just compensates this difference. This is
The thermoelectric power, defined as Q = -AV/AT,
the Seebeck effect.
AV is the voltage developed
where
across the sample due the
temperature gradient AT, is a measure of the Seebeck effect.
Metals
3.1.2.1
Seebeck
The
coefficient
of a metal can
be expressed
as
[Ashcroft and Mermin, 1976]:
Q_(nk)2T alnD(E)
[
3e
E_
E _
(3.12)
where D(E) is the density of states and EF is the Fermi level.
In the
free electron limit
2
Q
2,
kT
(2e EF .(3.13)
We note that it depends linearly on T and the sign of the carrier.
A
low carrier density also implies a large Q value.
3.1.2.2
Semiconductors
For semiconductors in which a mean free path can be defined
the thermoelectric power becomes [Mott, 1987]
(3.14)
Q = k/e((Ec - EF)/kT + 5/2 + r),
where r = d(In r)/d(ln E) with r the relaxation time.
For non-degenerate, broad band semiconductors [Smith, 1978]
the
thermoelectric
power
for
electrons
62
becomes
Q=
In (N)+Ae
q
(3.15)
n
and for holes
Q=. kq
n
P
+ Ah
-(,
(3.16)
where Ne and N. are the densities of states in the conduction and
valence bands; n and p are the electron and hole concentrations; Ae
and Ah are the transport energies per kT carried by the charge
carriers and are generally small in oxides.
as fixed by dopants or can be
can be temperature independent
thermally
activated
in
the
The carrier concentration
intrinsic
regime.
The temperature
dependence of the Seebeck coefficient and its magnitude can usually
distinguish between metals and semiconductors.
In
extrinsic
the
conductivity
regime,
where
a and Q are
determined by one type of charge carrier only, the conductivity and
thermoelectric rower can be related by the following equations:
Q=-k
In Nce eIAe
e
k Inae-ln(Nceleexp(A))]
e
(e
3.17)
and
Qh= e lnNyeabh
h+Ah1 =_
When Q is plotted vs. log a,
e
Inah-ln(NeL hexp(Ah))]
(3.18)
a pear-shaped curve (Jonker pear)
results, whose shape depends only on the intrinsic parameters such
as the band gap and the mobility ( ) of electrons and holes [Jonker,
1968].
By judging the shift of the straight parts of the curve with
respect to temperature, one can also determine whether the mobility
63
of the charge carrier is thermally activated or not [Choi, Tuller and
Goldschmidt, 1986].
In
narrow
band
semiconductors,
where
hopping
between
available lattice sites (polaron) is the transport mechanism,
(1-c)
kQ=In@
q
H*
AS
c
+--~
k
kT-
(3.19)
where c is the fraction of available lattice sites occupied by carriers
in conduction;
participating
ALSR
is the difference in vibrational
entropy between an occupied and an unoccupied site with ASR/k on
the order of 0.1 to 0.2;
P = 2 if the carriers are electrons with spin
degeneracy and P = 1/2 if the carriers are electron holes; values of P
= 1 are also possible if the orbital occupation numbers of an ion on a
lattice site are such that the charge carrier is restricted to one spin
orientation; H* is the heat of transport for conduction.
two
terms
are
they
are
usually
omitted
in
c can be related to the concentration of the charge
calculations.
carrier.
small
relatively
Since the last
For example c has been taken as the number of holes per Cu
site, which is equal to I - 2x in (Lai.xBax)2CuO4 for x < 0.1 [Cooper et
According to the small polaron theory [Nowotny and
al., 1987].
Rekas, 1990], the thermopower of YBa 2Cu30 6+8 can be expressed by
the following relation for p and n carriers respectively:
Q
k=-n @h
q
Q=- k In
q
where
Ph
+---
p
P
k)
(3.20)
+
,
(3.21)
and P. are the degeneracy factors including the spin and
orbital degeneracy of corresponding electronic carriers, and Sh and
64
Se
denote
the
vibrational
terms
entropy
associated
with
ions
surrounding the polaron on a given site.
For a conductor consisting of both electrons and holes as charge
carriers, the thermoelectric power can be calculated by [Smith, 1978]
Q = aeQe+ahQh
ae+ah
(3.22)
where Qe and Qh are the Seebeck coefficients for electrons and holes,
This equation
and ae and ah are the corresponding conductivities.
can be generalized to include other contributions such as the ionic
power:
thermoelectric
(3.23)
tot .
Bosman and van Daal [1970] pointed out that in the case of the
simultaneous presence of partially compensated n-type conduction
and impurity conduction the thermoelectric power can be expressed
as:
Q=- keA
+A
L
)'
''tot
'
'
(3.24)
'
where ED is the donor energy and ato = an + aimp.
is dominated by on,
hand side of equation.
When conduction
Q is determined by the first term on the rightAt temperatures below the exhaustion region.
-Q will rise with decreasing
temperature.
where aimp dominates conduction,
At low temperatures,
Q is determined by the second
term on the right-hand side of equation.
In this region
Q
may be
expected to have a low, temperature-independent
value which can
or a negative sign, depending
on compensation
degree and multiplicity factor of the acceptor level.
Even though this
have a positive
65
equation
specifies the relative
contributions of the electron and
impurity conduction, yet it is almost impossible to separate the two
contributions because the temperature dependence of the impurity
conduction is not known.
The major problem of applying thermoelectric power equations
to real data is that the equations discussed above do not always
explicitly specify the carrier concentrations except in the case of
In the case of two band conduction
nondegenerate semiconductors.
it is almost impossible to separate the individual contributions to the
total value.
Localization
3.1.3
As
mentioned
Metal-Insulator
and
in
the
previous
Transitions
chapter,
metal-insulator
transitions are common in the superconducting oxides.
It is thus
worth while to discuss these interesting phenomena here.
3.1.3.1
In
Localization
the
following
we
categorize
three
main
sources
of
localization which may exist in high Tc superconducting oxides.
(i) Mutual Electrostatic
Repulsion
The simplest approach to electronic repulsion is the Hubbard
model which assumes that the only important repulsion effect occurs
between two electrons on the same atom.
In this model the set of
bound and continuum electron levels of each ion are reduced to a
singly localized orbital level.
The bonding interaction will give rise to
a band of crystal orbitals as in metals.
However when the overlap
between orbitals is small an energy (U) is required to delocalize the
66
electron, which is equal to the difference between the ionization
energy of an electron (I) and the affinity of the neutral atom (A).
This energy is the gap between the two sub-bands resulting from the
so-called Mott-Hubbard splitting [Mott, 1974].
Each sub-band is
broadened by inter-atomic overlap, and they meet when the width
W of the bands and the repulsion parameter U are approximately
Beyond this point there is no energy gap, and the solid is
equal.
metallic.
The clearest illustration of the Hubbard model is provided
by solids containing elements from the lanthanide series with 4f
orbitals which have only a very small overlap with other valence
orbitals [Cox, 19871.
In many compounds of transition metals the d
band is narrow, and quite often a Mott-Hubbard splitting is seen
with localized electrons.
A range of electronic properties can result
from the competition between the different effects.
Thus changes
from metallic to insulating character and then back again to metallic,
are sometimes exhibited by a single series of compounds.
(ii)
Charge-Lattice
Interactions
In ionic solids, the electron or hole can produce local lattice
distortions
resulting
neighboring ions.
from
their
electrostatic
interactions
with
This type of distortion accompanies the electron as
it moves through the lattice, and the result is known as a polaron.
When the distortion is sufficiently strong, an electron or hole may be
trapped at a particular lattice site (small polaron), and can only move
This picture is
by thermally activated hopping through the solid.
most commonly applied to transition-metal compounds, especially in
the 3d series where the d bands are rather narrow.
67
(iii)
Electron-Defect
Interactions
One of the best known sources of localization is the Anderson
1958]
which
results
from a disordered
localization
[Anderson,
potential.
This phenomenon
following.
Suppose an array of atoms is to have a disordered
can
be qualitatively
as
described
potential field so that the energies of the atomic orbitals vary
randomly from site to site. Atoms with near-average energies are
very likely to have some neighbors at similar energies, and can form
delocalized orbitals by their overlap.
Atoms at exceptionally high or
low energies however, are unlikely to have similar neighbors, and so
their orbitals may remain
boundary between
as isolated or localized
The
states.
localized and extended states is known as the
mobility edge.
There are some other mechanisms which cause localizations.
For example a change of crystal structure may lead to a band gap.
Another important mechanism is antiferromagnetic
ordering.
Even
though there are different mechanisms which cause localization it is
not easy to disentangle the various effects operating in real solids
unless there are other obvious accompanying physical transitions.
3.1.3.2
Metal-Insulator
Transitions
It is obvious that the metal-insulator transition occurs when
there is a crossover from delocalized states to localized states
Due to the
resulting from temperature or composition change.
different sources of localization there are also different proposed
mechanisms that induce the transitions.
68
For the Mott insulators the transition can occur upon doping.
At low doping levels in semiconductors, impurities are on average
At higher concentrations the donor
well separated from each other.
or acceptor orbitals will begin to overlap with one another to form an
impurity band.
Even though they are formally half full they do not
immediately lead to metallic conduction because electrons in these
narrow bands are localized by repulsion effects.
The insulator-metal
transition (Mott transition) occurs when the following Mott criterion
[Mott, 1974] is met, (which is derived from the requirement that W >
U):
nd'/ 3 aH ~0.25,
(3.25)
where nd is the doping concentration and aH is the hydrogenic radius
of the donor orbital.
The existence of a mobility edge in the Anderson localization
model can also give rise to a metal-insulator transition, the so-called
Anderson transition.
When there are very few electrons present, the
Fermi level may be below the mobility edge.
level are then in localized states.
Electrons at the Fermi
At higher electron concentrations
the Fermi level may cross the mobility edge so that electrons are in
extended states and metallic conduction is possible.
However if they
are compensated to a certain level, the Fermi level will be shifted to
beyond the mobility edge and the electrons then become localized
again.
Though
localization
the metal-insulator
and
transition
are
closely related to each other, it must be noted that compounds can be
non-metallic
for reasons that have nothing to do with electron
localization.
For example the d band of some transition metal
69
compounds can be split by crystal field effects, and certain electron
configurations can
semiconductors.
give rise
to filled bands as in conventional
The band gaps in these compounds may sometimes
have a contribution from electron repulsion, but they are primarily
due to chemical bonding effects, similar to those treated by the
conventional band model.
3.2 Defect
Chemistry
The defect chemistry of the high Tc superconductors is similar
to other ceramic systems, involving intrinsic disorder, redox and
substitution reactions.
On the other hand, it is more complex given
of
nature
the multivalent
the Cu
ions
nonstoichiometry that they can accommodate.
defect models
which
depict
the large
and
oxygen
In this section the
the effect of the oxygen activity,
temperature, and dopant on the defect concentration in each system
will be presented.
These models are to predict and also to be tested
in relation to the electrical behaviors exhibited by the specimens
under the experimental conditions.
Before going into the individual
systems, we first consider the following reactions which apply to all
the systems:
(a). Intrinsic oxygen ion and electronic disorder:
O - + VO''
nil -+ e' + h*,
K,= [OI"[Vo*
(3.26)
K= n p
(3.27)
(b). Redox reactions:
Oox -+ 1/2 02 +
= n 2[Vo"P02/ 2
(3.28)
Ko = [Oi"]p2/p02 1/ 2
(3.29)
+ 2e', KR
1/2 02 -+ O" + 2h',
(c). Ionization of oxygen defects:
70
Vox
V 0 ' + e',
Kv 1 = [V 0 *]n/[Vox]
Kv 2 = [Vo**]n/[Vo*]
V0 * - V 0 9* + e',
0-
Oi-
K11 = [Oi']p/[Oi]
Oi' + h*,
Oi" + h',
3.2.1 La 2 .SrxCuO4.8
K 12 = [Oi"]p/I[Oi']
(LSCO)
The LSCO system is ideally suited for studying the effects of
dopants on the defect and transport properties given that it retains a
stable K2 NiF 4 structure over a wide compositional range (0.0 < x <
1.33) [Nguyen et al., 1981].
It is generally accepted that the initial
doping of Sr (x < 0.33 in 1 atm oxygen) is compensated by the
generation of electronic holes with the oxygen stoichiometry being
fixed at 4.0.
The substitution equation for the dopant can thus be
written as:
2SrLa' + CUCux + 2h' + 400x
CuO + 1/202 + 2SrO La2CuO4
(3.30)
Above that level, Sr is to be compensated by the oxygen vacancies
while the electron hole concentration remains rather constant. The
doping effect can thus expressed as the following equation:
2SrO + CuO
La2CuO4-
2Srta' + Cucux + 3 0ox + V 0 9*.
(3.31)
The charge neutrality equation in the general case is:
n + [SrLa'] + [Oi'l + 2 (Oi"] = p + [Vo*] + 2[V 0 **].
Theoretically we can solve all these equations analytically.
(3.32)
But for
the purpose of simplicity the last equation is usually approximated in
several regimes in which only certain reactions and defects are
dominant so that the above equations can be solved easily. In the
following the major defects will be solved in terms of equilibration
constants, oxygen partial pressure and dopant concentration.
71
oxidizing environment and a lightly doped
I: In a highly
Region
sample, the charge neutrality equation is approximated by:
(3.33)
2[Oi"]
p
so that
(3.34)
Sr',
)1/3[P021/6
p =
[0"] = (Ko/4)1/ 3P0 2 1/ 6 # f([SrLa'),
(3.35)
6
[Vo**] = KF/[Oi"] = KF(Ko/4)-1/3P02-1/ # f([SrLa']).
(3.36)
n = Ke/P = Ke(2KO)1/3pO 2-1/6 * f([SrLa'I)
(337)
II In
Region
a
atmosphere
oxidizing
moderately
and
moderate
doping level,
(3.38)
p = [SrLa'] * f(P 0 2 ),
[0f"] = KOP0 2 1/2/[SrLa']
(3.39)
2
[Vo**] = KF/[Oi"] = KF[SrLa'] 2/(KOP0
2
1/2).
(3.40)
(3.41)
n = Ke/p = Ke/[SrLa'] * f(PQ 2 ),
III In a relatively reducing atmosphere or when [SrLa'] is
Region
large,
2[Vo**] - [SrLa']
#
(3.42)
f(PO 2)
p = (KO[SrLa']/2KF) 1/2p0
2
(3.43)
1/ 4
f(P0 2)'
(3.44)
n = Ke/p = Ke(2KF/KO[SrLa']) 1/2p0 2-1/4
(3.45)
[0i"] = KF/[o**] = 2KF/[SrLa']
The P0
2
#
dependence of the major defect concentrations are plotted in
Fig. 3.2.1 [Opila and Tuller, 1990].
Association of the oxygen vacancy and the Sr substituent may
become important at high Sr levels, as evidenced by the ordering of
oxygen vacancies as observed by TEM [Nguyen, 1981].
One possible
reaction and mass action equation may be expressed by
2 SrLa'
+ Vo** -+ (SrLa')2VO'',
72
(3.46)
III
II
U
S
S
U
U;
a
Log (oxygen parttal pressure)
Fig. 3.2.1
Log (defect concentration) vs. log (Po 2 ) of La2-x.SrxCuO4.3
(after Opila and Tuller [1990]).
73
Kass = [S2V]/[SrLa'] 2 [Vo**]
(3.47)
where [S2V] is a short-hand form of [(SrLa')2VO**].
Assuming nearly
full association, i.e., 2[S2V] = [Sr]tot
[SrLa']
=
= (4[Sr]tot) 1/3 /Kass 1 / 3
*2[V*D]
(3.48)
The concentrations of the major defect in this system are plotted as a
function of the total Sr content in Fig. 3.2.2 [Opila, Tuller, Wuensch
and Maier, 1990].
3.2.2
Nd 2 .CeCuO
4 .3
Because of the multivalent nature of the Ce ion (3+
and 4+),
substitutional Ce on the Nd site can serve either as a donor or an
acceptor.
In the following we discuss both possibilities and solve the
defect concentrations
in terms of equilibrium constants and oxygen
partial pressure explicitly for regimes in which certain reactions and
defects are dominant as before.
(I) CeNdx as a donor (Nd2-xCex.y3+Cey
4+CUO48)
The ionization reaction and corresponding mass action equation
are
CeNdx -+ CeNd' + e',
(3.49)
KD = [CeNd n/[CeNdx]
(3.50)
and mass conservation requires:
[CeNd'] + [CeNd"I = [CeNdltotal = x-
(3.51)
The general charge neutrality equation is given by:
n + [Oi'] +2[Oi"] = p + [Vo*] + 2[Vo**] + [CeNd*].
(3.52)
Region I: For very low P0 2, n = [V 0 *] so that
n = [Vo*] = (KR/Kv2)/ 2 P02-1 4 ,
[Vo**] = Kv 2 ,
74
(3.53)
III
II
IV
U
S
S
N
m
0
Log [Srltotal
Fig. 3.2.2
Log (defect concentration) vs. log ([Srhtot) of La 2 .SrxCuO4.
5 (after Opila, Tuller. Wuensch and Maier (1990]).
75
[VoX]= (KR/Kv1Kv2)PO2- 2,
p = Ke/n = (Ke2KV2/KR) 1/2p02 1/4'
[Oi"l= K/Kv2,
[0') = (KOKF/Kv 2K122)1/2po
1 4
2 '
[Oi] = (KO/K11K12)P021/2,
[CeNdi = XKD/[KD + (KR/Kv 2 )1/2 po 2
4] '/
Region II: For low P0 2 , n = 2[Vo**] so that
n = 2[Vo**] = (2KR)1/ 3 P02-1/ 6 ,
(3.54)
[V 0 *] = (KR/4)1/3P02-1/6,
[Vo*] = (2KR2/3 /2Kv 2 )PO2-1/ 3,
[Vox] = (KRIKvIKv2)Po 2-1/2 ,
P = Ke/n = Ke/(2KR 1 /3)p0 2 1/6 ,
[Oi"]
[Oi']
KF(4/KR)l/3p021/ 6,
= 21/3KeKF/(KR 2/3 K12)P0 21/ 3,
[Oix] = (Ko/K 11 K 12)P? 21 / 2 ,
[CeNd ] = xKD/IKD + (2KR)1/3p02-1/6].
Region III: For intermediate P0 2 , n = [CeNd ] so that
2
n = [CeNd] = Y = ([KD(KD + 4x)] 1/ - KD}/2,
[Vo**] = (KR/y 2 )P02-1/ 2,
[VO*] = (KR/yKv2)PO2-1/ 2,
[Vox] = (KR/Kv 1 Kv2)Pa2-1 /2 ,
p = Ke/n - Ke/y,
[Oi"] = (KFy 2/KR)PO 2 1/ 2 ,
[Oi'] = (KeKFY/KRK12)P0
[Oix] =(Ko/KIIK
12 )Po2/
1 2
2 / ,
2.
Region IV: For high Pa 2 , 2[0"] - [CeNd'] So that
2[0j"] ~[CeNdi =
76
(3.55)
[Vo'']
=
2KF/y,
[Vol= (2KRKF/yKvl) 1/ 2 P021
[Vol]= (K/Kv1 Kv 2 )Po 2
49
,
(3.56)
n = (KRy/2KF)1/ 2Po 2 -1/4 ,
p = K/n = (2Ke 2KF/KRY)1/ 2PO2 1 /4
,
[Oi"]= y/2,
[Oi' = (Ke2KFy/2KRKIi 2)1/2p02 1/4
[Oix] = (Ko/K 1 1 KI2 )P0
The P0
2
1 2
/ .
dependence of each defect species is tabulated in Table 3.2.1
2
and plotted in Fig. 3.2.3.
(II) CeNd' as an acceptor (Nd 2 .xCex.y 3+Cey4 +CuO4+):
The ionization reaction and corresponding mass action equation are
CeNd
KA
=
-*
CeNdx
+
(3.57)
h',
(3.58)
[CeNdx]p/[CeNd])
and the mass conservation requires:
[CeNd'] + [CeNdxI = [CeNd total =
(3.59)
X.
The general charge neutrality equation will be:
n
+
[O'] +2[Oi"] = p
+
[Vo]
We can also separate the P 0
to low PO 2 for discussion.
2
+
2[Vo"]
+
(3.60)
[CeNd].
range into four regions from very high
Regions I and II are just mirror-symmetric
of the donor doping case; Region IV is exactly same as the donor
doping and
Region III: For [Oi']
[CeNd'] so that
[Oi'] = [CeNd*] = [Ko2pO2 +4KAxKoP021/2)1/2 - KOP0
2
1/ 2 }/2KA
= Y,
p = KAy/(x - y) (p m y when y << x),
(3.61)
n = Ke/p = Ke(x - y)/KAy,
(3.62)
77
Electron-
neutrality
2[01']=
n = [Vl n= 2[VoI n=[Ceial
P0 2 range very low
low
[Ce0al
high
interm.
n
-1/4
-1/6
0
-1/4
P
1/4
1/6
0
1/4
[Vo1
0
-1/6
-1/2
0
101"1
0
1/6
1/2
0
[Vo'J
-1/4
-1/3
-1/2
-1/4
1/4
1/3
1/2
1/4
[oil
[Vol
-1/2
-1/2
-1/2
-1/2
[Oi
1/2
1/2
1/2
1/2
[C 's]ll
Table 3.2.1
------
I------
0
I
Po 2 dependence of defect concentrations
,CeCuO 4.- system for Ce as a donor.
78
in Nd 2 -
II
n =2V6')
I
n = IV- ]
I
IV**0
-
-
-
IV
210 i'I = [Ce;d'
I
I
-
III
n = Ice Ndl = X
-
(_ =
1'
-
0
-
1
-
-
-
Vvc3]N-~
-i/
6m
-----------
Nd i
n
.1/2
-1/2
.
Log P02
Fig. 3.2.3
Log (defect concentration) vs. log (P 0 2) of Nd 2 .xCexCuO 4 .
for Ce as a donor.
79
[Oix] = yp/Kji = KAy 2 /KIl(x - y),
[Oi"I = [Oi'IK 12/p = (x - y)K12/KA (= const when y << x),
[Vo**] = KF/[Oi"] = KFKA/(x - y)K12 (= const when y << x),
[Vo*] = n[Vo**]/Kv 2 = KeKFKA/KL2KAyKV2,
[Vox] = n 2 [Vo'']/Kv 2Kvi= Ke 2KFKA(X - y)/KI 2 KA 2y 2KvIKv 2=KA(x
-
y)/Kvly 2 ,
[CeNdXI= X - y'
The P0
2
dependence of each defect in this case is plotted in Fig.
3.2.4.
3.2.3 YBa 2 TixCu 3 .,06+
For the Ti substitution on the Cu site two possible substitution
reactions can occur.
(i) Ionic compensation:
Y203 + 4BaO + 6TiO2 YBa2Cu306.5
2Yyx + 4 BaBax + 130ox
(3.63)
+ 6Ticu** + 60i"
If this reaction dominates then
(3.64)
[Oi"] = [Ticu''l * f(P0 2),
p = (Ko/[TicuO''l)"/2p0
(3.65)
14
2/ .
(ii) Electronic compensation:
4
Y203 + 4BaO + 6TiO 2 YBa2Cu3O6.54 2Yyx + BaBax + 130ox
+ 6Ticu** + 12e'
+
(3.66)
302-
If this reaction dominates then
n -2[Ticu''l
p
(3.67)
* R(PO2),
(3.68)
Ke/2[Ticu''I * f(PO2),
[Oi"] = 4KolTicufl 2P02/'2/Ke 2.
80
(3.69)
IV
21V6 I = ICe Nd
II
III
p =Nd
p = 210 '
Log P0
Fig. 3.2.4
P=
li)
2
Log (defect concentration) vs. log (P 0 2) of Nd 2-xCeCuO4 .s
for Ce as an acceptor.
Since this material
has a large intrinsic
oxygen
nonstoi-
chiometry, for low levels of doping the redox reaction may be
dominant in determining the carrier concentration as in the region I
in Fig.
3.2.2
where
the
hole and
oxygen
nonstoichiometry
is
independent of the dopant concentration.
All the defect models discribed above are based on dilute
solutions, in which the interaction between the defects is small or
negligible.
The interaction between defects can on one hand change
the mobility of the charge carrier and change the formation energy
of the defects.
not insignificant
For concentrated solutions where the interaction is
and the Henry's law breaks down, the activity
instead of concentration should be used in the mass action equations.
When there is an association of defects or formation of an ordered
structure due to heavy doping a different defect model pertaining to
that paticular defect association and structure should be used.
82
Chapter 4
Experimental
the procedures
In this chapter
characterization
properties
electrical
of
principles
and
procedures
of the
Details
presented.
for sample preparation
by
characterization
structure
and
phase
X-ray
by
for the
conductivity
thermoelectric power measurements are then illustrated.
are
and
Finally the
diffraction
and
transmission electron microscopy are discussed.
4.1
Sample
Preparation
The purpose of sample preparation is to ensure a product of
precise
and
composition
microstructure.
homogeneity
as
well
as
satisfactory
Simplicity in procedure and economy in time and
resources are the two other factors which may determine the proper
method in practice.
To achieve these goals we chose the following
two methods in this research.
4.1.1 Citric Solution
Method
through a modified Pechini solution
Powders were prepared
technique [Pechini, 19671.
In this method a proper amount of a
metal salt such as a nitrate (Y, La, and Nd) or carbonate (Sr or Ba) is
dissolved
in
distilled
water
at room
temperature.
Ammonium
hydroxide is added to precipitate the metal ions until the pH value
reaches 9-10.
After filtering and flushing with alcohol two or three
times to remove the ammonium and water, the precipitate is then
83
put into a solution of citric acid and ethylene glycol. After stirring
and heating to 70-80 0 C the solution becomes clear in a few hours.
Upon further heating, the metal ion remains in solution while the
acid and glycol react to form a polyester. The polyester is pyrolyzed
at 700 - 800 *C in an alumina crucible.
identified by XRD.
The residue phases are
Most metal ions form oxides except barium and
The actual concentration of the
strontium which form carbonates.
metal oxide or carbonate in the solution is thus calibrated by the
weight. La, Sr, Y, Ba, and Nd anions are prepared and assayed by this
method.
The Cu solution is made directly by dissolving the copper
nitrate into the citric and ethylene glycol solution.
This solution
method has the advantage of producing pure, homogeneous powder
with precise cation mole ratios.
It is also favorable for adding trace
amounts of dopants since the solution can be diluted to any extent as
needed.
This procedure proves to be a very effective way to produce a
Samples made from this route are
fine and homogeneous powder.
usually denser and stronger than from oxide-mixing. However when
La 2 -xSrxCuO4.8 samples were made by this method an increasing
amount of second phase La2 SrCu 2 0 6 with increasing Sr concentration
This problem was not found with the oxide-mixing
It is speculated that Sr carbonate precipitates out after
was observed.
method.
calcination which makes the sintering difficult especially for heavily
doped La2-xSrCuO4-8. Depletion of Sr from the nominal composition
La2-xSrCuO4.- then causes the phase separation.
4.1.2
Oxide-Mixing
Method
84
has
method
the solution
though
Even
its advantages,
the
powder obtained is no purer than the precursors and raw materials
since this method does not provide further purification. Further all
In the
nonvolatile impurities will concentrate in the final product.
mixed oxide
method,
oxide
stoichiometric
or carbonate
powders
containing the required cations were mixed directly to give - 10 gm
Mixing and grinding were performed in a plastic or glass jar
with a teflon bar in it. The bar is used as a grinder and mixer and is
total.
An intermittent
agitated by a stirrer for no less than 24 hours.
grinding
the
between
homogeneity
before
alumina crucible
calcination
two-stage
pressing.
was
to
Calcination was performed
in air overnight
ensure
in an
- 800 *C for
at temperatures
YBa 2 Cu 3 -x.Ti06+5.and 900-950 'C for La2 .xSrxCuO 4 -8 and Nd2 .
Tables 4.1.1.and 4.1.2 list all the chemicals used for the
xCeCuO4+..
processing.
Traditional
sintering
methods
applied to obtain the pellet specimens.
for
ceramic
materials
were
Powders weighing about 2.5
gm were uniaxially pressed at 5 Kpi to form disks of 3/4" diameter.
These disks were then coated with plastic wraps and put into a
plastic bag which was evacuated for isostatic pressing.
After being
pressed at 40 kpi isostatically the pellets were slightly polished on
the surfaces. Sintering was then performed for 12-16 hours in air or
flowing 02.
Samples were placed on Pt foil (La 2 -xSrCu04.8 and Nd2 .
CexCuO4+s) or on buffer powder of the same composition(YBa 2 Cu3.
xTix06+8) on alumina crucibles since the latter will react with Pt.
Sintering temperatures range from 930 *C (YBa 2Cu 3 -xTix06+a) to 1100
0C
(Nd 2-xCexCu0 4+) to 1150-1200 *C (La 2-xSrxCu04.5).
85
Chemical
Formula
Source
Purity (%)
Y-Nitrate
Y(N0 3)3-6H 20
Alfa Chemical
99.9%
Cu-Nitrate
Cu(N0 3) 2*3H20
Alfa Chemical
99.9%
La-Nitrate
La(N0 3 )3.6H 20
Fluka Chemie
99.99%
Nd-Nitrate
Nd(N0 3)3 .6H 20
Asar
99.9%
Sr-Carbonate
SrCO 3
Mallinckrodt
Reagent grade
Ba-Carbonate
BaCO 3
Mallinckrodt,
Reagent grade
Ethylene Glycol
C2 H60 2
Mallinckrodt,
Reagent grade
Citric Acid
Monohydrate
C 6H 80 7*H20
Mallinckrodt
Reagent grade
Ammonium
Hydroxide
NH 4OH
Mallinckrodt
Reagent grade
Table 4.1.1
Chemicals used for powder preparation by solutions.
86
-A
Chemical
Formula
Source
Purity (%)
Y-Oxide
Y20 3
Asar
99.9%
Cu-Oxide
CuO
Asar
99.9%
La-Oxide
La 203
REacton
99.99%
Nd-Oxide
Nd 203
As ar
99.9%
Sr-Carbonate
SrCO3
Mallinckrodt
Reagent grade
Ba-Carbonate
BaCO 3
Mallinckrodt
Reagent
Ce-Oxide
CeO2
Research Chem
99.99%
Ti-Oxide
TiO 2
Fluka Chemie
99%
Table 4.1.2
grade
Chemicals used for powder preparation by oxides.
87
The as-sintered pellets are all black in color, indicating that the
specimens are conductive.
Over-reduced YBa 2 Cu 3 06+3 samples show
green color as an indication of formation of a reduced second phase.
The density measured by the Archimedes method shows that they
are in the range of 85-95%
measure
the electrical
of the theoretical density.
properties
in situ,
particularly heat-treated after sintering.
the
samples
Since we
are not
All annealing is performed
in-situ in the measuring furnaces.
Sintered samples were stored in air and we observed that some
samples (especially those not isostatically pressed) became soft with
time and finally crumbled into powder.
Though the x-ray diffraction
patterns do not show a second phase, we believe that they are
attacked by the moisture or carbon dioxide in the atmosphere.
phenomenon
propensity
exposed
that
oxygen
deficient
The
La2-x Sr CuO 4.-8 shows a
to absorb moisture and become hydrolyzed when kept
in the ambient atmosphere
for a long
time has been
reported in the literature previously [Sreedhar and Ganguly, 1990].
It
seems
that
the
calcined
powders
of La2-xSrxCuO4.3
YBa 2 Cu 3 06+8 also absorb moisture from the air.
and
Pellets made from
these powders exposed to air for a long time are soft and weak.
Table 4.1.3 summarizes the compositions and the processing of
the samples made and studied in this research.
Two
of
the
samples
have
been
chemically
analyzed
by
inductively coupled plasma emission spectrometry.
Table 4.1.4 lists
the nominal compositions and the analyzed results.
It shows that our
samples are slightly cation deficient.
The implication of this cation
deficiency on the defect properties will be discussed in Chapter 6.
88
Composition (x)
0.00
0.05.0.10
0.15,0.18
Powder Preparation Sintering Conditions
C. S. and O. M.
1150*c, 02, 16hrs
0. M.
1 150*C, 02, 16hrs
0. M.
1150*C, 02, 16hrs
0.20.0.30
0.40,0.50
0.60,0.80
0.90, 1.00
0.00
NO
:
C. S. and 0. M.
1 100 0 C, air, 16hrs
0. M.
I 100*C, air, 16hrs
C. S. and O. M.
930*C, 0 2 , 16hrs
0 M.
930*C, 0 2 , 16hrs
0.01,005
0.10.0.15
0.20
0.00
0
S..
*i*
j-"
0.01.002
0.035.005
0.10
0. M Oxide-Mixng
C. S.: Citric Solution
Table 4.1.3
Compositions and processing
this research.
89
of the
samples made
in
Table 4.1.4
Nominal
Composition
La2CuO4
La
1.95
1 83
Sr
-----
0.14
La1.s5Sr.15
CuO4 .6
Cu
1.00
1.00
0
3.97
4.00
Compositions of Laz.xSrCuO 4. - (x= 0.0 and 0.15)
analyzed by inductively coupled plasma emission
spectrometry.
90
4.2
Property Measurements
Electrical
Bar shaped samples cut from pellets are used for conductivity
Grooves on all surfaces
power measurements.
and thermoelectric
were cut for easier winding of the electrodes.
Platinum was applied
by either sputtering or by painting (Englehard 6082) on the surfaces
Because of the
to ensure contact and reduce the electrode resistance.
conductive nature of these samples, contact is not a very serious
problem compared to semiconductors or insulators.
Ag instead of Pt
samples since they react with
paint was used for YBa 2 Cu 3.Ti,06+8
In some cases, after winding the electrodes, more conductive
the Pt.
The sample geometry
paint was applied to ensure better contact.
Because
was then measured for the calculation of the shape factor.
of the imperfectness of the sample shapes and electrode painting the
factors
shape
uncertainty
in
obtained
the
in
conductivity
would
way
this
The
data.
cause
greatest
the
calculation
of
the
For
uncertainty caused by the length measurements follows:
(4.1)
S ± AS = (w ± Aw) x (h ± Ah)/(l ± Al)
where S is the calculated shape factor; w is the width and h is the
height of the sample; I is the length between the two inner electrodes
Ax means the measurement error of x and
(4.2)
a ± Aa = 1/[(R ± AR) x (S ±AS)]
where
a
is the conductivity
and
R is the measured
resistance.
According to the principle of error propagation
Aw Ah Al AR
Aa
w
a
Taking
typical
h
values
I
(4.3)
R
of the length
errors say,
91
measurements
and
estimated
w ± Aw = h ± Ah = 0.20 ± 0.01 (cm) (5%),
1 ± Al = 0.40 ± 0.02 (cm) (5%),
and for a typical resistance and standard deviation
R ± AR = 1.00 ± 0.01 (ohm) (1%)
we obtain
a ± Aa = 10.0 ± 1.6 (s/cm).
So the uncertainty in log a will be
[log (10 + 1.6) - log (10 - 1.6)] = 0.14.
There
is
less
of a problem
comparing
under
the conductivity
different conditions for the same sample for obvious reasons.
when
the
comparison
is
made
between
different
samples
But
the
uncertainty in the shape factor has to be taken into account.
Both type K and type S thermocouple wires have been used for
temperature measurement and as electrodes.
No apparent difference
in the measurements of temperature, conductivity or thermoelectric
power were found.
In practice type K wires are stiffer and stronger
than type S of the same gauge making the contact more secure.
However they serve to more easily break fragile samples during
Type K thermocouples can also be used to
electrode
winding.
measure
temperatures
down
thermocouples become useless.
to
-200
*K
at
which
type
S
The vulnerability of type K wires to
oxidation shortens their useful life in oxidizing atmospheres at high
temperature.
The oxide formed on the wire surface also makes the
electrodes more and more resistive with time.
So even though type
K wire is much cheaper than type S wire, in most cases, type S wire
was used.
92
4.2.1
Conductivity
Conventional 4-probe dc conductivity measurements are used
to eliminate
voltages
(from
meter/voltage
-10
Stepwise positive
effects.
electrode
to
10
V)
generated
by
a
and negative
HP4140B
pA
source were applied to eliminate any complications
due to steady-state offset voltage and to nullify the thermoelectric
effect of the current during measurements.
Currents flowing through
the sample are maintained within mA ranges by an inserted resistor
Voltages were measured between
and measured by the HP4140B.
the inner electrodes by a Keithley
resistance > I GQ.
the I-V curves.
The resistances are calculated from the slopes of
A typical DC I-V curve is shown in Fig. 4.2.1.
standard deviations
contacts
181 multimeter with an input
are good.
The
are usually smaller than 1% as long as the
4-probe ac impedance measurements
with a
HP4192A LF Impedance Analyzer were used only in cases of more
resistive samples, where the grain boundary effect could be large, to
separate the contributions from the bulk and the grain boundary.
Use of a multi-sample holder illustrated in Fig. 4.2.2 enabled us to
take measurements of six samples nearly simultaneously under the
It is important to compare the properties of
same conditions.
different samples under the same conditions and thermal history.
With the multi-sample holder, the instruments were successively
switched to each sample through an ERB-24 (MetraByte) relay board
In the case of
controlled by an IBM AT personal computer.
measuring conductivity and tep simultaneously, the Pt wires of the
thermocouples at the two ends of the sample were also used as the
outer electrode
as shown in Fig. 4.2.3.
93
In this setup only one sample
~2
.01
%-o
-. 01 1
-
.
.
.
a
.
I
3
3
a
0040
.0 040
V (volt)
IW4140b and KISI DVM
C +-
1.0 C
Fig. 4.2.1
NCU-0 annealed at SOOC
799.9
15:15:39 08-29-89 Ra 3.707e-01 +- 3.89o-04
Typical
I-V
measurement.
curve
of
4-probe
DC
conductivity
=~2
6-bore A1 2 0 3 tube
PI
weies
"b.I ISyjI
6,
a1
4.
\I
()
4
1.11
11 JI4.
Ie
111iisb
A\
___~::i
11:1 1
5 I-'
pI
~
I ii
()
O
NINE-_
ii.
e
tilw
Fig. 4.2.2
_
Configuration of multi-sample holder.
can be measured at a time.
Thermoelectric
4.2.2
Power
Thermoelectric power is calculated from the voltage (AV) and
difference
temperature
(AT) measured between two electrodes by
the following equation:
Q=
- AV/AT + QR
(4.4)
Both type S
where QR is the thermoelectric power of the electrodes.
and type K thermocouples have been used and the results are very
In order to measure tep and conductivity simultaneously
consistent.
The e.m.f. of
a sample holder shown as in Fig. 4.2.3 was designed.
the
were
thermocouples
by
read
multimeters
(Keithley
181
Nanovoltmeter and Keithley 196 Digital Multimeter) and converted
through a formula which
to temperatures
is obtained by curveThe temperature
fitting of the published data [NBS, Monograph 125].
gradients
for
are
measurement
this
generated
by either of the
following methods.
4.2.2.1
In
Heat-Pulse
essence
this
Technique
a thermal
consists of generating
method
gradient along a bar of the sample for a short period and measuring
the resultant e.m.f.
A heat pulse is applied by a separate small
heater in the form of a platinum coil placed next to the sample to
create
the
measurement,
desired
current
temperature
at the
Just
before
the
(= I amp) is allowed to flow through the
heater for a certain duration
temperatures
gradient.
to generate the heat pulse.
electrodes
96
and the sample
emf
The
are then
'I
&
Pt wire
Pt + 10% Rh wire
Gas out
Sample
A --A
grove
A
(as
Sample
heater
in
A1,2 0 3 tube
Pt and Pt /I ORh wires
A/
Quartz tube
....
....
......
I Ig. 4.2.3
Configuration
of
sample
holder
conductivity and thermoelectric power.
for
measuring
measured and recorded continuously as the heat pulse fades away.
The Seebeck coefficient of the lead wire (type S or type K ), is
subtracted from the values calculated from the slopes of curves in
AV vs. AT plots to obtain the absolute thermoelectric power of the
sample.
A typical AV vs. AT plot is shown in Fig. 4.2.4.
always
a
time
lag
temperature change.
the
between
heat
pulse
and
There is
the
sample
Due to the varying response speed of the
sample to the heat pulse in different temperature ranges, the heating
and cooling periods of the sample are not the same and vary with
temperature.
A hysteresis always exists in the curve.
For the
purpose of consistency only the cooling (relaxation) part of the curve
is used for the calculation
since the heating period is always
relatively short.
4.2.2.2
Constant
Temperature
Gradient Technique
In this arrangement, the temperature difference is provided by
the
natural
temperature
gradient
in
the
furnace.
Since
the
temperature gradient changes with the average temperature of the
sample the relative position of the sample and furnace were shifted
to keep the temperature difference smaller than 10 *C. Hodge [1980]
has proved that in the case that the ionic mobility is small the tep is
independent of the temperature gradient and the derived tep should
be
same as that derived from the
heat pulse technique.
Consistent
data within ±10 p.V/K have been obtained by both methods in most
cases as shown in Fig. 4.2.5 (note expended scale) in which the
thermoelectric power of LaSrCuO4.- is measured as a function of
temperature.
98
~~1
I
1291.6
-
2391.1
A
p
A
A
A
A
A
13.5
10.0
6 .5-
AT
648.6 C +- 1.4 C 06: O9 12 01-12-69
0O-136.69 +-5.20 microV/K 1s15210
LSU-0 cooled in 02
Iig. 4.2.4
Typical
AV vs. AT curve
thermoelectric
power
by heat-pulse
technique
for
measurement
fi
To test how the temperature
in
which
constant average
the tep and conductivity were
measured at
temperature
with varying
temperature
the
an experiment on LaSrCuO 4. 8 was
measured tep and conductivity
conducted
affects
gradient actually
gradients.
This was performed by shifting the relative positions of the sample
and the furnace
while keeping the average temperature
constant.
We found the conductivity to be consistent throughout the whole
The result of thermoelectric power is
temperature gradient range.
shown in Fig. 4.2.6. Q remains a constant with AT as long as AT is
larger than a certain value (two to four degrees depending on the
It seems that when the AT is smaller than a
temperature range).
certain value, the fluctuation in the temperature reading will induce
a relatively large uncertainty (SAT) in AT so that the calculated Q is
It is this reason that the temperature gradients are
always kept above 3 0C or only tep's evaluated at temperature
less reliable.
gradient larger than 3 0 C were used.
With
the
constant
temperature
gradient
method,
the
temperature gradient induces a chemical gradient of each component
ion. This chemical gradient is independent of time and will induce a
concentration
gradient
in
ions.
the
The
thermoelectric
power
measured by this method thus includes both the electronic and ionic
part. By heat pulse technique, on the other hand, the ionic part is
reduced because the mobility of the ions is much slower than that of
In the time span of the heat pulse and
the electronic charges.
measurement (tens
insignificant.
the transport of ions should be
of seconds)
Judging from the similar results obtained from both
methods, we can
conclude that
the ionic tep in these
100
materials is a
100
80
0
60
;14
40
20-
00
Temp. (C)
Fig. 4.2.5
Thermoelectric power of LaSrCuO 4 .8 vs. 1000/T in oxygen
measured by both constant temperature gradient and
heat-pulse methods.
101
400
-
.
.
5-
.
.
.
W
.
.
.
W
-
LaSrCu0 4 in iN O
320
0
-- 240
1000C
GE..
.....
Mooo900C
850C
160
s0
0
OC
++++
---
6I
F
9
800c
15
delta T (C)
Fig. 4.2.6
Thermoelectric power vs. temperature gradient
LaSrCuO 4 .8 at constant average temperatures in oxygen.
102
minor component of the total tep.
One
of the difficulties of measuring
tep is to ensure the
accuracy of the temperature readings of the sample.
reliability of the electrode contact.
The other is
The latter alone can be easily
overcome just like the regular conductivity measurement.
But in
order to measure the temperature and voltage at the same spot the
electrode
has to contact the thermocouple on the sample.
The
simplest way to do this is to use one of the thermocouple wires as
the electrode.
As long as the thermocouple is attached to the sample,
the electrode
is also attached
at the same spot.
Usually
the
thermocouples are welded at the tip and then wound by a separate
wire to the sample.
This often leads to a poor point contact because
of the spherical bead shape at the tip.
After several refinements a
much more simple and secure contact was designed as shown in Fig.
4.2.3.
Grooves are cut into the sample of depth and width about the
size of the wires.
The two wires of the thermocouple are wound onto
the sample at the groove and twisted at both ends.
The bundle is
made as small as possible so that the last contact of the two wires is
close to the sample surface.
The advantage of this method is clearly
seen: no welding is necessary, line contact of the electrode around
the specimen and more precise sample temperature measurement.
4.2.2.3 Thermoelectric
Power of Pt
Even though we are confident with the quality of the tep data
(in terms of reproducibility) few tep data exist in order for these
materials in the literature which we can compare with to verify their
accuracy.
The exact configuration of the sample holder was therefore
103
used
of
tep
the
measure
to
in
wire
Pt
of
function
as
air
temperature
Fig.
and compared with published data [Cusack and Kendall, 1958].
4.2.7 shows that our data and the published data are almost identical
over
part
major
the
of
the
indicating
range
temperature
the
reliability of our data.
4.2.3
Measurement
and
temperature
of
schedules
composition,
P0 2 besides
measurements
usually
are
properties
electrical
the
Since
Strategy
were
used
functions
the following
during
the
of
three
automatic
measurements to separate the individual effects:
4.2.3.1
Isothermal
Measurements
Annealing
were taken in various P0
2
ranges at constant
temperature.
Gases were changed only after the properties reached
equilibration.
The oxygen partial pressure was controlled by flowing
pre-mixed 02/Ar gas mixtures (from Matheson and Airco).
Various
ratios of the mixtures ranging from 100% to 100ppm of oxygen were
The actual oxygen partial pressure was monitored by flowing
used.
the gas through a ZrO2 cell in a separate furnace.
The ratios of the
By the
pre-mixed gases were thereby found to be very reliable.
isothermal measurements we are able to determine the P0 2 dependence of the conductivity and tep.
These relationships are critical for
confirmation of defect models as described in Chapter 3.
4.2.3.2
Isobaric
Measurements
Cooling:
were
taken
104
during
cooling
or heating in a
A
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-26
0.2
0.4
D
Fig. 4.2.7
0.6
0.8
(Thousands)
temp. (C)
meosured
Thermoelectric power of Pt vs. temperature.
Usually data taken from the cooling
constant oxygen atmosphere.
cycle are used unless otherwise mentioned. Stepwise cooling (25 or
50 *C step change per hour or several hours) were used to ensure
sample equilibration at least at high temperatures.
temperature
For some low
(~ -200 - 25 *C) the sample holder is
measurements
Temperature variations arise from
submerged into liquid nitrogen.
the relative position of the sample and the liquid nitrogen level and
were monitored
measurements,
by a type
K thermocouple.
From the isobaric
the temperature dependence of the conductivity and
tep is obtained and the activation energy of each property can be
calculated.
4.2.3.3
Cooling:
Fixed-Composition
During the usual isobaric cooling or heating, redox reactions
proceed at higher temperatures because of the change of the oxygen
activity with temperature.
The oxygen stoichiometry and the carrier
concentration in the material change accordingly.
If the oxidation
reaction is exothermic as in the general case, cooling will result in an
uptake of oxygen from the environment (see Chapter 6).
However if
the sample is isolated from the environment at the beginning of the
cooling process, this reaction will be prohibited and the oxygen
stoichiometry of the sample will remain constant.
can separate the ionization
reactions
By this method we
from redox reactions.
In
practice the samples were annealed at high temperature in reducing
atmospheres (0.1 %, 350ppm and lOOppm 02) for equilibrium and
then cooled with the valves of the sample holder closed.
The seals of
the apparatus were checked by submerging the sample holder into
106
water while pressurizing the sample chamber.
of
period
24
hours
or
sample
the
longer
After cooling for a
became
holder
partially
evacuated so that when it was opened a sucking sound could be
heard, indicating that the seals were good and there was little or no
oxygen exchange
between
the sample chamber and the ambient
Caution was taken to ensure that the sample holder
atmosphere.
contained as little oxygen as possible before cooling.
The sample was
kept stabilized in a reducing atmosphere and the volume of the
sample chamber was minimized to (= 15 c.c.) and a buffer sample
The maximum change of oxygen
was placed next to the test sample.
stoichiometry (A~max) of the sample (Nd 2 -xCeCu04+s) in this way is
calculated to be no more than 6.3
x
10-4 for 0.1% 02 and 6.3
x
10-5
for 1OOppm 02 (compared to the regular value of S > 0.01) if all the
oxygen molecules in the sample chamber go into the sample during
cooling.
4.3
4.3.1
Structural
X-Ray
and
characterizations
phase
Diffraction
Powder X-ray diffraction with Cu radiation was used for phase
identification.
The pyrolized citrate solutions of Y, Cu, La, and Nd
were identified as pure oxides (Y2 0 3 , CuO , La2 0
3
and Nd 2 0 3 ). The
pyrolized citrate solutions of Sr and Ba were SrCO3 and BaCO 3 Sintered
pellets
were
into
ground
powders
and
measured.
Diffraction patterns of the most highly doped samples of each system
are shown in Figs. 4.3.1-4.3.3.
It was found that La2-xSrXCuO4.6
samples are isomorphous with K2 NiF 4 and Nd 2 .xCexCuO4+4 samples
have the same structure as Nd2 Cu0 4 +8 . No apparent second phases
107
were found in these samples.
This is expected since the dopant
concentrations
solubility
are within
the
literature [Huang et al., 1989].
limits reported
in
the
However we do not exclude the
possibility that a small fraction of second phase might exist that is
No data on the solubility of Ti on
beyond the XRD resolution.
According to the XRD results of this
YBa 2 Cu 3 0 6+8.has been reported.
study, it is greater than 10% mo.
4.3.2
Electron
The
Microscopy
morphology
and
microstructure
examined by the electron microscopy.
micrographs
of
the
calcined
of the
samples
were
Figs. 4.3.4 shows the SEM
powders
of
LaSrCuO4.s(a)
and
Nd 2 CuO 4 , 8 (b) made by oxide-mixing and citric solution methods
respectively.
Generally the particles of the powder made by the
solution method are finer (= 0.5 microns) and more uniform in size
and shape.
Figs. 4.3.5 a and b are the TEM images of the as-sintered
It can be seen that
La 1 .82 Sro. 18 Cu0 4.s(a) and LaSrCu0 4 .8(b) samples.
the grain size of both samples is of the order of 1 micron, not much
No inclusions or
different from the particle size of the powders.
precipitates were found in either sample.
series of micrographs of a La 2 C u 04
between 300 - 350 *C in
Figs 4.3.6a - 6d are a
sample which
a hot stage in the TEM.
microtwinning is clearly seen by these in-situ images.
was heated
The evolution of
The twinning
forms and grows into the matrix as the temperature decreases.
difficult to identify the tetragonal-orthorhombic
electron diffraction
lattice constants.
It is
transition from the
patterns because of the small change in the
Nevertheless
the twinning is characteristic of the
108
20
30
40
50
60
50
60
20 (degrees)
(a)
20
30
40
29 (egrees)
(b)
Figs. 4.3.1
X-ray diffraction patterns of LaSrCuO 4 .8(a), and La 2CuO 4.
b(b).
20
30
40
20 (degrees)
50
60
50
60
(a)
20
30
40
20 (degrees)
(b)
Figs. 4.3.2 X-ray diffraction patterns of Nd 3 gCeo.2CuO 4 .6(a), and
Nd 2CuO 4 .6(b).
U-
20
30
40
50
60
20 (degrees)
(a)
30
20
40
50
20 (degrees)
(b)
Figs. 4.3.3
X-ray diffraction patterns of YBa 2Cu 2 .9 Tio. 106+8(a), and
Y Ba2Cu 30 6 +6(b).
60
(a)
(b)
Fig. 4.3.4
SEM micrographs of the calcined powders of LaSrCuO 4 .6
(a) and Nd2CuO 448 (b).
112
(a)
(b)
Fig. 4.3.5
Im
I Lm
TEM images of the as-sintered Lat.8 2 Sro. 1 sCuOs4- (a) and
LaSrCuO 4 -8 (b) samples.
113
(a)
(c)
(b)
1pam
Figs. 4.3.6 TEM images of La 2CuO 4.6 taken in-situ at (a)348 'C, (b)340
*C, (c)320 *C, and (d)300 "C.
orthorhombic phase and the formation of twinning does provide an
This structural transition is
indirect evidence of such transition.
related to a small anomaly in the conductivity at that temperature
The kinetics of the transition and growth of twinning is very
fast, occurring even when the sample is cooled through the transition
The high transition temperature observed here (- 590
in minutes.
range.
*K) compared to that reported in the literature (for example 530 *K
by Longo and Raccah [1973]) is probably due to the lower oxygen
content in the specimen when examined in high vacuum (< 10-7 tort)
in the TEM chamber.
Possibly the onset of the transition happens at
a lower temperature before the twinning is observed.
In accompanying research on the La 2 -xSrxCuO4.8 system with
our research group, valuable and unique data have been obtained
regarding the oxygen stoichiometry by thermogravimetric analysis.
This information is critical in providing a quantitative description of
the ionic defect density as functions of temperature, oxygen partial
pressure and dopant concentration.
Some of this data will be
combined with the transport properties in our later discussion of the
defect properties.
115
Chapter 5
Results
In
chapter
this
for
separately
presented
are
measurements
electrical
from
results
experimental
each
system.
Comparison with published data is made when they are available.
The general implications of individual features of each system are
also investigated.
5.1 La2.xSrxCuO4-
system
For the purpose of clarity, the results for La 2 -xSrxCuO
4
are
presented in three compositional regions: the end members of the
solid solution (x = 0 and x = 1) and the compositions in between (0 < x
<1).
5.1.1 La2CuO4
The electrical resistivity of this composition was first measured
with temperature,
the resistivity
In Fig. 5.1.1
isobarically.
of
La2CuO4 is plotted vs. temperature for P0 2 's ranging from 1 atm to
10-4 atm.
For the most part, resistivity increases slightly with
temperature as is typical for metals.
even
though the resistivity
surprisingly,
dependence
the
on
resistivity
PO
2.
It is interesting to note that
shows little temperature dependence,
does
It becomes
show
a
reasonably
more resistive
atmosphere typical of a p-type semiconductor.
usually reasonably fast and the
resistivity
116
reaches
strong
in reducing
The kinetics are
its
equilibration
0.5
0.4
La 1 CuO, 7 c ooled
in various PO,'s
00oCe 10*
3OMMOD
at=
10"" atm
10-4 atm
10-6 atm
10
atm
00..
C
0 3
0.2
hk~...
0.1
-
I-
mm.
-
~).4-~* SC
0.0
z
=z
e
eme-e-9e ee2
G
*6-~OoOQQ
~ffi
200
*u- --a
IhSU.,.U~iI*
--
L
400
600
800
1000
Temp. (C)
Fig. 5.1.1
Resistivity of La2CuO 4. 8 vs. temperature in various Po 2 's.
1 17
But the
value in less an hour when the gas is changed at 800 *C.
kinetics become
atmosphere so that different
slower in reducing
cooling rates usually end up with different R-T curves in 100 ppm
02.
Even
though
is not
resistivity
the
a strong
function
of
temperature, a few small kinks exist in the resistivity curves. These
kinks occur at different temperatures in different heating and
cooling
cycles
and
samples
for different
changes
microstructural
they
are
These features may be due to
prepared under the same conditions.
some
even when
(structural
twinning
transition,
formation and grain size effect) occurring during heating or cooling.
It has been shown that a structural transition from tetragonal to
orthorhombic phase occurs at = 500 - 550 *K as it is cooled down.
This structural transition is always accompanied with the formation
of twinning (Figs. 4.3.6a - d).
However, the absolute values of
resistivity all fall within a small range.
Considering the uncertainty
of the shape factors of the samples, they are not very significant.
We
conclude that the microstructural changes have a only minor effect
on transport properties in the normal state.
Fig. 5.1.2 is the resistivity of another La 2 Cu04.8
temperature
ranges
orthorhombic-tetragonal
The
of
antiferromagnetic
transition
and
transition reported in the literature are also
There are some slope changes of resistivity above room
shown.
temperature.
But basically the resistivity increases linearly with
temperature as a metal.
phase
*C.
of temperature down to -176
measured as a function
sample
or
The different slopes may be associated with
microstructural
change as
118
mentioned
before.
At high
0.05
-
0 0.04
C
n0.03-
No
0.02 ±
-200
0
200
400
600
Temp. (C)
Fig. 5.1.2
800
1000
Resistivity of La 2CuO 4.6 vs. temperature cooled in 1 atm
02.
119
temperature (T > 600 'C) where redox reaction accompanied with the
temperature
variation may play a role in determine the carrier
density the resistivity shows a different slope.
It is clearly seen that
a transition from metal to semiconductor occurs at = 170 *K.
the resistivity increases
this temperature
rapidly
Below
with decreasing
This transition can be related to the antiferromagnetic
temperature.
transition reported in the literature [Guo et al., 1988; Johnston et al.,
1988] of this composition and will be discussed later in the next
Fig. 5.1.3 shows the thermoelectric power measured in the
chapter.
The values are positive for the entire
range.
same temperature
temperature range, indicating p-type conduction.
200 *C are nearly constant at - 70 - 80 gV/*K.
The values above
This value is smaller
iV/K) reported by Ganguly and Rao [1973] and
than that (= 250
Our sample was cooled in oxygen so that it had
Nguyen et al. [19831.
a higher oxygen content and hole concentration and thus has smaller
resistivity and tep values.
Below 200 *C the tep increases rapidly
with decreasing temperature,
implying a rapid decrease in carrier
density with decreasing temperature as for a semiconductor.
Fig. 5.1.4 shows conductivity and thermoelectric power data of
La2CuO4.3 measured isothermally over the P0
10-4
atm.
In
this
figure
log
2
range from 1 atm to
(conductivity)
and
thermoelectric power are plotted together vs. log (P0 2 ).
of the
slopes
thermoelectric
material.
both
the
activated.
conductivity
power
both
curves
indicate
and
the
p-type
reduced
The positive
positive
conduction
values
in
of
this
The overlapping of the isotherms is another indication that
carrier
concentration
and
mobility
are not
thermally
It is also found that log (a) " log (P0 2)1/ 6 and - eQ/2.3k 120
220
LaCu04
180
in 02
0
.2140
T-0 Trans.
a'
100
Neel Trans.
80
1000
-I
Temp. (C)
Fig. 5.1.3
Thermoelectric
atm 0,.
power of La2CuO 4.5 vs. temperature in I
121
2.0
I
I
I
I
2.0
I
La2 Cu04
1.0
1.0 Cb
0.0
slope = 1/6
0.0
40-1.0
0
-1.0g
++++e
-2.0
-~~
-
950 C
00
0~~
C
850
C
-
-2.00(a,
+-+-+800 C
-3.0
1
-=5.0
I
-4.0
I
-3.0
Log
Fig. 5.1.4
I
-2.0
P0 2
I
-1.0
I
0.0
'-3.0
1. 0
(atm)
Log (a) and normalized thermoelectric power of La 2 CuO 4.3
vs. log(PO 2 ) at various temperatures.
122
log (P0 2 )1/ 6 .
Since the thermoelectric power is usually a function of
carrier density only, it implies that the mobility is independent of
oxygen partial pressure and the change in the conductivity with P0 2
is due to the change in carrier concentration.
The relationship
between conductivity and thermoelectric power is further shown in
Fig. 5.1.5 in which a portion of a Jonker pear with slope of minus one
is clearly seen.
The intercept of log (a)
at thermoelectric
power
(eQ/2.3k) = 0 is = 1.7.
5.1.2 La 2 .SrxCuO
4.8
(0 < x < 1)
Fig. 5.1.6 shows the conductivity of La 2 -xSrCuO4 .8 for 0
0.3 measured with temperature in pure oxygen.
s
x
All compositions
show metal-like behavior i.e. the resistivity increases slightly with
temperature.
It also shows a monotonic increase of conductivity
with Sr concentration.
The increase in conductivity is believed to be
due to the increasing hole concentration accompanied with doping.
The mobilities of charge carrier calculated at 800 *C in oxygen are
about 1.1, 1.5, 1.1 and 1.2 cm 2 /Vsec for x = 0.05, 0.10, 0.15 and 0.20
respectively, assuming complete hole compensation of Sr.
carrier concentration
Since the
is fixed by the dopant in this compositional
range it is expected that the conductivity is not a strong function of
oxygen partial pressure and this is shown in Fig. 5.1.7, in which the
conductivity is plotted vs. P0 2 . This P0 2 independence of conductivity
in Sr-doped compositions serves as a strong contrast to that of x = 0.
The resistivity of La1 .85 Sr 15CuO 4 is shown in Fig. 5.1.8 as a
function of temperature in various Po 2 's to exemplify the properties
in this
composition range.
It
is
123
seen that
the
resistivity
increases
2.0
01.5
0
er4
S1.0
C\2
0.
0.0
Fig. 5.1.5
0.5
1.0
1.5
2.0
Log a (S/cm)
Normalized thermoelectric power of La 2CuO 4 -8 vs. log (a)
at various temperatures.
124
800 800
a I
600800
3.5
400 300
200
400 300
200
100
50 'C
50 C
9: e-0
0
100
~ Laa--.Sr.Cu04.,7
1 atm O2
3.0 -in
~2.5
2.0
b
1.5
0
ep
0
j~g~pOOO
1.0
eee
~ 3eeee
-*Awaree
0.5
0.00
0.05
0.10
0.15
0.20
0.30
0.0
0.4
i
Fig. 5.1.6
1.0
1.4
I
1.8
I
2.2
I
2.8
I
3.0
3.4
1000 /T (K~')
Log (a) of La., SrxCuO4.8
various x's (0.0 s x s 0.3).
125
VS.
1000/T in 1 atm 02 for
3.0
La2.- SrCu0 4...7
I-.
S2.0
A
ii
0
0
'-4
1.0
GeeeO X=0.0
Mese
x=0.05
AAAAA x=0.1
M44"
x=0.15
+++++ x=0.2
x+++(*x x=0.3
0.0
-5 .0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
Log Pa (atm)
Fig. 5.1.7
Log (a) vs. log(Po 2 ) of La2 -xSrCuO4-8 at 800 *C for various
x's (0.0 s x 0.3).
126
0.010
La. 5 Sro.j
5 Cu
y
4..
0.008
0.004 -
0.002 -
0.00
-
e++e1 atm OS
--
0.000 0
200
400
*--100
600
ppm
800
0-
1000
Temp. (C)
Fig. 5.1.8
Resistivity of Lai.
various Pos.
8 5 Sro. 1 5 CuO4.3
127
vs. temperature
for
t
linearly with temperature as a metal and is almost independent of
P02. Even though the highest Tc of this system occurs near this
composition, no special behavior in terms of conductivity of this
composition was observed.
When further increases in x, the conductivity decreases with x
as shown in Fig. 5.1.9 in which the conductivity is plotted vs l/T in
pure oxygen as before for comparison.
In this range (0.4
gradual change in slope is observed as x increases.
obvious temperature
regimes.
s x s 1.0) a
There are two
At high temperatures the slope of
conductivity (positive) with respect to l/T increase with increasing x.
At low temperatures the conductivity is relatively insensitive
to
from positive
to
temperature
but
the
slope
changes
gradually
negative with increasing x.
Combining the conductivity data of Fig. 5.1.6 and Fig. 5.1.9 and
plotting it vs. x, we obtain Fig. 5.1.10 in which the conductivities
under the same equilibration conductions (800 *C in 02) of all
compositions are compared.
It is clearly seen that the conductivity
reaches a broad maximum at 0.3 < x < 0.4.
This is consistent with the
data by Nguyen et al. [19831 although their data were based on room
temperature
measurements.
The PO 2 dependence of conductivity in this compositional range
is shown in Figs. 5.1.11 a-f.
An increasing P0
2
dependence is found
with x in contrast to the almost P0 2 -independence for 0.05
s x s 0.3
For x = 0.90 and 1.00 the conductivity follows a nearly
P0 2 1/4 power law (Figs. 5.1.lle and f). There is also an indication of
the beginning of a transition from p to n type conduction at high
in Fig. 5.1.7.
temperatures and low Po 2 's for these
128
two compositions.
The gradual
*c'
fjoll
lbrill
(tO
NrJQ tbQo
3.5
52.5
b
0
- 1.5
keeee
x
=
0.4
eeex =0.5
x= 0.8
+++x =0.8
*w4wx
= 0.9
++++.x = 1.0
0.50.6
Fig. 5.1.9
I
1.0
1.4
I I -
2.) 3.0
1000 /T (K ~ )m
2.2
1.8
3.4
Log (a) of La2 .,SrCuO4.s vs. 1000/T in 1 atm 02 for
various x's (0.4 5 x 5 1.0).
129
3.0
2.5
b2.0-0
0o-1.5
0.
.4
0.
0.
1.0
Sr concentration (x)
Fig. 5.1.10 Log (a) of La1.,SrCu0 4 .8 vs. x at 800 *C in 1 atm 02.
130
3.0
Laj.
1 Sr.4Cu04.y
.5
b
0
0-2.0
slope
1/4
a~os900
C
850 C
--++++ 800 C
750 C
700 C
15I
-5
-4.0
-3.0
-2.0
Log P0
2
f
-1.0
0.0
1.0
(atm)
Fig. 5.1.11 (a)
Fig. 5.1.11
Log (c7) of Laz.xSrxCu O 4- vs. log(Po 2 ) at various
temperatures for (a) x = 0.4, (b) x = 0.5, (c) x = 0.6, (d) x =
0.8, (e) x = 0.9, and (f) x = 1.0.
131
2.5
La..Sr.5 Cu04-,
2.0 -
slope = 1/4
0
4 1.5
moo-
50
4.0
-0
1.geg_de
_4
-2.0
_d~o
++
850 C
-+++
+++++
800 C
750 C
*-W
700
-1.0
_il
Log P0 2 (atm)
Fig. 5.1.11 (b)
132
900 C
0.0
~1.0l
C
1.
MEMEM
2.5
1
,
1
1
i
La1 .4Sr.6CuO4.
S2.0 -
b
0
01.5
slope = 1/4
a-~ee
900 C
+++
850 C
A-1--++
--
1.2.0
-4.0
-3.0
-2.G
*--
-1.0
Log P0 2 (atm)
Fig. 5.1.11 (c)
133
800 C
750 C
700
0.0
C
1.0
2.2
La1 .aSr.aCuO4..
1.2 -
slope
=1/4
13e8wa.e
slop
900
850 C
1 C~ 1/
0-++++ 800
++++i+ 750 C
0700
-4.0
-3.0
-2.0
-1.0
Log P0 2 (atm)
Fig. 5.1.11 (d)
134
C
C
0.
1.
2.0
Lal.1Sr.9 CuO4..
#.OM
$1.5
%*MO
slope = 1/4
0
0
-I
-4.0
-
-1.)
-3.0
Log P02 (atm)
Fig. 5.1.11 (e)
135
4
900
850
800
750
700
U.U
A
t.U
mommm
1.5
-LaSrCuO4,,
b
slope = 1/4
90.5
e~~e900
a~en850
-
0.0 5.
-4.0
-800
-3.0
C
+++++
750 C
*-
700 C
-2.0
-1.0
Log P0 2 (atm)
Fig. 5.1.11 (f)
136
C
C
0.0
-
.
change of the P 0
2
dependence is better seen in Figs. 5.1.12 a-c, in
which the conductivity of each composition is plotted vs. log(P 0 2 ) at
different
temperatures.
Table 5.1.1
conductivity
summarizes
measured
in
the activation energies (AE) in eV of
I
atm
02 and the PO 2 power
law
dependence (n) of conductivity at 800 'C (a - (P 0 2)n) of La 2 -xSrCu0 4.
8 for the entire x range (0
5.1.3
x
1.0).
LaSrCuO 4 .8
This composition was studied in more detail.
Fig. 5.1.13 shows
the conductivity of this composition as a function of 1/T in 100%, 1%
and 350 ppm oxygen atmospheres.
0 C/hour).
rate (25
The conductivity
All runs were cooled at the same
was found initially to increase
with decreasing temperature (in constant Po,) down to - 400 - 500
C followed by a change of sign in slope so that the conductivity
decreases slightly with decreasing temperature at low temperatures.
The almost identical shape of the cooling curves in various P0
2
seems
to exclude the possibility that the mobility is a strong function of Po2The maximum conductivity of each cooling curve decreases from 35
to 12 and to 3.5 S/cm as the P0 , is reduced from 1 to 10-2 and to 103.5 atm.
The activation energies for conduction at high temperature
-0.31,
are
-0.29, and -0.23 eV respectively.
The decrease in
energies may be due to the slower kinetics of the redox reaction in
reducing
atmospheres.
The activation energies at lower temperatures are small and
positive.
increase
Although relatively small, the activation energies tend to
with
decreasing
oxygen
137
partial
pressure.
At
low
3.0
I
I
I
Lail -Sr 1Cu04.. at 700 C
2.0
b
0
x=0.4
-
x=0.5
x=0.8
x=o.8
X=0.9
X=1.0
0.0L
-5.0
-4.0
-3.0
-2.0
-1.0
Log PO (atm)
0.0
1.0
Fig. 5.1.12 (a)
Fig. 5.1.12 Log (a) vs. log(Po 2) of La2-xSrxCuO4. for various x's (0.4 S
x s 1.0) at (a) 700 *C, (b) at 80V3C and (c) 900 *C.
138
3.0
La2.. Sr.Cu0 4.., at 800
2.0
b
to
0- 1.0
ee"
Seeee
x=0.4
X=0.5
x=0.8
x=0.8
x=0.9
X=1.0
0.0 '
-5.0
-4.0
-3.0
-2.0
-1.0
Log POa (atm)
Fig. 5.1.12 (b)
139
0.0
1.0
3.0
.
La2a-Sr.CuO4.., at 900
02.0
0
0
x=0.4
Gesee x=0.5
3*0+0
x=0.8
x=0.8
x=0.9
x=1.0
0.0'
-5 .0
I
-4.0
I
I
-3.0
-2.0
I
-1.0
Log P02 (atm)
Fig. 5.1.12 (c)
140
I
0.0
1.0
x
0.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
0.90
1.00
Table 5.1.1
EHiT
'LoT
(eV)
(eV)
-0.01
-0.03
-0.08
-0.08
-0.09
-0.11
-0.26
-0.32
-0.33
-0.40
-0.39
-0.34
-0.01
-0.03
-0.03
-0.03
-0.03
-0.03
-.0.05
-0.04
-0.03
-0.02
-0.01
0.03
n
0.16
0.01
0.00
-0.01
0.00
0.06
0.11
0.13
0.15
0.20
0.23
0.26
Activation energies (AE) in eV of conductivity and Po 2
power law dependence (n) of conductivity of at 800 *C
( cc (Po 2)n) of La2.SrxCuO4-a.
141
800800
400 300
100
200
50 'C
2.0
LaSrCu04..
1.5
0
0.5
+++++
-
i
1.0
00
+++++350ppm Os-
I
t
1.4
1.8
2.2
2.8
3.0
3.4
1000 /'r (Km')
Fig. 5.1.13 Log (a) of LaSrCuO4-5 vs. 1000/T in various Po2's.
142
temperature the ionic species are frozen in and no redox reactions
These small slopes at low temperature (=
need to be considered.
0.03 eV) are thus referred to electronic ionization processes.
There is
the initiation of an upturn in the curve at high temperature in 350
As discussed later, we believe this is a sign of a p-n
The minimum value of conductivity at the transition is
ppm 02.
transition.
1.4 S/cm.
measured
shows
5.1.14
Fig.
the
thermoelectric
under the same conditions.
power
1000/T
vs.
Under all conditions,
the
thermoelectric power is positive, indicating that the major carrier is a
hole.
The low value of tep at low temperature implies a high carrier
Increasing values of tep are observed under reducing
concentration.
atmospheres, indicating a decrease in carrier concentration.
There is
also an obvious transition in the slope which roughly corresponds to
the transition in the conductivity at about 500 'C in Fig. 5.1.13. The
transition also becomes broader under reducing atmospheres.
slopes
of tep vs.
1000/T at high
temperature
similar values for the different atmospheres.
regime
The
approach
However the activation
energy calculated at high temperatures is = -0.15 eV which is about
half of that of conductivity (-0.31 eV).
If this represents the carrier
formation energy the activation energy of mobility will be - -0.16 eV
(negative!),
which
discussed later.
is
physically
unlikely.
Alternatives
will be
The other interesting comparison of Figs. 5.1.13 and
5.1.14 is that the difference of conductivity in different atmospheres
is nearly constant with temperature
power is not.
while that of thermoelectric
These phenomena suggest that the thermoelectric
power is a complex function of carrier
143
concentration including mixed
400 300
800800
40I
80080I
0.8
100
200
20-005
30
50 '1C
C
La rCu04..,
9:0.4
0
+
,P. 0.2
+e
i+ 0
350ppm 0.
C\2
0. 5
I
I
1.0
I
I
1.4
I
I
1.8
I
2.2
1000/'
Fig. 5.1.14 Normalized
thermoelectric
1000/T in various Po2's.
144
3.0
2.8
3.4
(IC')
power
of
LaSrCuO 4 .6 vs.
conduction at high temperatures.
in reducing atmosphere
At the highest temperature (> 900 'C)
iV/*K
at 100
a maximum
the tep reaches
with
decreases
and
This change in slope we believe corresponds
increasing temperature.
to the p-n transition observed in the conductivity.
The PO 2 dependence of conductivity and thermoelectric
power
of LaSrCuO4.3 was measured at high temperatures and is shown in
Fig. 5.1.15.
The absolute values of conductivity are slightly lower
It could be due to the uncertainties in the
than that in Fig. 5.1.1 If.
The
shape factor for different samples as mentioned in Chapter 4.
slopes of conductivity are however quite consistent and all follow A decrease in slope observed at low PO 2 's and high
1/4 power law.
suggests
temperatures
consistent with
a
to
transition
n-type
the cooling experiments (Fig.
dependence of conductivity
conduction,
also
The PO 2 1 /4
5.1.13).
is consistent with Eq. 3.41 in Section
3.2.1 i.e. p - PO2/4, which suggests that the Sr doping is compensated
by oxygen vacancies and 2[Vo']
compositional system.
[SrLa'] for large Sr content in this
The thermoelectric
follows a much weaker PO,
power on the other hand
The difference in slopes of
dependence.
these two properties with PO)
is surprising and will be discussed in
relation to the p-n transition
in this region.
thermoelectric
relationship.
power
plotted
is
vs.
In Fig. 5.1.16
conductivity
to
The absolute slope is much smaller than 1.
show
the
their
If the holes
were not degenerate, a slope of -1 would be expected at higher PO2's
as part of the Jonker pear.
It is interesting to compare properties of LaSrCuO4-8 and YBCO.
It
is found that
the
conductivity
145
and
thermoelectric
power
of
1.00
1.00
0.75
0.5
0.50
0
0"
0
0.25 -
0ca
10.00
Log P0 2 (atm)
Fig. 5.1.15 Log (a) and normalized thermoelectric power
LaSrCuO 4- vs. log (Po 2 ) at various temperatures.
146
of
1.0
0.8
~0.8
-
, _--
-
C\2
0.4
0eemu 1000 C
b***
-*w*eK
00
950 C
900 C
0.2
0.4
0.6
Log a (S/cm)
0.8
1.0
Fig. 5.1.16 Normalized thermoelectric power vs. log (a) of LaSrCuO 4 -.
at various temperatures.
147
LaSrCuO 4.- (Figs. 5.1.13 and 5.1.14) are very similar to those of YBCO
(Fig. 2.3.3 a and b) in terms of temperature dependence and absolute
It
values.
transport
a similar
suggests
2
dependence of both
is different,
suggesting that the
However the P 0
density for both compounds.
properties of these two compound
carrier
and
mechanism
defect structures differ.
It has been found in undoped La 2 CuO 4 .8 that the kinetics are
slower
in
Sluggish
at
kinetics
than
atmospheres
reducing
Po ,
low
in
oxidizing
environments.
in LaSrCuO 4 .
are also found
as
demonstrated in Fig. 5.1.17 which shows how the conductivity varies
with time as the gas is changed at 950 *C.
It shows a typical
relaxation behavior i.e. most of the change in conductivity occurs in
The relaxation time becomes longer so that it
the first few hours.
The strong P 0
reaction
dependence
2
the
dominates
in reducing atmospheres.
equilibration
to reach
takes longer time
conductivity
of
carrier
generation
processes
redox
the
suggests
so
the
that
relaxation time can be related to the diffusion coefficient of oxygen
in the material.
The curve implies that the diffusion coefficient is a
function of the oxygen content and becomes smaller at lower oxygen
content.
A
fixed-composition
cooling
experiment
as
below
described
was conducted for further confirmation of the redox reaction effect.
The sample was annealed at 100%, 1% 02 and 1OOppm 02 for
hours at
1000 0 C.
isolated from the
-
10
Just before it started to cool, the sample was
environment by
sealing the sample
holder so that
no or very little oxygen exchange could occur between the sample
and
the environment.
The
conductivity
148
results
are
shown
in Fig.
1.51
IVIIA
1.0
00
040.5
40
Time (hrs)
Fig. 5.1.17 Log (a) vs. time of LaSrCuO 4 .8 annealed at 950 *C
various P0 2's.
149
In pure oxygen, ample oxygen molecules still remain in the
5.1.18.
sample holder for at least partial oxidation to occur when the sample
Thus the slope at high temperatures is smaller than in the
is cooled.
flowing gas situation.
at
For the 1% 02 case, a change in slope appears
so
temperatures
high
For
temperature.
increasing
100ppm oxygen, the
conductivity
the
that
the
annealed
specimen
with
increases
initially in
negative slope regime is much more obvious
with an activation energy of = 0.38 eV.
The conductivity minimum
(0.6 S/cm) occurs at approximately the same temperature as in the
1% 02.
The smaller slope in the 1% 02 is suspected to be caused by
oxidation due to the higher level of residual oxygen molecules in the
At low temperatures (< 400
sample holder.
defects must dominate the
conductivity
carrier
4C)
generation
the ionization
of
so that
all
process
curves are similar for both fixed composition cooling
and isobaric cooling (Fig. 5.1.13) cases.
The ionization energies are
only = 0.01 eV.
Fig. 5.1.19
shows both conductivity and thermoelectric power
as functions of l/T in 100 ppm 02 with fixed composition.
though
there
is a drastic
difference
Even
in conductivity for isobaric
cooling and fixed composition cooling the thermoelectric power is
almost
identical
thermopower is
for
both
coolings.
As
mentioned
before
the
a complex function of carrier concentration for more
than one type of charge carriers.
It does not represent explicitly the
carrier concentration when it is close to the p-n transition, a region of
two band conduction.
5.2 Nd2-xCexCuO4,+
150
800800
400 300
50 *C
100
200
1.5
1.0
LaSrCu0 4 , sealed in
1 11
4-On
+++++
0 0.5
00
-++++100ppm
Os
0
0.0
-
-0.5
-wI
i
1
8
1.0
1.4
1.8
2.2
2 .8
3.0
3.4
1000 /T (K~ )
Fig. 5.1.18 Log (a) vs. 1000/T of LaSrCuO4.S cooled in various Po 2 's at
constant S.
151
400 300
800600
1.5
8000
40
200
20
30
50 'C
100
50 C S1.5
10
LaSrCu0 4.., cooled in 10Oppm
O at cons tant v
1.0
1.0 N
0
N,
C~2
+++++ cond.
b
0.5
0.5
**wwtep
0
-4
0
0.
0.0
-0.
0.8
-
}
5
1.0
1.4
1.8
1000 /T
2.2
(C')
2.6
3.0
3
Fig. 5.1.19 Log (a) and normalized thermoelectric power vs.
of LaSrCuO 4. in 100ppm 02 atcastant a.
152
-0.5
.4
1000/T
The results obtained for Nd2.xCexCuO
446
are also separated into
three compositional parts: x = 0, 0 < x < 1.5 and x = 1.5.
5.2.1 x = 0
The conductivity and thermoelectric power of Nd 2 CuO 4 -8 were
with
behavior
semiconductor
(NTCR)
three
of
resistance
of
negative-temperature-coefficient
typical
a
shows
function
The conductivity
The results are shown in Fig. 5.2.1.
temperature.
a
as
continuously
oxygen
pure
in
measured
first
temperature
distinct
regimes, with activation energies of 0.51, 0.12 and 0.31 eV from high
viewed
in
slope
negative
as
only
represent
intermediate
the
an effective
temperature
It
may simply
absolute
The
regimes.
two
should be
regime
energy.
activation
between
transition
the
Because of its narrow range, the
respectively.
to low temperature
conductivity reaches moderately high semiconducting values.
Log(a)
1.4 which is very close to the values obtained by Su et
at 800 'C is
al. [19891 (= 1.3) and by Hong et al. [19891 (= 1.5) under the same
condition but is about one order of magnitude higher than the result
The tep values are negative throughout the
of Ganguly et al. 119731.
indicative
range,
temperature
No saturation-like
regime is observed.
high temperatures
vary
0.27
eV
at
temperatures.
Fig.
in
varies
gradually
highest
the
Below
with
temperature
The activation energies at
ranging
temperature,
to
0.45
at
from
intermediate
300 0C the activation energy is about 0.14 eV.
5.2.2 shows the conductivity
PO2's
Only two
however appear in this measurement.
regimes
distinct temperature
conduction.
of electron
It
atmospheres.
153
is
measured with temperature
seen
that
the conductivity
800600
400 300
200
100
50 'C
1.0
C.)
0.0
b
0
0
-
-2.
0.6
I
1.0
-
1.4
I
1.8
- -- I
2.2
1
2.8
1
3.0
1 3 .0
3.4
1000/T (IC)
Fig. 5.2.1
Log (a) and normalized thermoelectric power vs. 1000/T
of Nd 2 CuO 4. 8 in 1 atm 02.
154
increases
with
conduction.
much
reducing
an
indication
of
n-type
The activation energies for each regime do not vary
in different
1OOppm
atmosphere,
02,
atmospheres
which
independent of PO 2 .
implies
except
the
that
at
low
transport
temperatures
in
mechanism
is
Based on the relative conductivities, the carrier
concentration in 100 ppm 02 at 450 *C is about 1.36 times of that in
Fig. 5.2.3 shows the thermoelecl.ic
02, assuming a constant mobility.
power measured under the same conditions as in Fig. 5.22.
values increase
The tep
slightly with decreasing P0 2, consistent with the
trend of conductivity, which suggests that the electron mobility is not
a strong function of P0 2 .
The difference in activation energy between
conductivity and thermoelectric power can usually be attributed to
the activation energy of mobility.
At first sight it seems that at least
in the high temperature regime the electron mobility is thermally
activated from Fig. 5.2.1.
The high temperature data of Fig. 5.2.1 was
re-plotted as log (aT) vs. l/T as in Fig. 5.2.4 for an activated process.
Data by Su et al. [19891 are also incorporated in this figure for
comparison.
Differences
in
slopes
the
of
conductivity
thermoelectric power are clearly seen for both, sets of data.
and
Su et al.
[19891 concluded that polaron hopping is the transport mechanism.
changes
Howevemgradual
in
slope
with temperature
intrinsic
generation
of electrons
both
At high temperature
properties area also seen but not explained.
where
for
and
holes
by
thermal
excitation across band gap may control the carrier concentration, the
thermoelectric power would have contributions from both carriers so
that
the
slope
of
thermoelectric
power
would
represent the activation energy of carrier generation.
155
not necessarily
800600
400 300
200
100
50 *C
2.5
2.0
1.5
i4 1.0
b0.50
0
0.0
10* atm (-
-
-0.5 -104
atm
++4 103 atm
++++
-
-1.0
.A
0.4
101 atm (-0)
1.0
(+ 0.2)
10-
atm (+ 0.4)
10"* atm (+ 0.6)
1.4
1.8
1000/T
Fig. 5.2.2
2.2
2.8
3.0
3.4
(KIC)
Log (a) vs. 1000/T of Nd 2 CuO 4 .8 in various PO 2 'SNumbers in the parentheses indicate how much the true
magnitudes of conductivity have been shifted on the
vertical log scale for clarity.
156
800800
400 300
200
100
50 *C
0.5
0.0
0
.0-
S-0.5CO
ICY
100
1.0
1.8
1.4
10
Fig. 5.2.3
2.2
2.8
3.0
3.4
oo/T (K-')
Normalized thermoelectric power vs. 1000/T of Nd 2 CuO 4 .
6 in various PO 2's.
157
1000 900
800
700
500 '6C
800
5.0
4.0
3.0
AD
C.)
2.0
1.0
9L
400.0
0
-. 0
-2.0
-3. .
Fig. 5.2.4
0.8
0.9
1.0
1.1
1.2
1.3
1000/T (Km')
Log (aT) and normalized thermoelectric power vs. 1000/T
of Nd2CuO 4 .8 in 1 atm 02.
158
The increase in carrier concentration with temperature at high
temperatures can be due to intrinsic excitation of electrons and holes
and/or from the redox reaction.
In order to clarify the ambiguity, an
experiment which involves cooling samples in isolated chambers was
carried out as before to eliminate or minimize the redox reaction
effect on both properties.
Results are shown in Figs. 5.2.5 and 5.2.6.
The activation energies of conductivity and thermoelectric power in
various
and
temperature
in Table
summarized
5.2.1.
regimes were observed.
for
atmosphere
conductivity
temperatures
temperatures
creation
all
in
PO,
ranges for both cooling processes are
The conductivity
temperature
different
PO 2's
is
process,
the
intrinsic
the conductivity
oxygen defect concentration.
increases with reducing
the
but
ranges,
more
difference
prominent
at
in
low
This is because at higher
than at high temperatures.
wIhere
only two temperature
In Fig. 5.2.5
dominates
reaction
the
carrier
is relatively independent of the
At lower temperatures the one with
higher initial oxygen vacancy concentration will have higher carrier
concentration, so that the conductivity in
that in 0.1 % 0?.
the
sealing,
independent
the
of PO
If the redox reaction is completely prohibited by
activation
,
energy
of
conductivity
should
be
and correspond to half of the band gap if the
mobility is not activated.
difference
OOppm 02 is higher than
From Table 5.2.1 it is shown that there is a
in activation energy of conductivity between coolings in
0.1 % and 100 ppm 02 (0.18 and 0.13 eV), indicating that the redox is
not entirely suppressed, at least in 0.1 % 02.
It
also
the band gap is no greater than 0.26 (2 x 0.13) eV.
the
corresponding
thermoelectric
159
power.
Except
indicates that
Fig. 5.2.6 shows
for some
low
2.00
1.75
Nd2 Cu0 4..,
1.50
1.25
1.00
=+eue 100 ppm O
0.75
350
-~
+0.1s
0.5
Fig. 5.2.5
ppm 0,
6
I
I
1.0
1.4
I
1.8
2.2
1000/T (I<-)
I
2.8
I
3.0
3.4
Log (a) vs. 1000/T of Nd2CuO 4.-8 in various PO2's
constant S.
160
800600
800800
0.00
400 300
400 300
200
100
200
100
50 'C
50 C
Nd2Cu0 4..,
o -0.50
-0.75
C -1.00
C2
-
-1.25
-1.50so
Fig. 5.2.6
ppm 0,
@100
350 ppm OS
+++++ 0.1 O4
8
1.0
1.4
1. 8
1000 /T
2.2
2.8
3.0
3.4
(K- 1
Normalized thermoelectric power vs. 1000/T of Nd 2 CuO 4 8 in various P02's at constant S.
161
I. Isobaric cooling
560-280 C
800-560 C
Log(PO 2 ) AE(GT)
AE(Q)
(atm)1
-4
-3.5
-3
-2
-1
0
AE(a)
AE(aT)
AE(Q)
280 C-RT
&E(a)
&E(CFT)
&E(Q)
AE(a)
1
0.57
0.57
0.57
0.52
0.50
0.62
0.37
040
032
026
029
0.27
050
0.50
0.51
0.50
0.48
0.51
0.16
0 15
0.13
0.15
0.14
0 17
0.10
0.09
0.10
0,09
0.09
0. 14
009
009
0.08
0.08
0.08
0.12
0o18
0.27
0.25
0.30
0.30
0.35
0.10
0.09
0.10
0.09
0.09
0.14
0.16
0.22
0.24
0.26
0.27
0.31
I1. Fixed-composition cooling
440 C-RT
800-440 C
Log(P0 2 ) &E(aT)
(atmn)1
-4
-3.5
-3
-2
0.19
022
025
0.32
Table 5.2.1
AE(Q)
AE(aT)
&E(a)
&E(Q)
AE(a)
1
0.11
0.17
0.17
0.18
0.13
0.17
018
025
0.12
0.12
0.11
0.14
0076
0061
0076
0091
0056
0068
0077
0090
Activation energies (AE) in eV of conductivity (a),
thermoelectric power (Q), an d (aT) of Nd 2 CuO 4. in
various temperature and P0 2 ranges for both isobaric
cooing and fixed composition cooling.
162
temperature
data,
conductivity
data
results
the
very
are
consistent
with
the
error and agree with the
within experimental
argument that the mobility is not thermally activated and does not
vary much in this P0 2 range. Fig. 5.2.7 shows the direct relationship
between conductivity and thermoelectric
power for various PO2's.
Straight lines with slope equal to unity further prove the validity of
a nondegenerate, broad band semiconductor model in Section 3.1.2.2,
The
in which the mobility of electrons is not thermally activated.
conductivity at zero thermoelectric power is - 80 S/cm. This value is
roughly the same as the result of Su et al. [1989].
To illustrate the redox reaction effect, the results from isobaric
cooling and fixed-composition cooling in 100 ppm 02 are plotted
together in Fig. 5.2.8.
between
Differences in both properties are observed
The difference
the two experiments.
in thermoelectric
Since the
power should be primarily due to the redox reaction.
carrier concentration is additive (n = Zni) the enthalpy of the redox
reaction can not be calculated simply from the difference in the slope
But the
(aln(n )/a(1/T) aln(n I + n 2 )/a(1/T) - aln(n 2 )/a(1I/T)).
difference in the conductivity should arise from the redox reaction.
Fig. 5.2.9 shows the conductivity of Nd 2 CuO 4 +s as a function of
P02 for various temperature.
It shows - -1/7 - -1/20 power law for
the PO 2 dependence of the conductivity with weaker dependence in
lower PO2's and higher temperatures. It can be compared to the 1/6
power law of La 2 CuO 4 .8.
decreases
with
increasing
The activation energy of conductivity
temperature
and
reducing
atmosphere
which is consistent with the continuous cooling experiment.
The
temperature
range
average
activation energy
calculated
163
from
this
0.0
i0.1~xO0
C
-0.5SLOB
I
c -1.0
0
1.5
10
Log a' (S/cm)
.,0
Fig. 5.2.7 (a)
Fig. 5.2.7
Normalized thermoelectric power vs. log (a) of Nd 2 CuO 4.6
at constant S in (a) 0.1% 02, (b) 350 ppm 02 and (c) 100
ppm 02164
0.0
-
I
-
-
NdaCu0%,
.
cc oled
at constant y
in 350 ppm Os
.2EO-0.5
SAM=, I
'C
C!-1.0
cq
1.5
1.0
Log c' (S/cm
Fig. 5.2.7 (b)
165
8.0
0.0
1
1
1
1
1
NdaCuO4, cooled
at constant y
in 100ppm O
.0-0.5eem4
C, -1.0
C\2
1.0
1.5
Log a (S/cm)
Fig. 5.2.7 (c)
166
2.0
400 300
800800
200
100
50 *C
.0
2.0
Nd2CuO 4 in 100ppm O
- 1.0.A
-
1.0
Ca
0
-
b 0.0
- 0 .0
0
I10'
-0
-
suee*
&****
1.0
Fig. 5.2.8
,2o
2-0
isobaric
fixed composition
1.4
1.8
(K2
1000O/T (KCL)
2.0
3-0
Log (T) and normalized thermoelectric power vs. 1ooo/T
of Nd2 CuO 4.8 in 100ppm PO 2 isobarically and at constant
167
2.5
NdaCuO+.,.
2.0
slope
= -1/10
0
b1.5
0
1.0
Gee
1000 C
.MO" 900 C
****& 800 C
++++ 700 C
I
-4.0
I
-3.0
-
-2.0.
Log P 0
Fig. 5.2.9
0.0
1.0
(atm)
Log (a) vs. log (Po2 ) of Nd2CuO 4
168
I
-1.0
at various temperatures.
(700-
1000 *C) is
0.56 eV in I atm 02
slightly
greater than
previous results of the isobaric cooling experiment (0.51 eV). This is
in good agreement with the results of Hong et al. (19891 (Fig. 2.2.5a).
Fig. 5.2.10 shows the thermoelectric power measured under the same
conditions.
and P0
2
It is seen that it is n-type throughout the temperature
ranges.
However compared to the conductivity the
thermoelectric
power
shows
weaker
temperature
and
PO 2
dependences.
results.
This is also consistent with the continuous cooling
Fig. 5.2.11 is a Jonker plot of isotherms of Nd2 Cu0 4 . 6 from
Figs. 5.2.9 and 5.2.10.
In most cases the slopes of all curves are
smaller than 1.
It appears that the material is tending towards an np transition at high PO, and low temperature.
At high temperatures
the magnitude of thermoelectric
power is small, implying a large
carrier density or intrinsic conduction.
5.2.2 0 < x s 0.2
To determine the doping effect of Ce on transport properties,
samples of Nd2 .,CeCu0
4
s with x = 0, 0.01, 0.05, 0.10, 0.15 and 0.20
were prepared and measured under identical conditions.
Fig. 5.2.12
shows the conductivity of all six samples as functions of temperature
in 1 atm oxygen.
The results for the undoped sample is very similar
The conductivity increases with x
to previous results (Fig. 5.2.1).
from x = 0 up to x = 0.15 and then decreases.
is
a
gradual
semiconductors
transition
that
from
a relatively
With increasing x there
nondegenerate
to
degenerate
temperature-independent
conduc-
tivity is observed for temperatures between 400 - 800 *C for x >
0.01.
Because of the
high and
169
degenerate conductivity, the intrinsic
0.0
.o -0.5eC4
0
Nd2 Cu04..
.eee. 1000 C
M
cy
Gseee 900 C
Boo C
A700
"+++&
C
1.
I
-
1
.985.0
I
-4.0
-3.0
-2.0
-1.0
LI.U
1.0
Log P0 2 4 atm)
Fig. 5.2.10 Normalized thermoelectric power
Nd 2 CuO4.6 at various temperatures.
170
vs.
log
(PO 2 )
0.4
0.2
Nd2CuO 4 in various P0a's
Ca
0 -0.
0-0.42
I
SLOPE = 1
p~4
C,,
C'?
N -0.6a)
-0.8
-
1000 C
se4ee4goo
04**
C
8oo C
700 C
-1..
5
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Log a (S/cm)
Fig. 5.2.11 Normalized thermoelectric power vs. log (a) of Nd 2 CuO 4 -6
at various temperatures.
171
800800
2.5
400 300
200
100
50 *C
1.5
0.5
**"Ma
40-0.5
0
-1.5
0.
1.0
1.4
1.8
2.2
2.8
3.0
3.4
1000/T (K-1)
Fig. 5.2.12 Log (a) vs. 1000/T of Nd 2.CexCuO
for various x's.
172
4 .6
cooled in 1 atm 02
conduction is not seen for large x's at temperatures as high as 1000
0 C.
However all samples seem to approach the same conductivity
At
value at high temperatures, an indication of intrinsic conduction.
low temperatures the activation energies of ionization are = 0.24 eV
for x = 0 and 0.01
and 0.21
of unintended
concentration
eV for the others, implying a high
impurities
s x
5.2.13 shows the conductivity as functions of x for 0
atm 02.
A maximum of conductivity occurs at x = 0.15.
conductivity
0.2 in I
The drop of
at x = 0.20 could be due to the interaction between
dopant and/or the precipitation of a second phase.
increases
Fig.
or nonstoichiometry.
temperature
with
temperature for x > 0.10.
for
x
The conductivity
< 0.10 and then decreases with
This result is qualitatively in agreement
with data by Pieczulewski et al. [19891 (Fig. 2.2.6c).
annealing was performed to examine the effect of
Isothermal
P02 on the conductivity.
A typical result is shown in Fig. 5.2.14
where the conductivity is measured continuously with time as P 0
changed
compositions.
compositions
doping.
very quickly
in a matter of an hour for all
Figs. 5.2.15 a-e show the conductivity vs. P0
at
various
temperatures
to
illustrate
the
It is seen that as x increases the PO 2 dependence
2
for all
temperatures
effect of temperature.
for
compositions
individual
The reverse
decreases.
2
at
the
seen
These results are in agreement
with Figs. 2.2.5a and b by Hong et al. [19891.
173
to illustrate
temperature dependence is
for x > 0.1, consistent with Fig. 5.2.13.
of
effect
Figs. 5.2.16 a-f on the other hand show the conductivity vs. P0
various
is
It is seen that the conductivity
at constant temperature.
reaches equilibrium
2
2.5
2.0
1.5
40
1.0
0.00
0.05
0.15
0.10
0.20
x (Ce concentration)
Fig. 5.2.13 Log (a) vs. x of Nd 2 .CeCuO
temperatures.
174
4-
in I atm 02 at various
2.5
52.0
Q
b
0
-4 1.5
1.0'
200
400
800
800
1000
Time (min.)
1200
1400
Fig. 5.2.14 Log (a) vs. time of Nd2-xCeCuO 4.8 annealed at 900 *C in
various PO2's.
175
2.5
52.0
b
0
3eee-e X=0.01
. **rA x=0.05
0++
x=0.10
+++
i!iiX=0.15
x=0.20
5.0
-4.0
-3.0
Log
-2.0
P0 2
-1.0
0.0
1.0
(atm)
Fig. 5.2.15 (a)
Fig. 5.2.15 Log (a) of Nd 2 .xCexCuO 4 -8 vs. log (P0 2 ) for various x's at
(a) 800 *C, (b) 850 0 C, (c) 900 *C, (d) 950 *C, and (e) 1000
*C
176
2.5
Nd..Ce.Cu0 4.., at 850C
$2.0
to
0
0-41.5
000ee x=0.00
x=0.01
x=0.05
x=0.10
x=0.15
x=0.20
1.05
-M5.0
I
-4.0
I
I
-2.0
-3.0
I
-1.0
Log P0 2 atm)
Fig. 5.2.15 (b)
177
I
0.0
1.0
2.5
52.0
b
0
-4 1.5ee
x=0.00
. **"*x=0.05
*++4 X=0.10
+++++ X= 0. 15
-
1.0
-5 .0
-4.0
x=0.20
-3.0
Log
-2.0
-1.0
P0 2 (atm)
Fig. 5.2.15 (c)
178
0.0
1.0
2.5
,
.
.
at 950C
Nda-xC e1 CuO~.,
02.0
b
0
X=0.00
x=0.01
x=0.05
x=0.10
x=0.15
.**I*&
x=0.20
4~I
I
I
a
-1.0
-4.0
1.2
4:0
Log POi
atm)
Fig. 5.2.15 (d)
179
u.u
1.0.
2.5
Nd 2.. Ce.CuO4y
at 1000C
S2.0
00
b
0
GO".
eeeee
x=0.00
x=0.01
x=0.05
x=O.10
x=O.15
x=0.20
-
-4.0
-3.0
Log
-2.0
P0 2
-1.0
(atm)
Fig. 5.2.15 (e)
180
0.0
1.0
2.5
52.0
0
0
1.5
Fig. 5.2.16 (a)
Fig. 5.2.16 Log (a) of Nd2 .x Ce xCuO 4 .3 vs. log (Po 2 ) at various
temperatures for (a) x = 0.00, (b) x = 0.01, (c) x = 0.05, (d)
x = 0.10, (e) x = 0.15, and (f) x = 0.20.
181
2.5
5
Nd 1 ... Ceo.oCuO4.,
S2.0 -
b
31.5--
C
850 C
see800
.GOOee
,&1666
1.Q
900 C
+++++
950
*oW-W-
1000
-4.0
C
C
-3.0
-2.0
-1.0
Log POg (atm)
Fig. 5.2.16 (b)
182
0.'
1.0
2.5
Ndi.sMCeO.OsCuO"
O2.
b
0
0000
800 C
.aee 850 C
&haha
++++
W-K1000
1.25.0-
900 C
950 C
C
'
-4.0
Log
-2.0
-1.0
P0 2 (atm)
Fig. 5.2.16 (c)
183
'
0.0
1.b
2.5
I
Ndi.gCeo.,CuO4.y
2.0 -
b
0
G
800 C
wG2850 C
900 C
950 C
w**x-
.0
-4.0
1000 C
-3.0
Log
-2.0
P0 2
-1.0
(atm)
Fig. 5.2.16 (d)
184
0.0
1.0
2.5
j2.0
Ndl.aMCeo.1 5CuO4 7
b
to
0
0-1.5
GOC0 800 C
3*eee 850 C
*
900 C
+++++ 950
*f
-4.0
C
1000 C
I
-3.0
Log
I
-2.0'
-1.0
PO2 (atm)
Fig. 5.2.16 (e)
185
0.0
1.0
n
2.5
Ndj.sCeo.2CuO4,
S2.0
b
0o
0
1.5
00000 800 C
meeee 850 C
900 C
++++ 950 C
h****
1000 C
**
'
*-5.O
-4.0
-3.0
Log
'
-2.0
-1.0
P0 2 (atm)
Fig. 5.2.16 (f)
186
0.0
1.0
5.2.3 x = 0.15
Because of the monotonic change in the conductivity in the
range 0 < x < 0.15, it seems that doped Nd2 -xCexCuO443 materials have
Since Nd1 .85 Ce.i 5 CuO 4 .s has the highest
similar electrical properties.
Tc and conductivity in this system, the thermoelectric power of this
composition was also measured and deemed as being representative
of the group.
Fig. 5.2.17 shows both properties as function of
temperature in 1 atm 02.
The conductivity is almost identical to that
in Fig. 5.2.12, indicating good reproducibility.
of conductivity changes
positive
activation
sign at
energy
decreases
with
thermoelectric
power
the
on
400 *C, below which it has a
of
conductivity
2
increasing
other
dependence of both properties.
insensitive.
The thermoelectric
Above 400 *C the
0.21 eV.
hand
independent with very' ,mall absolute values.
P0
The thermal coefficient
The
temperature.
is nearly
temperature
Fig. 5.2.18 shows the
Both parameters are Po 2 -
power of the other heavily doped
samples are also expected to be temperature- and P0 2 - independent.
5.3 YBa2Cu3-xTix06+S
The electrical conductivity of the system YBa2Cu2-xTix06+ for
x
= 0.005, 0.01, 0.02, 0.035, 0.05, and 0.1 were measured as a function
of temperature upon cooling for a variety of PO2 s.
illustrated in Figs. 5.3.la-e.
behavior.
These results are
All samples were found to show similar
The absolute conductivity values are comparable to that of
the undoped sample (Fig. 2.3.3a), indicating little effect of doping.
In
fact the conductivity differences of all sample (< ±0.1 s/cm) is within
the
uncertainty
of
measurements.
187
They
are
practically
identical
2.5
800800
400 300
800600
400 300
100
100
200
200
momm
50 *C
50 *C
2.5
Conductivity
2.0
2.0 tm
1.5
M
b
1.0
.
Nd1 .wCe., 5 CuO4.
in 1 atm Os
0
0.5
0.5
0.0
Adlo&-i b
I
I
1.0
I
I
1.4
I
0.0
-
-If.
I
I
1
2.2
1.8
1000/T
(K~
I
2.8
1
I
3.0
t
3% *
Fig. 5.2.17 Log (a) and normalized thermoelectric power vs. 1000/T
of Nd.s 85Ceo. 5 Cu0 4 .8 in 1 atm 02.
188
2.5
2.5
0
-
8
- 9
- 9-
2.0
1.5
0
2.0
Ndl.,mCe .15Cu0 .4-y,annealed
at 800 C
1.0
M
1.5
1.0
CL
0
0.5
0.5
0.0
0.0
-0.*5_ 5
-4
-M3
-2
-1
1-0.5
Log P0 2 (atm)
Fig. 5.2.18 Log (a) and normalized thermoelectric power vs. log (P0 2 )
of Ndl. 8 5Ceo.i 5 CuO4.6 at 800 *C.
189
800800
800600
3.0
400 300
400 300
50 'C
50 C
100
200
200
100
YBaaTi.Cu3..0 7..., in 1 atm O
-4
2.5
S2.0
0
0
0
1- 1.0
Gee" x
0.005
0.01
SX
0.5
***-.
,
0.0
b
3
I
I
1.0
I
II
1.4
I
II
1.8
I
2.2
0.02
ZX
X
1X
4+4--
I
1000/T (K''')
0.035
0.05
0.10
I
2.8
I
I
3.0
I
3.4
Fig. 5.3.1 (a)
Fig. 5.3.1
Log (a) vs. 1000/T of YBa 2Cu 3.xTix0 6 +6 in (a)1 atm 02, (b)
10% 02, (c) 1.0% 02, (d) 0.1% 02, (e) 100 ppm 02.
190
800800
3.0
i
-
400 300
I
'C
00105
0
40
800I
100 ,50
200
I
in 10% Os
YBaTi.Cus...o0.
2.5
52.0
b
1.5
o
0
0.41.0
0.005
0.01
++44
-,
- 0.02
seese0.035
-- ~X
0.05
0.10
0.5
0..8
I
I
I
1.0
I
a
I
I
1.4
I
I
I
~
I
~'
8 2.2)
1000 /T (Kr')
I
I
I
1.
Fig. 5.3.1 (b)
191
I
I
I
2.8
~
I
I
3.0
3.4
3.0
800 600
400 300
800600
400 300
50 'C
50 *C
100
200
200
100
YBa2TizCu3..O 7 -, in 1% 02
2.5
~2.0
Q
*%MO
1.5
0
0.4
1.0
+++++
0.005
IX
0.01
0.02
0.035
0.05
I
+++++ IX
-
0.5
o.0
I
-4
x
0.10
x
1
3
' I
1.0
I
'
I
1.4
'
I
1.8
1000 /T
I
2.2
(K~')
Fig. 5.3.1 (c)
192
I
I
I
2.6
I
I
3.0
I
3.4
800800
1 t
3.0
2.5 -
400 300
200
YBaiTiCu3 ..1 07 .. , in
100
0.1%
50 'C
02
0 2.0--
b1.5 -0
= 0.005
x = 0.01
x
1.0-++
x
=
0.02
x
=
=
0.05
0.10
++++-+
--
0.5
0.
x
0.
1.0
1.4
1.8
2.2
1000/T (K)
Fi g. 5.3.1 (d)
193
= 0.035
2.8
3.0
3.4
800800
2.0
1.5
400 300
I
1
F
200
r
50 'C
100
I
9
YBaaTizCu 3 -207 -7 in 100 ppm OQ
.- 4
S1.0
b 0.5
0
0.0
4
++e..e
1
0.005
....-
x
0.01
0.02
0.035
0.05
X
-0.5
+++++
1
+++++X
M-
0-0
J.s
t
1.0
I
I
I
1.4
iI
1.8
I
1I
1000 /T (K
194
0.10
X
I
2.2)
Fig. 5.3.1 (e)
1X
I
2.8
i
I
I
3.0
3.4
They
show
all
temperatures
a
metal-semiconductor
moderate
at
transition
This transition occurs at about the same
(= 400 'C).
temperature, independent of dopant concentration, P0
2
and absolute
The conductivity of all compositions decreases as
decreases, indicating hole conduction in all cases. The slope
conductivity value.
the P0 2
in the semiconducting region increases slightly as the P0 2 is reduced.
In reducing atmospheres (0.1%
from
p-type
to
n-type
OOppm 02) all show a transition
and
at high
conduction
conductivity irregularities found in the
due to slow kinetics.
atmospheres.
The
temperatures.
OOppm 02 are believed to be
The kinetics are much slower under reducing
In Fig. 5.3.2, it shows how the conductivities of all
samples vary with time when the temperature was changed in 100
In oxidizing atmospheres the conductivities usually reach
ppm 02.
equilibration within one hour when the temperature is changed. Fig.
5.3.3 shows the conductivity of YBa 2 Cu 2 .9 Tio. 1 06+8 measured as a
function of temperature in various PO2 's.
The curves were obtained
at the same cooling rate (25 *C/hr) except the one indicated "slowly
cooled", which was cooled at (25 OC/3 hrs).
clearly seen.
100ppm
The effect of PO2 is
From the comparison of the two cooling curves in
02, it can be concluded that the irregular and abnormally
resistive
conductivity
limitations.
at
low
temperatures
is
due
to
kinetic
This reasoning can be also applied to Fig. 2.3.3a.
Figs. 5.3.4a and b shows the results of isothermal annealing in
The conductivity of YBa 2 Cu2.995Ti.oo506+8 and
various Po,'s.
and low
YBa 2 Cu 2 .9Ti.O6+6 is shown as functions of P0 2 . At high P0
2
temperature,
less
dependent.
the
samples
become
They all undergo what
195
more
metallic and
appears to be a p-n
P0
2
transition in
1.0
0.5
0.0
b
0.o
0
-0.5 -
- 1.0 F..0
Fi g. 5.3.2
200
400
G00
800
1000
1200
Time (min.)
Log (a) vs. time of YBa 2Cu 3-xTix0 6+8 cooled in 100 ppm 02.
196
800600
400 300
200
100
50 *C
2.5
1.5
b
1.0
0
0- 0.5
0.0
1.0
1.4
1.8
2.2
2.6
3.0
3.4
1000/T (K-i)
Fig. 5.3.3
Log (a) vs. 1000,T of YBa 2Cu 2.9 Tio.iO 6+a cooled in various
Po2's.
197
N
Cl)
Log P02 (atm)
Fig. 5.3.4 (a)
Fig. 5.3.4
Log (a) vs. log (P0 2 ) at various temperatures of YBa 2 Cu 3 .
,Ti,06+a for (a) x = 0.005, and (b) x = 0.10.
198
YBa2Tio.jCuL9 07..
1.5
slope = 1/2
0
0.5
.44++
a-eo-
-
-4.0
-
199
750 C
700 C-
+-++-+
650 C
-*-X
800 C
-. 0 -2.0 -1.0
Log PO2 (atm)
Fig. 5.3.4 (b)
800 C
0-0
1.U
reducing
atmospheres
Poa
at
temperatures.
high
In
the intermediate
ranges the data follows a log a - P 0 2 1/2
temperature
and
dependence.
This behAvior is similar to undoped YBa 2 Cu 3 0 6+8 . (Fig.
2.3.4a)
Judging from the conductivity results, which show little effect
upon Ti doping, thermoelectric power results similar to those in Figs.
2.3.3b and 2.3.4b are expected.
measurements were conducted
Hence,
no thermoelectric
on this compositional system.
200
power
Chapter 6
Discussion
In this chapter we will discuss the experimental results of the
three compositional systems.
In each system, information relevant
towards confirming the theoretical predictions based on the defect
models will be elucidated first.
Models available in the literatures
will be reviewed in comparison with our results.
Issues requiring
clarification will also be addressed.
6.1 La 2 .xSrXCuO4.8
System
6.1.1 Defect Model and Transport of La 2 CuO 4 . 8
The most important observations from the previous chapter
about
La 2 C u 0 4
are that both log (a )
and
thermoelectric power are proportional to P0 2 1/6.
the
normalized
This implies that
hole conduction is dominant and that the hole concentration
is
proportional to P0 21/6.
Since La 2 CuO 4 .8 is a p-type conductor, it is very natural for us
to consider a defect model involving the equilibration between holes
and oxygen interstitials (p -2[0"])
as predicted in Section 3.2.1
Region I. Following that prediction, p = (2Ko) 1/3p0
16
2 / ,
where KO is
the equilibration constant of the oxidation reaction in the following:
1/202 -+ Oi" + 2h'.
(3.29)
This model fits the experimental results very well.
The oxygen
content in our sample as sintered in 02 is also shown to be slightly
oxygen excess (Table 4.1.4), which is consistent with this model.
If
we assume 5 (oxygen excess) = 0.01 at 900 *C in 1 atm 02, since p ~
201
2[01"]
=
(2Ko) 1 /3 p 0 2 1/ 6 , KO will have a value of 7.3 x 1058
(#/cm 3 )3 (atm)-1/2.
Based on the same experimental results, Tsai et al. [1989] on
the other hand derived a defect model involving doubly ionized
oxygen vacancies and electrons as dominant defects since in reducing
conditions the material is more likely to be oxygen deficient [Nguyen
et al., 1981; Mitsuda et al., 1987; Johnston et al., 1987]. In this model
the oxidation reaction and mass action equation are as following:
VO" + 2e' + 1/202 -+ 0%x,
KO- = 1/(n 2 [V-]P021/)
The charge neutrality equation involves:
n = 2[VO
so that
p = Ke/n
=
Ke(Ko./2) 1/3po 211/6.
where Ke is defined in Eq. 3.27.
(6.1)
Since La 2 CuO4 remains a p-type
conductor as shown by the P0 2 dependence of a and the sign of tep,
then
ah >> ae or pqph >> n9e,
which implies
h4te >> n/p = np1hq/ah = nyhq/a.
In the case that n = 2 x [Vo''] = 2 x 0.11/F.U. (from Opila and Tuller,
[1990]) and a - 3 S/cm (Fig. 5.1.4) at 900 *C in 10-4 atm 02 and
assuming that g = 1 cm 2 /volt*sec
(around the borderline between
large and small polaron regimes), then for p-type conduction
to
dominate in the oxygen deficient regime,
(6.2)
h/pe >> 100,
which is not unreasonable in this material judging from the nature of
valence band and conduction band [Mattheiss,
202
1987; Takegahara et
We can also calculate the hole concentration p, which is
al., 1987].
1-9 x 1019 cm- 3 or 1.8 x 10-3 /F.U ~ n/100.
= a/qgh =
ah/q9h
argument
This
thermoelectric power.
Q
can
be
also
applied
to
positive
the
For mixed conduction:
= GeQe+OhQh
Ge+
h
(3.22)
When n > p, it generally implies IQel < IQhl if the density of states of
conduction and valence band (Nc and Ny) are not very different.
Since ah >> e, it implies ahQh + aeQe - GhQh. So the thermoelectric
power is determined primarily by the hole conduction (Q
-
Qh).
The oxygen stoichiometry of undoped material is a matter of
controversy.
Both oxygen excess and deficiency have been reported
[e.g. Johnston et al., 1987 and Cheong et al., 1989].
Allan and
Mackrodt [1988] predicted that oxygen vacancies are energetically
preferable and even calculated that oxygen vacancies have lower
energy in the a-b plane than in the c-axis, which has also been
confirmed experimentally
[Nguyen, Choisnet, Hervieu and Raveau,
On the other hand Chaillout et al.
1981 and Shafer et al., 1987].
[1989] observed by neutron diffraction La 2 CuO4 annealed under high
pressures (1-3 kbar at 600 *C) the existence of oxygen interstitials
which sit between two La planes.
Opila and Tuller [1990] recently
found from a TGA study that the oxygen stoichiometry of this
composition actually varies from 4.01 to 3.89 when the oxygen
partial
pressure
temperatures.
changes
from
1 atm
to
10-4
atm
at high
It may be concluded that there are both oxygen
203
excess and deficiency in La 2 CuO4 within the P0 2 range studied in this
research.
For the complete PO 2 range in which the phase is stable, a
charge neutrality equation should thus involve all of the electrons,
holes, oxygen vacancies and oxygen interstitials. It is expressed as
2[Oi
(6.3)
+ n = 2[Vo 0 ] + p
in which the background impurity is neglected and doubly ionized
oxygen defects are assumed. This equation can be rearranged as the
following equation when the mass action equations of other reactions
are combined:
2KFn 4 + yn 3 - Keyn - 2y 2 = 0,
(6.4)
where KF is the Frankel constant for doubly ionized oxygen defects;
Ke is the equilibration constant of intrinsic electron-hole generation;
and y is defined as KRP02-1 2 in which KR is the equilibration constant
of the reduction reaction. Eq. 6.4 can be solved by computer as a
function of P0 2 if the constants are known or assumed. A schematic
diagram, illustrating defect densities versus P0
2
is shown in Fig. 6.1.1.
The ranges and curvatures of the transition regions are dependent on
the equilibration constants. The hole and electron conductivities are
also shown for the condition in which p-type conduction dominates
for most P0 2 ranges given much higher hole mobility than electron
mobility.
Schirber el al. [1988] and Rogers et al. [1988] reported oxygen
excess and suggested the excess oxygen is present as 02-.
their
argument
the
reaction
and
corresponding
relation will be:
02 = (02)' + h*
KR = [(0
204
2 )']p/PO2 ,
mass
Following
equation
Q
0MO
Fig. 6.1.1
Kroger-Vink diagram for La 2CuO 4±a
205
with the charge neutrality equation
p = 1/2[(02)']
Solving
p = (KR/2)1/2p02 1/2,
(6.5)
which is not consistent with the experimental results of this study
Su et al. [1990] estimated, in a study of the same system, the
density of conduction states (N)
the followin
Q=
and the transport entropy (Ah) from
equation:
kIn
+Ah
q
P
-p
(3.16)
Incorporating results of thermoelectric power similar to ours and the
relationship between oxygen excess and P 0
2
from the literature, they
derived a relationship between oxygen excess (8)
and thermoelectric
power as
In (8) = In (const) - Qe/k
is (1/2
where the constant
According to our data this constant is ~ 4.0 x
1.22 x 10-2 per F.U.).
3.16,
Nvexp(Ah)) = 8.704 x 10-2 per F.U.
(A more careful calculation shows that it should be
(formula unit).
10-2 /F.U.
(6.6)
Despite their effort, however, the validity of applying Eq.
which
is derived
from
non-degenerate
metal as La2CuO 4 .3 needs further justification.
good only for oxygen excess (positive 8).
semiconductor,
to a
Besides, Eq. 6.6 is
Possible oxygen deficiency
was not considered.
Another important feature of this composition observed in this
study
is
that
conductivity
both
and
2
dependences
it
implies
that
206
power
are
Combined with their strong
relatively independent of temperature.
PO
thermoelectric
the
equilibrium
constants
of
oxidation and reduction (Ko and KR) are not strong functions of
temperature,
nearly zero.
which means the enthalpy of the redox reaction is
In other word, there is little energy gain or loss for the
oxygen to enter or leave the sample.
In
the
previous
chapter
we
observed
also
a
metal-
semiconductor transition in this composition at - -100 *C (Fig. 5.1.2).
This transition temperature is comparable to that of the
antiferromagnetic
transition (Neel temperature,
According to
TN).
the calculation by Guo, Temmerman and Stocks [1988], this metalsemiconductor transition is caused by the antiferromagnetic ordering
and the TN increases with decreasing oxygen content. The TN has
been
shown
experimentally
to be
a strong function
of oxygen
stoichiometry [Johnston et al., 1987 and 1988; Cheong et al., 1989].
However there remains substantial discrepancy between the
relationship
of TN
and
oxygen
the corresponding
stoichiometry.
Johnston et al. [1987 and 1988] established a relationship between
TN and oxygen deficiency of La 2 CuO4.y, for which TN = 0 at y = 0 and
TN = 300 'K at y = 0.03.
According to that relationship the oxygen
deficiency of our sample is ~ 0.015 in pure 02.
Cheong et al. [1989]
on the other hand pointed out the highest TN (= 328 *K) of La 2 Cu04+
is achieved
by vacuum annealing
with 8
-+
0.
Accordingly our
sample, when cooled in oxygen, is on the oxygen excess side, in
agreement with the ICP results (Table 4.1.4)
6.1.2 Doping Effects of Sr
The doping effects of Sr on conductivity as functions of
In
temperature and P0 2 were illustrated in Figs. 5.1.6-5.1.12.
207
Chapter 3 we predicted that initial Sr doping of La 2 Gu04 (x < 0.33)
would increase the hole concentration by the substitution reaction:
CuO + 1/202 + 2SrO La2CuO4-+ 2 SrLa' + CuCux + 2h' + 400x
(3.30)
Under the same conditions a linear increase of the conductivity (a)
with the dopant concentration (x) is expected from the following
equation:
a = plelp4
if p is equal to x (full ionization of the dopant) and g is constant.
6.1.2 is plotted from Fig. 5.1.10 as log (a) vs. log (x) for x
illustrate this effect.
Fig.
0.3 to
It is seen that the conductivity increases
monotonically with Sr concentration, consistent with the model.
The
deviation from the ideal slope of unity could be due to (1) the
uncertainty
of the absolute conductivity
as indicated in Chapter 4
and/or (2) an increasing tendency of oxygen vacancy compensation
with x and/or (3) the mobility becomes a function of Sr content.
From (2) and (3) we will expect a saturation of conductivity with x.
We
dependence
have
observed
of conductivity
temperatures in the 0.4
- P0
20
experimentally
with
x
an
increasing
of La2-xSrxCuO4.-
x s 1.0 range (Figs. 5.1.11 a-f).
and at x = 1.0, a m P 0
2 1/4.
PO 2
at high
At x = 0.4, a
This compositional region can thus
be viewed as a transition state between Regime II and Regime III
predicted in Fig. 3.2.1.
In Regime II the dominant defects are p and
SrLa' and the charge neutrality equation is approximated by
p = [SrLa'] # f(P 0 2 ).
(3.37)
In Regime III the dominant defects are VO** and SrLa' and the charge
neutrality equation is approximated by 2[Vo**] = [SrLa'] (Eq. 3.42) so
th at
208
2.5
2.3
2.0
to
0
1.8
1.5-1.4
Fig. 6.1.2
-1.2
-1.0
-0.8
-0.8
-0.4
Log x (Sr conc.)
Log (a) vs. log (x) of La 2 .xSrxCuO 4 -6 (0
209
< x
S 0.3).
p = (Ko[SrLa']/2KF)1/ 2p0 2 1/4.
(3.43)
The change of compensation mechanism in this compositional
range is also consistent with the defect model predicted in Fig. 3.2.2,
in which the relationship between defect and Sr concentration is
When the Sr concentration reaches a certain value (Regime
shown.
III in Fig. 3.2.2) it becomes compensated by oxygen vacancies as Eq.
In agreement with Eq. 3.41 a is found to
3.42 (2[Vo**] = [SrLa'])follow
PO2 1/4 law at x = 1.0.
requires that p m [SrLa']1/ 2 .
In this regime the defect model also
However the experimental results show
that the conductivity decreases with [SrLa'] in this compositional
x
conductivity
includes
mobility.
This is because the
1.0) (Figs. 5.1.9 and 5.1.10).
range (0.4
contribution
of carrier
concentration
and
In this region the hole mobility decreases with [SrLa'] due
to the disorder induced by increasing oxygen vacancies [Sreedhar
and Ganguly, 1990].
By conductivity measurements alone, this model
can not be verified unless the hole mobility is known.
Additional
measurements of thermoelectric power in this range is required to
confirm the defect model.
Another solution to this is to prove 2[Vo**]
[SrLa'] by directly measuring the oxygen vacancy concentration as a
function of SrtLa'] by TGA.
Although a strict relationship as Eq. 3.42
was not obtained, a general trend (Opila and Tuller [1990])
that the oxygen content decreases with [SrLa'].
shows
If this model is
correct the hole concentration can be calculated by p = c*[SrLa']1/ 2 ,
where c is a constant.
Assuming the boundary of the two regimes is
at [SrLa] = 0.33 /F.U. [Michel and Raveau, 1984] so that c = 0.57.
hole concentration at [SrLa'] = I is - 0.57 /F.U.
compositions calculated
from Fig. 5.1.10
210
are
The
The mobilities of all
shown in Table 6.1.1.
Sr Conc.
(#/F.U.)
0.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.80
0.90
1.00
Hole Conc.
(#/F.U.)
Vol/F.U.1
3)
(X
95.3
95.0
94.9
94.3
94.6
94.6
94.4
94.2
93.8
93.0
92.9
92.7
0.0 2 T
0.05
0.10
0.15
0.20
0.30
0.36
0.40
0.44
0.51
0.54
0.57
Conductivity ole Mobility
cm 2/volt*sec)
(S/cm)
14
57
150
169
268
278
339
2 19
117
85
46
19
0.41
0.68
0.88
0.66
0.79
0.55
0.55
0.32
0.16
0.097
0.049
0.017
# From Sreedhar and Ganguly (19901.
T From Jorgensen et al., (19881.
Table 6.1.1
Conductivity, hole concentration and mobility of La-.
,SrCu04.8 at 800 *C 1 atm 02.
211
assuming that p = x for x
0.3 and p = 0. 5 7 *[SrLa']1/ 2 for x > 0.33 per
The hole mobility data shows that the transport mechanism
(F.U.).
falls in the large polaron regime for small x's and in small polaron
regime at high x's, consistent with the transition from metallic or
semimetallic to semiconducting state with x [Michel and Raveau,
1984; Sreedhar and Ganguly, 1990].
As mentioned in Chapter 3 the defect models derived above
are based
increases
on
dilute solution.
the interaction
between
When
the
defects
defect concentration
also increases.
The
decrease of conductivity with increasing dopants can be explained by
the decrease
of either carrier mobility or mobile charge carrier
concentration.
Since ordering of oxygen vacancy has been observed
in heavily doped La 2 -xSrxCuO 4 .3 [e.g. Sreedhar and Ganguly, 19901,
most of the oxygen vacancies are part of the structure and can no
longer be viewed as defects.
In that case even though the oxygen
content decreases with increasing [SrLa'] from TGA data [Opila and
Tuller 1990], the model of Eq. 3.42 (2[Vo''] = [SrLa']) may not be true.
The diffusion coefficient and oxidataion enthalpy are also shown to
decrease with increasing [SrLa'] [E. J. Opila, private communication],
which implies that [Vo''] may actually decrease
with increasing
[SrLa'] in this regime. The tep's of La 2CuO 4 .3 and LaSrCuO4.3 are also
similar (Figs. 5.1.3 and 5.1.16), implying that the hole concentrations
are comparable for these two compositions.
If this is the case the
in conductivity with increasing
[SrLa'] for [SrLa'] > 0.4
decrease
observed in Fig. 5.1.10 may be partly due to the decrease of mobile
hole concentration.
Further tep measurements of samples in this
compositional range are needed to confirm this model.
212
From the conductivity data (Fig. 5.1.9) it is seen that there is a
metal-insulator transition in La 2.SrxCuO4.3 at x = 0.9. For x 0.9 the
material
conductivity
are
they
and
high
of
400 *C i.e. the absolute values
below
is metallic
decrease
with
increasing
At x = 1.0, the conductivity increases with temperature
and has relatively low values (~ 20 S/cm in 02 and 1.2 S/cm in 100
temperature.
This transition with
ppm 02), an indication of semiconductivity.
increasing dopant concentration implies it is of the Anderson type i.e.
localization due to the disordering effect by the increasing dopant
and oxygen vacancy concentrations.
The rapid decrease of conductivity at high temperatures and
high x 's (Fig. 5.1.9) can not be simply explained by lattice scattering.
Generally the hole mobility decreases linearly with temperature if
The resistivity vs. temperature plot'
phonon scattering is dominant.
shows
nonlinearity
phenomenon
however
at
can
(Fig.
temperatures
high
be
explained
by
the
6.1.3).
This
redox reaction
occurring at high temperatures and will be discussed in the next
section.
At very high Sr levels, ordering of oxygen vacancies has been
reported by X-ray and electron diffraction [Nguyen et al. 1983 and
Sreedhar and Ganguly, 1990].
The defect concentrations as functions
of total Sr concentration are predicted in Regime IV of Fig. 3.2.2.
In
this regime the dominant defect was assumed to be an association of
Sr and oxygen vacancies e.g. two SrLa' and one VO** ((SrLa')2Vo**}.
It
can be proved that in this regime the hole concentration also follows
1/4 power law of P0 2. So from conductivity measurements alone we
can not determine whether there is defect association or not.
213
0.020
0.015
0.010
0.005
0.000
0
200
400
600
800
1000
Temp. (C)
Fig. 6.1.3
Resistivity vs.
temperature of La 2 -xSrxCuO 4.6 (0.4 s x s
0.8) in 1 atm 02.
214
6.1.3 Defect Model of LaSrCuO4.8
One of the most important observations of LaSrCuO 4 .8 in this
study
is the conductivity
oxidation conditions.
temperature
at
variation
with temperature
in various
The decrease of conductivity with increasing
(or
temperatures
high
positive
temperature
coefficient PTC of resistance) leads to a negative activation energy (From the fixed
-0.3 eV) of conductivity (Figs. 5.1.9 and 5.1.13).
composition experiment it was also concluded that the conductivity
variation
is due
temperatures.
to
the different
oxidation
states at different
In the previous section, we demonstrated
that the
defect model assuming Vo** compensation of SrLa' applies for the
case of x = 1.0. Rewriting Eq. 3.43 as
(6.7)
p = ([Vo**]/KR)1/ 2 po 2 1/4,
and given that KR = KRoexp(- AHR[RT), AHR is thus
= - 2AEod - 0.6 eV.
If the hole concentration is 0.57 /F.U. (as in Table 6.1.1) or 6.1 x 1021
cm- 3 , KR can also be obtained as 1.43 x 10-22 (cm 3 .atmi/ 2 ) at 800 *C
10-20 (cm 3 .atml/ 2 ) at I atm 02.
In the log (a) vs. log (P0 2 ) diagram (Fig. 5.1.15) the slopes start
and KRo = 9.53
x
to decrease at low P02's which suggests that the conductivity is
approaching a minimum.
If the mobilities of electrons and holes are
comparable, the minimum of conductivity corresponds to intrinsic
conduction where n = p.
If the hole mobility is higher than that of
the electron, which is more likely judging from the nature of valence
and conduction bands, there will be an offset in P0
2
between intrinsic
conduction and conductivity minimum as shown in Fig. 6.1.1.
It
implies that the conduction may have reached the intrinsic regime at
1000 *C and 100 ppm 02 (Fig. 5.1.15).
215
In the fixed composition
cooling experiment, the conductivity curve in Fig. 5.1.19 behaves like
a typical semiconductor.
If there is no leakage into the sample
prohibited
is
and
need
not
to be
holder, the
redox reaction
considered.
The activation energy of conductivity observed at high
temperature
in
100ppm
0.4 eV) is then
02 (activation energy
mostly due to band gap and the activation energy of the hole
mobility (Fig. 5.1.19).
with
temperature
at
The rapid decrease of thermoelectric power
high
is
another
An increasing contribution of
conduction is no longer negligible.
conduction
5.1.19)
In the intrinsic regime, electron
evidence of intrinsic conduction.
electron
(Fig.
temperature
will decrease
the magnitude
of tep.
(As
suggested in Section 6.1.1, if hole conductivity is higher than electron
conductivity due to mobility difference, the tep may not be equal to
zero at p = n).
.1.4
Oxygen Stoichiometry
of LaSrCuO 4 .8
We have shown that the transport properties of LaSrCu0 4 .8
depend strongly on the oxygen content.
involves the oxygen defect.
The defect model also
It is necessary for us to clarify the
oxygen stoichiometry of this composition.
The solubility of Sr in La 2 .SrxCu0
=
1.33 [Nguyen et al., 1981].
4.- 8
is reportedly as high as x
Sr is regarded as a dopant in this
notation and the materials are oxygen deficient except under high
oxygen pressures [Goodenough, 1973].
But as the Sr concentration
becomes comparable to the La content, as in the case of LaSrCuO 4. 8 ,
the definition of doping and hence the exact oxygen stoichiometry
becomes less clear.
The reason of adopting the form of "La 2 .
216
xSrxCuO4-,
x =
1.0" is that this composition retains the structure of
K 2NiF 4 as the parent phase La 2 CuO 4 . 8 . By this formula one assumes
electronic compensation of Sr ideally.
Any oxygen content less than
On the other hand as the pseudo-
4 is regarded as oxygen deficient.
ternary diagram of LaO1 .5 -CuO-SrO (Fig. 6.1.4) shows, LaSrCuO 4 -8 sits
It is not easily perceived that Sr is a dopant from
right in the center.
This composition also sits half way between
this point of view.
La 2 CuO 4 and Sr2 CuO 3 . As a result it seems more reasonable to write
this composition as LaSrCuO 3.5 ± or La2-xSrxCuO4-x/2+a, which assumes
ionic compensation is more likely.
The oxygen vacancy compensation
mechanism have been confirmed by this study and others [e.g. Opila
and Tuller, 1990] at high x.
Any oxygen content higher than 3.5 is
regarded as oxygen excess although the sites on which the oxygen
interstitials sit are the normal oxygen sites of the K2NiF 4 structure.
4 .S
6.2 Nd2 .CexCuO
System
6.2.1 Transport Properties of Nd2 CuO 4 .8
We have shown in the last chapter that Nd 2 CuO 4 is an n-type
The
semiconductor for a wide range of temperature and atmosphere.
conductivity can
be separated
into three temperature regimes (Figs.
5.2.1 and 5.2.2) as for a typical semiconductor.
One of the important
features of this material is that the high temperature regime is
dominated by a redox reaction, in contrast to intrinsic electron-hole
disorder.
This character is evidenced by the fixed composition
experiment
different
where
observed (Fig. 5.2.8).
observed by
the
conductivity
and
tep
curves
were
The - Po 2 -1/10 dependence of the conductivity
isothermal
annealing
217
experiment
also
serves
as
CuO
SrzCuO.
LazCuO4
LaOI.5i
SrO
-----
Laz-zSrzCuO4-z,2
---
La2 -zSri-xCu 2 06 -x/2
A: LaSrCuO-3.s
B: La2 SrCuZO6
Fig. 6.1.4
Pseudo-ternary diagram of La 2 0 3 -SrO-CuO system.
218
additional evidence that the redox reaction does occur and plays an
important role in determining the transport properties.
It is a common practice to obtain the activation energy of
mobility by comparing the activation energies of conductivity and
tep, since the former is a combination of carrier density and mobility
while the latter is usually a function of carrier density only.
It is
interesting to find in Fig. 5.2.8 that the electron mobility is thermally
activated in isobaric cooling process and is not in fixed composition
cooling process.
They seem to be contradictory
to each other.
However it is possible if the electron mobility is a function of oxygen
content other than temperature.
When the material is cooled with
fixed composition the oxygen content does not change so that the
electron mobility does not change.
On the other hand when the
material is cooled isobarically, the oxidation state of the material
changes accordingly (see the following section), resulting in change of
oxygen content.
So the mobility seems to vary with temperature.
(Note that the change of conductivity with temperature in both
coolings is still primarily due to the change of carrier density.
And
the difference in conductivity between the two coolings is primarily
due to the redox reaction.)
Since the lower temperature represents a
more oxidizing state, it implies that the electron has a lower mobility
in a higher oxygen content.
The difference in oxidation state for the isobaric and fixedcomposition cooling processes can be understood by the following
reasoning.
At equilibration, the oxygen content in the material is
related to the oxygen partial pressure (assuming ideal gas) and
219
Considering the following reaction
temperature of the environment.
and mass action equation
1/2 02
Ko = Kooexp(AHo/RT) = [Oi]/Po 2 1/2
-> Oix,
(6.8)
so that
[Oix] =
(6.9)
P 0 2 1/2Koexp(AHo/RT)
Suppose that the material is cooled from TH to TL, then
[Oix)T > [OixTL
for an endothermic reaction (AHo > 0) and
[Oix]TI < [Oi]TL
for exothermic reaction (AHo < 0) for the same P0 2 , assuming that Koo
At temperature TL the
and AH O are not functions of temperature.
oxygen
interstitial
concentrations
at equilibrium in both cooling
processes are just [Oix]TH and [Oix]TL respectively.
So from comparison
of oxygen contents at both temperature it is possible to determine
the sign of AHo.
In this derivation, the oxygen excess is assumed, but the result
is also valid for the oxygen deficient case.
In that case, the following
oxidation equation is used rather than Eq. 6.9:
1/202
+
Vox -+ 00', KO = KoOexp(AHo/RT) = [Vox]-IP
0
2-1 2 (6.10)
From the change of conductivity with temperature, it is concluded
that the oxidation reactions for both LaSrCuO4.6 and Nd 2 CuO 4 .a are
exothermic.
For
the results
of the
fixed composition
experiment
we
attributed the high temperature conductivity to intrinsic conduction
because (1) the redox reaction is mostly prohibited, (2) the tep
approaches zero at high temperature, suggesting n - p. and (3) there
are
turn-overs
in
the Jonker
220
plot
(Fig.
5.2.11)
in
oxidizing
atmospheres indicating the vicinity of n-p transition.
If this is true
the band gap is twice the activation energy of conductivity (Fig.
5.2.8), which is - 2 x 0.15 = 0.3 eV in 100 ppm 02.
For a typical semiconductor with three temperature regimes of
conduction, due to phonon scattering, the conductivity should have a
positive slope with 1/T in the saturation regime where the carrier
density is fixed by ionized dopants or impurities as in Fig. 5.1.19.
However in Fig. 5.2.1, the conductivity of Nd 2 Cu0 4 .,. increases with
temperature at all temperatures.
This is due to the narrowness of
the saturation regime so that only the transitions between regimes
are found at intermediate temperatures.
regime is
1 S/cm.
The conductivity in this
If the electron mobility is not a strong function
of dopant, it has a value of = 0.87 cm 2 /voltesec (see Section 6.2.4).
The carrier density is calculated to be - 7.2 x 1018 cm- 3 , which
corresponds to a singly-ionized impurity level of = 0.068%.
concentration
The electron
is related
to the thermoelectric
power by the following e uation for a non-degenerate semiconductor
Q=- kIn
q L
When
n
+Ae
j
(6.11)
Q and n are known Ncexp(Ae) can be calculated. For example
at 500 'C in 1 atm flowing oxygen, conductivity (a) - 3.2 S/cm and
electron
mobility (g) = 0.87 cm 2 /voltesec
6.2.4). Thus n - 2.3 x 1019 cm- 3 . For
(assumed, see Section
Q - -188 gV/*K, Ncexp(Ae) is -
2.05 x 1020 cm- 3 . From the coincidence of the curves in Fig. 5.2.7 it is
concluded that this constant is not a function of temperature and P0 2 However with the advent of the intrinsic conduction and degeneracy
221
at high temperatures, Eq. 6.11 is no longer good and it explains why
the tep saturates at very high temperatures (Fig. 5.2.8).
6.2.2 Defects in Nd2 CuO 4. 8
The magnitudes of tep and conductivity of Nd 2 CuO 4 4 8 were
found to increase with reducing atmosphere (Figs.5.2.5 and 5.2.6).
The = -1/10 power law dependence on P0 2 of conductivity however
can not be easily fit into any simple defect model. In the intrinsic
regime, n = p and conductivity is not a function of P0 2 . On the other
hand in the regime where n = 2[Vo**], n is proportional to P0 2 -1/6. So
in the transition between these two regimes, n will follow a PO 2 a
This reasoning can
power law with c varying from 0 to -1/6.
qualitatively explain the low P0 2 dependence of both properties. To
solve the problem quantitatively we have to consider the charge
neutrality equation as Eq. 6.3, in which all possible defects may play
Theoretically by fitting Eq. 6.4 to the
a role in different P0 2 ranges.
curves in Fig. 5.2.9, the equilibration constants can be obtained as
functions of P0 2 and temperature. However such an attempt was not
because
successful
of the
saturation
temperatures in highly reducing
of conductivity
atmospheres,
at
high
which can only be
explained by degeneracy of electrons at high concentration.
6.2.3
Oxygen
Stoichiometry
The oxygen content of Nd 2 -xCeCuO448 is still a matter of
Suzuki et al. [1990] reported a deficiency at 900 *C, 10of 8 is - 0.04 for x = 0 and - 0.008 for x = 0.15 by TGA and-
controversy.
3 atm Po
2
chemical titration analysis.
But Moran et al. (1989),
222
by using
that the both oxidized and
iodometric titration techniques reported
reduced samples show an oxygen level above the nominal value of 4.
on the other hand reported
Wang et al. (1990)
content of as sintered Nd 2 .Ce,Cu0
is always greater than 4 but
N 2 it could be either smaller or larger than 4
in
reduced
when
4 43
that the oxygen
depending on the Ce content.
In all cases, it is agreed that the
oxygen content decreases with reducing atmosphere and the electron
concentration increases with Ce doping up to x = 0.15.
to the following
According
redox reaction
and mass
action
1 2
2 / ,
(6.12)
equation:
00 -> 1/202
+
KR = n 2 [V'*
VO** + 2e,
0
so that
log(KR)
=
log([Vo''1)
+
(6.13)
2log(n) + 1/2log(PO2).
Eq. 6.13 holds regardless of any defect model.
Since aoe n and
n is
not a strong function of P0 2 , and assuming that the concentration of
oxygen
Nd
vacancies
2 CuO4.8
to the oxygen
is equal
8 in
nonstoichiometry
(by this we define the oxygen reference state in the
formula as exactly 4) then a slope of 1/2 is expected in the [2log(a) +
log(6)] vs. log(Po 2 ) plot.
We incorporate our conductivity data with
It is
TGA results from Suzuki et al. 119901 to verify this assumption.
found from Fig. 6.2.la that the slope is only - 3/10 suggesting that
the oxygen stoichiometry is less than 4 or there is cation excess.
adjusting
the
oxygen
stoichiometry
to
-
3.993 or a formula as
Nd 2 Cu03. 9 9 3. 3 we can obtain a 1/2 slope (Fig. 6.2.1b).
suggests that the
This value
average valence state of copper is < +2.
deviation from 1/2 slope at high temperatures and lower Po
be
understood following
the
argument in Section 6.2.1
223
By
that
The
2
s can
charge
3.01
1
Nd 2CuO 4
.3
1.0
0.0-
-1e.0 800 C
-.
-Oe
e'100
C
C
>++ 650 C
.
-2.0
-3.0
-4.0
-8.0
75)
-1.0
0.0
1.0
0.0
1.0
Log PO, (at=)
(a)
3.0
Nd2CuO3.9993.-.
1.0 +
0.0
~1.01..
seee
-e
4+++.
-4.0
0C
75 0c
700cc
65
-2.0
-3.0
-1.0
Log PO, (atm)
(b)
Fig. 6.2.1
[Log (a)
+
2Log (5)] vs. log (Po 2 ) of (a) Nd 2 CuO 4 .o.8 and (b)
Nd2CuO3.9993-8-
224
carriers begin to degenerate at high concentration.
6.2.4 Doping Effects of Ce
The apparent doping effect of Ce on Nd 2 CuO 4 is to increase the
conductivity
monotonically
up to [Cetot - 0.15 (Fig. 5.2.12 and
5.2.13), which is consistent with the donor nature of Ce 4 + on the Nd 3 +
site.
In Fig. 5.2.12 we also observed an increasing temperature range
in which the conductivity is relatively independent of temperature.
The redox effect on the conductivity of the undoped sample at high
temperature is no longer observed for x > 0.01 %.
If this regions
correspond to the saturation of ionization of Ce the electron mobility
can be derived assuming electron concentration is equal to the donor
concentration (n = [CeNd']).
For example, a = 220 S/cm at 450 *C and
1 atm 02 for Ndi. 85 Ceo. 15Cu04+8 and n = [CeNd'] = 15% so that g - 0.87
cm 2 /voltesec.
However the average valence state of Ce in Nd 2 .
is smaller than +4 (e.g. +3.84, Huang et al. [1989]) which
xCexCu04+s
means that some Ce 3 + exist in these materials or n < [Ce]tot in the
saturation regime.
than
0.87
mechanism.
The actual electron mobility may thus be higher
cm 2 /voltesec,
implying
a
large
polaron
transport
In Fig. 5.2.12 we also observed a slight decrease of
conductivity with temperature above 450 *C for large x's.
This can
be explained by the decreasing electron mobility due to increased
phonon
scattering
at higher temperature
as in LaSrCuO 4 .8 (Fig.
5.1.18).
This
transition
from
the
semiconducting
behavior
of
the
undoped sample to the metal-like behavior (temperature-insensitive
and high conductivity) of the heavily doped samples (Fig. 5.2.12)
225
appears to be in accord with the Mott transition described in Section
3.1.3.2.
According to the Mott theory, Nd 2 -xCexCuO443 will become a
metal when the following Mott criterion is met.
nd 1/3 aH - 0.25,
(3.25)
where nd is the doping concentration and aH is the hydrogenic radius
of the donor orbital.
From Fig. 5.2.12 it is found that the transition
occurs when 1% < nd < 5%, which implies 3.1 < aH < 5.3
A.
aH is related
to the static dielectric constant of the host material (Kst) and the
effective mass of the electron (m*) by the following equation
aH = (h/2te)2 (Kst/m*).
Values of aH ranging from 0.9 to 640
A
range of materials [Edwards and Sienko,
have been reported for a
1978].
Since a highly
conducting material such as Nd 2 CuO 4 . 8 usually has a low dielectric
constant, the relatively low value of aH obtained in this system is not
unexpected.
The other effect of Ce doping is manifested by the even smaller
P0
2
dependence of both conductivity (Figs. 5.2.15, 5.2.16) and tep
(Fig. 5.2.18).
is approaching
It serves as a further evidence that the electron density
saturation due to heavy doping and is relatively
The TGA data by Suzuki et al.
independent of redox processes.
[1990]; Takayama-Muromachi et al. [1989]; and Wang et al. [19901
also show the insensitivity of oxygen stoichiometry to Po 2 at high x,
consistent with this argument.
The effect of the average valence state of Ce in Nd 2-xCeCuO4+a
mentioned before needs further discussion.
take on 3+ or 4+ valence states.
In general Ce ions can
When Nd is substituted by isovalent
Ce 3+, there will be no direct effect on the net charge carrier density
226
But the multivalent nature of Ce ions in Nd 2 xCexCuO4+6 can affect the behavior of the electrical properties in a
Consider the following redox and
way different from others.
and oxygen content.
ionization reactions and mass action equations:
KR' = [Vox]P021/ 2
Oo -+ 1/202 + Vox
K, = n2[V 0 **]/[Vox].
Vox -+ Vo** + 2e'
In the undoped material, electrons are released from the Vo level
and are excited to the conduction band.
Ce 4 +, it increases the electron
When Nd is substituted by
density and/or oxygen interstitial
concentration by either of the following reactions.
2CeO 2 + CuO Nd2Cu04-+ 2CeNd' + Cucux + 2e' + 40 0 X + 1/202,
2CeO2 + CuO Nd 2Cu4-+ 2CeNd' + Cucux + 400x + Oi".
Under reducing conditions,
the Ce 4 + levels will serve as traps for
electrons released from the oxygen vacancy levels (see the following
schematic diagram) by the following reaction:
2CeNd' + 00 = 1/202
+ VO**
+ 2 CeNdx
2
K = [CeNdx] 2 [Vo**]P021/ 2 /[CeNd*] 2 = KR'KI[CeNdx] /(n[CeNd*] )2
Conduction Band
Vo e
2Ce 4 +
Conduction Band
Vo
t
V0
2Ce 3 +
alneBand, ooz
VlneBand
Reducing
Oxidizing
It is seen that the the electron concentration and oxygen vacancy
concentration are direct functions of [CeNdx/[CeNd-].
227
The conductivity
of Nd 2 -xCexCuO 4+8 is thus dependent on the initial amount of Ce4+ and
the relative position and density of states of these two levels (Ce 4 +
and Vox) in the band gap.
Above x = 0.15 a decrease of conductivity of Nd 2 -xCexCuO 4+8
The electron conductivity
with x was observed (Figs. 5.2.12, 5.2.13).
may decrease with donor doping for several reasons.
It could be due
to (1) as in La 2 -xSrxCuO4.8 case, that ionic defects begin to overtake
the compensation
reaction
so that the carrier density does not
increase much with doping; the mobility on the other hand may
decrease due to the interaction of electrons with a more disordered
lattice; and/or (2) the formation of a second phase which could
decrease the hole concentration and complicate the defect structure.
For case (1), it has been shown by Moran et al. [1989] that the
electron concentration increases and [Ce4+] decreases monotonically
with Ce doping up to 15 %.
Huang et al. [1989] and Wang et al.
[1990] in their analysis of lattice constants also imply that an abrupt
change of ionic defect concentration with x is unlikely up to x = 0.2.
The decrease in electron mobility with x may thus be very plausible.
But it needs further evidence.
In the case of (2), even though the solubility of Ce is reported
to be
0.20 [e.g. Wang et al.,
1990],
we can not exclude the
possibility that our samples contain a second phase above 0.15 Ce
since the effective solubility limit of Ce seems to be dependent on
material processing and reportedly ranges from 10% [Markert et al.
1989] to 20% [Wang et al., 1990].
1%)
of NdCe 3 0 7 has been
A very small amount (less than
confirmed
microprobe analysis in Nd1 . 85 Ce.
228
15 CuO 4.y
by X-ray
and
electron
sample by Huang et al.
[1989].
When a second phase forms, the conductivity may change
due to the second phase as well as the compositional change of the
Further structure analysis may be needed to clarify
parent phase.
this problem
6.3 YBa 2 Cu 3.Tix0
6+ 8
System
It is observed in this study that YBa 2 Cu 3 -xTix0 6 +8 (0
exhibits
essentially
the
transport
same
properties
sxs
and
0.1)
defect
chemistry as the undoped material (Figs. 5.3.1-5.3.4), which is rather
unexpected, judging from the donor nature of Ti substitution on Cu.
To explain the possible mechanism, let us consider the following
charge neutrality equation for this system:
(6.14)
2[Ticu**] + p = 2[Oi"] + n.
Ti
Presumably
doping
interstitial concentrations.
will
increase
electron
and/or
oxygen
But since the 1-2-3 compound is believed
to have a large oxygen nonstoichiometry,
there is a reservoir of
oxygen defects (interstitials) which is of the order of 8/F.U.(0 ! 8 s 1).
It is very likely that the Ti doping in this study (s 01./F.U.) is still
outnumbered by the oxygen interstitials so that the charge neutrality
can be approximated by the following equation
(6.15)
p = 2[Oi"],
which means that Ti doping does not affect the carrier density
substantially.
This is why the conductivity shows no doping effect
(Fig. 5.3.1).
Recently, in a study on the effect of La doping on the Ba
site of YBa 2Cu 3 06+8 by Hong et al. [1990], little change of conductivity
was observed.
They viewed this material as highly acceptor-doped
due to the built-in large oxygen nonstoichiometry.
229
The addition of
even substantial amounts of aliovalent impurities results in only
modest changes in the net excess acceptor content. This is consistent
with our argument proposed above.
Following the mass action equation of the oxidation reaction
that p = 2 [Oi"] = (2Ko) 1/3P02 1/6 , it implies that the normalized tep
(eQ/2.3k) should be proportional to 1/6 log(PO 2 ) if the tep is a direct
function of hole concentration as Eq. 3.16. The reason why it is not
observed at low temperatures and high PO 2's (Fig. 2.3.4b and Fig. 9b
in the paper by Nowotny et al. [1990]) can be explained as the result
of the degeneracy effect at high hole concentration as discussed
before.
Even though no literature report exists for the solubility limit
of Ti on YBa 2 Cu 3 0 6+5 , it should be no less than 10% of all Cu ions
according to Xiao et al. [1987].
If all the Ti4+ ions go on the Cu(l) site,
this substitution can be as high as 30% since the number of Cu(I) site
is only one third of the total Cu sites.
of Ti and Cu [Huheey,
A comparison of the ionic radii
1983] indicates that Ti ions are generally
slightly smaller than Cu ions.
This solubility then seems to be limited
only by the amount of the compensating oxygen interstitials the
Since the YBa 2 Cu 3 0 6 +8 structure can
structure can accommodate.
accommodate as much as 7 oxygens in a unit cell it is not surprising
that it has high solubility of Ti.
No data on the oxygen stoichiometry of Ti-doped YBa 2 Cu 3 06+
has been reported in the literature.
The oxygen content of Fe-doped
YBa 2 Cu 3 0y samples are shown to be constant at y = 6.87 ± 0.05
[Obara et al., 1988] with Fe concentration.
230
From the electrical data
and the argument stated above, a constant S with Ti concentration
can be expected.
231
Chapter 7
Conclusions
Both the conductivity and thermoelectric power measurements
of La 2 CuO 4.8 lead to the conclusion that the hole concentration is
proportional to Po 2 1/6 , which is consistent with a defect model
It also requires a high hole mobility
interstitials, electrons and holes.
with
outnumber
electron
to
respect
mobility
interstitials
oxygen
temperature and P0
2
oxygen vacancies,
doubly-ionized
involving equilibration between
when
for a p-type
ranges studied.
vacancies
oxygen
the
conduction
in
The thermal-insensitivity
conductivity implies a near zero redox enthalpy.
The metal-insulator transition of La 2 CuO4.
all
of
observed at low
temperature can be related to the antiferromagnetic ordering.
The electrical conductivity of La 2 -x.SrxCuO4.3 increases with x in
the range of 0
0.3 and decreases with x beyond that range.
x
It
can be explained by a transition from electronic compensation to
ionic compensation of the dopant.
The gradual increasing P0
dependence of conductivity in the range of 0.4
x
2
1.0 also reflects
the increasing role of oxygen nonstoichiometry on the conductivity.
The decreasing hole mobility with increasing x suggests that the
metal-insulator transition with x observed in La 2 -x.SrxCuO4.3 above x
= 0.9 is of the Anderson type.
On the other hand the change of slopes
in log (a) vs. 1/T plot observed in La 2 -x.SrxCuO 4 .8 (0.4 s x
400 *C is
due
to
the
reduction
concentration.
232
which
decreases
0.9) at -
the carrier
The conductivity of LaSrCuO 4 -8 follows a - P0 2 1/4 law, which is
consistent with the defect model that the dominant defect species is
the oxygen vacancy.
At high temperatures in reducing atmosphere
LaSrCuO4-8. undergoes a p-n transition.
Nd 2 CuO 4+ 8 is an n-type semiconductor, based on the P0
2
dependence of conductivity and the sign of thermoelectric power.
The oxidation reaction occurring during isobaric cooling at high
The electron
temperatures dominates the carrier formation process.
mobility
is
not
thermally
activated
as
proved
from
a fixed-
composition cooling experiment.
The conductivity of Nd 2 CuO 4 +8 follows a = P0 2 -1/10 law, which
confirms with n-type semiconduction approaching degeneracy in low
PO2's and intrinsic conduction in high PO2's.
Upon doping with Ce, the conductivity Nd 2CuO 4 +8 increases with
Ce concentration
and becomes temperature
and P 0
insensitive,
2
indicating the donor nature of Ce substitution on Nd sites.
semiconductor-metal
transition is a Mott type transition and the
hydrogenic radius of this system is in between 3.5 - 5.3
Ti-doped
This
A.
YBa 2 Cu 30 6+8 has electrical properties similar to the
undoped material
in terms of magnitude,
Po2
and
temperature
dependence, indicating that the Ti doping (up to 3.3% of total Cu site)
of
YBa 2 Cu
properties.
3 0 6 +8
has little effect on the transport and defect
The aliovalent nature of Ti is swamped due to the large
oxygen nonstoichiometry.
233
Chapter 8
Future Work
Since the conductivity
of La 2 .SrxCu O4.
becomes PO2-
independent at x = 0.05 the defect model proposed in Regime I in Fig
A similar transport and
3.2.1 was not verified in this research.
defect study at low dopant concentration range (0 < x < 0.05) would
be necessary to further support the defect model.
In La2-xSrxCuO4.6 we observed that the conductivity decreases
with [SrLa'] at high x's because of the decreasing mobility with [SrLa'I.
In any case it does not support the prediction of the defect model
that p oc
[SrLa']1/
2
explicitly.
Further
measurements
thermoelectric power of La2.xSrXCuO4- in the 0.4
s xs
of
the
1.0 range to
see how the hole concentration varies with [SrLa'] may be necessary
to verify the defect model.
The strong similarity of the electrical properties of YBa 2Cu 306.6
and
LaSrCuO 4 .8 (or Lai. 2 SrO. 8 CuO 4 .8) is a rather interesting
phenomena.
It implies a similar transport mechanism and defect
structure for these two materials.
The reason why the latter is not a
superconductor [Sreedhar and Ganguly, 1990] could be due to the
lower conductivity (hole concentration and mobility) of the latter.
If
we can increase the hole concentration by annealing the material in
pressurized oxygen it may become superconducting.
A further study
may prove to be constructive and worthwhile.
La2.xSrxCuO 4 .6, when prepared
by the chemical
solution
method, was observed to contain an increasing amount of the second
234
phase La 2 SrCu 2 0 6 at high Sr concentration.
This phase is closely
It can be
related to LaSrCuO 3 .5 +8 structurally and compositionally.
considered as an intergrowth of double oxygen perovskite and SrO
layers (Fig. 8.1.1a) compared to the intergrowth of one oxygen
perovskite layer and one SrO layer in La 2 -x.SrxCu0 4.- (Fig. 8.1.lb).
Fig. 6.1.4 also shows how these two compositions sit closely to each
LaSrCuO 3 .5 +8 will decompose into La 2 SrCu 2 0
other.
6
in reducing
conditions or when there is SrO deficiency through the following
chemical reaction:
2LaSrCuO 3.5 +
--
La 2SrCu 20 6 + SrO + 802-
When the calcination temperature is not high enough, SrCO 3 instead
of SrO is formed or if the calcined powder is exposed to air for a
period of time before sintering, SrCO 3 tends to precipitate out as a
result of CO 2 absorption [Sreedhar and Ganguly, 1990], making the
This is probably the reason why an increasing
powder Sr-deficient.
amount of second
phase of La 2 SrCu 2 0
preparation of La 2 .xSrxCuO4-8.
6
was
observed
during
However a more careful and detailed
study on the processing and structural analysis is necessary to clarify
this confusion.
The true reason for the decrease of conductivity
xCexCu04+ with x above x = 0.15 is still unknown.
in Nd 2 -
The decreasing
electron mobility or creation of a second phase are just two possible
causes.
A detailed study in the 0.15 s x s 0.20 range may be useful
to solve the problem.
When the sample is exposed to a temperature gradient the
thermal diffusion will bring about the compositional gradient across
the sample, also denoted as the Soret effect.
235
In measuring the tep of
0
K2 NiIFS sabs
K2NiF4
(b)
(a)
Fig. 8.1.1
6
Structures of La 2 SrCu206-8 (a) and LaSrCuO4.8 (b).
236
these materials by constant temperature gradient method this effect
has to be considered.
large
oxygen
defect
Since the materials studied all have relatively
concentrations
and
probably
high
oxygen
diffusivities the ionic contribution to the thermoelectric power may
not be trivial.
By careful comparison of the thermoelectric power
between the two measuring techniques one should be able to provide
information about ionic conduction.
237
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