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1967
An x-ray study of the lead titanate-bismuth
chromate system
Tsen-tsou Shih
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Shih, Tsen-tsou, "An x-ray study of the lead titanate-bismuth chromate system" (1967). Masters Theses. Paper 5164.
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AN X-RAY STUDY OF THE LEAD TITANATE-BISMUTH
CHROMATE SYSTEM
BY
TSEN-TSOU SHIH -I tj tf ()
A
129:-=;19
THESIS
submitted to the faculty of
THE UNIVERSITY OF MISSOURI AT ROLLA
in partial fulfillment of the requirements for the
Degree of
MASTER OF SCIENCE IN CHEMISTRY
Rolla, Missouri
. 1967
Approved by
~~~-'~~=~~~---
(advisor)
ii
ABSTRACT
The lead titanate-bismuth chromate system was studied
employing x-ray diffraction techniques at both room and
high temperatures. Samples were prepared by sintering
stoichiometric mixtures of the corresponding oxides
followed by air quenching,
Bismuth chromate was prepared
by resintering and air quenching for four times.
The
results of the analyses show the structure of BiCr0
be tetragonal with 8 molecules per unit cell,
3
Solid
to
solutions exist over the range 100 to 35 mole percent
PbTi0 3 of the binary system, although small amounts of
other phases are present in some regions.
X-ray data at room temperature indicate the tetragonal perovskite structure exists over the range of 100
to 65 mole percent PbTi0 ,
3
PbTi0
From 60 to 35 mole percent
the structure is cubic.
3
Dielectric measurements show that the specimen
containing 95 mole percent PbTi0
3
is ferroelectric with
a Curie point of 475°C, slightly lower than that of pure
PbTi0 .
3
From 90 to 50 mole percent PbTi0
3
the samples
are too conductive for meaningful dielectric ' measurements.
High temperature x-ray results show that the Curie
point drops almost linearly from 100 to 65 mole percent
PbTi0 ,
3
The phenomenon is exhibited by ferroelectric
binary systems containing PbTi0
PbTi0 -BiFe0 system.
3
3
3
with the exception of the
iii
ACKNOWLEDGEMENTS
The author wishes to thank Dr. William J. James,
Director of the Graduate Center for Materials Research and
Professor of Chemistry, and Dr. Robert Gerson, Professor
of Physics, for their guidance, support, and
during the course of this investigation.
e~couragement
The author is
also greatly indebted to Mr. Gary D. Achenbach and Mr.
Harlen Rice for their assistance with the high temperature
x-ray unit.
The financial assistance of the Atomic Energy
Commission in the form of a research fellowship is also
gratefully acknowledged.
iv
TABLE OF CONTENTS
LIST OF TABLES.
Page
...........
vi
.
LIST OF FIGURES
I.
II,
.
~
.
B.
Lead Titanate, PbTi0 • . .
3
Solid Solutions ·of PbTi0 ,
3
Bismuth Chromate, BiCr0
vii
1
2
Perovskite Ferroelectrics.
D.
,
,
A.
C.
"III.
.
INTRODUCTION .
REVIEW OF LITERATURE ,
......
3
..·...
2
11
·...
.
1.8
21
EXPERIMENTAL • .
25
·...
25
. , • . • . ••
25
1.
Analytical balance . . . . . . . •
25
2.
Ball mill. . .
25
A.
Materials.
.
B.
Apparatus . . . . . . ,
3. Pill die
4. . Crucible .
..•.• .
.......
, . .
....
... . .......
5.
Furnace,
6.
Mortar and pestle.
7.
X-ray diffractometer
8.
High temperature, high vacuum
25
25
25
26
"
....
attachment . . . . • . • . . .
26
26
C.
Preparation of Samples .
26
D.
Sintering Procedure . .
28
E.
X-ray Diffraction Analysis at Room
Tempera ture .
F.
. . . . .
. . . . . . ..
High Temperature Techniques . .
29
30
v
IV.
RESULTS AND DISCUSSION .
.
...
.....·..
Sintering.
B.
Crystallographic Results at Room ,
·..
Temperature . . .
c.
High Temperature X-ray Analysis. •
36
37
.. ...·..
BIBLIOGRAPHY
35
35
A.
. ..
Page
44
APPENDICES
A.
Materials.
B.
Apparatus.
C.
X-ray Data for PbTi0
III
.
•
•
•
•
•
.. ....
47
and BiCr0 3 . ••
D.
3
Sintering Data . . ' . •
E.
X-ray Diffraction Data for the PbTi0 BiCr0
F.
3
·.....
·
System . . . . •
.
46
49
51
3
56
High Temperature X-ray Diffraction
Data for the PbTi0 -BiCr0
3
VITA
f
•
3
System. , . ,
. . . . . . . .. . . . · . . .
65
71
vi
LIST OF TABLES
Page
Table
I.
II.
III.
IV.
Representatives of perovskite-type compounds.
Bond length in tetragonal and cubic PbTi0
3
,
structures • .
...... .
Comparison of observed and calculated intensities from neutron diffraction of PbTi0
3
X-ray data on the PbTi0 -BiCr0 system. .
3
3
6
17
17
41
vii
LIST OF FIGURES
Figure
1.
Page
Typical hysteresis loop of a ferroelectric
..... .
. ... ..
3
2.
Crystal structure of cubic barium titanate .
5
3.
Crystal structure of barium titanate showing
crystal.
.
.
"
"
"
"
octahedra of oxygen atoms about titanium
atoms. .
4.
.
.
5
.
perovsk~te
Classification of the
A
2+ 4+
B 03-
type compounds according to the constituent
ionic radii.
5.
B
Graph of ionic radii of B4+ ions and po1arizabi1ity of A2+ ions for some of the
compounds of the A2+B4+0 perovskite structure type.
6.
. . ..
. . . .
.. . .
3
.
. . .. ..
... ..
.
8
Three dimensional graph of theperovskite2+ 4+
type A B 03 compounds using ionic radii of
the A2+ and B4+ ions as two coordinates and
the polarizability of the A2+ ions as the
third coordinate .
7.
Classification of the A3 +B 3 +0 -type
3
compounds according to the constituent ionic
radii . .
8.
,
., ..
3
.
.
. .
.
.
.
.
.
12
.
"
. . . .
"
.
.... ..
"
12
Unit cell volume as a function of temperature of PbTi0
11.
3
Axial ratio as a function of temperature of
PbTi0
10.
10
Lattice parameters as a function of temperature of PbTi0
9.
9
3
.
.
.
.
.
.
.
.
.
.
.
.
Specific heat of lead titanate PbTi0 ,
3
.
13
13
viii
Figure
12.
Page
Variation of permittivity with temperature
of PbTi0 .
3
13.
. .•
14
Crystal structure of tetragonal PbTi0 : oxy3
gen octahedron defining the lattice . . . . •
16
.
.
• .
.
.
• .
.
. .
.
.
.
14.
Environment of Ti in PbTi0 . . . . . . . . •
3
16
15.
Environment of Pb in PbTi0 . . . . • .
3
16.
16.
Lattice spacing of the PbTi0 -CaTi0 system
3
3
at room temperature.
19
Lattice spacing of the PbTi0 -CaZr0 system
3
3
at room temperature.
19
Lattice spacing of the PbTi0 -casn0 system
3
3
at room temperature.
•
19
········....
17.
·· · · ·
18.
· ·
19.
20.
21.
·
···....
····
Phase diagrams of the PbTi0
side of the
3
systems PbTi0 -CaTi0 , PbTio -Cazro , and
3
3
3
3
PbTi0 -Casn0 · . . . . . . • . . • . . . . •
3
3
Phase diagrams of the systems PbTi0 -BaTi0 ,
3
3
PbTi0 -srTi0 , and PbTio -CaTi0 . . . . . .
3
3
3
3
24.
. •
Complete phase diagram of the PbTi0 -BiFe0 3
3
system .
. . .
.............
Siemens high temperature x-ray diffractometer.
25.
22
The volume and axial ratio cia of the unit
cells of solid solutions in the PbTi0 3
BiFe0 system versus the composition . .
3
23.
20
Change in the lattice constants in a system
of solid solutions of PbTi0 -BiFe0 as a
3
3
function of the composition . . . . . . . . .
22.
20
.
.
.
...
.
.....·
"
.
"
.
22
22
..
27
.
27
Siemens high temperature x-ray diffractometer and high vacuum system .
. .
.
.
.
ix
Page
A typical plot
ot
the lattice parameters
versus temperature for
';.7.
28.
29.
~bTi03-BiCr03
system.
Lattice parameters of
PbTiO 3 -BiCrO 3
-. the
system . . ..
".
....
Variation of the
v9~ume
cia ratio of-the
PbTiO~-BiCro3
Curie points of the
34
38
of the unit cell and
system . . . .
~bTi03-Bicro3
system .
.
39
42
1
I.
In 1960, BiFe0
structure.
3
INTRODUCTION
was reported(6) to have the peroYskite
The compound is believed to be ferroelectric
.(19) with a Curie point of about 900 o C, which is the
The ionic radius of cr 3 +,
highest Curie point known.
°
0.63 A, is about the same as that of Fe
3+
0
,0.64 A.
There-
fore a perovskite-type structure might be predicted for
BiCr0 .
3
Single phase Bicr0
was reported (21) in 1965 to
3
have a tric1inic pseudocubic perovskite structure.
The Curie point of pseudo-binary solid solutions of
perovskites containing PbTi0
3
usually decreases upon
substitution of other perovskite components as discussed
in Sec. II-C.
system.
The sole exception is the PbTi0 -BiFe0
3
3
Here the tetragonal distortion from the ideal
peroyskite structure varies from 1.063 for pure PbTi0
1.17 for 32 weight percent PbTi0
3
3
to
causing the Curie point
to increase as the concentration of BiFe0
3
is increased.
The purpose of this investigation was to prepare and
study solid solutions of PbTi0
3
containing Bicr0
3
with
regard to crystallographic symmetry and electrical
properties.
It was of particular interest to see if ferro-
electric properties were enhanced upon substitution of
Bicro ,. as found in the PbTi0 --BiFe0 system, or diminished,
3
3
3
. as observed in other pseudo-binary systems containing
2
II.
A.
REVIEW OF LITERATURE
Perovskite Ferroelectrics
Crystals lacking a center of symmetry may be piezo-
electric.
A piezoelectric crystal shows a displacement of
electric charge upon an application of external stress.
This behavior is exhibited by 20 of the 21 non-centrosymmetric crystal classes.
shows pyroelectricity.(l)
A subgroup of piezoelectrics
The spontaneous polarization of
a pyroelectric crystal is altered with change in temperature.
Both piezoelectricity and pyroelectricity are
inherent properties of a crystal wnich require a crystal
structure to contain a polar axis along which atomic
displacement can take place asymmetrically.
Ferroelectrics are a class of pyroelectrics with the
additional property that spontaneous polarization can be
reversed by applying a sufficiently intense electric
field.
The presence of domains* in the ferroelectric
crystal produces a hysteresis in the polarization when an
alternating field is applied.
A typical hysteresis loop
for a ferroelectric crystal is shown in Figure
i.
The
hysteresis disappears at a certain temperature, called the
Curie point.
The structure undergoes a transition at
this temperature from the polar to non-polar state; the
high temperature form of the crystal is known as para-
*
A part of a twinned crystal which is itself a true
single crystal.
3
E
Figure 1.
crystal.
Typical hysteresis loop of a ferroelectric
4
electric. (2)
At the structure transformation, the Curie
point, the dielectric constant reaches a maximum.
this temperature the dielectric constant
~
Above
taIls off
according to the Curie-Weiss law: (2)
E -
1 = C!(T-T )
c
where
TC is · a temperature close to the eurie point.
e is a constant with the dimensions of temperature,
Among the various types of ferroelectrics, the perovskite family has received much attention following the
discovery of ferroelectricity in barium titanate BaTi0 ,
3
The general formula of compounds belonging to this family
is AB03' where A is a monovalent, divalent, or trivalent
cation and B is a pentavalent, tetravalent, or trivalent
cation respectively.
The structure of the ideal perovskite
can be visualized from Figures 2 and 3 for cubic BaTi0 ,
3
The larger cation Ba (orA ion) is located in the center
of the cubotetrahedron and has a coordination number 12.
The smaller cation Ti Lor B ion)
is 6 coordinated and is
located in the center of the octahedral framework of
oxygens.
In general, the structure is slightly distorted
from the ideal cubic type.
Table I lists several
perovskite-type compounds.
Not all compounds with the
formula AB0 , however, have a perovskite-type structure.
3
An important factor that determine~ the structure type is
the geometrical packing of the ions in the lattice.
The
5
-@o)(ygen
Figure 2.
Crystal structure of cubic barium titanate. (3)
0"
Figure 3.
Crystal structure of barium titanate showing
octahedra of oxygen atoms about the titanium atoms. (3)
6
TABLE I
C - cubic; T = te~ragon3.1; 0 = orthorhombic. A star in front of the
values of the lattice paramcters denotes a multiplc unit cell. The orthorhombic distortion is described in terms of monoclinic Ilxes. (F) in the
last column indicates that the phase transition to the cubic phase
coincides with the ferroelectric Curie point .
.Transition
Structure at 20°C
Compound
Symmetry
a=b
BaTi03
SrTi0 3
CaTi03
PhTi0 3
CdTi03
tcmperaturo
to cubic phase
Lattice parameters
T
C
0
T
0
3.992
3.905
*3.827
3.905"
*3.791
I
cia
1.010
-
I
y
I
(OC)
120 (F)
-220
12GO
0.999
90° 40'
1.063
1.004
9P 10'
230
215
490 (F)
-
PbZr0 3
PbHfO.
0
0
*4.159
*4.136
0.988
0.991
90° "
90°
KNbOa
Np,NbO.
AgNbO.
0
0
0
4.038
*3.!)14
*3.944
0.933
0.991
0.993
90° 15'
90° 41'
90° 34/
435 (F)
G40
550
KTI1.03
NaTaO a
AgTa0 3
C
3.989
*3.890
*3.931
0.998
0.992
90° 29'
90° 21'
-260 (F)
470
485
0
0
-
. (1)
Representatives of perovskite-type compounds.
7
packing of this structure can be related to the ionic radii
by the following equation:
RA + R0 ::: t
12 (~ + RO)
where
t
=
tolerance factor.
RA
=
ionic radius of larger cation A.
~ = ionic radius of smaller cation B.
R
o
= ionic radius of oxygen.
For an ideal perovskite, t
is exactly equal to unity.
For perovskites of the type A2 +B 4 +o
3
and A3 +B 3 +0 , the
3
tolerance factor has been assigned a value between 0.99
and 0.77(4) (5) although exceptions have been reported.
(4)
Roth
classified perovskites according to the ionic radii
of the constituents (Figures 4-7).
A three-dimensional
4
graph was also constructed for the perovskite type A2 +B +0
3
,
'
compoun d s uS1ng
A2+ an d B4+ 10ns
as t wo co or d'1na t es an d
2
the polarizability of the A + ions as the third coordinate
(Figure 6).
As very little is known quantitatively about
the polarization of the trivalent ions in perovskite
A3 +B 3 +o
3
compounds, this factor has not been used to
°3 , .
3+ 3+
classify these structures for A B
It can be seen
from Figure 7 that all the perovskite-type structures occur
in the upper left portion of the diagram,
3 3
No A +B +0
3
compound is known to have a simple cubic perovskite-type
structure.
As Bi
3+
0
3+
has a radius of 0.96 A (between Y
and
sm 3 +), Figure 7 predicts the possibility of Bier0
3
being
8
O. c;nrnp'"l1l1IS sturU",! in the per'sent work thut hove the ~truct"r{' shown by
tlw arp;ls 1lOllUdf'!l hy dnslll'(111l1l's:~. compollnds notsturli('11 in til{' pl'l':-:C'nt work
t.hht. ar .. w.. :-:llInl·d to h.:.l.\'{' th(~ !itrtlC:llln~ shown by thn an'as hOUllfi('d hy cla~il(·d
11rH's; 0, tmTlII011f\(b stuclierl in th(~ prrsent work that do not han' the pcrovskite
tYJJr. ~lrll('t,lll"f'; X, pn:-:itioTl or Coml)o:.;itions studicu in th(~ prc~('nt work that do
not [orrn A+2B H O J (,CHT 1POIlWl,s.
_A~ til<' N)mpOlinci Ca;\lnO.l hn' not hern sti,,1ic~ in thr ]>rr~cnt work nml confllctmJ.!' rC'port.'i on its symuwtry rxist. it is t('ntativ("ly It'ft on the borclt'r bd\\"Prtl
orthorhomhic arlu pSl'uuocuhic typl'S und is shown by t[ucstion mark on'r symhol.
Figure 4.
.
2+ 4+ -type
Classification of the perovsklte
ABO
compounds according to the constituent ionic radii.
14 )
0, Compounds -having ferroelectric or antiferroelectric
structure types; 0, compounds having cubic or pseudocubic
structure types; X, position of composition that does not
form A2+B4+0 compound.
3
Graph of ionic radii of B4+ ions and polarizability of A2+ ions for some of the compounds of the
A2+B4+0 perovskite structure type. (4)
3
Figure 5.
9
PI
--t
T/11. lW
c" f ·
o
C1
:
:
"
I
Pb
j~ :
~""::-I"
I
.~':·":'.:.:I:·>:':~:
'.' _ ... :.j::_:::::'.:'.::.:.::-:.:.. :'{.:..1
;"'"
'f},Q
Bo
N
+c:c
I.L.
a
Cd ~
.J
Sr . iii
<C
N
Co
ir
<C
.J
fr
I ,. i:-::J-:::;'T1;:' r
~.
,;;, .1 l
1r
u
r
• •
Co
~"'l'
v. - - _ .. - - - - - - - - - -. - - - - - Cd
~,
j,
lin V Ti Sn
tr----r-r
HI Z,
RADIUS OF SH
Ce U
'O~lS. A
n.
0, Position of compounds of the orthorhombic perovskite
structure
type;~,
position of compounds of the cubic or
pseudocubic perovski te structure type i 0, position of
compounds having ferroelectric or antiferroelectric perovskite structure types.
Coarse shading indicates boundary between orthorhombic
and pseudocubic structure types; medium shading, boundary
enclosing compounds of ferroelectric and antiferroelectric
structure types; crosshatch shading, boundary between
perovskite and SrV0 3 structure types. The boundary between
cubic and pseudocubic perovskite types has not been shown
on this diagram for the sake of clarity.
Figure 6.
Three dimensional graph of the perovskite-type
' "lon1C ra d'11- 0 f th e A2+ an d B4+
A2+B4+ 03 compound
s uS1ng
ions as two coordinates and the polarizability of the A2+
ions as the third coordinate. (4)
10
o~
li'
Ce+~
Nd+ S
Sm"
,\,+3
I
.SO
.l...- r
.90
1.00
•
IJIJ
Radius of B3 + ions,
0, Rhombohedral perovskite,
~
>
~t._
120
1:30
A
90 0
;
DI orthorhombic
perovskite (CaTi0 3 type) ;~, T1 2 0 3 structure typei<>,
corundum structure type; 0, La 2 0 3 structure typei 0,
compounds not studied in the present work that are not
assumed to have the structure shown by the areas bounded
by dashed lines.
3+ 3+
Figure 7. Classification of the A. B 03-type compounds
according to the constituent ionic radii. (4)
11
a perovskite-type structure of low symmetry.
Recently,
Filip'ev(6) and Fedulov(7) reported that bismuth ferrate,
BiFeo 3 , has a rhombohedral distorted perovskite structure.
This provides further evidence of the possible existence
of perovskitic Bicr0 3 , since the ionic radius of cr 3 +
o
3+
0
(0.63 A) is essentially equal to that of Fe
(0.64 A).
B.
Lead Titanate, PbTi0 3
Lead titanate has been studied extensively by many
investigators.
Naray-Szabo(8) first reported the structure
to be a tetragonal perovskite with
a = 3.89
o
A, and
~ =
o
4.13 A, one molecule per unit cell.
Precise lattice para-
meters at room temperature were determined in 1951 by
Shirane et al(9) with a
=
3.894
A,
and c
=
4.140
A.
The
space group is P4mm.
The axial ratio cia at room temperature is 1.063,
markedly larger than any other perovskite with the same
structure.
Above room temperature c decreases and a
increases until just below the transition point, 490°C,
cia is 1.02.
Figures 8-12 show the temperature dependence
of the lattice parameters, the axial ratio, the'cell
volume, specific heat, and dielectric constant respectively.
.
A furt h er p h ase transl. t 'lon (12) occurs a t approxlmately -100°C as the crystal is cooled slowly.
The low
temperature phase appears to be non-ferroelectric and
possesses a multiple tetragonal cell.
The
ne~v
dimensions
12
~.I
S
"""""--.,-----r----r----,---...:.,..---.
~IO
4.05
.
...
~
.
s:
E
lJ.oo
A
~
u
3·'f°L~~---
1.8S0L---IO.LO---:-2..LOO--:-"30.J.O--""7"'~070---::5-!-O=-O---;,-:lOO·
Tempe-rat.", C·C)
Figure 8. Lattice parameters as a function of temperature
of PbTi0 3 . (10)
'.08 r----r---,---,---,----,------.,
I. 0 Ij.
5'a.
I·O~
\
.
I
I
I
1.0° 0L _ _ _
, o.Lo--~:----::!:-;:---::-:!-;:-- ~LOO----",.,JoO
Figure 9. Axial ratio as a function of temperature of
PbTi0 3 . (10)
13
'2·8J:::""""--r--...---.,.---r--r---,
Figure 10. Unit cell volume as a function· of temperature
of PbTi0 3 . (10)
100
tJ"I
Q)
rtj
Q)
80
r-I
0
S
""r-I
60
+l
cO
40
cO
0
Q)
.r::
0
-.-I
lI-I
20
-.-I
0
Q)
~
CI)
0
0
100
200
300
400
500
600
Temperature ( °C)
Figure 11.
Specific heat of lead titanate PbTi0 3 , (9)
14
8
6
2
o
o
400
200
T
600
(DC)
Figure 12. Variation of permittivity with temperature
of PbTi0 " (11)
3
15
are a'
=
4a,
£' =
2c.
The atomic positions of the room temperature phase
of lead titanate were determined in 1956 by Shirane et
al(13) using both x-ray and neutron diffraction.
The
results are given in Figures 13-15 and Tables II-III.
Taking Pb at the origin, both 01 (located above and below
Ti along the tetragonal axis) and 0Il (the other oxygen
atoms) are shifted in the same direction by the same
o
0
amount, 0.47 A.
Ti is shifted by 0.17 A in the same
direction as the three oxygens.
remains undistorted.
The oxygen octahedron
Figure 13 shows the structure of
tetragonal PbTi0
with oxygen defining the lattice. The
3
large shifts of Ti and Pb ions cause the change in bond
length.
The bond lengths in the cubic structure at 490°C
and those of the tetragonal structure at room temperature
are given in Table-.II.
Passing from the cubic structure
above the Curie temperature to the tetragonal structure,
the oxygen octahedron suffers only a uniform elongation
due to the tetragonal distortion.
The Ti-O
I
bond under-
goes a drastic change as can be seen from Figure 14.
The
o
Ti-O (+) bond length is 1.78 A, much shorter than the sum
I
o
of the Goldschmidt radii which is 1.96A. The Pb-OII
o
0
length is 2.53 A, and the Goldschmidt radius is 2.78 A.
Megaw(2) (14) explained the large axial ratio and high
Curie point of PbTi0
3
as a consequence of homopolar bond
2
formation by Pbi the tendency of Pb + to form unsymmetrical covalent bonds, as is found in tetragonal PbO.
pb
@)Pb
00
aTI
Figure 13. Crystal structure of tetragonal PbTi0 3 : oxygen
octahedron defining the lattice. (13)
Ou
(a)
Figure 14. Environment of
Ti in PbTi0 3 . (13)
(b) II
Figure 15. Environment of
Pb in PbTi0 3 . (13)
17
TABLE II
o{(+> means the 01 is close to Ti; Onc+) is cl080 to Pb
All distances in Angstrom units
Tetragonal
+ 0·040
dzo = +0·112
Tetragonal
0%=0
3·90
4·15
3·90
4·15
3'07
Ti-OI(+>
Ti-OI(_)
Ti-Ou
1·78 }
2·38
1·98
2·08 }
1·95
1·98
Ph-OI
Ph-OII(+)
Pb-Orr(""",)
2·80
2·53 }
3·20
2·76 }
2·85
2·80
dZTl =
a
c
Cubio
(a.t 490 0 C.)
Bond length in tetragonal and cubic PbTi0 3 structures. (13)
TABLE III
First run
(Counts/O'l min.)
.
hkl
001
100
101.110
Io-A
207
224
llO
III
002
200
012
201.210
1I2}
211
202
220,003
122
221,
300
103
310,301
113
311
222,023
~
Ic- A
205
254
2625
104
624
290
216
III
2627
203
585
305
242
182
185
Second run
(Counts/0'5 min.)
"
Io-B
192
218
90
2594
214
633
262
247
{ 142
68
361
318
304
238
Ic- B
206
264
109
2549
191
563
292
246
129
73
353
346
307
249
282
307
1230
347
1307
305
Comparison of observed and calculated intensities from
t 'lon OL~ PbTl'0 3 " (13)
· ~
neutron d lfLrac
18
lies at the apex of a flat pyramid with a square base
containing O's at the corners.
o
The pyramid height is
0
0.46 A as compared vlith 1.16 A in PbO.
This covalent
system of Pb-O bonds creates conditions which favor the
development of unsymmetrical Ti-O bonds, or the off-centering of Ti in the oxygen octahedron, to produce a polar
axis.
C.
Solid Solutions of PbTi0 3
Lead titanate has the highest Curie point among the
perovskite-type ferroelectrics.
Almost any substitution
of Pb or Ti with suitable atoms which form a perovskitetype lattice causes a lowering of the Curie point.
The
systems PbTi0 3 -caTio3 ,(lS) (~6) PbTi0 3 -CaZr0 3f (17) and
PbTi0 3 -CaSno 3 (17) were studied in recent years.
The
crystallographic .results are given in Figures 16-18.
The
phase diagrams of the systems of the lead titanate side
were constructed from x-ray phase analysis and the dielectric measurements as shown in Figure 19.
It can be seen
that the Curie point falls with the increase of the con--:
centration of the second component in all three systems.
Figure 20 shows the dependence of the Curie point
upon composition when Pb is replaced by Bar Sr, or Ca.
In
three cases the Curie point decreases almost linearly with
increasing content of the substituted atoms.
The axial
ratio cia of the tetragonal solution at room temperature
decreases accordingly.
The two lower transition tempera-
19
Q
A
l/J
if!
It'll
1J!1l
42
It
U.ft7
4.1
4.0
,I
•
3.9
UJt7
a
I
/J
cia I.{/ul/
3.8
.12'
f.dJI/
flO
0
Call0.
20
60
40
.\. (%)
80
I.IU
100
PbTlO,
UI7Il
I'h 1(03
Figure 16.
Lattice spacing
Figure 17.
of the PbTio 3 -CaTi0 3 system
A
I.lJt'
B!J
PI •
1t'1/
Wt.% CnZrO,
Lattice spacing
of the PbTi0 3 -CaZr0 3 system
at room temperature. (171
at room temperature. CL6)
o
iQ
Mole "/0 CaSn03
ZO
'Il
51/
IIIJ
IflO
MJIl
J..9J1J
b
I.t711J
Figure 18.
Lattice spacing of the PbTi0 3 -Casno 3 system at
room temperature. (17)
20
t>
0
.....+'
~
500
400
300
-.-\
0
04
200
C)
-.-\
1-1
::s
100
C)
a
0
10
20
PbTi0 3
30
40
50
Mole% AB03
Figure 19.
Phase diagrams of the PbTi0 3 side of the
systems (1) PbTio j -caTi0 3f (2) PbTi0 3 -CaZro 3 , and (3)
PbTio 3 -CaSn0 3 " (17
6oo.----r-.,.-~--r~.--,--.,_-.__r__,600
.
Cubic
400(,)
(,) 400
o
oj
o
200
.2
e
(I)
Co
E
:retrogonal
o
~
Mole % of Sr or Co .
Figure 20.
Phase diagrams of the systems PbTi0 3 -BaTi0 3 ,
PbTi0 3 -srTi0 3 , and PbTio 3 -caTio 3 .(2)
21
turesof BaTi0 , however, decrease with increasing
3
concentration of Pb.
The PbTi0 -BiFe0 system was investigated by Fedulov.
3
3
(18) (19)
A continuous series of solid solutions was found
existing in the entire range of the sys'tem.
A narrow two
phase region was observed from 65-72 weight percent BiFe0
as seen from Figures 21-23.
3
In the tetragonal phase the
lattice parameter c increases sharply with increasing bisThe cia ratio
muth ferrate whereas a decreases somewhat.
increases from 1.063 for 100 percent PbTi0
68 weight percent BiFe0 "
3
3
to 1.17 for
On transferring from the tetra-
gonal modification to the rhombohedral modification, the
°3
~v
unit cell volume decreases sharply,
= 3.5 A.
rhombohedral region the parameter
~,
unchanged with increase in BiFe0
concentration.
3
is practically
rhombohedral angle remains constant.
known system containing PbTi0
3
Bismuth Chromate, BiCr0
in which the Curie ' point
3
decreases.
3
The earliest report of BiCr0
(8) in 1947.
The
This is the only
increases as the concentration of PbTi0
D.
In the
3
was made by Naray-Szabo
He described the structure of Bicr0
tetragonal perovskite with a
= 7.75
with B molecules per unit cell.
o
A, and
3
as a
0
S
= 7.95 A,
The ceramic sample was
prepared by heating a stoichiometric mixture of oxides
(nitrates or carbonates) at 700-800 o C for 3 hours.
Detailed X-ray results of his studies are given in
22
Ufo mol.
Ufo mol.
1I.1J5
I'
"
"
11..050
Rhombohedra
II
Tetragonal
::
,
1.10
Te~agonal 63.00
£050 Rhombohedral I[ ap" 1i9
°Rh
62.00
a
IJ.n
Ufo wt.
Figure 21.
60
80
q.0 60
Ufo wt.
100
Bl F'eD l
Change in the
Figure 22.
80
roo
BiFeOJ
The volume and
lattice constants in a
axial ratio cia of the unit
system of solid solutions
cells of solid solutions in
of PbTi0 3 -BiFe0 3 as a
function of the composi-
the PbTi0 3 -BiFe0 3 system
versus the composition. (18)
(18)
.
t 1on.
T. ·C
800
600
1100
200
o
,
110
Gn
BiFeCl, cone .• wt.
Figure 23.
80
100
~.
Complete phase diagram of the PbTi0 3 -BiFe0 3
system.
(I) Tetragonal region; (II) tetragonal +
rhombohedral region; (III) rhombohedral region. (19)
23
Appendix C.
In 1954, Keith(5} reported that it was not possible
tp confirm the structure reported by Naray Szabo.
stated that the volatility of Bi 0
2 3
He
made it difficult to
obtain solid state reaction.
.
(20)
In 1962, Buhrer
tried to synthesize BiCr0
from
3
He failed,
both oxides and coprecipitated hydroxides.
however; to obtain a single-phase perovskite.
More recently, Sugawara et al. (21) prepared single
phase BiCr0
3
by sintering the mixed oxides at 700°C under
a pressure of 40 kbars and then quenching.
X-ray diff-
raction showed it to have a distorted perovskite structure
with a triclinic pseudo-cubic unit cell.
parameters were
a
= 89°10'.
~
=£ =
o
3.90 A, b
=
The lattice
°
3.87 A,
~
=
y
=
90°35',
Sugawara attributed the complicated distorted
structure to the covalent character of Bi3+.
information was reported except that Bicr0
3
No further
was not ferro-
magnetic down to 77°K.
Venevtsev et al(22)
studied the effect of the addition
of Bi 0 'cr 0 to BaTi0 .
2 3
2 3
3
It was found that in the range
of small additions, the Curie temperature was not lowered,
and for some specimens it was even somewhat higher than
that of the initial BaTi0 .
3
The tetragonal distortion
disappeared and the cells of the perovskite phase became
.cubic at a content of more than 2.6 mole percent BiCro ,
3
Ikeda and Okano(23) studied the change in the piezo~
electric behavior of the PbTi0 -Pbzr0 system upon addition
3
3
24
of BiCr0 "
3
They investigated mainly the rhombohedral-
tetragonal phase boundary of the system upon addition of
BiCr0 "
3
The width of the investigated region was from 40
to 70 mole percent Bicro "
3
The boundary between the
tetragonal (F t ) and rhombohedral (F ) phases, lies at 55
r
mole percent Pbzro ,and ,does not shift with
3
up to the Curie point, 370°C.
PbTi0
3
side gradually with
t~mperature
This boundary shifts to the
incre~sing
Bicr0
3
substitution.
The ferroelectric Curie point was found to decrease with
increasing BiCr0
3
content.
25
III.
A.
EXPERIMENTAL
Materials
The materials used in the preparation of the various
samples were PbO, Ti0 2 , Bi 0 , and cr 0 , The purity and
2 3
2 3
manufacturer of each of these oxides are listed in
Appendix A.
B.
Apparatus
The uses of the various- apparatus will be described
here, and a list of apparatus is given in Appendix B.
1.
Analytical balance . . A single pan electric balance
was used in weighing the materials to make the samples.
The sensitivity of the balance was 1/10,000 gram.
2.
Ball mill.
A ball mill was used for mixing the
samples for sintering.
The ball mill was constructed from
a 250 ml plastic bottle that contained about 25 ceramic
balls of 0.4 inch in diameter and could be rotated at an
inclined angle by a variable speed motor.
3.
pill die.
A stainless steel die of 3/8 inch
diameter was used to press the mixed oxides to form discs
for sintering.
4.
crucible.
A morganite crucible with a lid, lined
with platinum foil, was used to sinter the samples.
The
crucible was approximately O.B inch in diameter and 0.875
inches high.
5.
Furnace,
Two furnaces . were used to sinter the
26
samples.
One was a platinum-wound resistance furnace with
a maximum temperature limit of 1300 oC.
The other was a
Kanthal-wound resistance furnace with a maximum temperature
of 100QoC.
controls.
Both furnaces were equipped with automatic
Temperatures were accurate to within
f
8°C.
The furnaces were each calibrated twice to ensure correct
temperature.
6.
Mortar and pestle.
An agate and a porcelain mortar
and pestles were employed to grind the sintered sample
.
~
in preparation for x-ray diffraction analysis.
7.
X-ray diffractometer.
A Siemens diffraction unit
was used for crystallographic analysis.
radiation, A
8.
=
Ni filtered CuKa
° was used.
1.542 A
High temperature, high vacuum attachment.
The high
temperature unit was employed to determine the Curie
points of the samples in the system.
ture of the unit was l300 oC.
torr.
The maximum tempera4
The vacuum was below 10-
A tantalum heating element with the dimensions
3/16" x 5/16" was used as both sample holder and heating
stage.
Figures 24 and 25 show the construction of the
high temperature attachment and the high vacuum system.
C.
preparation of Samples
The compositions were arbitrarily selected at 5 or 10
mole percent intervals between 100 percent lead titanate
and 100 percent bismuth chromate.
stoichiometric amounts
of materials were weighed to an accuracy of 1/10,000 grams.
27
Figure 24.
Siemens high temperature x-ray diffractometer.
Figure 25.
Siemens high temperature x-ray diffractometer
and high vacuum system.
28
The materials were mixed in a ball mill.
was added to form a slurry.
Distilled water
After rotating the sample
for 4-5 hours, the slurry was filtered with distilled
water and then dried in a drying oven.
Samples were then
ground, by hand, to a fine powder (approximately 300 mesh)
and pressed into discs 3/8 inch in diameter and 1/8 to
3/8 inches in
height~
The pressure applied was 50,000 psi
in most cases.
D.
Sintering
Proc~dure
The discs were placed in a platinum-lined morganite
crucible with a stainless steel spatula.
crucible was put into a preheated furnace.
The covered
After a
temperature recovery period of about 10 minutes, the
sample was usually sintered for 2 hours under one atmosphere pressure.
After the reaction period, the crucible
was removed from the furnace and air 9uenched.
The discs
shrank only slightly because of the high pressure applied
before sintering.
As the sintering temperatures used in
this system were generally above 900°C, incomplete reactions on the surface of the discs were evident due to the
volatility of Pba and Bi 0 "
2 3
The outer parts of the discs
were removed using a sheet of abrasive paper.
was
The sample
ground by hand with a mortar and pestle to a fine
pO\vder of approximately 300 mesh.
The sample was then
used for x-ray diffraction studies.
For compositions of 40 mole percent PbTi0
3
to
Bi~r03
29
resintering techniques were employed in an attempt to
obtain complete reaction.
This was accomplished by re-
peating the procedures stated in the last paragraph, that
is; regrind, repress, and resinter.
For 100 percent Bicr0
3
the sample was preheated at a
temperature of 400°C for 1-2 hours.
The temperature was
then increased and sintering continued for about the same
period of time.
Sintering under an oxygen atmosphere was
also carried out.
Thesintering temperatures and the
other conditions during sample preparation are listed in
Appendix D.
E.
X-ray Diffraction Analysis at Room Temperature
X-ray diffraction patterns were made of each sintered
sample.
The samples were mounted on the center of
a 3/2" square glass plate.
A minute quantity of
vaseline was spread on the glass for adhension of the
powdered sample.
The surface of the sample '1as made flat
by pressing it against another glass plate.
A scanning
speed of lO/min and a chart paper speed of 1 ern/min were
generally used.
A slower speed of 0.25°/min and a chart
paper speed of 2.5 em/min were used to increase the
resolution of certain reflections.
An entrance slit of
1 rom and an exit slit width of 0.1 rom were used.
The x-ray
unit was aligned frequently and provided very good
resolution for Ka
reflections.
1
and Ka , especially for the high angle
2
30
The lattice parameters were determined from the x-ray
patterns.
The "d" values for all possible values of "hkl"
were calculated using the digital IBM-360-40 computor
located on the V.M.R. campus.
The volume of the unit cells
was determined from the following equations.
Tetragonal
Cubic
F.
High Temperature Techniques
The Curie point of each specimen was determined using
a high temperature x-ray diffractometer.
A tantalum,
instead of platinum, sample holder was used because
tantalum has a very simple structure and d-spacings which
are quite different from those of the perovskites.
The
reflections contributed by the tantalum stage did not
superimpose upon those of the perovskites.
Since tantalum
reacts readily with oxygen and nitrogen at moderate
temperatures, it was necessary to use a vacuum of the
order of 10 -4 torr.
This was accomplished by using a
forepump and a diffusion pump.
The procedure for determining the phase transformation, ferroelectric
+
paraelectric, was as follows:
A fine powder sample, mixed with drops of ether to
form a slurry, was mounted on the surface of the Ta heating
element with a stainless steel : spatula.
The amount of
the sample was just enough to fO:r1l1 a thin layer.
The
surface of the sample was made as even as possible.
'rhe
31
heating element was then fixed in place.
Alignment was
made according to the procedures listed in the Manual.*(24)
The vacuum pump system was connected to the high temperature attachment and the system evacuated to the desired
pressure.
To obtain the best resolution, a scanning rate of
O.25°/min and a chart paper speed of 2.5cm/min were chosen.
An entrance slit of I.nun and an exit slit of O. 2mm were used
to obtain reasonably high intensities.
The temperature
was measured with a chromel-alumel thermocouple, attached
to the back of the Ta element, and a portable millivolt
potentiometer.
When a vacuum of 10
-4 torr
was reached, the x-ray
diffraction pattern of a particular pair of
was recorded.
refle~tions
In this series of samples studied, the pair
of reflections (200) and (002) was selected because these
peaks possess the maximum splitting among the sets of
reflections with strong intensities in the room temperature x-ray pattern.t
*
For an unknown reason the correct reflection angles
could not be obtained. Therefore a correction of the
true angles. was made with true angles obtained from
the room temperature stage as a standard.
t
The (100) and (001) reflections had stronger intensities but their separation was less. The same was true
for (110) and (all).
(211) and (112) had nearly the
same peak separation as (200) and (002) but the
intensities were too low for good resolution.
32
starting at room temperature, x-ray patterns for
various temperatures were obtained.
The temperature
interval varied from lOO°C at temperatures far below the
Curie point to within lODe in the vicinity of the Curie
point.
X-ray patterns of temperatures above the Curie
point up to 700°C were obtained.
The equilibrjum tem-
perature of each setting could be attained within 10
minutes.
A slight fluctuation of the temperature (±2°C)
during the measurements was observed occasionally.
For a few samples, x-ray patterns of 26 range 15-60
degrees at room temperature were made.
The relative inten-
sities and the sharpness differed from those patterns
obtained with a room temperature stage.
The low angle
reflection intensities were lower and the high angle reflection intensities were higher; all the peaks were broader.
These were the consequences of the ~neven surface of
the sample on the Ta stage and the smaller amount of
sample mounted on the sample holder.
A complete x-ray
pattern, from 15-60 degrees of 26, was made of the 90 percent PbTi0
3
Curie point.
composition at a temperature just above the
Only lines belonging to a simple cubic
pattern of the high temperature phase of the sample were
evident as well as several peaks of the Ta stage.
The tetragonal and cubic lattice parameters, ' S and
~,
were calculated for each temperature from x-ray data obtained at the various
temperature5~
A typical plot of the
lattice parameters versus temperature is shown in Figure
33
26.
The Curie point was determined from the intersection
of the lattice parameters of tetragonal and cubic regions.
The x-ray data are given in Appendix F.
4.00
3.99
Composition:
80% PbTi0 -20% B
3
3.98
......
3.97
o,::t;
'-'
~
(])
3.96
\
\
+J
<l)
\
S
cU
~
co
\
3.95
\
I
0,
<l)
C)
-~
-p
4J
rO
H
\
3.94
3.93
3.92
3.91
100
0
200
300
400
500
60
Temperature (oC)
Figure 26.
A typical plot of the lattice parameters versus temperature
BiCr0 3 ::>ystem.
35
IV.
A.
RESULTS AND DISCUSSION
Sintering
The determination .of the time and the temperature
for sintering the mixed oxides was a trial and error process.
Bismuth chromate was made by repetitive sintering
at 800, 850, 900, and 950°C for a period of 2 hours in each
sintering.
Resintering techniques were required because
the higher temperatures necessary to provide sufficient
reaction caused some Bi 0 to melt in the mixture.
2 3
A
temperature of 1000 to 1050°C and a period of 2 hours were
used for samples on the PbTi0
3
side of the system.
Higher
sintering temperatures were required to ·obtain complete
solid state reactions as the concentration of BiCr0
increased.
was
3
For example, sintering at 950°C for 95 mole
percent PbTi0
3
sample gave complete reaction, whereas sih- .
tering at the same temperature for 50 mole percent PbTiO j
gave incomplete reaction.
For samples : frotn
45 mole
percent PbTi0
to 100 percent BiCr0 temperatures beb'leen
3
3
800 and l200 0 c were employed. Resintering and multplestage sintering were also carried out in an att~mpt to go
to higher temperature without melting the samples.
In
several cases, the sample fused.
Each sample was pressed into a disc before sintering,
in part to shorten the diffusion path length and to prevent
the vaporization of low melting point oxides.
Weight
36
losses during sintering were found to be negligible extil.e pt
for those samples sintered at temperatures higher than
llOOOC in which case the discs were found to be nonhomogeneous after sintering.
Therefore, a closed system would
be required for high temperature sintering.
The color of PbTi0
3
is brown • . As the BiCr0
3
content
is increased in samples of the PbTi0 -BiCr0 system, the
3
3
color of the powders changes gradually to dark green.
The
hardness of the sintered discs generally increases as the
BiCr0
B.
composition is increased.
3
Crystallographic Results at Room Temperature
Pure PbTi0
3
was prepared by sintering equimolar
mixtures of PbO and Ti02 at IOOOoe.
X-ray results were in
good accordance with Shirane'.s .• lattice constants and
indexing for pure PbTi0
3
as given in Appendix E.
The
method for preparing bismuth chromate was described in the
previous section.
X-ray diffraction
patte~ns
showed
primarily a single phase with a perovskite tetragonal
structure.
The lattice parameters are a
=
° c
7.855 A,
=
o
7,902 A.
The pattern is similar to that of Naray-Szabo's
except for a few extraneous peaks.
Peaks at d
= 3.56,
o
2.64, 2.46, and 1.67 A, corresponding to the positions of
er 0 are evident, but strangely there is no evidence of
2 3
Bi 0 in the x-ray spectra.
2 3
Weight losses were too small
to account for the absence of Bi 0 as resulting from
2 3
evaporative loss.
Attempts to index x-ray data by using
.37
Sugawara's triclinic lattice constants were unsuccessful.
Further studies of Bicr0
3
are necessary and it is probable
that high pressure techniques will be required to prepare
single
p~ase
material.
In the PbTi0 -Bicr0 system, single phase solid
3
3
solutions were prepared over the range 100 to 50 mole
percent PbTi0 . From 100 to about 60 mole percent PbTi0
3
3
the structure is tetragonal. The lattice parameter £
decreases sharply and a increases gradually with increasing concentration of BiCr0
3
(Figure 27).
The cia ratio
(Figure 28) decreases from 1.064 for pure PbTi0
for 65 mole percent PbTi0 .
3
to 1.008
The volume of the unit cell
(Figure 28) decreases as the BiCr0
content is increased.
3
Between 60 to 50 mole percent PbTi0
apparently cubic.
3
3
the structure is
Below 45 mole percent PbTi0 , x-ray
3
results show multiple phases with a predominance of cubic
phase up to 35 mole percent PbTi0 .
3
appear at this composition.
Some cr 2 0 peaks
3
Below 30 mole percent PbTi0 ,
3
the x-ra.y patterns were too poor to be analyzed.
Further
studies in the region below 45 mole percent PbTi0 are
3
required.
The application of high pressure during sinter-
ing may be helpful. ·
c.
High Temperature X-ray Analysis
The Curie points of ferroelectric materials are
generally determined from dielectric constant measurements.
It was not possible to do so for the solid
38
4.14
4.12
4.10
4.08
4.06
-
o~
........
4.04
I-l
Q)
+J
Q)
4.02
~
I-l
to 4.00
O!
Q)
0
·n
3.98
.jJ
.jJ
to
H
3.96
3.94
\
\
\
I
.
P-D-o-ou-o
'
3.92
.
3.90
3.88
100 90
80
70
60
50
40
30
Mole percent PbTi0
Figure 27.
system.
20
10
0
3
Lattice parameters of the PbTi0 3 -Bicr0 3
39
1.06
1.04"
63.0
--.
1. 02
C"1
o&<tl
.....
r-I
r-I
Cl.l
,
()
\
\
cd
~
1.00
62.0
4.l
•.-1
~ .
p
"
()
Cl.l
~
0
4-l
0
Cl.l
.§
61.0
60.0
100
90
80
70
60
50
40
30
Mole percent PbTi0
Figure 28.
20
10
0
3
Variation of the volume of the unit cell
and cia ratio of the PbTi0 -Bicr0 3 system.
3
r-I
~
40
solutions of this system.
The samples were too conductive,
no doubt as a consequence of electron hopping, to give
sharp peaks in the dielectric constantvs. temperature
plot. The room temperature resistivity varies from about
8
6
10 ohm-cm for 10 mole percent BiCr0 to 10 ohm-ern for 40
3
mole percent BiCro , as measured by Mr. James Canner of the
3
physics department. The Curie . point of only a 95 mole
percent PbTiOi 'sample could be determined from dielectric
measurements and it was found to be 475°C.
It was therefore necessary to obtain the Curie points
of the solid solutions from 95 to 65 mole percent PbTi0 3
by high temperature x-ray techniques. The results are
given in Table IV and illustrated in Figure 29.
The Curie
point of the 95 mole percent PbTi0 3 sample determined by
this method is 465°C, in resonable agreement with that
obtained from the dielectric measurement.
were measured twice.
measurements was
±
Several samples
The average deviation between
10ce.
possible errors that can occur
in high temperature x-ray diffraction techniques are as
follows:
First, the thermocouple is attached to the back
of the sample holder; therefore, the temperature registered
might differ from that of the sample itself.
Second, the
surface of the sample is rough, causing some local variation in temperature from point to point.
Third, the thick-
ness of the sample mounted on the sample holder is difficult to reproduce from measurement to measurement, making
it difficult to assure temperature reproducibility.
TABLE IV
No.
PbTi0 3
X-ray data on the PbTi0 -BiCr0 system
3
3
Parameters
Volume of
Curie Pt.
cia
0
0
03
(OC)
a (A)
c (A)
Unit Cell(A )
I-A
2-A
100
95
3.888
3.893
4.137
4.080
62.556
61.828
1.064
1.048
3-13
90
3.898
4.041
61.391
1.037
4-A
5-A
85
80
3.906
3.910
4.020
3.999
61.339
61.144
1.029
1.023
6-A
7-A
75
70
3.912
3.911
3.979
3.961
60.888
60.587
1.017
1.013
8-A
9-A
10-A
Il-B
12-A
13-B
14-B
65
60
55
50
45
40
35
3.916
3.926
3.925
3.924
3.924
3.920
3.922
3.947
60.521
60.495
60.458
60.421
60.421
60.236
60.328
1.008
1.000
1.000
1.000
1.000
1.000
1.000
2l-D
0
7.955
7.902
60.945
1.006
Sample
t
*
1101e%
490
475t
465
410
440
345
325
310
290
250
240
190
Phases . Pr
Tetragona
Tetragona
Tetragona
Tetragona
Tetragona
Tetragona
Tetragona
Tetragona
Cubic
Cubic
Cubic
Cubic and
Cubic and
Cubic and
and Cr 2 0
Tetragon~
Determined from dielectric measurement by James Canner in the Physics D
The other phase is not yet identified unambiguously, possibly the tetrag
structure.
42
500
400
.-..
C,)
0
.......
+l
s::
'r-!
0
0.,
300
Q)
.r-!
H
~
U
200
100
100
95
90
85
80
Mole percent PbTi0
Figure 29.
system.
70
75
65
60
3
Curie points of the PbTi0 3 -BiCr0 3
43
It is seen from Figure 29 that the Curie point drops
almost linearly as the concentration of BiCr0
increased.
is
3
This is consistent with the crystallographic
results at room temperature; one would expect in the simplest case that the less the distortion from the ideal
cubic perovskite, the lower the Curie point.
The crystal
structure of 60 to 50 mole percent PbTi0
room temperature.
is possible.
is cubic at
3
A Curie point below room temperature
Therefore low temperature x-ray studies are
necessary in order to construct the complete phase diagram of the single phase solid solution region of the
system.
Inasmuch as PbTi0
is reported to have a .low
3
phase transition at -lOO°C, low temperature x-ray studies
over the single phase solid solution region would be of
interest.
It is worth noting that as in other pseudo-binary
systems, PbTi0
3
has an extraordinary capability for
bringing Bicr0
into its perovskitic lattice.
3
.
The similarity of Cr 3+ to Fe 3 +rn1ght
lead one to
expect the behavior of the PbTi0 3 -Bicr0 3 to approximate
that of PbTi0 -BiFe0 , Such is not the case, and these
3
3
results clearly show that ionic size of the ferroactive
ion is not a unique factor in determining the tendency
to form perovskitic structures of similar properties.
44
V.
BIBLIOGRAPHY
1.
Jona, F. and G. Shirane (1962) Ferioe1ectric Crystals,
Pergamon Press, New York.
2.
Megaw, H. D. (1957) Ferroelectricity in Crystals,
Methuen, London.
3.
Kittel, C. (1965) Introduction to Solid state Physics,
John Wiley & Sons, Inc.
4.
Roth, R. s. (1957) J. Res. U. S. NatL Bureau of
Standards, ~, 2, p. 75.
5.
Keith, M. L. and R. Roy (1954) Am. Mineralogist,
p. 1.
6.
Fi1ip'ev, S. A., N. P. Smo1yaninov, and E. G. Fesenko
(1960) Soviet Physics-Cryst., ~, 6, p. 913.
7.
Fedulov S. A., Y. N. Venevtsev, G. S. Zhdanov, and E.
G. Smazhevskaya (1961) Soviet Physics-Cryst., 6,
5. p. 640.
-
8.
Naray-Szabo, I.
30.
!.'
p.
9.
Shirane, G. and S. Hoshino (19S1) J. Phys. Japan,
4, p. 265.
!,
10.
Shirane, G., S. Hoshino (1950) Phys. Rev., 80, p.
1105.
11.
Bhide, V. G., K. G. Deshmukh, and M. S. Hegde (1962)
Physica, ~, p. 871.
12.
Kobayashi, J.,and R. Ueda (1955) Phys. Rev.,
1900.
13.
Shirane, G., and R. Pepinsky (1956) Acta Cryst.,
p. 131.
14.
Megaw, H. D.
15.
Sauer, H. A' I S. S. F1aschen, and D. C. Hoersterey
(1959) J. Am. Ceram. Soc., ~, p. 363.
16.
Sa\.;aguchi IE., T. Mi tsuma I and Z. Ishi (1956) J. Phys.
Soc. Japan, 11, 12, p. 1298.
1\
(1947) Muegyetemi Koz1emenyek,
(1954) Acta Cryst.,
1,
~,
~.'
p.
~,
p. 187.
45
17.
Fedu1ov, S. A., and Y. N. Verievtsev (1964) soviet
. Physics-Cryst.,!, p. 286.
18.
Fedulov, S. A., Y. N. Venevtsev, G. S. Zhe1anov, E. G.
Smazhevskaya, and I. S. Rez (1962) Soviet PhysicsCryst., 2, 1, p. 62.
19.
Fedu1ov, S. A., P.B. Ladyzhinskii, I. L. Pyatigorskaya, and Y. N. Venevtsev (1964) Soviet PhysicsSolid State, ~, 2, p. 375.
20.
Buhrer, C. F. (1962) J. Chern. Physics,
21.
Sugawara, F., and S. Iida (1965) J. Phys. Soc. Japan,
20, p. 1529.
22.
Venevtsev, Y. N., G. S. Zhdanov, S. N. Solov'ev, E. V.
Bezus, V. V. Ivanova, S. A. Fedu1ov, and A. G.
Kapyshev (1961) Soviet Physics-Cryst., ~, p. 594.
23.
Ikeda, T., and T. Okano (1964) J. Applied Physics, 3,
2, p. 63.
24.
~,
3, p. - 798.
-
High Temperature High Vacuum Horizontal X-ray Diffractometer Attachment, Instruction Manual,
Materials Research Corporation, Orangeburg, N. Y.
June, 1964.
APPENDICES
A.
Materials
B.
Apparatus
C.X-ray Data for PbTi0
3
and Bicr0
3
D.
Sintering Data
E.
X-ray Diffraction Data for the
F.
PbTi0 -BiCr0 System
3
3
High Temperature X-ray Diffraction
Data for the
PbTi03~Bicro3
System
46
APPENDIX A
Materials
The following is a list of the materials used in this
investigation.
Lead oxide (FbO).
1.
yellow)
2.
I
Laboratory chemical grade (mono-
Fisher Scientific Company, Fairlawn, N. 'J.
Titanium oxide (Ti0 2 ).
Certified reagent grade,
Fisher Scientific Company, Fairlawn, N. J.
3.
Bismuth oxide (Bi 2 0g).
Certified reagent grade,
Fisher Scientific Company, Fairlawn, N. J.
4.
Chromium oxide (CrZ03)'
Chemically pure grade,
J. T. Baker Chemical Company, Phillipsburg, N. J.
47
APPENDIX B
Apparatus
The following is a list of the appar.atus used in ·this
investigation.
1.
Analytical balance.
Sartorius (multi-purpose),
Type 2.403 (single-pan), 0-100 gm, Aloe Scientific Company I
st. Louis, Missouri.
2.
Mortar and pestle, agate.
Fisher Scientific
Company, Fairlawn, N. J.
3.
Mortar and pestle, porcelain.
Fisher
Scienti~ic
Company, Fairlawn, N. J.
4.
Ball mill, variable speed.
Located in Graduate
Center for Materials Research, University of Missouri. at
Rolla.
5.
Crucible, recrystallized alumina.
Type N4429,
Morgan Refractories, England.
6.
Pl~tinum
foil, high purity.
0.001 inch thickness,
A. D. Mackey, Inci., New York, N. Y.
7.
Furnace, electrical.
Platinum-wound resistance,
located in ChemicaJ. Engineering building, University of
Missouri at Rolla.
8,
;Furnc3.c·e,
-electrical.
<
4.
' .
.,
c. ,
. . ' ..
Kanthal-wound resistance,
located in Graduate Center for Materials Research,
University of Missouri at Rolla.
9.
X-ray Diffractometer.
Siemens Crystalloflex IV,
48
Type U13, Siemens America, Inc., Long Island, N. Y.
10.
High temperature-high vacuum horizontal
diffractometer attachment.
x-ra~
Model X-86G, Materials Research
Corporation, Orangeburg, N. Y.
49
APPENDIX C
X-ray Data for PbTi0
A-.
and Bicr0
3
3
Tetragonal PbTi03*
0
Parameters:
=
a == 3.905 A, c
0
4.151 A.
0
d
(A)
4.150
3.899
2.842
2.758
2.297
2.076
1 •.950
1.833
1.765
1.744
1.658
1.608
1.421
1.384
1.379
1.335
1.308
1.3045
1.3000
1.2403
1.237
1.2333
1.1819
1.1484
1.1287
1.1016
1.0841
1.0816
1.0601
1.0465
1.0383
1.0031
0.9766
0.9747
0.9715
0.9593
0.9491
0.9476
0.9457
1/1 0
hk1
26
49
100
52
40
15
32
13
10
11
19
42
13
3
001
100
101
110
9
7
3
5
11
10
3
7
10
5
3
2
7
3
9
B
1
2
3
4
1
3
2
2
4
III
002
200
102
201
210
112
211
202
003
220
212
221
103
300
301
113
310
311
222
203
302
213
320
312
321
004
104
223
400
114
322
401
303
410
50
A.
(Cont'd)
o
d
*
B.
(A)
hk1
0.9222
411
Taken from ASTM card number 6-0452.
Tetragonal BiCr03**
Parameters: . a
26
(0)
27.96
32.82
33.98
36.78
41.54
45.90
53.42
56.78
56.96
65.42
67.88
73.66
**
=
0
7.75 A, c
=
0
7.95 A.
d (A)
I/Io
hk1
3.188
2.727
2.636
2.442
2.172
1.975
1.713
1.620
1.615
1.425
1.380
1.285
7
3
1/2
1/2
1/2
2-3
112,211
202,220 .
212
301,310
203,302
004···
214,420
332
224-.
521
440
116,600
2
5-6
2
4/2
1/2
1
Reported by Naray-szabo{8) at room temperature for CuKa
radiation.
APPENDIX D
Sintering Data
A.
Sintering Data for Samples of the PbTi0 -BiCr0 System
3
3
Sample Composition
Pressure* Time Temperature Sintering Quenching Phase
(mo1e%PbTi0 )
( °C)
No.
(psi)
(hrs)
System
3
I-A
2-A
2-B
2-C
3-A
3-B
3-C
4-A
5-A
6-A
7-A
7-B
8- A
9-A
lO-A
11-A
11-B
12-A
12--B
12-C
13-A
13-B
13-C
14-A
100
95
95
95
90
90
90
85
80
75
70
70
65
60
55
50
SO
45
45
45
40
40
40
35
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
-50000
50000
50000
50000
50000
50000
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1000
1050
1000
950
1050
1000
950
1050
l050
1000
1000
1050
1050
1050
l050
950
1050
1050
1150
1200
1100
1050
1150
1050
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
l\1
S
M
M
M
M
M
M
A.
(Cont'd)
Sample Composition
Pressure* Time Temperature Sintering Quenching-Phase
No.
(mole%PbTi0 )
( °C)
(psi)
(hrs)
System
3
14-B
ilS-A
lS-B
15-C
15-D
lS-E
35
30
30
30
30
30
50000
50000
50000
50000
50000
50000
15-F
30
50000
- 16-A
16-B
16-C
16-D
16-E
16-F
20
20
50000
50000
50000
50000
50000
50000
17-A
17-B
10
10
17-C
10
17-D
10
20
20
20
20
2
2
4.5
2
2
1
2
1
2.5
2
2
2
2
2
1
2
17-E
17-F
17-G
18-A
10
10
10
5
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1000
1100
1050
900
850
900
1050
900
1100
1050
1000
900
850
875
900
1050
800
800
900
-800
900
950
800
900
950
1000
1050
1000
900
800
9pen
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Air
Air
Air
Air
Air
M
M
Air
M
Air
Air
Air
Air
Air
Air
M
M
Air
Air
Air
Air
Air
Air
Air
Air
- Air
Air
Air
Air
Air
Air
Air
M
M
M
M
M
M
M
M
M
M
M
M
M
(Cont'd)
A.
Sample Composition
Pressure* Time Temperature Sintering Quenching Phas
(psi)
(mole%PbTi0 )
(hrs)
( °C)
System
No.
3
19-B
3
19-C
3
50000
50000
50000
50000
50000
800
850
800
850
900
2
2
2
2
2
Open
Open
Open
Open
Open.
Air
Air
Air
Air
Air
M
M
applied before sintering.
* Pressure
t
S means single phase; M means multiple phases.
** R means resinter.
B.
Sintering Data for the BiCr0
3
Samples
Pressure* Time Temperature Sintering Quenching Pha
Sample Composition
System
(psi)
(hrs)
( °C)
No.
(rnBi2o~+nCr203)
20-A
20-B
1.00+1.00
1.5
400
2
750
400
750
800
400
750
800
850
400
750
1.00+1.00
1.5
1.00+1.00
1
1.5
2
20-C
2
3
20-D
20-E
1.00+1.00
1.00+1.00
2
1.5
2
.Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Air
M
Air
Air
M
Air
Air
Air
Air
M
(Contrd)
B.
Sample Composition
Pressure* Time Temperature Sintering Quenching Ph
(hrs)
System
(psi)
( °C)
No.
(mBi 2 0 3 +nCr 2°3)
2
20-G
20-H
20-K
1.00+1.00
1.00+1.00
1.00+1.00
20-M
1.00+1.00
20-N
20-0
1.00+1.00
1.00+1.00
75000
75000
75000
75000
75000
75000
75000
3
99
3
3
3
2
3
1.S
2
2
21-A
21-B
21-D
21-E
1.05+1.00
1.05+1.00
1.05+1.00
1.05+1.00
75000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
50000
2
3
3
2
2
3
2
2
2
3
2
2
2
2
850
800
800
800
850
800
900
800
400
750
850
950
800
800
850
900
800
850
900
950
800
850
900
950
950
Open
Open
Oxygen
Open
Open
Open
Open
Open
Open
. Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Open
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
ti" This sample was inserted in the tube and heated to 800°C and sintered.
*
t
**
See page 54.
M
M
M
56
APPENDIX E
X-ray Diffraction Data for the PbTi0 -BiCr0 System
3
3
Notes:
1.· All x-ray patterns are based on CuKa radiation
with a wavelength of
2.
1~542
o
A.
The indices of the x-ray patterns of each
composition include only the main phase (see
Table III)ithe structure is indicated in each
table.
3.
For the tetragonal patterns, expect Bicro ,
3
the parameters
~
and £ were calculated from
the 200 and 002 lines, respectively.
Bicr0
3
For
c was calculated from the 004 reflect-
ion and a was calculated from
2~1,
112, 202,
and 220 lines.
4.
In the cubic
r~gion,
the parameter a was
determined from the 200 line.
5.
The samples used here for each composition
are the same as given in Table IV.
57
a.
100% PbTi0
3
Structure: Tetragonal 0
Parameters:
a = 3.888 A, c
26
(° )
21.54
22.95
31.58
32.54
39.32
43.72
46.68
49.85
51.92
52.55
55.44
57.36
65.75
67.76
70.55
72.22
72.79
76.90
77.40
81.43
84.35
90.67
93.27
94.85
95.95
b.
=
0
4.137 A.
0
d
(A)
4.122
3.872
2.831
2.749
2.289
2.069
1.944
1.828
1.760
1.740
1.656
1.605
1.419
1.382
1.334
1.307
1.298
1.239
1.232
1.181
1.147
1.083
1. 060
1.046
1.037
l/Io
hk1
44
62
100
45
43
44
67
12
12
6
16
42
15
14
6
5
001
100
101
110
111
002
200
102
201
120
112
211
202
003
212
221
300,103
301
130,113
311
222
213
132
231
004
8
8
9
5
6
9
7
7
4
95% PbTi0 -5% BiCr0
3
3
Structure: Tetragonal 0
0
Parameters:
a = 3.893 A, c = 4. 080 A.
0
28 (0)
d
21.86
22.90
31.74
32.48
39.42
44.37
46.62
50.42
52.00
52.50
4.062
3.880
2.817
2.754
2.284
2.040
1.947
1.808
1.757
1.742
(A)
r/Io
hk1
13
35
100
55
43
001
100
101
110
111
602
200
102
201
120
5
26
7
8
8
58
b.
(Cont'd)
28
0
( 0 )
55.94
57.40
66.21
67.95
70.90
76.86
77.10
81.38
84.65
91.67
93.49
94.80
c.
d
(A)
1.642
1.604
1.410
1.378
1.328
1.239
1.236
1.182
1.144
1.074
1.058
1.046
90% PbTi0 -10% Bicr0
3
3
structure: Tetragonal 0
Parameters: a = 3.898 A, c
·· ~e
(0 )
22.14
22.96
31.96
33.58
39.57
44.82
46.56
50.90
52.07
52.50
56.47
57.51
66.54
67.96
71.40
74.34
77.18
81.44
85.00
93.86
94.78
1/1 0
hk1
10
33
8
5
4
4
5
5
3
3
3
3
112
211
202
220
212
031
130
311
222
213
132
231
= 4.041
0
A.
0
d
(A)
4.012
3.870
2.798
2.667
2.276
2.020
1.949
1.792
1.755
1.742
1.628
1.601
1.404
1.378
1.320
1.275
1.235
1.181
1.140
1.054
1.047
1/1 0
hk1
21
42
100
49
38
8
32
7
7
7
10
31
8
4
4
3
5
3
2
3
5
001
100
101
110
111
002
200
102
201
120
112
211
202
220
212
013
301,130
131
222
132
231
59
d.
85% PbTi0 -15% Bicr0
3
3
Structure: Tetragonal 0
0
Parameters: a = 3.906 A, c = 4.020 A.
28
0
( 0 )
22.16
22.80
31.90
32.37
39.53
45.07
46.45
51.01
52.00
52.29
56.53
57.43
66.60
67.80
71.44
72.28
74.81
76.90
81.37
85.05
93.75
94.50
e.
d
(A)
4.008
3.897
2.803
2.763
2.278
2.010
1.953
1.789
1.757
1.748
1.627
1.603
1.403
1.381
1.319
1.306
1.268
1.239
1.182
1.140
1.055
1.049
1/1 0
hk.1
20
36
100
51
38
9
26
7
8
8
11
28
7
3
4
3
3
6
2
1
2
2
001
100
101
110
III
002
200
102
201
120
112
211
202
220·
212
221
013
031
131
222
132
321
80%'PbTi0 -20% BiCr0
3
3
Structure: Tetragonal 0
Parameters: a = 3.910 A, c
=
0
3.999 A.
0
28
( 0 )
22.28
22 •.7 9
32.00
32.34
39.60
45.32
46.flO
51.31
52.15
56.78
57.41
66.71
67.61
d
(A)
3.987
3.899
2,794
2.766
2,274
1.999
1.955
1,779
1.752
1.620
1.604
1.401
1.384
I/1S!
hkl
16
33
100
52
39
001
100
101
110
8
27
6
7
12
31
7
5
III
002
200
102
201
112
211
202
220
. 60
e.
(Cont'd)
29
(°)
71.49
75.06
76.82
81.20
85.01
92.86
93.90
94.60
f.
0
d
212
103
301
311
222
213
132
231
3
3
6
3
1.319
1.264
1.240
1.184
1.140
1.063
1.054
1.058
3
3
4
4
75% PbTi0 -25% Bicr0
3
3
structure: Tetragonal 0
Parameters:
a = 3.912 A, c
26
(O)
22.42
22.78
32.14
32.31
39.64
45.56
46.38
51.39
52.10
56.93
57.39
66.94
67.53
71.58
75.58
76.70
81.10
85.19
94.40 ·
g.
hkl
1/1 0
(A)
= 3.979
a
A.
a
d
(A)
3.962
3.900
2.783
2.768
2.272
1.989
1.956
1.777
1.754
1.617
1.604
1.397
1.386
1.317
1.257
1.241
1.185
1.138
1.050
1/1 0
hk1
15
31
100
50
35
6
24
5
8
10
26
001
100
101
110
111
002
200
102
201
112
121
202
220
212
103
301
131
222
312,231
6
4
2
2
6
3
3
5
70% PbTi0 -30% BiCr0
3
3
Structure: Tetragonal 0
Parameters:
a = 3.911 A, c
=
0
3.961 A.
0
26
( 0 )
22.48
22.75
d
(A)
3.952
3.905
1/1 0
hk1
14
31
001
100
61
g.
(Cont'd)
0
28
( 0 )
32.15
32.30
39.65
45.78
46.39
51.64
52.10
56.99
57.33
67.00
67.40
71.88
76.68
81.72
85.24
94.15
h.
d
(A)
2.782
2.769
2.271
1.980
1.956
1.769
1.754
1.615
1.606
1.396
1.388
1.312
1.242
1.177
1.138
1.052
65% PbTi0 -35% BiCr0
3
3
Structure: Tetragonal 0
Parameters:
a = 3.916 A, c
1/1 0
hk1
100
66
36
101
110
III
002
200
102
201
112
211
202
220
122
301,130
131
222
312
8
22
6
8
12
26
7
6
2
6
2
2
4
=
0
3.947 A.
0
28
( 0 )
22.55
22.75
32.20
32.27
39.72
45.95
46.33
51.80
52.08
57.20
57.40
67.10
67.33
71. 70
72.01
76.00
76.67
81.10
85.35
94.23
d
(A)
3.940
3.910
2.778
2.772
2.267
1.973
1.958
1.763
1.755
1.609
1.604
1.394
1.390
1.315
1.310
1.251
1.242
1.185
1.136
1.051
1/1 0
hk1
21
34
100
98
34
7
21
6
9
11
24
7
6
3
3
3
6
3
3
4
001
100
101
110
III
002
200
102
201,120
112
121
202
220
212,003
221
013
301
131
222
312
62
i.
60% PbTi0 -40% Bicr0
3
3
Structure:
Cubic
0
Parameter:
a = 3.926 A.
0
26
( 0 )
22.70
32.28
39.71
46.21
52.02
57.37
67.32
71.96
76.54
85.40
94.19
j .
(A)
3.914
2.771
2.268
1.963
1.756
1.605
1.390
1.311
1.244
1.136
1.052
I/I o
hk1
45
100
22
21
8
23
8
4
5
1
5
100
110
111
200
120
211
220
221,030
103
222
231
55% PbTi0 -45% BiCr0
3
3
Structure:
Cubic
0
Parameter:
a = 3.925 A.
26
0
(0 )
22.70
32.29
39.80
46.22
52.00
57.40
67.35
72.01
76.60
85.50
94.25
k.
d
d
(A)
3.914
2.770
2.263
1.962
1.757
1.604
1.389
1.310
1.243
1.135
1.051
2!~
39
100
24
24
10
21
6
3
5
2
4
hk1
100
110
111
200
120
211
220
221,030
103
222
231
50% PbTi0 -50% BiCr0
3
3
Structure:
Parameter:
Cubic
°
a = 3.924 A.
2e (0)
d
22.72
32.29
39.74
46.23
3.910
2.770
2.266
1.962
°
(A)
I/I o
hk1
40
100
100
110
111
200
24
24
63
k.
1.
(Cont'd)
d
52.03
57.40
67.36
72.16
76.62
81.12
85.50
94.30
1.756
1.604
1.389
1.308
1.243
1.185
1.135
1.051
(A}
l/I Q
8
21
6
1
6
3
2
3
hkl
120
211
220
221,030
103
311
222
231
45% PbTi0 -55% BiCr0
3
3
structure:
. Parameter:
28
CO)
22,68
27.64
32.23
39.78
46.23
52.01
57.43
67.36
76.69
85.50
94.31
m.
0
28 (0)
Cubic
0
a = 3.924 A•
0
d
CA}
3.917
3.225
2.775
2.264
1.962
1.757
1.603
1.389
1.242
1.135
1.051
1/1 0
·hkl .
100
19
22
8
21
6
5
2
3
100
(BiCr0 )
3
110
111
200
120
211
220
103
222
231
I/I Q
hkl
33
11
100
22
22
7
22
7
4
3
100
(BiCr0 )
3
110
III
200
120
211
220
103
231
37
2
40% PbTi0 -60% BiCr0
3
3
Structure:
Parameter:
Cubic
0
a = 3.920 A.
28 '(0)
d
22.78
27.78
32.35
39.84
46.28
52.16
57.50
67.45
76.80
94.50
3.900
3.209
2.765
2.261
1.960
1.752
1.601
1.387
1.240
1.049
0
(A)
64
n.
35% PbTi0 -65% BiCr0
3
3
Structure:
Parameter:
Cubic
0
a = 3.922 A.
0
26
d
( 0 )
22.76
27.76
30.60
31.55
32.28
36.40
39.83
46.26
52.14
55.08
57.50
67.41
76.77
94.50
o.
100% BiCr0
(A)
3.904
3.211
2.919
2.878
2.771
2.466
2.261
1.961
1.753
1.666
1.601
1.388
1.240
1.049
(0)
37
21
100
(BiCr03)
8
5
100
5
24
26
6
3
21
6
4
3
110
(Cr2.°3 )
111
200
120
(Cr2. 0 g)
211
220
103
231
3
Structure: Tetragonal 0
Parameters: a = 7.855 A, c
26
hkl
I/~
= 7.902
0
d
(A)
0
A.
I/1..9-
hkl
(Cr2. 03)
25.00
27.80 ·
32.10
33.88
3.559
3.206
2.786
2.644
2
100
35
5
211/112
022,220
003,122,
36.46
2.462
5
301,310,
43.00
45.90
2.102
1.975
1.684
1.668
1.614
3
20
20
(Cr2. ° 3)
(Cr:£Og)
54.44
55.02
57.00
5
4
132,213,231
004
233,332
(Cr2.°3 )
224
65
APPENDIX F
High Temperature X-ray· Diffraction Data
for the PbTi0 3 -Bicr0 System
3
a.
95% PbTi0 -5% Bicr0
3
3
Curie point:
t
( DC)
.25
185
260
338
375
408
431
449
460
480
504
566
633
725
853
b.
26
465°C.
0
200
46.62
46.48
46.40
46.30
46.27
46.21
46.14
46.08
46.03
45.99
45.98
45.95
45.91
45.85
45.78
29
002
44.45
44.76
44.96
45.23
45.28
45.44
45.60 '
0
d 200
d OO2
a (A)
c (A)
1.9465
1. 9521
1.9552
1.9592
1. 9604
1. 9628
1. 9656
1.9681
1. 9701
1. 9717
1. 9721
1. 9733
1. 9750
1.9774
1. 9803
2.0363
2.0230
2.0145
2.0030
2.0010
1.9943
1. 9877
3.8930
3.9042
3.9104
3.9184
3.9208
3.9256
3.9312
3.9362
3.9402
3.9434
3.9442
3.9466
3.9500
3.9548
3.9606
4.0726
4.0460
4.0290
4.0060
4.0020
3.9886
3.9754
d
d
°
a (A)
c (A)
3.8978
3.9002
3.9026
3.9112
3.9136
3.9216
3.9312
3.9386
3.9410
3.9410
3.9458
3.9474
4.0392
4.0332
4.0332
4.0290
4.0104
3.9970
3.9786
90% PbTi0 -10% BiCr0 3
3
Curie point:
t
( DC)
--25
45
75
131
188
267
330
368
374
384
415
445
475
29
200
46.56
46.53
46.50
46.39
46.36
46.26
46.14
46.05
46.02
46.02
45.96
45.94
45.94
410°C.
2e
002
44.84
44.91
44.91
44.96
45.18
45.34
45.56
200
1. 9489
1.9501
1.9513
1.9556
1.9568
1. 9608
1. 9656
1.9693
1.9705
1. 9705
1.9729
1.9737
1. 9737
OO2
2.0196
2.0166
2.0166
2.0145
2.0052
1.9985
1.9893
3.9474
0
66
b.
(Cont'd)
t
( °C)
496
550
590
640
700
750
812
c.
28
200
002
45.93
45.91
45.90
45.89
45.87
45.82
45.80
d
200
d
002
°
a (A)
°
c (A)
3.9482
3.9500
3.9508
3.9516
3.9532
3.9572
3.9588
1. 9741
1.9750
1. 9754
1. 9758
1. 9766
1.9786
1.9794
90% PbTi0 -10% Bicr0
3
3
Curie point:
t
( °C)
25
86
175
240
310
334
345
366
386
412
424
433
453
493
540
577
632
702
d.
28
26
200
46.56
46.51
46.41
46.34
46.27
46.25
46.25
46.21
46,19
46,13
46,10
46.07
46 ',05
46.02
45,99
45.97
45,95
45.93
440°C.
28
002
44.82
44.93
45.08
45.22
45.36
45.48
45.53
45.60
45,66
d
200
d
002
°
a (A)
°
c (A)
4.0408
4.0314
4.0188
4.0070
3.9952
3.9852
3.9810
3.9754
3.9704
1.9489
1. 9509
1.9548
1.9576
1. 9604
1. 9612
1.9612
1. 9628
1,9636
1.9660
1,9673
1,9685
1,9693
1,9705
1,9717
1,9725
1.9733
1,9741
2.0204
2.0157
2.0094
2.0035
1. 9976
1.9926
1.9905
1. 9877
1,9852
3.8978
3,9018
3.9096
3.9152
3.9208
3.9224
3.9224
3.9256
3.9272
3,9320
3.9346
3.9370
3.9386
3,9410
3.9434
3.9450
3.9466
3.9482
d
d
a (A)
°
c CA)
3.9064
3.9096
3.9112
3.9152
3.9192
4.0196
4.0170
4.0120 '
4.0052
4.0010
85% PbTi0 -15% Bicr0
3
3
Curie point:
345°C.
0
t
( °C)
25
70
100
150
180
28
200
46.45
46.41
46.39
46.34
46.29
26
002
45.07
45.10
45.16
45.24
45.29
200
1. 9532
1.9548
1.9556
1.9576
1. 9596
002
2.0098
2.0085
2.0060
2.0026
2.0005
67 .
d.
(Cont'd)
t
( °C)
206
234
264
284
306
332
376
405
442
475
574
608
666
764
e.
28
200
46.25
46.21
46.12
46.09
46.04
46.00
45.96
45.92
45.93
45.90
45.86
45.84
45.80
45.75
28
002
45.35
45.41
45.54
d
200
d
002
°
a (A)
°
c CA)
3.9960
3.9910
3.9802
1. 9612
1. 9628
1.9664
1.9677
1. 9697
1. 9713
1. 9729
1.9746
1. 9741
1.9754
1.9770
1. 9778
1. 9794
1.9815
1.9980
1. 9955
1.9901
3.9224
3.9256
3.9328
3.9354
3.9394
3.9426
3.94S8
3.9492
3.9482
3.9508
3.9540
3.9556
3.9588
3.9630
d
d
a CA)
c (A)
3.9104
3.9120
3.9136
3.0168
3.9208
3.9232
3.9248
3.9264
3.9296
3.9336
3.9346
3.9362
3.9386
3.9410
3.9442
3.9482
3.9492
3.9508
3.9532
3.9986
3.9970
3.9952
3.9926
3.9836
3.9786
3.9736
3.9712
3.9654
80% PbTi0 -20% BiCr0
3
3
Curie point:
325°C.
t
(OC)
25
52
75
124
155
208
229
260
282
310
315
328
372
411
478
570
618'
628
690
0
28
200
46.40
46.38
46.36
46.32
46.27
46.24
46.22
46.20
46.16
46.11
46.10
. 46.08
46.05
46.02
45.98
45.93
45.92
45.90
45.87
26
002
45.32
45.34
45.36
45.39
45.50
45.56
45.62
45.65
45.70
200
1. 9552
1.9560
1.9568
1.9584
1. 9604
1.9616
1.9624
1.9632
1.9648
1.9668
1.9673
1.9681
1.9693
1.9705
1.9721
1.9741
1.9746
1.9754
1.9766
002
1.9993
1.9985
1.9976
1.9963
1.9918
1. 9893
1. 9868
1.9856
1. 9827
0
f.
80% PbTi0 -20% Bicr0
3
3
Curie point:
310°C·.
0
t
( °e)
25
84
140
. 185
214
242
268
297
324
370
412
500
562
626
694
g.
28
200
46.40
46.35
46.28
46.23
46.18
46.12
46.07
46.03
46.00
45.98
45.97
45.94
45.92
45.87
45.81
28
002
45.32
45.41
45.54
45.66
45.69
d
200
d
002
0
a (A)
c (A)
3.9986
3.9910
3.9802
3.9704
3.9678
1.9552
1.9572
1. 9600
1. 9620
1. 9640
1. 9664
1. 9685
1. 9701
1. 9713
1. 9721
1.9725
1.9737
1.9746
1. 9766
1. 9790
1. 9993
1.9955
1.9901
1. 9852
1.9839
3.9104
3.9144
3.9200
3.9240
3.9280
3.9328
3.9370
3.9402
3.9426
3.9442
3.9450
3.9474
3.9492
3.9532
3.9580
d
d
a CA)
c (A)
3.9120
3.9160
3.9192
3.9224
3.9272 ·
3.9304
3.9312
3.9354
3.9370
3.9386
3.9402
3.9418
3.9434
3.9458
3.9802
3.9704
3.9638
3.9606
3.9516
75% PbTi0 -25% BiCr0
3
3
Curie point:
t
(OCl
25
105
154
177
228
260
286
313
384
433
477
527
582
649
290°C.
0
26
200
46.38
46.33
46.29
46.25
46.19
46.15
46.14
46.09
46.07
46.05
46.03
46.01
45.99
45.96
29
002
45.56
45.66
45.74
45.78
45.89
200
1.9560
1.9580
1. 9596
1.9612
1.9636
1. 9652
1.9656
1.9677
1.9685
1. 9693
1.9701
1. 9709
1. 9717
1.9729
OO2
1. 9901
1. 9852
1. 9819
1. 9803
1. 9758
0
69
h.
70% PbTi0 -30% BiCr0
3
3
Curie point:
250°C.
t
(OC)
25
57
69
84
110
119
119
134
143
153
160
169
173
186
189
222
270
300
372
426
471
518
i.
29
200
46.39
46.35
46.36
46.32
46.31
46.32
46.31
46.30
46.29
46.28
46.26
46.26
46.25
46.24
46.24
46.20
46.15
46.14
46.11
46.09
46.06
46.04
26
0
002
45.78
45.88
45.88
d
200
d
002
1.9556
1.9572
1.9568
1.9584
1.9588
1. 9584
1.9588
1.9592
1.9596
1.9600
1.9608
1.9608
1.9612
1.9616
1.9616
1.9632
1.9652
1.9656
1.9668
1.9677
1.9689
1.9697
1.9803
1.9762
1.9762
29 002
d
d
45.78
45.85
45.90
45.99
1.9556
1.9572
1.9588
1.9600
1.9616
1.9628
1.9640
1.9652
1.9656
1.9664
1.9677
1.9681
1.9697
1.9713
1.9733
45.96
1. 9729
a
(A)
3.9112
3.9144
3.9136
3.9168
3.9176
3.9168
3.9176
3.9184
3.9192
3.9200
3.9216
3.9216
3.9224
3.9232
3.9232
3.9264
3.9304
3.9312
3.9336
3.9354
3.9378
3.9394
0
c
(A)
3.9606
3.9524
3.9524
3.9458
70% PbTi0 -30% BiCr0
3
3
Curie point:
t
240°C.
0
( °C)
25
67
93
129
164
190
215
239
284
354
428
491
550
600
670
28
200
46.39
46.35
46.31
46.28
46.24
46.21
46.18
46.15
46.14
46.12
46.09
46.08
46.04
46.00
45.95
200
002
1.9803
1.9774
1. 9754
1. 9717
a (A)
°
c (A)
3.9112 3.9606
3.9144 3.9548
3.9176 3.9508
3.9200 . 3.9434
3.9232
3.9256
3.9280
3.9304
3.9312
3.9328
3.9354
3.9362
3.9394
3.9426
3.9466
70
j.
65% PbTi0 -35% BiCr0
3
3
Curie point:
190°C.
0
t
( °C)
25
68
104
133
157
180
213
224
254
260
284
323
386
436
460
28
200
46.33
46.29
46.25
46.22
46.17
46.17
46.14
46.14
46.13
46.12
46.12
46.11
46.10
46.08
46.06
29
002
45.95
45.96
45.98
d
200
1.9580
1.9596
1.9612
1. 9624
1.9644
1.9644
1.9656
1.9656
1.9660
1.9664
1.9664
1.9669
1. 9673
1.9681
1.9689
0
d OO2
a (A)
c (A)
1.9733
1.9729
1.9721
3.9160
3.9192
3.9224
3.9248
3.9288
3.9288
3.9312
3.9312
3.9320
3.9328
3.9328
3.9338
3.9346
3.9362
3.9378
3.9466
3.9458
3.9442
71
VITA
Tsen-tsou Shih was born in Kiangsu, China, on January
28, 1940.
He graduated from Chiang-Kuo High School in
June 1958.
He enrolled in the Chung-Hsing University,
Taichung, Taiwan, China, in September 1958, and received
the Bachelor of Science degree in Chemistry in June 1962.
He worked in the Chemistry Department, Chung-Hsing
University as a full time teaching assistant during the
period of August 1963 to February 1964.
He entered the Graduate School of the University of
Missouri at Rolla in September 1964.
From September 1965
to April 1967, he was appointed a research assistant in
the Graduate Center for Materials Research of the Space
Science Research Center ,.,i th funds provided by the U. S.
Atomic Energy Commission.
12~~1. 9