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X-ray investigations of the cubic to tetragonal phase transition in CsCaCl3 at Tc = 95 K
Solid State Communications, Printed in Great Britain.
Vol. 60, No. 2, pp. 139-141,
X-RAY INVESTIGATIONS
OF THE CUBIC TO TETRAGONAL
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
1986.
PHASE TRANSITION
IN CsCaCls AT T, = 95 K
Y. Vaills and J.Y. Buzare Laboratoire
de Spectroscopic
du Solide, U.A. No 807 C.N.R.S., Faculte des Sciences, Route de Laval, 72017 Le Mans Cedex, France and A. Gibaud and Ch. Launay
Laboratoire
de Physique de 1’Etat Condense U.A. No 807 C.N.R.S., FacultC des Sciences, Route de Laval, 72017 Le Mans Cedex, France (Received 24 April 1986; in revised form 20 May 1986 by E.F. Bertaut) Some new crystallographic data on the cubic to tetragonal phase transition at T, = 95 K in CsCaCla allow us to infer the space group Dii for the low temperature phase connected with alternate rotations of the CaC16 along (00 1) directions. From the relative distorsion (c_a)/a we estimate the rotation angle which is the order parameter of the transition, smaller than in other chloride perovskites as CsPbCla and CsSrCls.
INTRODUCTION MANY PEROVSKITE COMPOUNDS AMX3 have been investigated by several kinds of experimental techniques with regard to the cubic to tetragonal phase transition. It has been established that these phase transitions are connected with the condensation of certain soft phonons whose eigenvectors correspond to the displacements of some atoms in the structure stabilized below the transition temperature T, [l] . Two kinds of phonon modes have been observed to soften. In some perovskites such as BaTiOs, KNbOs . . . the transverse optical model F2s at the zone centre becomes unstable which involves the shifting of both ions A and X along the principal axes and leads to ferroelectric phase transitions. In other class of perovskites (SrTiOs , LaAlOs, KMnFs, RbCaFs, CsPbCls . . .), the zone boundary mode like Ms or Rzs in the cubic phase condenses at T,. These latter modes can be related to the tilting of the MX6 octahedra around the cubic directions (0 0 1). Stereochemical considerations lead to similar conclusions. Let us consider the two quantities: &AX
&MX
=
=
a
rA + rX
2
d2
--
f-(rM
’ +rx),
where a is the cubic lattice parameter and rA, rx and TM the ionic radii tabulated by Shannon [2]. It may be seen that a structural phase transition may be expected to occur due to shifting when bAx < 0 and &Mx > 0. Rotations of the MX6 octahedra at the transition may be expected for bAx > 0 and Aijux < 0 [3]. 139
In this paper we are mainly concerned with CsCaCls which is a cubic chloride perovskite at room temperature (space group 0; or Pm3m). It is one of the few AMCIB perovskites that retains the 0; symmetry at room temperature. It undergoes a cubic to tetragonal phase transition at low temperature (T, = 95 K) and there is no evidence for further transitions down to 40K [4-61. Thus it seems a good candidate for studying critical phenomena near T, in connection with the strong anharmonicity of the Cl- motion [7] without disturbance from other phase transitions as it would be the case in CsPbCls [8] for instance. We present preliminary X-ray measurements on CsCaC13 owing to the lack of a firmly established space group in the low temperature phase. CRYSTAL PREPARATION The phase diagram for CsCl-CaC12 [9] shows that CsCaCls melts congruently at 910°C. The CsCaCls single crystals were prepared by a Bridgman-Stockbarger technique from high purity powders of CsCl and CaCls . Pure anhydrous CaCls was obtained from CaCls , 4Hs 0 dried in primary vacuum at 180°C for 48h. CsCl was dehydrated as well. After weighing in a glove box and mixing in equimolar proportions the mixture was inserted in a conical graphite crucible shut by a screw cap at the top and provided with a capillary tube at the bottom in order to prevent supercooling. The charged crucible was heated in a vertical furnace to approximately SO’C above the melting point of CsCaCla (Tf = 910°C) for 12 h. Then the temperature was lowered at a rate of 2_4”C/h using a programmed cooling. Single crystals so obtained
CUBIC TO TETRAGONAL
140
PHASE TRANSITION
Table 1. Atomic positions in the tetragonal cell according to the Dif, spacegroup
Ca2+ cs’ Cl, Cl,
Site
X
Y
Z
4(c) 4(b) 4(a) 8(h)
0 0 0 x
0 1
0
were transparent one cm3.
and
: J_+x
hygroscopic
X-RAY DIFFRACTION
measuring
a 1 i about
EXPERIMENTS
These experiments were carried out on powdered single crystal with a Philips powder X-ray diffractometer using the CuK, radiation. First, the lattice parameter a in the cubic phase was measured at room temperature a (300K) = (5.382 + 0.001) A. A liquid helium cryostat previously described [lo] allowed us to perform measurements at variable temperature from 40 to 300K. At IOOK we determined a = (5.373 + O.OOl)W. At lower temperature, the hhh lines remained single, while the hhl lines were split into two lines of relative intensity 2: 1 and the hkl lines gave three lines of equal intensity. This behaviour is in agreement with a distance between two successive lattice planes given by: dhk, = jhF+$li2.
Thus it may be inferred that a tetragonal distortion occurs at low temperature in CsCaCls. The variations of the lattice parameters a and c, vs temperature were investigated through the behaviour of several cubic lines (310, 400, 420). The corresponding Bragg angles were found in the following order: 0013 =
6103 <
eoo4
em
<
0301 =
eo31
<
elm
=
IN CsCaCls
Vol. 60, No. 2
recalled in the introduction, we may expect the structural transition to be due to rotations of Car& octahedra. With this assumption and according to Megaw’s classification of tilted rigid octahedra in perovskites [l I], the low temperature phase symmetry space group is either D&, (P4/mbm) or Dif, (14/mcm); the former is connected with the condensation of the M3 zone boundary mode in which the octahedra remain undistorted but rotated along one of the cubic directions (0 0 1). Adjacent octahedra are rotated in the same sense along the rotation axis (Fig. 1b). The latter corresponds to the condensation of the Rzs zone boundary mode in which the octahedra are still undistorted and rotated along one of the cubic directions, but in this case the octahedra rotations alternate along the rotation axis (Fig. la). The rotation of the octahedra results in a modification of the unit cell axes and then extra reflections are produced which correspond to half integer Miller indices in the pseudo-cubic unit cell. Furthermore, it appears that the two space groups result in distinct extra reflections. In fact, the matrix transformation which allows to relate the Miller indices of the tetragonal D$, unit cell ad2, ad2, 2c to the cubic one may be written:
Taking into account the extinction rules for Dii ht, k, of distinct parity of I, odd, we should observe superstructure lines such as 3/2, l/2, l/2; 5/2, l/2, l/2; 312, l/2,3/2. . . For the D:,, unit cell ad2, ad2, c, the matrix transformation is
eJlo
which shows that the ratio c/a is greater than 1. Some values of (c/a - 1) for various temperatures are given in Table 2. These results were obtained through a computer adjustment of experimental and calculated line positions. From these measurements, the transition temperature may be located between 95 and 100K. After that, we began the search for the space group of the crystal in the low temperature tetragonal phase. At first, from Shannon’s ionic radii, we have &os-or = +O.llAand&,_or=-0.12A. Thus, from the stereochemical considerations we
The extinction rules for Dih are h,, k, of distinct parity. The extra lines observed in this case should be: 312, l/2, 0; 312, l/2, 1; 312, l/2, 2; S/2, l/2, 1; 312, l/2,3. . . A systematic search for extra reflections led us to observe only the 312, l/2, l/2 and 312, l/2, 312 lines corresponding to the D$, space group. According to this latter space group atomic positions in the tetragonal cell are given in Table 1. DISCUSSION On the basis of these results, it is possible to relate the tetragonal distorsion c/a of the cubic cell to the
CUBIC TO TETRAGONAL
vol. 60, No. 2
PHASE TRANSITION
IN CsCaCls
141
(a)
&I'
OCa"
(b)
Fig. 2. Projection of rotated octahedra in the (00 1) plane: cpis the order parameter of the transition. drawn from our measurements. New experiments are now in progress, with regard to precise transition temperature and tetragonal lattice parameters determinations. To conclude, we would like to outline that contrary to other chloride perovskites as CsPbCls or CsSrC13, the low temperature phase symmetry group is Dif, when we assume the transition to be due to Fig. 1. Octahedra rotation modes. (a) Rzs mode (b) octahedra rotations. It corresponds to the condensation Ms mode. of a Rzs zone boundary mode connected with alternate rotations of the CaCle octahedra around the cubic displacement of the Cl atoms in the CsCaCla lattice of the tetragonal phase and hence to the rotation angle cp directions (0 0 1) as in SrTi03 or RbCaF3. Furthermore, the tetragonal distorsion is smaller in CsCaC13 than in of the octahedra which is the order parameter of the CsPbC13 for which Aleksandrov et al. [14] quote transition. Fig. 2 shows the CaCle octahedra rotation cp= 4.3’ at T = T, - 1 K or in CsSrC13 for which the in the (0 0 1) plane. According to Alefeld [ 121, we can same authors determine cp= 5.4’ at T = T, - 2K. relate the relative distorsion to the square of the order parameter: REFERENCES c/a-l = $cp’. W. Cochran, Adv. Phys. 9,307 (1960). The values of cpdeduced from our estimates of c/a R.D. Shannon, Acta. C’ryst. A32,75 l(1976). :: 1 at various temperatures are collected in Table 2. These 3. M. Rousseau, J.Y. Gesland, J. Julliard, J. Nouet, results give smaller values of the order parameter than J. Zarembowitch & A. Zarebowitch, Phys. Rev. B12,1579 (1975). EPR measurements on CsCaC1a:Gd3+ which led to 4. K.S. Aleksandrov, Femoelectrics 19,436 (1978). cp= 3” at T = T, [6]. It may be outlined Alefeld’s 5. A.E. Usachev, Yu.V. Yablokov & K.S. Alexsandrov, model underestimates cpin fluoperovskites as well. Though Sov. Phys Solid State 21,1445 (1979). some indications [6, 131 seem in favor of a slight jump 6. A.E. Usachev & Yu.V. Yablokov, Sov. Phys. of cp at the transition, no definite conclusions may be Solid State 24,852 (1982). 7. J. Hutton & R.J. Nelmes, J. Phys. C: Solid State Phys 14,1713 (1981). 8. Y. Fujii, S. Hoshino, Y. Yamada & G. Shirane, Table 2. Phys Rev. 9,4549 (1974). 9. J. Julliard & J. Nouet, Rev. Phys. Apple 10, 325 TOO (1975). 10. I.V. Shakhno & V.E. Plyushchev, Russ. J. Inorg. Chem 5,564 (1960). 11. A.M. Glazer & H.D. Megaw, Phil. Msg. 25, 1119 0 0 100 (1972). 8 1.3 95 12. B. Alefeld,Z. Phys. 222, 155 (1969). 87 19 2.0 Y. Vaills & J.Y. -Buzard (to be‘published). 80 26 2.4 ::: K.S. Aleksandrov, K.A. Pozdnyakova & T.A. Orlova, Sov. Phys CkistaZZogr. 22,52 (1977).
Vol. 60, No. 2, pp. 139-141,
X-RAY INVESTIGATIONS
OF THE CUBIC TO TETRAGONAL
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
1986.
PHASE TRANSITION
IN CsCaCls AT T, = 95 K
Y. Vaills and J.Y. Buzare Laboratoire
de Spectroscopic
du Solide, U.A. No 807 C.N.R.S., Faculte des Sciences, Route de Laval, 72017 Le Mans Cedex, France and A. Gibaud and Ch. Launay
Laboratoire
de Physique de 1’Etat Condense U.A. No 807 C.N.R.S., FacultC des Sciences, Route de Laval, 72017 Le Mans Cedex, France (Received 24 April 1986; in revised form 20 May 1986 by E.F. Bertaut) Some new crystallographic data on the cubic to tetragonal phase transition at T, = 95 K in CsCaCla allow us to infer the space group Dii for the low temperature phase connected with alternate rotations of the CaC16 along (00 1) directions. From the relative distorsion (c_a)/a we estimate the rotation angle which is the order parameter of the transition, smaller than in other chloride perovskites as CsPbCla and CsSrCls.
INTRODUCTION MANY PEROVSKITE COMPOUNDS AMX3 have been investigated by several kinds of experimental techniques with regard to the cubic to tetragonal phase transition. It has been established that these phase transitions are connected with the condensation of certain soft phonons whose eigenvectors correspond to the displacements of some atoms in the structure stabilized below the transition temperature T, [l] . Two kinds of phonon modes have been observed to soften. In some perovskites such as BaTiOs, KNbOs . . . the transverse optical model F2s at the zone centre becomes unstable which involves the shifting of both ions A and X along the principal axes and leads to ferroelectric phase transitions. In other class of perovskites (SrTiOs , LaAlOs, KMnFs, RbCaFs, CsPbCls . . .), the zone boundary mode like Ms or Rzs in the cubic phase condenses at T,. These latter modes can be related to the tilting of the MX6 octahedra around the cubic directions (0 0 1). Stereochemical considerations lead to similar conclusions. Let us consider the two quantities: &AX
&MX
=
=
a
rA + rX
2
d2
--
f-(rM
’ +rx),
where a is the cubic lattice parameter and rA, rx and TM the ionic radii tabulated by Shannon [2]. It may be seen that a structural phase transition may be expected to occur due to shifting when bAx < 0 and &Mx > 0. Rotations of the MX6 octahedra at the transition may be expected for bAx > 0 and Aijux < 0 [3]. 139
In this paper we are mainly concerned with CsCaCls which is a cubic chloride perovskite at room temperature (space group 0; or Pm3m). It is one of the few AMCIB perovskites that retains the 0; symmetry at room temperature. It undergoes a cubic to tetragonal phase transition at low temperature (T, = 95 K) and there is no evidence for further transitions down to 40K [4-61. Thus it seems a good candidate for studying critical phenomena near T, in connection with the strong anharmonicity of the Cl- motion [7] without disturbance from other phase transitions as it would be the case in CsPbCls [8] for instance. We present preliminary X-ray measurements on CsCaC13 owing to the lack of a firmly established space group in the low temperature phase. CRYSTAL PREPARATION The phase diagram for CsCl-CaC12 [9] shows that CsCaCls melts congruently at 910°C. The CsCaCls single crystals were prepared by a Bridgman-Stockbarger technique from high purity powders of CsCl and CaCls . Pure anhydrous CaCls was obtained from CaCls , 4Hs 0 dried in primary vacuum at 180°C for 48h. CsCl was dehydrated as well. After weighing in a glove box and mixing in equimolar proportions the mixture was inserted in a conical graphite crucible shut by a screw cap at the top and provided with a capillary tube at the bottom in order to prevent supercooling. The charged crucible was heated in a vertical furnace to approximately SO’C above the melting point of CsCaCla (Tf = 910°C) for 12 h. Then the temperature was lowered at a rate of 2_4”C/h using a programmed cooling. Single crystals so obtained
CUBIC TO TETRAGONAL
140
PHASE TRANSITION
Table 1. Atomic positions in the tetragonal cell according to the Dif, spacegroup
Ca2+ cs’ Cl, Cl,
Site
X
Y
Z
4(c) 4(b) 4(a) 8(h)
0 0 0 x
0 1
0
were transparent one cm3.
and
: J_+x
hygroscopic
X-RAY DIFFRACTION
measuring
a 1 i about
EXPERIMENTS
These experiments were carried out on powdered single crystal with a Philips powder X-ray diffractometer using the CuK, radiation. First, the lattice parameter a in the cubic phase was measured at room temperature a (300K) = (5.382 + 0.001) A. A liquid helium cryostat previously described [lo] allowed us to perform measurements at variable temperature from 40 to 300K. At IOOK we determined a = (5.373 + O.OOl)W. At lower temperature, the hhh lines remained single, while the hhl lines were split into two lines of relative intensity 2: 1 and the hkl lines gave three lines of equal intensity. This behaviour is in agreement with a distance between two successive lattice planes given by: dhk, = jhF+$li2.
Thus it may be inferred that a tetragonal distortion occurs at low temperature in CsCaCls. The variations of the lattice parameters a and c, vs temperature were investigated through the behaviour of several cubic lines (310, 400, 420). The corresponding Bragg angles were found in the following order: 0013 =
6103 <
eoo4
em
<
0301 =
eo31
<
elm
=
IN CsCaCls
Vol. 60, No. 2
recalled in the introduction, we may expect the structural transition to be due to rotations of Car& octahedra. With this assumption and according to Megaw’s classification of tilted rigid octahedra in perovskites [l I], the low temperature phase symmetry space group is either D&, (P4/mbm) or Dif, (14/mcm); the former is connected with the condensation of the M3 zone boundary mode in which the octahedra remain undistorted but rotated along one of the cubic directions (0 0 1). Adjacent octahedra are rotated in the same sense along the rotation axis (Fig. 1b). The latter corresponds to the condensation of the Rzs zone boundary mode in which the octahedra are still undistorted and rotated along one of the cubic directions, but in this case the octahedra rotations alternate along the rotation axis (Fig. la). The rotation of the octahedra results in a modification of the unit cell axes and then extra reflections are produced which correspond to half integer Miller indices in the pseudo-cubic unit cell. Furthermore, it appears that the two space groups result in distinct extra reflections. In fact, the matrix transformation which allows to relate the Miller indices of the tetragonal D$, unit cell ad2, ad2, 2c to the cubic one may be written:
Taking into account the extinction rules for Dii ht, k, of distinct parity of I, odd, we should observe superstructure lines such as 3/2, l/2, l/2; 5/2, l/2, l/2; 312, l/2,3/2. . . For the D:,, unit cell ad2, ad2, c, the matrix transformation is
eJlo
which shows that the ratio c/a is greater than 1. Some values of (c/a - 1) for various temperatures are given in Table 2. These results were obtained through a computer adjustment of experimental and calculated line positions. From these measurements, the transition temperature may be located between 95 and 100K. After that, we began the search for the space group of the crystal in the low temperature tetragonal phase. At first, from Shannon’s ionic radii, we have &os-or = +O.llAand&,_or=-0.12A. Thus, from the stereochemical considerations we
The extinction rules for Dih are h,, k, of distinct parity. The extra lines observed in this case should be: 312, l/2, 0; 312, l/2, 1; 312, l/2, 2; S/2, l/2, 1; 312, l/2,3. . . A systematic search for extra reflections led us to observe only the 312, l/2, l/2 and 312, l/2, 312 lines corresponding to the D$, space group. According to this latter space group atomic positions in the tetragonal cell are given in Table 1. DISCUSSION On the basis of these results, it is possible to relate the tetragonal distorsion c/a of the cubic cell to the
CUBIC TO TETRAGONAL
vol. 60, No. 2
PHASE TRANSITION
IN CsCaCls
141
(a)
&I'
OCa"
(b)
Fig. 2. Projection of rotated octahedra in the (00 1) plane: cpis the order parameter of the transition. drawn from our measurements. New experiments are now in progress, with regard to precise transition temperature and tetragonal lattice parameters determinations. To conclude, we would like to outline that contrary to other chloride perovskites as CsPbCls or CsSrC13, the low temperature phase symmetry group is Dif, when we assume the transition to be due to Fig. 1. Octahedra rotation modes. (a) Rzs mode (b) octahedra rotations. It corresponds to the condensation Ms mode. of a Rzs zone boundary mode connected with alternate rotations of the CaCle octahedra around the cubic displacement of the Cl atoms in the CsCaCla lattice of the tetragonal phase and hence to the rotation angle cp directions (0 0 1) as in SrTi03 or RbCaF3. Furthermore, the tetragonal distorsion is smaller in CsCaC13 than in of the octahedra which is the order parameter of the CsPbC13 for which Aleksandrov et al. [14] quote transition. Fig. 2 shows the CaCle octahedra rotation cp= 4.3’ at T = T, - 1 K or in CsSrC13 for which the in the (0 0 1) plane. According to Alefeld [ 121, we can same authors determine cp= 5.4’ at T = T, - 2K. relate the relative distorsion to the square of the order parameter: REFERENCES c/a-l = $cp’. W. Cochran, Adv. Phys. 9,307 (1960). The values of cpdeduced from our estimates of c/a R.D. Shannon, Acta. C’ryst. A32,75 l(1976). :: 1 at various temperatures are collected in Table 2. These 3. M. Rousseau, J.Y. Gesland, J. Julliard, J. Nouet, results give smaller values of the order parameter than J. Zarembowitch & A. Zarebowitch, Phys. Rev. B12,1579 (1975). EPR measurements on CsCaC1a:Gd3+ which led to 4. K.S. Aleksandrov, Femoelectrics 19,436 (1978). cp= 3” at T = T, [6]. It may be outlined Alefeld’s 5. A.E. Usachev, Yu.V. Yablokov & K.S. Alexsandrov, model underestimates cpin fluoperovskites as well. Though Sov. Phys Solid State 21,1445 (1979). some indications [6, 131 seem in favor of a slight jump 6. A.E. Usachev & Yu.V. Yablokov, Sov. Phys. of cp at the transition, no definite conclusions may be Solid State 24,852 (1982). 7. J. Hutton & R.J. Nelmes, J. Phys. C: Solid State Phys 14,1713 (1981). 8. Y. Fujii, S. Hoshino, Y. Yamada & G. Shirane, Table 2. Phys Rev. 9,4549 (1974). 9. J. Julliard & J. Nouet, Rev. Phys. Apple 10, 325 TOO (1975). 10. I.V. Shakhno & V.E. Plyushchev, Russ. J. Inorg. Chem 5,564 (1960). 11. A.M. Glazer & H.D. Megaw, Phil. Msg. 25, 1119 0 0 100 (1972). 8 1.3 95 12. B. Alefeld,Z. Phys. 222, 155 (1969). 87 19 2.0 Y. Vaills & J.Y. -Buzard (to be‘published). 80 26 2.4 ::: K.S. Aleksandrov, K.A. Pozdnyakova & T.A. Orlova, Sov. Phys CkistaZZogr. 22,52 (1977).