Structures in the System CaTiO3/SrTiO3

Article abstract of DOI:10.1006/jssc.1998.7836

At room temperature the sequence of phases with increasing amounts of strontium in the system CaTiO₃/SrTiO₃is orthorhombic (Pnma), orthorhombic (Bmmb), tetragonal (I4/mcm), and cubic (Pm3m). All phase boundaries shift toward smaller strontium contents with increase of temperature. Volume changes resulting from phase transformations are small for all compositions. Shape changes are greatest (~0.3%) for theBmmb/I4/mcmtransition, but would probably be accommodated by microtwinning and so are unlikely to affect the mechanical integrity of a specimen.

Full text of DOI:10.1006/jssc.1998.7836

JOURNAL OF SOLID STATE CHEMISTRY 139, 238—247 (1998)
ARTICLE NO. SC987836
Structures in the System CaTiO3/SrTiO3
C. J. Ball,ꢀ B. D. Begg, D. J. Cookson, G. J. Thorogood, and E. R. Vance
Materials Division, ANSTO, Menai, New South Wales 2234, Australia
Received November 12, 1997; accepted March 24, 1998
the cell parameters for any of these phases. McQuarrie (3)
At room temperature the sequence of phases with increasing found only orthorhombic, tetragonal, and cubic phases. By
amounts of strontium in the system CaTiO3/SrTiO3 is ortho-
rhombic (Pnma), orthorhombic (Bmmb), tetragonal (I4/mcm),
and cubic (Pm3m). All phase boundaries shift toward smaller
strontium contents with increase of temperature. Volume cha-
nges resulting from phase transformations are small for all
compositions. Shape changes are greatest (&0.3%) for the
Bmmb/I4/mcm transition, but would probably be accommodated
by microtwinning and so are unlikely to affect the mechanical
integrity of a specimen. ( 1998 Academic Press
extrapolation of the cell parameters of the orthorhombic
phase he placed the orthorhombic/tetragonal phase bound-
ary at x"0.55 at room temperature, which is close to the
‘‘nearly cubic’’/tetragonal boundary reported by Granicher
and Jakits. McQuarrie also found that the phase boundaries
shifted to lower strontium contents at higher temperatures,
though at room temperature the rate of change of composi-
tion with temperature for both phase boundaries was small.
Mitsui and Westphal (4) investigated only the strontium-
rich end of the phase diagram (x50.8). They confirmed the
existence of the tetragonal phase, and put the tetrag-
onal/cubic phase boundary at x"0.9 at room temperature.
A sample with x"0.8 changed from tetragonal to a differ-
ent structure, which appeared to be the ‘‘nearly cubic’’
structure of Granicher and Jakits, near 110 K. More re-
cently Ceh et al. (5) questioned the existence of the tetrag-
onal phase. They reported cell parameters for the
orthorhombic phase for 04x40.9, though they also
stated that for x"0.6 only lines characteristic of a cubic
structure were present.
INTRODUCTION
Perovskite, CaTiO , is one of the major phases of Synroc,
ꢁ
a titanate ceramic designed for immobilization of high-level
radioactive waste (1). It is the major host phase for stron-
tium, an important radwaste element, and will also incor-
porate significant amounts of the actinides. Obviously, the
limits of solubility of strontium and other waste elements,
and the phases formed when these limits are exceeded, are of
interest. It is known that CaTiO and SrTiO are com-
Because of the importance of this system, and the lack of
agreement between previous workers, we have reexamined
ꢁ
ꢁ
pletely miscible and cubic at high temperatures, but the
temperatures of transformation to the less symmetrical low-
temperature phases, and any volumetric and shape changes
associated with such phase changes during cooling from the
temperature of formation, are not known. There is even
some uncertainty as to what the room temperature phases
are.
the phases in the (Ca/Sr) TiO system. In this we have been
ꢁ
greatly helped by the excellent resolution obtainable with
synchrotron radiation.
EXPERIMENTAL
The ternary system BaTiO /SrTiO /CaTiO is of con-
ꢁ
ꢁ
ꢁ
siderable technological importance on account of the
ferroelectric behavior of many of its compositions. While
most attention has been given to Ba-rich compounds, the
Ca Sr TiO binary system has been studied by several
Materials of composition Ca
Sr TiO , with x"0 and
ꢀ\V
V
ꢁ
0.10 up to 1.0 in steps of 0.05, were prepared by first
hydrolyzing a known quantity of Ti-isopropoxide with an
aqueous Sr-nitrate solution. An appropriate amount of
ꢀ\V
V
ꢁ
groups of workers. Granicher and Jakits (2) reported the
existence of orthorhombic, rhombohedral, ‘‘nearly cubic,’’
tetragonal, and cubic structures with increasing proportions
CaCO was slurried with water and converted to Ca-nitrate
ꢁ
solution by addition of HNO , before being added to the
ꢁ
other precursors. The sample was then stir dried and cal-
of SrTiO , at room temperature, but they did not measure
°
cined at 600 C for 1 h. The resulting powder was pelleted
ꢁ
°
and sintered at 1400 C for 96 h in air. The sintered pellet
°
was ground to (0.1mm, repelleted, and refired at 1550 C
for 85 h before final grinding.
ꢀTo whom correspondence should be addressed.
238
0022-4596/98 $25.00
Copyright ( 1998 by Academic Press
All rights of reproduction in any form reserved.

STRUCTURES IN THE SYSTEM CaTiO /SrTiO
239
ꢁ
ꢁ
XRD measurements at room temperature were made clearest splitting is of the 400 line, since higher-order lines
with Debye—Scherrer geometry on rod-shaped specimens of (visible with j"1 A) are overlapped by other lines. Unfor-
s
diameter &0.2mm, using the X-ray diffractometer installed tunately this is a relatively weak line; another indication
at the Australian National Beamline Facility at the Photon that the structure is not cubic is provided by the 310 com-
Factory in Tsukuba, Japan (6). Wavelengths of &1 A were plex, since although the 310 and 301 lines are overlapped,
s
°
used. Elevated temperature measurements (up to 500 C) they are clearly separated from the 103 line. A change of
were made in the same diffractometer, but using a thin layer dimension along two (or three) 11002 directions gives rise to
of powder on the flat end of an electrically heated hot finger. an orthorhombic structure. For these cases hhh lines are not
Resolution was maximized by narrowing the incident beam split, but again may be overlapped by lines that are. We
to a ribbon of width &0.1 mm, and the number of grains have examined the 222 and 444 lines. An orthorhombic
contributing to a reflection was increased by rocking the structure can also be obtained by a [100] (010) shear (or
°
specimen through 1 during the exposure. This arrangement variant thereof ), with or without a change of dimension
was not entirely satisfactory. The diffraction arcs were along [010]. The shear leads to splitting of hhh lines, into
spotty in appearance, so although the splitting of lines could two approximately equal components, and the change
be clearly seen, the intensities of the lines were greatly along [010] leads to splitting of h00 lines, as for the tetrag-
affected by particle statistics and any attempt at Rietveld onal structure.
analysis of the patterns would have been pointless. The hot
It is important to notice the difference between the two
finger stage did have the merit of being cheap and easily ways of developing an orthorhombic structure. In the first
assembled.
case the axes of the subcell remain orthogonal so the subcell
also has orthorhombic symmetry and hhh lines are not split.
In the second case the angle between two of the subcell axes
is changed by the angle of shear, leading to monoclinic
DATA ANALYSIS
The simplest structure in the (Ca/Sr) TiO system is that symmetry for the subcell. It is because these two axes remain
ꢁ
of SrTiO , which is cubic with cell parameter a+3.905 A. equal in length that the overall symmetry becomes orthor-
ꢁ
The structure consists of TiO octahedra with Sr ions be- hombic, but hhh lines are split, by an amount proportional
ꢂ
tween them. Other structures can be derived from that of to the angle of shear.
SrTiO by small distortions of this cubic cell. As discussed
A rhombohedral structure [reported by Granicher and
ꢁ
by Glazer (7, 8), these distortions consist of (i) tilts of the Jakits (2)] is obtained by a change of dimension along [111].
octahedra, (ii) displacements of the cations, and (iii) distor- In this case the h00 lines are not split but the hhh lines are,
tions of the octahedra. The tilts of the octahedra lead to into two components with intensities approximately in the
splitting of the X-ray diffraction lines of the simple cubic ratio 3:1.
structure and the appearance of additional (superlattice)
By profile fitting of h00 and hhh lines [using the program
reflections with half-integral indices when referred to the XFIT (9)], we have been able to determine the lattice type in
cubic cell. These reflections indicate that the true unit cell is all cases and hence to deduce the likely space group. This
a multiple of the pseudocubic subcell. As shown by Glazer has been confirmed and cell parameters obtained by Riet-
(8) the nature of the tilts, and hence the space group, can be veld analysis, using the program LHPM [Howard and Hill
deduced by examining the superlattice reflections from (10)].
a single crystal, but the problem is more difficult with a
powder pattern since the superlattice reflections are always
very weak and difficult to locate precisely, and therefore,
given that the departure from the cubic cell is small, almost
impossible to index unambiguously. The lattice type, how- orthorhombic, with space group C62. The cell parameters
ever, can be determined by inspection of the strong lines, in the setting Pnma and the angle of shear of the pseudo-
and once this is known the possible space groups consistent cubic subcell vary with composition as shown in Figs. 1 and
with tilts of regular octahedra are quite restricted. Since in 2, respectively. The variation of the shear angle with x
may cases the tilts are very small, the resultant splitting of suggests transformation to another phase between x"0.45
the strong lines is also very small and may only be apparent and x"0.5, but this is very uncertain for two reasons:
in some of the lines. In these cases it helps to know where to (i) there is significant curvature in the plot, making a linear
RESULTS
At room temperature, Ca Sr TiO with 04x40.40 is
ꢀ\V
V
ꢁ
look.
extrapolation from any short section of the plot highly
A tetragonal structure is obtained by expansion (or con- subjective, and (ii) there is no reason to suppose that the
traction) along [001] (all indices are based on the pseudo- angle of shear differs only infinitesimally from zero at the
cubic subcell, unless otherwise stated). The greatest splitting transformation.
in this case is of the h00 lines, which split into two compo-
nents with intensities approximately in the ratio 2:1. The ating a zero angle of shear and therefore a space group other
At x"0.5 the 222 line (Fig. 3a) shows no splitting, indic-

240
BALL ET AL.
FIG. 1. Unit cell parameters of Pnma phase of (Ca,Sr) TiO . #, a; *, b/(2; ;, c.
ꢁ
than Pnma. The 400 line (Fig. 3b), however, is split, suggest- observed superlattice lines. Figure 4 shows the portion of
ing a tetragonal structure with c/a(1. Tilt system No. 16 the pattern between the lines 222 and 321, indexed on the
of Glazer’s (8) classification gives rise to such a structure subcell and on a unit cell with all axes double those of the
ꢃ
ꢃ
ꢃ
but the space group (I4/mmm) is not consistent with the subcell. The presence of lines with h #k #l O2n shows
FIG. 2. Angle of shear, ꢀ, of pseudocubic subcell of Pnma phase of (Ca,Sr) TiO .
ꢁ

STRUCTURES IN THE SYSTEM CaTiO /SrTiO
241
ꢁ
ꢁ
same as for x"0.5, i.e., Bmmb. The 400 line (Fig. 6b)
confirms this. The 222 and 400 lines for x"0.4 are shown in
Figs. 6c and 6d. Splitting is not obvious but the 222 line is
significantly wider than the 222 line for x"0.45 and the
shape of the peak is consistent with splitting into two nearly
equal components, suggesting that the space group is Pnma.
In principle it is possible to distinguish between the phases
by observing (or not, as the case may be) the reflections 121
and 323 in Bmmb (indexed on the true unit cell), which
would be the reflections (120, 021) and (320, 023), but are
forbidden, in Pnma. These reflections arise from cation dis-
placements, not tilts of the octahedra. However, with the
FIG. 3. (a) 222 and (b) 400 X-ray diffraction lines of Ca Sr TiO
(j+1.00A).
ꢄꢅꢆ ꢄꢅꢆ
ꢁ
that the lattice is not body-centred. The most likely alterna- parameters of Table 1 the intensities of these lines are less
tives are Glazer’s (8) tilt system Nos. 17 and 18, both of than 1% of the intensities of other superlattice lines, which
which give rise to an orthorhombic structure with space themselves are less than 1% of the intensities of the main
group No. 63 (Bmmb). These tilt systems differ in that No. 18 (subcell) lines, so the fact that they were not observed is not
leads to equality of the b and c parameters, whereas No. 17 very informative. Refinement in Pnma of the X-ray pattern
does not. Neither of these tilt systems will account for all of from the sample with x"0.4 gave the data shown in Figs.
the observed superlattice reflections, but the space group 1 and 2, which are close to the values predicted by extra-
allows for A-cation displacements from their positions in polation of the data for lower values of x, confirming that
the cubic subcell and for distortion of the TiO octahedra, this is the correct space group for x"0.4. We conclude
ꢂ
which will account for the extra lines. The structure refined from this that the structure is orthorhombic with space
satisfactorily in space group Bmmb with the results shown in group Pnma unless the splitting of h00 lines suggests a tet-
Fig. 5 and Table 1, confirming that this is the correct space ragonal structure with c/a(1, in which case the structure is
group and that the tilt system is No. 17.
actually orthorhombic with space group Bmmb.
It is difficult to determine the composition of the bound-
ary between the two orthorhombic phases. As noted above, c/a'1. The superlattice lines are consistent only with tilt
For 0.654x40.9 the structure is tetragonal with
extrapolation of the angle of shear in the Pnma phase system No. 22 giving rise to space group No. 140, I4/mcm,
suggests transformation between x"0.45 and x"0.5, but which is the space group of SrTiO below 90 K (4) and of
ꢁ
°
the 222 line for a specimen with x"0.45 (Fig. 6a) shows no CaTiO above 1100 C (11). For x50.95 the structure is
ꢁ
evidence of splitting, indicating that the space group is the cubic (Pm3m).
FIG. 4. Portion of X-ray diffraction pattern of Ca Sr TiO . Values of hꢃ#kꢃ#lꢃ are shown for the lines when indexed on the pseudocubic
ꢄꢅꢆ ꢄꢅꢆ
ꢁ
subcell and on the super cell with all parameters double those of the subcell (j+1.00A).

242
BALL ET AL.
FIG. 5. Observed (2), calculated (—), and difference X-ray diffraction patterns from Ca Sr TiO at room temperature (j+1.00 A).
ꢄꢅꢆ ꢄꢅꢆ
ꢁ
The relations between the phases can best be seen by servation that samples with x50.95 were cubic, but, as for
comparing the parameters of the subcells which, except for the transformation between the two orthorhombic phases,
the phase Pnma, have the symmetry of the true unit cell. The extrapolation may not be a valid procedure. The boundary
subcell parameters for specimens with x50.45 are shown in between the phases Bmmb and I4/mcm cannot be obtained
Fig. 7. For the phase Bmmb the true cell parameters are by extrapolation since there is a discontinuity in the para-
twice the subcell parameters, for the phase I4/mcm the meters at the boundary. However, we observed a small
amount of the phase Bmmb in the sample with x"0.65,
relation is a"(2a , c"2c , where a and c are the sub-
ꢀ
ꢀ
ꢀ
ꢀ
cell parameters, and for the cubic phase the subcell is the
true unit cell. For the phase Pnma the subcell is of mono-
clinic symmetry, but with a "c .
ꢀ
ꢀ
Extrapolation of the parameters for the phase I4/mcm
suggests that the boundary with the cubic phase is at
x&0.925 at room temperature, in agreement with our ob-
TABLE 1
?
Structural Parameters in Ca0.5Sr0.5TiO3, Space Group Bmmb
Atom
u
v
w
B (Aꢃ)
(Ca,Sr)1
(Ca,Sr)2
Ti
O1
O2
4c
4c
8d
8e
8f
0
0
ꢀ
ꢇ
ꢀ
ꢇ
0
!0.007
1.02
ꢀꢆ
ꢀ
ꢀ!0.006
0.98
ꢃ
ꢀ
ꢇ
0
ꢀ
ꢀꢆ
ꢀ
0.60
ꢀꢄ
ꢇ
ꢀ#0.018
0
2.05
ꢇ
ꢇ
ꢇꢄ
0
0.034
ꢀ!0.019
0.67
ꢃꢄ
ꢃ
ꢇ
ꢁ
ꢀ
O3
8g
ꢀ#0.028
ꢀ
ꢀ!0.000
0.72
ꢇ
ꢁ
ꢇ
ꢇ
ꢁꢄ
? Decimal fractions show displacements of atoms from positions in cubic
aristotype. Estimated standard errors (suffixes) apply to least significant
figure of parameter. a"7.7378 A, b"7.7440 A, c"7.7446 A, Bragg
FIG. 6. X-Ray diffraction lines from Ca Sr TiO : (a, b) x"0.45,
ꢀ
ꢁ
ꢁ
ꢀ\V
V
ꢁ
R factor"1.7.
j+1.00 A; (c, d) x"0.4, j+1.05 A; (a, c) line 222; (b, d) line 400.

STRUCTURES IN THE SYSTEM CaTiO /SrTiO
243
ꢁ
ꢁ
FIG. 7. Cell parameters of pseudocubic subcell in Ca Sr TiO . Phase Bmmb: #, a; *, b; ;, c. Phase I4/mcm: ꢀ, a; ꢁ, c. Phase Pm3m: E, a.
ꢀ\V
V
ꢁ
possibly due to compositional inhomogeneity or to hyster- diffraction patterns. We have estimated the temperature of
esis in the transformation, which shows that the boundary is the transformation between the two orthorhombic phases
very close to this composition.
Determination of the phase boundaries at elevated tem- the 222 line to zero, although as mentioned above, this may
peratures is difficult, because of the poorer quality of the not be a valid procedure. The data are shown in Fig. 8.
for a sample with x"0.35 by extrapolating the splitting of
FIG. 8. Ca
Sr
TiO : angular separation of lines 440
and 044
(j+1.05 A).
ꢄꢅꢂꢆ ꢄꢅꢁꢆ
ꢁ
.LK?
.LK?

244
BALL ET AL.
FIG. 9. Ca
Sr
TiO : splitting of pseudocubic subcell line 400 (j+1.05 A).
ꢄꢅꢁꢆ ꢄꢅꢂꢆ
ꢁ
Close to the transformation temperature we could not de- McQuarrie (3) agree less well with our results, and he did
tect splitting of either the h00 or hhh lines. The boundary not identify the phase Bmmb.
between the tetragonal and cubic phases could also be
The sequence of phases that we find with increasing
obtained by extrapolation, in this case of the splitting of the strontium at room temperature is exactly the same as the
400 line. Data for the sample with x"0.65 are shown in sequence of phases in SrZrO with increasing temperature
ꢁ
Fig. 9. We have tried to bracket the temperature of the observed by Carlsson (12). He found a few very faint lines
boundary between the Bmmb and I4/mcm phases but have indicative of an enlarged unit cell, but he did not determine
found that both phases are present at some temperatures. the structures of the two phases intermediate between the
This could have been due to compositional inhomogeneity, room temperature orthorhombic and high-temperature cu-
but temperature variation within the specimen may also bic phases, which he described as tetragonal with c/a(1
have been significant. We take the transformation temper- and c/a'1. Ahtee et al. (13) determined the structures and
ature as the temperature at which there are about equal showed that the phases were orthorhombic (Bmmb) and
amounts of the two phases.
tetragonal (I4/mcm), as we have found in the (Ca,Sr) TiO
ꢁ
The positions of the phase boundaries found in this work system. They explained this sequence of phases by con-
are shown in Fig. 10. Also shown are the results of Mitsui sidering the sequence of tilting which, in Glazer’s (7)
and Westphal (4) for Sr-rich materials at low temperatures notation, is
and some of the phase boundaries reported by Granicher
and Jakits (2).
Pnma
a\b>a
Bmmb
ꢄ > \
a b c
I4/mcm
ꢄ ꢄ \
Pm3m
ꢄ ꢄ ꢄ
a a a
\
%
%
a a c
%
DISCUSSION
with condensation of soft modes, which consist of oscilla-
tions of the octahedra, at each transformation on cooling
Our results are in good agreement with the results of from the cubic phase.
Mitsui and Westphal (4). From the positions of the phase
With this interpretation of the phase transitions we might
boundaries we can conclude that the ‘‘nearly cubic’’ phase expect to find the same sequence of phases on heating
reported by Granicher and Jakits (2) is the phase Bmmb, but CaTiO . Vogt and Schmahl (14) found no intermediate
ꢁ
we find no evidence of a trigonal-rhombohedral phase. phases between the room-temperature orthorhombic and
Instead, the phase Pnma persists up to the boundary with high-temperature cubic phases, but Redfern (11) has found
Bmmb. The boundaries of the tetragonal phase reported by the tetragonal phase with space group I4/mcm between 1400

STRUCTURES IN THE SYSTEM CaTiO /SrTiO
245
ꢁ
ꢁ
FIG. 10. Variation with temperature of phase boundaries in the system CaTiO /SrTiO : E, Pnma/Bmmb; #, Bmmb/I4/mcm; ;, I4/mcm/Pm3m; ꢀ, ꢁ,
ꢁ
ꢁ
data of Mitsui and Westphal (4); lines, data of Granicher and Jakits (2).
and &1500 K; he did not find the phase Bmmb. Matsui of the octahedra. The tilt about the x axis produces reflec-
et al. (15) have also examined CaTiO at high temperatures. tions which (indexed on the supercell) have all indices odd
ꢁ
Their XRD patterns are very similar to those of Redfern, but and kOl. Reflections with all indices odd and hOk will
they identified the intermediate phase as Cmcm (an alterna- also be present, on account of the tilts about the z axis, as
tive setting of Bmmb). They based this identification on the they are in Bmmb. Consequently, for example, the line with
ꢃ
ꢃ
ꢃ
continued presence of the unresolved group of lines 121, h #k #l "51 in Fig. 4 would be a superposition of the
103, and 211 (indexed on the low-temperature orthorhom- lines 515, 155, 711, and 171 in Bmmb, and of the same lines
bic phase, in the setting Pbnm), which are the lines 311, 131, plus 551 and 117, but with all lines split, in Pnma (indexed
and 113 when indexed on the supercell with all axes twice on the monoclinic supercell). However, lines 551 and 117,
those of the pseudocubic subcell, but the only alternative present in Pnma but not in Bmmb, would be exactly super-
space group they considered was P4/mbm, which results imposed on 155 and 711, respectively, since in the mono-
ꢄ ꢄ >
from the tilt system a a c . It is true that none of the 311 clinic supercell a"c. The difficulty of distinguishing
group of lines would appear in P4/mbm, but 311 and 131 between these cases is apparent and reduces to the problem
would appear in I4/mcm (supercell space group F4/mmc). of resolving the splitting, as for the main lines. Redfern (11)
Cmcm can be distinguished from I4/mcm through the pres- reported that peak splitting could be resolved at all temper-
ence, or otherwise, of the lines 120
and 210
. When atures up to the transition to I4/mcm, but that splitting of
.@LK
.@LK
indexed on the supercell these are the lines 310 and 130, peaks in the I4/mcm structure could not be resolved.
which should appear in Cmcm but not in F4/mmc (I4/mcm). Our experience with varying strontium content at room
The fact that these lines are not seen in the temperature temperature was that splitting in the low-Sr I4/mcm
range of the intermediate phase suggests that it is I4/mcm structure was greater than in the high-Sr Pnma and Bmmb
and not Cmcm.
structures. Near to the boundary with the cubic phase,
This is not to say that Bmmb does not occur at lower of course, the splitting approached zero. It is possible
temperatures. As we have noted, it is very difficult to distin- that the temperature range of stability of Bmmb fell entirely
guish between the phases Pnma and Bmmb, and inspection between temperatures investigated by Redfern. It is also
of the superlattice lines is of little use since, structurally, the possible that Bmmb does not form at all in CaTiO ,
ꢁ
>
phases differ only through the presence of tilts of the oc- which would be the case if the b tilt in Pnma disappeared
tahedra about the subcell x axis in Pnma, but not in Bmmb, at the same temperature as the a\ tilt, with one a conse-
and, possibly, through cation displacements and distortions quence of the other. We can think of no compelling reason

246
BALL ET AL.
FIG. 11. Angle of tilt, a, of a\ tilts in Pnma phase of Ca Sr TiO at room temperature.
ꢀ\V
V
ꢁ
why this should not happen. The heat capacity measure- of looking at the transformation is to note that equal tilts
ments of Guyot et al. (16) on CaTiO and of Nagarajan et al. about the x and z axes are equivalent to a single tilt about
ꢁ
(17) on Ca
Nd
TiO identified transitions at &1380 [101], and at the transformation the axis of tilt changes to
ꢄꢅꢈꢆ ꢄꢅꢀꢆ
ꢁ
and &1520 K, in agreement with the XRD data of Redfern [001].
(11) and Matsui et al. (15), but showed no sign of a transition
The variation of the volume of a subcell with composition
at a lower temperature. However, this is not conclusive at room temperature is shown in Fig. 12. The fact that the
evidence that no such transition occurs, since it would not subcell volumes are closely the same on either side of
necessarily be accompanied by a measurable heat capacity a phase boundary at room temperature does not prove that
anomaly: for instance, the heat capacity measurements of there is a negligible volume change in a given material when
Naylor and Cook (18) on CaTiO showed no evidence of it undergoes a transformation at some other temperature,
ꢁ
the transition at &1380 K.
but that is probably the case. There is certainly no evidence
The variation of shear angle ꢀ with composition in the to the contrary. Unfortunately our high-temperature data
phase Pnma was shown in Fig. 2. A more fundamental were not sufficiently precise to enable a worthwhile com-
quantity is the angle of tilt, a, of the octahedra about the parison of volumes to be made.
x and z axes. Since successive octahedra along both of these
Although there is little change in volume on transforma-
axes are tilted in opposite senses (!tilts, in Glazer’s nota- tion there is a change of shape, particularly in the trans-
tion) the axes are inclined to one another, as Glazer (8) has formation from Bmmb to I4/mcm. By extrapolating the
shown. For the tilt system resulting in the phase Pnma the parameters found in the phase Bmmb to a strontium content
magnitudes of the tilts about the two axes are the same, and of x"0.65 and comparing with the parameters of the phase
ꢃ
it can be shown that sin ꢀ"sin a. The variation of a with I4/mcm at that composition, we find that the biggest change
composition is shown in Fig. 11. No particular significance of dimension when Bmmb transforms to I4/mcm is an expan-
is attached to the approximately linear variation of a with x, sion of 0.31% along the c axis, with contractions of 0.04 and
but it is apparent that a, and therefore ꢀ, differs from zero 0.23% along a and b, respectively. These changes are cal-
by a significant amount at the transformation to Bmmb, culated on the assumption that the c axis in Bmmb becomes
which at room temperature, as we have shown, occurs the c axis in I4/mcm. In practice it is likely that microtwinn-
between x"0.4 and x"0.45. Of course, a discontinuous ing will occur which will greatly reduce long-range stresses,
change in at least one of the tilts was inevitable, since tilts so mechanical integrity of a specimen is unlikely to be
about one of these axes persist in phase Bmmb. Another way affected.

STRUCTURES IN THE SYSTEM CaTiO /SrTiO
247
ꢁ
ꢁ
FIG. 12. Volume of pseudocubic subcell in Ca Sr TiO at room temperature. E, phase Pnma, #, phase Bmmb; ᭜, phase I4/mcm; ;, phase Pm3m.
ꢀ\V
V
ꢁ
CONCLUSIONS
3. M. McQuarrie, J. Am. Ceram. Soc. 38, 444 (1955).
4. T. Mitsui and W. B. Westphal, Phys. Rev. 124, 1354 (1961).
5. M. Ceh, D. Kolar, and L. Golic, J. Solid State Chem. 68, 68 (1987).
6. R. F. Garrett, D. J. Cookson, G. J. Foran, T. M. Sabine, B. J. Kennedy,
and S. W. Wilkins, Rev. Sci. Instrum. 66, 1351 (1995).
7. A. M. Glazer, Acta Crystallogr. Sect. B 28, 3384 (1972).
8. A. M. Glazer, Acta Crystallogr. Sect. A 31, 756 (1975).
9. R. W. Cheary and A. Coelho, Collaborative Computational Project
No. 14 in Powder and Single Crystal Diffraction, Program: XFIT, http:
//www.dl.ac.uk/CCP/CCP14 (1996).
At room temperature the phases in the system Ca
ꢀ\V
Sr TiO are Pnma for 04x40.4; Bmmb for 0.454x40.6;
I4/mcm for 0.654x40.9; and Pm3m for x50.95.
Volume changes resulting from transformations between
phases are small.
The largest shape changes occur for the Bmmb/I4/mcm
transformation, but at most are &0.3% and would prob-
ably be accommodated by microtwinning, so the mechan-
V
ꢁ
10. C. J. Howard and R. J. Hill, AAEC Report No. M112 (1986).
11. S. A. T. Redfern, J. Phys. Condensed Matter 8, 8267 (1996).
ical integrity of a specimen is unlikely to be affected by 12. L. Carlsson, Acta Crystallogr. 23, 901 (1967).
13. M. Ahtee, A. M. Glazer, and A. W. Hewat, Acta Crystallogr. Sect. B 34,
phase transformations during cooling from the temperature
of formation.
752 (1978).
14. T. Vogt and W. W. Schmahl, Europhys. ¸ett. 24, 281 (1993).
15. T. Matsui, H. Shigematsu, Y. Arita, Y. Hanajiri, N. Nakamitsu, and
T. Nagasaki, J. Nucl. Mater. 247, 72 (1997).
16. F. Guyot, P. Richet, P. Courtial, and P. Gillet, Phys. Chem. Miner. 20,
141 (1993).
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R. C. Ewing, Eds.), p. 233. Elsevier, Amsterdam, 1988.
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2. H. Granicher and O. Jakits, Suppl. Nuovo Cimento 9, 480 (1954).
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