Evolution of crystallographic phases in (Sr1-xCax)TiO3 with composition (x)

Article abstract of DOI:10.1006/jssc.2001.9336

Results of X-ray powder diffraction, neutron powder diffraction, electron microdiffraction, and convergent beam electron diffraction (CBED) studies are presented to show that the space group of (S_1-xCa_x)TiO₃ (SCT) in the c

Full text of DOI:10.1006/jssc.2001.9336

Journal of Solid State Chemistry 162, 20}28 (2001)
doi:10.1006/jssc.2001.9336, available online at http://www.idealibrary.com on
Evolution of Crystallographic Phases in (Sr Ca
x
)TiO
3
1!x
with Composition (x)
Rajeev Ranjan,* Dhananjai Pandey,*ꢁꢀ W. Schuddinck,- O. Richard,- P. De Meulenaere,-
J. Van Landuyt,- and G. Van Tendeloo-
*
School of Materials Science & Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005, India; and -Electron Microscopy
for Materials Research (EMAT), Universiteit Antwerpen (RUCA), Groenenborgerlaan 171, 2020 Antwerpen, Belgium
Received March 28, 2001; in revised form July 17, 2001; accepted August 2, 2001
tration of Caꢃ> has been shown by Bednorz and Muller (7)
Results of X-ray powder di4raction, neutron powder di4rac- to stabilize X}Y-type quantum ferroelectricity above a criti-
tion, electron microdi4raction, and convergent beam electron
cal Caꢃ> concentration of x "0.0018. The phase transition
A
di4raction (CBED) studies are presented to show that the space
behavior changes from quantum to classical type for
group of (Sr1+xCa
x
)TiO
3
(SCT) in the composition range
x'0.016 (7). The peak in the dielectric constant becomes
increasingly smeared out with increasing x in the composi-
tion range 0.016(x40.12 (7). Ranjan et al. (14) have
proposed that this smearing is due to a dipole glass/relaxor
ferroelectric transition caused by the frustration introduced
by competing ferroelectric and antiferroelectric interactions.
0
.35<x40.55 cannot be Cmcm. The correct space groups
are Pbcm for 0.35 < x 40.40 and Pbnm for 0.40 < x 4 0.55.
The analysis of powder XRD data reveals that the structure of
SCT is noncubic for x 50.06. It is shown that four di4erent
types of orthorhombic phases appear in the SCT system with
2
؉
increasing Ca content. ( 2001 Academic Press
Key Words: (Sr1؊xCa
x
)TiO
3
; perovskites; electron microdif- Ranjan et al. (14) have also shown that (Sr Ca )TiO
ꢀ
\V
V
ꢂ
fraction; CBED; neutron powder di4raction; X-ray powder (SCT) undergoes an antiferroelectric phase transition in the
di4raction; antiferroelectrics; quantum ferroelectrics; tilt composition range 0.12(x(0.43. For x50.43, SCT ex-
transitions.
hibits incipient antiferroelectric behavior (15).
In addition to the zone-center soft mode, SrTiO has
ꢂ
a zone boundary soft mode also. The cubic (space group:
1
. INTRODUCTION
Pm3m) to tetragonal (space group: I4/mcm) phase transition
below 105 K in SrTiO is driven by the zone boundary
ꢂ
Strontium titanate (SrTiO ) has been the model system
R
mode (1). For the SCT system, Ranjan and Pandey (13)
ꢂ
ꢃꢄ
for studies related to structural phase transitions and critical have shown that, with increasing Caꢃ> content, the struc-
phenomena (1}3). Upon lowering of the temperature, the tural phase transition behavior changes from SrTiO -like to
ꢂ
dielectric constant of SrTiO gradually increases and be- CaTiO -like above a critical Caꢃ> concentration x+0.12.
ꢂ
ꢂ
ꢂ
comes nearly 20,000 at 4 K (4). This has been attributed to CaTiO , unlike SrTiO , exhibits an orthorhombic (space
ꢂ
the softening of a zone-center optical mode. Upon lowering group: Pbnm) to cubic (space group: Pm3m) phase transition
of the temperature below 4 K, the dielectric constant (eꢀ) mediated by an intermediate tetragonal phase (space group:
becomes temperature independent and does not lead to any I4/mcm) (16, 17) due to phonon instabilities at the R and
peak in eꢀ(¹), indicating the absence of a ferroelectric phase M points of the cubic Brillouin zone.
transition (4). This leveling o! of the eꢀ(¹) below 4 K has
While the phase transition aspects in the SCT system are
been attributed to zero-point quantum #uctuations, which reasonably well understood, there are several controversies
preclude the freezing of the soft zone-center optical mode. about the room-temperature structure of SCT as a function
SrTiO has accordingly been termed as a quantum para- of Caꢃ> content. As said earlier, the structure of SrTiO at
ꢂ
ꢂ
electric or an incipient ferroelectric (4).
room temperature is cubic (space group: Pm3m) whereas
A rich variety of phase transitions are known to result CaTiO has an orthorhombic structure (space group: Pbnm)
ꢂ
when Caꢃ> is substituted at the Srꢃ> site in SrTiO (5}14). (18). In the mixed (Sr Ca )TiO system, it is expected
ꢂ
ꢀ\V
V
ꢂ
In the (Sr Ca )TiO (SCT) system, a very small concen- that, above a certain critical Caꢃ> concentration, the struc-
ꢀ\V
V
ꢂ
ture will change from cubic to orthorhombic. In an early
work, McQuarrie (19) proposed that the structure of SCT
changes from cubic to tetragonal for 0.15(x(0.55 and
ꢀ
To whom correspondence should be addressed. Fax: 091-542-368147/
3
68428. E-mail: dpandey@banaras.ernet.in.
2
0
0
022-4596/01 $35.00
Copyright ( 2001 by Academic Press
All rights of reproduction in any form reserved.

CRYSTALLOGRAPHIC PHASES IN (Sr Ca )TiO
21
ꢀ\V
V
ꢂ
tetragonal to orthorhombic for x50.55. Mitsui and Wes-
tphal (6) investigated the room-temperature structure of
SCT in the composition range 04x40.20 and reported
that the structure of SCT becomes tetragonal (space group:
3. X-RAY DIFFRACTION STUDIES
3
.1. Superlattice Reyections Due to Octahedral Tilts
Figure 1 depicts powder X-ray di!raction patterns of
I4/mcm) for x'0.10. Ceh et al. (20) have questioned the SCT for x"0.00 (ST), 0.06 (SCT6), 0.09 (SCT9), 0.12
existence of the tetragonal phase in the SCT system and (SCT12), 0.25 (SCT25), 0.30 (SCT30), 0.35 (SCT35), 0.36
have proposed that the cubic}orthorhombic phase bound- (SCT36), 0.40 (SCT40), 0.43 (SCT43), 0.50 (SCT50), and 1.00
ary is located around x"0.40. Based on the observation of (CT) in the 2h range of 353}653. These patterns have been
two tilt transitions, Ranjan and Pandey (13) have argued zoomed to make the superlattice peaks visible. Because of
that the structure of SCT should be orthorhombic for this zooming, some of the main perovskite peaks are trun-
x50.12. Further, Ranjan et al. (12) have shown that the cated in the "gure. The superlattice re#ections are due to the
structure of SCT for x"0.50 is exactly identical to that of doubling of the elementary perovskite cell caused by tilting
CaTiO with the Pbnm space group. McQuarrie (19) and of the TiO octahedra (12). The Miller indices given in
ꢂ
ꢅ
Ball et al. (21) have, on the other hand, proposed that the Fig. 1 are with respect to a doubled elementary perovskite
structure of SCT does not become CaTiO -like until cell (2a ;2b ;2c ). As shown by Glazer (23, 24), super-
ꢂ
ꢀ
ꢀ
ꢀ
x50.55. According to Ball et al. (21), SCT has a Cmcm lattice re#ections with all-odd (ooo) Miller indices arise due
space group in the composition range 0.35(x40.55. As to &&anti-phase'' (!) tilting of the neighboring TiO oc-
ꢅ
per the phase diagram of SCT given by Ranjan et al. (14, 22), tahedra whereas superlattice re#ections with two-odd and
SCT for 0.35(x40.40 is antiferroelectric at room temper- one-even (ooe) type Miller indices are due to &&in-phase'' (#)
ature. According to Ranjan et al. (14, 22), the space group of tilting. The antiparallel displacements of Srꢃ>/Caꢃ> ions in
the antiferroelectric phase of SCT is Pbcm. This raises the neighboring elementary perovskite cells give rise to
doubts about the correctness of the Cmcm space group superlattice re#ections, which are of oee type (23, 24).
proposed by Ball et al. (21).
It can be seen from Fig. 1 that the superlattice re#ections
In the present work, we have examined the room-temper- of ooo, ooe, and oee types are present in the XRD patterns
ature crystal structure of SCT using X-ray powder di!rac- of SCT43, SCT50, and CaTiO . Based on the presence of
ꢂ
tion, neutron powder di!raction, electron microdi!raction, the three types of superlattice re#ections, the tilt system for
and convergent beam electron di!raction (CBED) tech- SCT43 and SCT50 are expected (12) to be identical to that
niques with a view to settle the existing controversies for CaTiO , that is, a\a\c> (space group: Pbnm) (23, 24).
ꢂ
about the structure of SCT as a function of Caꢃ>
content.
2
. EXPERIMENTAL
SCT samples were prepared using solid state ther-
mochemical reaction in a stoichiometric mixture of SrCO ,
ꢂ
CaCO , and TiO . The powders were mixed in a ball mill
ꢂ
ꢃ
using zirconia jars and balls for 6 h. Acetone was used as the
mixing media. Calcination of the mixed powder was carried
out at 11003C for 6 h. Before pelletization, the calcined
powders were ball-milled for 2 h for breaking the agglomer-
ates. Sintering of the pellets was carried out at 13003C for
6
h. The sintered pellets were crushed to "ne powders and
subsequently annealed at 5003C for 12 h for removing the
strains induced, if any, during the crushing process before
using it for di!raction studies.
X-ray di!raction studies were carried out using a 12-kW
Rigaku rotating anode based powder X-ray di!ractometer
operating in the Bragg}Brentano focusing geometry. Elec-
tron microdi!raction and CBED studies were carried out
on a Philips 200-kV electron microscope (model CM20).
For electron microscopy, the powder was ground in ethanol
and the small crystallites were dispersed on a holey carbon
grid.
FIG. 1. XRD patterns of di!erent compositions of SCT. The y-axis is
zoomed to enable the superlattice re#ections to become visible. As a result
of this, some of the main perovskite re#ections are truncated.

2
2
RANJAN ET AL.
The XRD patterns of SCT compositions with 0.09 Fig. 1, cannot be indexed with respect to a unit cell that is
(
x(0.36 contain superlattice re#ections of ooo type doubled along a , b , and c , the aꢆb\c> tilt system and
ꢀ
ꢀ
ꢀ
only. If we assume that ooe type superlattice re#ections are Cmcm space group for SCT36 and SCT40 are ruled out.
truly extinguished, the tilt system for SCT compositions Hence, the assignment of the Cmcm space group by Ball
with 0.094x(0.36 would be either aꢆaꢆc\ (space group: et al. (21) for the composition range 0.35(x40.40 is
I4/mcm), similar to the structure of the low-temperature incorrect.
(
(105 K) phase of SrTiO (2), or a\a\cꢆ (space group:
ꢂ
Ibmm) (12). However, the observation (13) of two tilt
4. SPACE GROUP OF (Sr1؊xCa )TiO IN THE
x 3
transitions clearly rules out the possibility of a aꢆaꢆc\ type
single-tilt system for SCT compositions with x50.12. The
similarity of the XRD pattern of SCT9 with that of SCT12
suggests that SCT9 may also exhibit two tilt transitions. X-ray powder di!raction patterns for these compositions in
Thus, the most plausible tilt system for the composition Fig. 1 do not contain the extra weak re#ections character-
COMPOSITION RANGE 0.40< x40.55
The Pbcm space group for x'0.40 is ruled out since the
range 0.904x(0.36 is a\a\cꢆ with space group Ibmm.
istic of the antiferroelectric phase. We now proceed to show
The 311 superlattice re#ection, which is the strongest that the correct space group of SCT in the composition
superlattice re#ection, is visible in the XRD patterns up to range 0.40(x40.55 is Pbnm, as proposed by Ranjan et al.
x"0.09, even though its intensity has become extremely (12) and not Cmcm proposed by Ball et al. (21). For this, we
low (10\ꢇ times the intensity of the strongest perovskite present the results of neutron di!raction, electron microdif-
peak 220). Mitsui and Westphal (6) did not observe any of fraction, and CBED studies on SCT50, which is representa-
the superlattice re#ections, shown in Fig. 1, for the composi- tive of the above-mentioned composition range.
tion range 04x40.20, presumably due to the low resolu-
tion of the old di!ractometers.
4
.1. Neutron Diwraction Study
To make a choice between the Pbnm and Cmcm space
groups, we have re"ned the structure of SCT50 with the
Cmcm space group also using the same neutron powder
3
.2. Superlattice Reyections in (Sr0.64Ca0.36)TiO (SCT36)
3
and Sr0.60Ca0.40TiO (SCT40) Due to Antiferroelectricity
3
The XRD patterns of SCT36 and SCT40 in Fig. 1 are di!raction data that was earlier used by Ranjan et al. (12) for
similar to those for 0.094x(0.36 with one important establishing the Pbnm space group.
di!erence. In addition to the &&ooo'' type superlattice re#ec-
For Rietveld re"nement, the various initial structural
tions, the XRD patterns of SCT36 and SCT40 contain extra parameters were taken from the re"ned values of Ball et al.
weak re#ections, which are marked with arrows in the (21). The minimum value of the R ("8.07) was attained
ꢁ
ꢀ
"
gure. Indexing of these extra weak re#ections requires after a few cycles of re"nement. The re"ned structural
doubling along two elementary perovskite cell parameters parameters are listed in Table 1. The re"ned positional
a , b ) and quadrupling along the third (c ), i.e., the multiple coordinates (X, >, Z) obtained by us are very close to those
(
ꢀ
ꢀ
ꢀ
elementary perovskite cell is 2a ;2b ;4c . Such a quadru- reported by Ball et al. (21). The isotropic thermal (B)
ꢀ
ꢀ
ꢀ
pling of the c parameter of the elementary perovskite unit parameters in our case are smaller than those reported by
cell has recently been reported in SCT30 below room tem- Ball et al. (21) for all the atoms except Sr/Ca(1). The cal-
perature by Ranjan et al. (14), who attributed it to the culated neutron powder di!raction pro"le for the re"ned
presence of superlattice re#ections characteristic of an anti-
ferroelectric phase. As per the phase diagram of Ranjan
et al. (14), SCT36 and SCT40 are antiferroelectric, even at
room temperature since the corresponding phase transition
temperatures lie above the room temperature. The extra
weak re#ections seen at room temperature in Fig. 1 for
SCT36 and SCT40 are therefore due to the antiferroelectric
nature of these two compositions at room temperature. The
space group of the antiferroelectric phase of SCT has been
con"rmed to be Pbcm (14, 22).
TABLE 1
Re5ned Structural Parameters of SCT50 with Cmcm Space
Group Using Neutron Powder Di4raction Data
Atom
X
>
Z
s
B (Aꢃ)
Sr/Ca(1)
Sr/Ca(2)
0.0
0.0
0.25
0.270(1)
0.0
0.285(2)
!0.001(3)
0.487(2)
0.25
0.0
0.225(1)
0.261(1)
0.25
0.25
0.0
0.0
0.033(2)
0.25
1.6(3)
0.1(2)
0.4(1)
0.9(1)
0.3(1)
0.7(2)
Ball et al. (21) have assigned the Cmcm space group and Ti
O(1)
O(2)
O(3)
aꢆb>c\ tilt system for the composition range 0.35(
x40.55. The three orthorhombic unit cell parameters
A , B , C for the Cmcm space group are approximately
ꢂ
ꢂ
ꢂ
equal to 2a , 2b , and 2c , respectively. However, the fact
Note. A "7.763(2) A
s
, B "7.776(1) A
s
, C "7.757(2) A
s
, R "5.92,
ꢀ
ꢀ
ꢀ
ꢆ
ꢆ
ꢆ
ꢀ
that the extra weak re#ections, marked with arrows in Rꢁꢀ"8.07, R "6.12, and R "6.11.
%

CRYSTALLOGRAPHIC PHASES IN (Sr Ca )TiO
23
ꢀ\V
V
ꢂ
position (not the intensity) of the re#ections on the patterns
and hence do not require accurate alignment of a zone axis
with respect to the electron beam since a slight misorienta-
tion of the di!racted beam does not signi"cantly a!ect the
position of the re#ections. The Bravais lattice, the glide
planes, and the partial extinction symbols are determined by
comparing the experimental patterns with the theoretical
ones given by Morniroli and Steeds (25). Taking into ac-
count the di!erent possibilities of the Bravais lattices and
the glide planes for each crystal system, all the theoretical
electron microdi!raction patterns have been computed by
Morniroli and Steeds (25). An individual partial extinction
symbol is given for each theoretical microdi!raction pat-
tern. By adding one, two, or three individual partial extinc-
tion symbols corresponding to di!erent zone-axis patterns
FIG. 2. Observed (...), calculated (**), and difference neutron pow-
der di!raction pattern of SCT50 after "nal re"nement with the Cmcm space
group.
(depending on the crystal system), one obtains a small
structure is in good agreement with that experimentally number of possible space groups. Usually, these possible
observed, as can be seen from Fig. 2. However, a similar "t is space groups belong to di!erent point groups, which may
observed even if one does the re"nement with the Pbnm be distinguished by the study of the positions as well as the
space group. The goodness-of-"t parameter, R , for the intensity distributions of the re#ections in the CBED pat-
ꢁ
ꢀ
Cmcm space group (R "8.07) is comparable to that ob- terns. Recording of the CBED patterns requires a very
ꢁ
ꢀ
tained by Ranjan et al. (12) for the Pbnm space group accurate orientation of the zone axis with respect to the
(
R "8.08). It is, therefore, not possible to make a unique electron beam since the di!racted beam intensity depends
ꢁꢀ
choice between the two space groups, Cmcm and Pbnm, greatly on the precise orientation. Using the combination of
purely on the basis of Rietveld analysis of powder di!rac- electron microdi!raction patterns showing the &&net'' sym-
tion data.
metries and CBED patterns showing the &&ideal'' symmetry,
The total number of re"nable positional coordinates in it is possible to identify the unique space group or at least
both Cmcm as well as Pbnm space groups is seven. Since the a small subset of consistent space groups.
number of atoms in the asymmetric unit is six and four for
the Cmcm and Pbnm space groups, respectively, the number
4.2.1. Electron microdi+raction studies. Figures 3a}3c
of re"nable isotropic thermal parameters for the Cmcm depict three whole patterns (zero-order Laue zone
space group is two more than that for the Pbnm (ZOLZ)#"rst-order Laue zone (FOLZ)) obtained for
space group. Further, the unit cell volume of the Cmcm SCT50, exhibiting the 2mm highest &&net'' symmetry, charac-
space group is double the unit cell volume of the Pbnm space teristic of the orthorhombic crystal system. To obtain these
group. As per crystallographic conventions, one chooses the patterns, the sample is tilted along the zero-order Laue zone
smallest size unit cell representing the lattice symmetry of mirrors until the "rst-order Laue zone re#ections appear on
the crystal. Since no improvement in re"nement results with the pattern. Using the lattice parameters A "5.50 A
s
,
ꢆ
the choice of the Cmcm space group, even after using a lar- B "7.75 A, and C "5.49 A, the zone axes of the three
s
s
ꢆ
ꢆ
ger number of re"nable parameters and a larger unit cell, it patterns in Figs. 3a}3c were con"rmed to be [001], [010],
is more appropriate to assign the Pbnm space group with and [100], respectively. This choice of axes (with
a smaller unit cell to SCT50. As shown in the next section, C (A (B ) is di!erent from those used in the interpreta-
ꢆ
ꢆ
ꢆ
analysis of ZOLZ and FOLZ microdi!raction patterns in tion of neutron di!raction data by Ranjan et al. (12) for
conjunction with CBED patterns uniquely "x the Pbnm which A "5.50 A
s
, B "5.49 A
s
, and C "7.75 A
s
(i.e.,
ꢆ
ꢆ
ꢆ
space group for SCT50.
B (A (C ). For the B (A (C choice, the space
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
ꢆ
group symbol is Pbnm, whereas for C (A (B , the space
ꢆ
ꢆ
ꢆ
group symbol becomes Pcmn (see &&International Tables for
Crystallography'' (26)). The two space group symbols rep-
4
.2. Electron Diwraction Studies
Electron microdi!raction patterns were recorded with resent the same structure in di!erent settings, i.e., cab and
a focused and nearly parallel incoherent beam. These pat- cba settings for Pbnm and Pcmn, respectively (26). The
terns allow one to obtain the crystal system and the Bravais theoretically calculated atlas of microdi!raction patterns
lattice and to reveal the presence of glide planes and screw (25) for the orthorhombic system correspond to the
axes of a crystal. The crystal system is obtained from the C (A (B choice of axes and hence the need to
ꢆ
ꢆ
ꢆ
electron microdi!raction patterns having the highest &&net'' change over from the Pbnm space group symbol to the
symmetry (25). The &&net'' symmetries take into account the Pcmn.

2
4
RANJAN ET AL.
FIG. 3. Electron microdi!raction pattern (ZOLZ#FOLZ) of SCT50 along the (a) [001], (b) [010], and (c) [100] zone axes of the orthorhombic cell.
For an orthorhombic crystal system, the determination of for the [010] and [100] zone-axis patterns, respectively. The
the partial extinction symbol requires analysis of the [001], addition of these individual partial extinction symbols leads
010], and [100] zone-axis patterns. On the [001] zone-axis to the Pc-n partial extinction symbol. This symbol, accord-
[
pattern (Fig. 3a), the mesh of re#ections of the zero-order ing to the &&International Tables of Crystallography'' (26), is
Laue zone (ZOLZ) constitutes a centered rectangle. The in agreement with the Pc2 n (m2m point group) and Pcmn
ꢀ
mesh of re#ections of the "rst-order Laue zone (FOLZ) (mmm point group) space groups. Thus, electron microdif-
forms a smaller noncentered rectangle. The periodicity dif- fraction studies suggest that the space group of SCT50 can
ference between the ZOLZ and FOLZ, plus the change from be either Pcmn or Pc2 n.
ꢀ
a centered to a noncentered rectangle is characteristic of the
presence of an &&n'' glide plane perpendicular to [001]. More-
over, re#ections belonging to the "rst-order Laue zone are
4.2.2. Convergent beam electron di+raction (CBED)
present on the two mirrors. The corresponding theoretical study. The point group of a crystal system can be deter-
pattern (Fig. 3a) has the individual partial extinction symbol mined by observing the &&ideal'' symmetries of CBED zone-
P..n where P stands for primitive cell and n for the n-glide axis patterns. As said earlier, these symmetries take into
plane perpendicular to [001]. The two dots stand for the account the position and the intensity of the re#ections. For
presence or absence of glide planes to be determined from SCT50, the zero-order Laue zone ideal symmetry of the
the [100] and [010] zone-axis microdi!raction patterns. [001] zone-axis pattern (Fig. 4a) is (2mm). The zero-order
A similar analysis is performed for the [010] and [100] Laue zone ideal symmetry of the [012] zone-axis pattern is
zone-axis patterns. The theoretical patterns corresponding also (2mm) (Fig. 4b) and that of the [212] zone-axis pattern
to the experimental ones are presented in Figs. 3b and 3c. (Fig. 4c) is (2). According to Table 2, which gives the ZOLZ
The individual partial extinction symbols are P.-. and Pc.. and the whole pattern ideal symmetry for the di!erent

CRYSTALLOGRAPHIC PHASES IN (Sr Ca )TiO
25
ꢀ\V
V
ꢂ
FIG. 4. Convergent beam electron di!raction pattern of SCT50 along (a) [001], (b) [012], and (c) [212] zone axes.
zone-axis patterns and for the di!erent point groups belong- group, on the other hand, has the point group symmetry
ing to the orthorhombic crystal system (25), these observed mmm. Thus, the space group of SCT50 is uniquely estab-
symmetries are in agreement with the mmm point group lished as Pcmn (or equivalently Pbnm in a di!erent setting of
only. This rules out the Pc2 n space group for the SCT50 for the axes).
ꢀ
which the point group symmetry is m2m. The Pcmn space
4
.2.3. Pcmn versus Cmcm in SC¹50. The [010] direc-
tion of the Pcmn space group is along the 11002 of the
elementary perovskite cell while [100] and [001] are 453
rotated with respect to the corresponding elementary perov-
ꢀ
TABLE 2
9
9Ideal:: Symmetries of the Di4erent Zone-Axis Patterns for
the Di4erent Point Groups Belonging to the Orthorhombic skite cell directions. For the Cmcm space group, all three
Crystal System
11002 directions are along the elementary perovskite cell
axes 11002 . Thus, the [010] direction of the Pcmn can be
parallel to any one of the three 11002 directions of the
Cmcm space group. Considering only the right-handed
coordinate system, the following orientation relationships
become possible between the unit cells for the Pcmn and
Cmcm space groups:
ꢀ
Ortho
rhombic
[001] [010] [100] [uv0] [u0w] [0vw] [uvw]
mmm
(2mm) (2mm) (2mm) (2mm) (2mm) (2mm)
(2)
1
(1)
1
(1)
1
(1)
1
2
(m)
m
mm
2mm
(m)
m
(2mm)
2mm
(m)
2mm
(2mm)
2mm
(m)
m
(m)
m
(m)
m
(m)
m
m
(m)
m
(m)
1
m
(m)
1
(m)
m
2
mm
m2m
mm2
(m)
(
i) [010] #[010] , [100] #[1 0 1ꢁ ] , [001] #[1 0 1] ;
m
. ! . ! . !
(2mm)
(m)
1
(m)
m
(m)
m
2
mm
m
m
(
ii) [010] #[100] , [100] #[0 1ꢁ 1] , [001] #[0 1 1] ;
. ! . ! . !
2
22
(2mm) (2mm) (2mm)
(m)
1
(m)
1
(m)
1
(1)
1
2
2
2
(
iii) [010] #[001] , [100] #[ 1ꢁ 1 0] , [001] #[1 1 0] .
. ! . ! . !

2
6
RANJAN ET AL.
FIG. 5. ZOLZ and FOLZ microdi!raction pattern for (a) C.c., (b) C-.., and (c) C..- partial extinction symbols.
The subscripts P and C refer to the Pcmn and Cmcm space means that similar di!raction patterns will be obtained for
groups, respectively. the [010] Pcmn structure and the [001] Cmcm structure. So
For the possibility (i), there is a c-glide perpendicular to the C..- partial extinction symbol of Fig. 5c cannot be ruled
010] for the Cmcm space group. The theoretically cal- out. The only di!erence is that the patterns in 3a and 3c
[
culated microdi!raction pattern for C.c. partial extinction cannot be explained with the Cmcm description.
symbol is shown in Fig. 5a. The two rectangles in ZOLZ The above analysis leads us to the conclusion that the
and FOLZ, drawn by joining adjacent di!raction spots, in space group of SCT50 cannot be Cmcm. Thus, the proposi-
Fig. 5a do not match with the corresponding rectangles tion of Ball et al. (21) that the space group of SCT50 is Cmcm
shown in Fig. 3b. Moreover, the FOLZ is shifted in such is incorrect. The correct space group of SCT50 is Pcmn (or
a way that along one of the ZOLZ mirrors (along [001]*) Pbnm in the cab setting of the orthorhombic axes), as al-
no FOLZ re#ections are present. This is not the case for the ready established in the previous section.
P.-. partial extinction symbol (Fig. 3b) where there are
FOLZ re#ections on both ZOLZ mirrors. This rules out the 5. COMPOSITION DEPENDENCE OF ORTHORHOMBIC
C.c. partial extinction symbol for Fig. 3b.
UNIT CELL PARAMETERS
Next, we consider the second orientation relationship (ii)
for which the partial extinction symbol should be C-... The
The room-temperature orthorhombic cell parameters
theoretical microdi!raction pattern for this is given in (A , B , C ) of SCT in the composition range 0.094
ꢆ
ꢆ
ꢆ
Fig. 5b. Again, the rectangles do not match with the corre- x40.50 are related to the equivalent elementary perovskite
sponding rectangles in Fig. 3b and also the FOLZ is shifted cell parameters (a , b , c ) as under
ꢀ
ꢀ ꢀ
in such a way that along one of the ZOLZ mirrors (along
001]*) no FOLZ re#ection is present. This rules out C-..
partial extinction symbol for Fig. 3b. It should be noted that
[
A +(2a , B +(2b , and C +2c
ꢆ ꢀ ꢆ ꢀ ꢆ ꢀ
the 100 and 001 re#ections of the Pcmn (see Fig. 3b), be-
(For 0.094x40.50 except for 0.364x40.40) [1]
A +(2a , B +(2b , and C +4c
comes 01
after unit cell transformation. For the Pcmn space group, the
00 and 001 re#ections are kinematically forbidden but
appear in Fig. 3b by multiple di!raction. On the other hand,
the 011 and 011 re#ections for Cmcm, obtained after unit cell
ꢁ 1 and 011 re#ections for the Cmcm space group
ꢆ
ꢀ
ꢆ
ꢀ
ꢆ
ꢀ
1
(For 0.364x40.40).
[2]
ꢁ
transformation, belong to extinct re#ections due to The development of the orthorhombic structures in the SCT
C centering. Such extinct re#ections due to lattice centering system may be visualized to occur in two ways: (i) the
cannot appear by multiple di!raction (25).
elementary cubic perovskite cell may become distorted in
For the third possible orientation relationship (iii), the a pseudotetragonal sense (a +b Oc , a"b"c"903) or
ꢀ
ꢀ
ꢀ
partial extinction symbol is C..-. The theoretically calculated (ii) the elementary cubic perovskite cell is monoclinically
microdi!raction pattern for C..- is shown in Fig. 5c, which distorted as in CaTiO (a "b Oc , a"b"903, cO903).
ꢂ
ꢀ
ꢀ
ꢀ
is, when turned over 453, similar to that observed for the P.-. For the pseudotetragonal distortion, the pro"le of the hhh
partial extinction symbol in Fig. 3b. After unit cell trans- type re#ections in the di!raction patterns will remain a sin-
formation the 200 and 020 re#ections of the Cmcm become, glet while the h00 type re#ections will be split into two,
respectively, 101 and 10 1ꢁ in the Pcmn space group and the where the Miller indices hhh and h00 are with respect to the
1
10 and 110 re#ections become 100 and 001, respectively. elementary cubic perovskite cell. For monoclinic distortion
ꢁ
Also, the FOLZ re#ections are not shifted. Along both of the elementary cubic perovskite cell, the hhh type re#ec-
ZOLZ mirrors, the FOLZ re#ections are present. This tions will also be split.

CRYSTALLOGRAPHIC PHASES IN (Sr Ca )TiO
27
ꢀ\V
V
ꢂ
FIG. 7. Variation of the magnitude of 2h di!erence between 004 and
00/040 pair of elementary perovskite re#ections with x.
4
x"0.055. This is, therefore, the critical composition above
which the structure of SCT should become noncubic at
room temperature, con"rming our conclusion about the
noncubic structure of SCT6 on the basis of the peak
broadening shown in Fig. 6. For x'0.35, the di!erence
*
(2h) decreases abruptly due to the sudden decrease of the
c parameter in the antiferroelectric phase of SCT (14, 22).
ꢀ
Granicher and Jakits (5) in their low-resolution XRD work
called this phase &&nearly cubic'', which we now know to be
orthorhombic (14, 22).
Table 3 gives the re"ned values of the orthorhombic cell
parameters (A , B , C ) for x50.09. The equivalent ele-
ꢆ
ꢆ
ꢆ
mentary perovskite cell parameters (a , b , c ) can be ob-
ꢀ
ꢀ ꢀ
tained from A , B , and C values using Eqs. [1] and [2] for
ꢆ
ꢆ
ꢆ
the appropriate composition range. The a , b , and c values
FIG. 6. XRD pro"le of +400, elementary perovskite re#ection for
di!erent SCT compositions. The indices are with respect to the elementary
perovskite cell.
ꢀ
ꢀ
ꢀ
are plotted as a function of composition in Fig. 8. The
equivalent elementary perovskite cell parameters show
a pseudotetragonal relationship (a +b ).
ꢀ
ꢀ
Figure 6 depicts the XRD pro"les for the 400 type ele-
mentary perovskite re#ections for the composition range
TABLE 3
Re5ned Orthorhombic Unit Cell Parameters and Unit Cell
Volume of Sr1؊xCa TiO
0
.04x40.50. It is evident from this "gure that these re#ec-
tions appear as a doublet for all the compositions in the
range 0.094x40.50, as expected for the pseudotetragonal
elementary perovskite cell. Even for SCT6, the structure
seems to be noncubic. This is because the 400 re#ection of
x
3
x
A
(A
s
)
B
(A
s
)
C
(A
s
)
s
< (Aꢂ)
ꢆ
ꢆ
ꢆ
ꢆ
SCT6 is much broader than that of SrTiO (ST). Evidently, 1.00
the 004 and the 400/040 re#ections are not superimposed in
SCT6 also.
5.3783(1)
5.4737(1)
5.4793(2)
5.4793(2)
5.4790(3)
5.4798(1)
5.4853(1)
5.4903(1)
5.5117(2)
5.5151(3)
5.4395(1)
5.4714(1)
5.4798(2)
5.4788(3)
5.4801(2)
5.4813(1)
5.4861(1)
5.4917(1)
5.5129(3)
5.5131(4)
7.6381(2)
7.7329(2)
7.7412(2)
15.5106(5)
15.5222(5)
7.7820(2)
7.7917(2)
7.7956(2)
7.8075(2)
7.8062(4)
223.45
231.59
232.43
465.62
466.06
233.74
234.47
235.04
237.23
237.34
ꢂ
0
0
0
0
.50
.43
.40
.36
The variation of the di!erence between the 2h angles for
the 004 and 400/040 re#ections (*(2h)"2h !2h
)
0.35
ꢇꢆꢆ
ꢆꢆꢇ
with Caꢃ> content (x) is shown in Fig. 7. This di!erence 0.30
0
0
0
.25
.12
.09
(
*(2h)) gradually increases with increasing Caꢃ> content
from x"0.09 to x"0.35. Extrapolation of *(2h) versus
x curve to *(2h)"0 intersects the composition (x) axis at

2
8
RANJAN ET AL.
rhombic phase OI for 0.094x(0.36, (iii) orthorhombic
phase OII for 0.364x40.40, (iv) orthorhombic phase
OIII for 0.40(x40.55, and (v) orthorhombic phase OIV
for x'0.55. The structure of SCT in the composition range
0
.064x(0.09 may be either tetragonal or orthorhombic
but it is de"nitely noncubic.
Rietveld analysis of neutron powder di!raction data is of
little help in making a choice between the two plausible
space groups (Pbnm and Cmcm) in the composition range
0
.40(x40.55. The electron microdi!raction and conver-
gent beam electron di!raction studies have revealed that the
correct space group of SCT in this composition range is
Pbnm (tilt system a\a\c>) and not Cmcm (tilt system
aꢆb>c\). For the composition range 0.364x40.40, the
correct space group is Pbcm.
FIG. 8. Variation of equivalent elementary perovskite cell parameters
with Caꢃ> concentration (x).
ACKNOWLEDGMENT
In the composition range 0.094x40.40, the 004 peak
occurs on the lower angle side of 400/040 position, indicat-
ing c 'a . For x'0.40, this situation is reversed since the
Partial support from Inter University Consortium for the Department of
Atomic Energy Facilities is gratefully acknowledge by the authors from
BHU.
ꢀ
ꢀ
0
04 peak now occurs on the higher angle side of the 400/040
position. Thus, for x40.40, c 'a whereas for x'0.40,
ꢀ
ꢀ
REFERENCES
c (a . As per the work of Ball et al. (21), the latter trend
ꢀ
ꢀ
may continue up to x+0.55. For x'0.55, the elementary
perovskite cell is monoclinically distorted in the sense dis-
cussed earlier.
1
2
3
. G. Shirane and Y. Yamada, Phys. Rev. 177, 858 (1969).
. A. D. Bruce and R. A. Cowley Adv. Phys. 29, 219 (1980).
. K. A. Muller, W. Berlinger, and E. Tosatti, Z. Phys. B: Condens. Matter
On the basis of the equivalent elementary perovskite cell
parameters (a , b , c ) and their relationship with the or-
8
4, 277 (1991).
4. K. A. Muller and H. Burkard, Phys. Rev. B 19, 3593 (1979).
ꢀ
ꢀ ꢀ
5
6
7
8
. H. Granicher and O. Jakits, Nuovo Cimento 9 (Suppl), 480 (1954).
. T. Mitsui and W. B. Westphal, Phys. Rev. 124, 1354 (1961).
. J. G. Bednorz and K. A. Muller, Phys. Rev. ¸ett. 52, 2289 (1984).
. J. Dec, W. Kleemann, U. Bianchi, and J. G. Bednorz, Europhys. ¸ett.
thorhombic unit cell parameters (A , B , C ), four di!erent
ꢆ
ꢆ
ꢆ
types of orthorhombic phases need to be distinguished in
the SCT system: (i) Orthorhombic (OI) for 0.094x(0.36:
In this composition range, the equivalent elementary perov-
skite cell is pseudotetragonal with c 'a (+b ),
2
9(1), 31 (1995).
9. W. Kleeman, U. Bianchi, A. Burgel, M. Prasse, and J. Dec, Phase
rans. 55, 57 (1995).
0. W. Kleeman, A. Albertini, Chamberlin, and J. G. Bednorz, Europhys.
ett. 37(2), 145 (1997).
ꢀ
ꢀ
ꢀ
¹
A +B +(2a , C +2c and the space group is Ibmm. (ii)
ꢆ
ꢆ
ꢀ
ꢆ
ꢀ
1
Orthorhombic (OII) for 0.364x40.40: In this composi-
tion range, the equivalent elementary perovskite cell is
pseudotetragonal with c 'a (+b ), A +B +(2a ,
¸
1
1
1. W. Kleeman, J. Dec, and B. West Wanski, Phys. Rev. B 58, 8985 (1998).
2. R. Ranjan, D. Pandey, V. Siruguri, P. S. R. Krishna, and S. K.
Paranjpe, J. Phys.: Condens. Matter 11, 2233 (1999).
ꢀ
ꢀ
ꢀ
ꢆ
ꢆ
ꢀ
C +4c and its space group is Pbcm. (iii) Orthorhombic
ꢆ
ꢀ
1
1
1
1
1
3. R. Ranjan and D. Pandey, J. Phys.: Condens. Matter 11, 2247 (1999).
4. R. Ranjan, D. Pandey, and N. P. Lalla, Phys. Rev. ¸ett. 84, 3726 (2000).
5. S. K. Mishra, R. Ranjan, and D. Pandey, to be published.
6. R. A. Redfern, J. Phys.: Condens. Matter 8, 8267 (1996).
7. B. J. Kennedy, C. J. Howard, and B. C. Chakoumakos, J. Phys.:
Condens. Matter 11, 1479 (1999).
8. H. F. Kay and P. C. Bailey, Acta Crystallogr. B 10, 219 (1957).
9. M. McQuarrie, J. Am. Ceram. Soc. 38, 444 (1955).
20. M. Ceh, D. Kolar, and L. Golic, J. Solid State Chem. 68, 68 (1987).
(
OIII) for 0.40(x40.55: In this composition range, the
equivalent elementary perovskite cell is pseudotetragonal
with c (a (+b ), A +B +(2a , C +2c and the
ꢀ
ꢀ
ꢀ
ꢆ
ꢆ
ꢀ
ꢆ
ꢀ
space group is Pbnm (,Pcmn). (iv) Orthorhombic (OIV) for
0
.55(x41.00: In this composition range, according to
1
1
Ball et al. (21), the equivalent elementary perovskite cell is
monoclinically distorted with a "b Oc with c slightly
ꢀ
ꢀ
ꢀ
ꢀ
greater than 903 while the space group remains Pbnm.
2
1. C. J. Ball, B. D. Begg, D. J Cookson, G. J. Thorogood, and E. R. Vance,
J. Solid State Chem. 139, 238 (1998).
2
2
2
2
2. R. Ranjan and D. Pandey, J. Phys.: Condens Matter 13, 4251 (2001).
3. A. M. Glazer, Acta. Crystallogr. B 28, 3384 (1972).
4. A. M. Glazer, Acta. Crystallogr. A 31, 756 (1975).
5. J. P. Morniroli and J. W. Steeds, ;ltramicroscopy 45, 219 (1992).
6
. CONCLUSION
Five di!erent phases appear at room temperature as
a function of Caꢃ> content: (i) cubic for x(0.06, (ii) ortho- 26. &&International Tables for Crystallography.'' Kluwer, Dordrecht, 1992.