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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S., Beznosikov B. V., Posdnjakova L. A.
Заглавие : Successive phase transitions in perovskites. II. Structures of distorted phases
Коллективы : European meeting on ferroelectricity
Место публикации : Ferroelectrics. - 1976. - Vol. 12, Spesial issue. - P.197-198. - DOI 10.1080/00150197608241424
Аннотация: Estimation of atomic displacements from the unit cell distortions is discussed for the perovskites having successive structural phase transitions. The distorted structures of CsPbCl3 and CsSrCl3 are proposed.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S.
Заглавие : The sequences of structural phase transitions in perovskites
Место публикации : Ferroelectrics. - 1976. - Vol. 14, Is. 1. - P.801-805. - DOI 10.1080/00150197608237799
Аннотация: A classification of the octahedral tilt systems in perovskites is given, based on the work of Glazer1 but extending it and using a new notation; this leads to a simple description of the sequences of phase transitions, and shows how they are related to the soft modes M3 and R25. Examples from the literature are discussed.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S.
Заглавие : Mechanisms of the ferroelectric and structural phase transitions. Structural distortions in perovskites
Коллективы : International meeting on ferroelectricity
Место публикации : Ferroelectrics. - 1978. - Vol. 20, Spesial issue. - P.61-67. - DOI 10.1080/00150197808239430
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sandler Yu. M.
Заглавие : Critical-behavior and elastic nonlinearity of perovskites at non-ferroelectric structure phase-transitions
Место публикации : Fiz. Tverd. Tela. - 1980. - Vol. 22, Is. 9. - P.2578-2587. - ISSN 0367-3294
Примечания : Cited References: 27
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sandler Yu. M.
Заглавие : Unstability and phase-transition splitting in perovskites at non-ferroelectric structural phase-transitions
Место публикации : Solid State Commun. - 1980. - Vol. 33, Is. 2. - P.265-266. - ISSN 0038-1098, DOI 10.1016/0038-1098(80)90369-5
Примечания : Cited References: 6
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Melnikova S. V., Anistratov A. T., Aleksandrov K. S.
Заглавие : Birefringes and structure phase-transitions in ABCl3 perovskites
Место публикации : Fiz. Tverd. Tela: Mezhdunarodnaya kniga, 1981. - Vol. 23, Is. 1. - P.246-250. - ISSN 0367-3294
Примечания : Cited References: 16
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Flerov I. N., Aleksandrov K. S., Tressaud A., Grannec J., Couzi M.
Заглавие : Phase transitions in elpasolites (ordered perovskites)
Место публикации : Materials Science and Engineering R: Reports. - 1998. - Vol. 24, Is. 3. - P.81-151. - ISSN 0927-796X
Примечания : Cited References: 174
Предметные рубрики: ELASTIC NEUTRON-DIFFRACTION
MII = CO
RAMAN-SCATTERING
THERMODYNAMIC PROPERTIES
CRYSTAL-STRUCTURE
SINGLE-CRYSTALS
RB2KMIIIF6 ELPASOLITES
CUBIC PEROVSKITES
TEMPERATURE FORM
HIGH-RESOLUTION
Ключевые слова (''Своб.индексиров.''): crystal atomic structure--crystal growth--crystal lattices--crystallization--crystallography--ferroelectricity--hydrostatic pressure--order disorder transitions--single crystals--thermodynamics--elpasolites--landau theory--perovskite
Аннотация: Many compounds with general chemical formula A2BB?X6 and with tolerance factor value t < 1 crystallize in the elpasolite (ordered perovskite) structure. Different preparative methods have been considered. For example, the Bridgman technique is the most suitable method of growing single crystals of halogenated elpasolites with monoatomic cations. Group-theory and symmetry analyses have allowed us to build a scheme of possible structural distortions connected with octahedral rotations and displacements of ions. Experimental observations have proven that ferroelastic phase transitions occurring most frequently in elpasolites are due to small octahedra tilts. Quantitative analysis allows the possibility of describing these transitions in the framework of the thermodynamic Landau theory. Hydrostatic pressure and the substitution of atoms in different crystallographic sites allow to change significantly the succession and the temperature of phase transitions. The hypothesis of bond stresses is able to predict the possible occurrence of a phase transition for a particular elpasolite and/or the role of the octahedra rotations in the transformation. The mechanism of phase transitions in elpasolites and related compounds has also been considered. One can assume that a displacive mechanism associated with a strong anharmonicity plays a large role in phase transitions occurring in compounds with monoatomic cations. On the other hand, for instance, in cryolites with ammonium cations, the transitions originate from an order-disorder phenomenon. В© 1998 Elsevier Science S.A. All rights reserved.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S., Beznosikov B. V.
Заглавие : Architecture and properties of perovskite-like crystals
Коллективы : USA-CIS-Baltic Seminar on Ferroelectricity
Место публикации : Ferroelectrics: Gordon Breach Sci Publ Ltd, 1999. - Vol. 226, Is. 1-4. - P.1-9. - ISSN 0015-0193, DOI 10.1080/00150199908230285
Примечания : Cited References: 9
Ключевые слова (''Своб.индексиров.''): perovskites--perovskite-like crystals--new representatives of ruddlesden-popper's phases--new representatives of ruddlesden-popper's phases--perovskite-like crystals--perovskites
Аннотация: A variety of the known structures of perovskite-like crystals including cation- and anion-deficient phases were considered as the intergrowth systems of slabs containing n-layers (n = 1,2, 3,...infinity) of corner-linked octahedra BX6, pyramids EX5 or square-planar nets BX4 (B-cation, X- anion) linked by intermediate blocks of different types.([1- 3]) Some new structural types and new representatives of ferroelectrics, ferroelastics and HTSC's can be constructed on this basis. The prognosis of new possible representatives in Ruddlesden-Popper's family is discussed.A variety of the known structures of perovskite-like crystals including cation- and anion-deficient phases were considered as the intergrowth systems of slabs containing n-layers (n = 1, 2, 3, . . . ?) of corner-linked octahedra BX6, pyramids BX5 or square-planar nets BX4 (B-cation, X-anion) linked by intermediate blocks of different types.[1-3] Some new structural types and new representatives of ferroelectrics, ferroelastics and HTSC's can be constructed on this basis. The prognosis of new possible representatives in Ruddlesden-Popper's family is discussed.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Gavrichkov V. A., Ovchinnikov S. G.
Заглавие : An impurity resistivity of doped manganese perovskites
Место публикации : Physica B: ELSEVIER SCIENCE BV, 1999. - Vol. 259-61: International Conference on Strongly Correlated Electron Systems (SCES 98) (JUL 15-18, 1998, PARIS, FRANCE). - P828-830. - ISSN 0921-4526, DOI 10.1016/S0921-4526(98)00875-8
Примечания : Cited References: 4
Предметные рубрики:
Ключевые слова (''Своб.индексиров.''): manganese perovskites--mobility--linear and quadratic magnetoresistance
Аннотация: We present a two-time of relaxation approach at an analysis of a magnetoresistance in ferromagnetic manganese perovskites La(1-x)(Ca,Sr)(x)MnO. To explain a change in the low-held response from predominantly quadratic dR/dH\(H--0) = 0 for T T(c) to linear dR/dH\(H--0) for T T(c) as noted in the measurements in thin films La(0.7)Ca(0.3)MnO(3) we calculated held and temperature dependences of a impurity contribution to a carrier mobility in a framework of the 2p(O)- and 3d(Mn)-scattering model elaborated for manganese perovskites. We obtained the field-dependent impurity contribution to the overall scattering of carriers that show a transition in the low-field (H) dependence of R from quadratic above T(c) to linear below consistent with an experiment. The calculated negative magnetoresistance ratio is sharply peaked at a temperature-near T(c) or below. (C) 1999 Elsevier Science B.V. All rights reserved.
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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Gavrichkov V. A., Ivanova N. B., Ovchinnikov S. G., Balaev A. D., Aminov T. G., Shabunina G. G., Chernov V. K., Petukhov M. V.
Заглавие : Comparison of negative magnetoresistance mechanisms in manganese perovskites and chromium spinels
Место публикации : Phys. Solid State: AMER INST PHYSICS, 1999. - Vol. 41, Is. 10. - P1652-1655. - ISSN 1063-7834, DOI 10.1134/1.1131064
Примечания : Cited References: 17
Предметные рубрики: ANISOTROPIC MAGNETORESISTANCE
TRANSPORT-PROPERTIES
THIN-FILMS
ALLOYS
Аннотация: A transition of the field dependence of the electrical resistivity from a square law (similar to H-2) above T-c to a linear function (similar to H) below T-c is observed in the degenerate ferromagnetic semiconductor HgCr2Se4(n). Together with the large negative magnetoresistance, these magnetoelectric effects correspond to effects observed in the perovskite-type oxides La1-xCaxMnOdelta. Inasmuch as the undoped semiconductor HgCr2Se4 is a ferromagnet with approximately the same critical temperature as the doped semiconductor and in view of the total lack of data on the Jahn-Teller effect in this compound, we infer that our results cast doubt on existing hypotheses (polaron and binary exchange) regarding the origin of the giant magnetoresistance in La1-xCaxMnOdelta. Impurity sd scattering is discussed as a possible magnetoresistance mechanism for both compounds. (C) 1999 American Institute of Physics. [S1063-7834(99)01710-4].
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11.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zinenko V. I., Zamkova N. G.
Заглавие : Theory of an Fm3m - I4/m structural phase transition in an Rb2KScF6 crystal
Разночтения заглавия :us: Theory of an Fm3mI4/m Structural Phase Transition in an Rb2KScF6 Crystal
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 2000. - Vol. 91, Is. 2. - P314-323. - ISSN 1063-7761, DOI 10.1134/1.1311990
Примечания : Cited References: 16
Предметные рубрики: FIRST-PRINCIPLES THEORY
LATTICE-DYNAMICS
PEROVSKITES
ELPASOLITES
Аннотация: An Rb2KScF6 crystal having an elpasolite structure undergoes a sequence of Fm3m -- I4/m -- P12(1)/n1 structural phase transitions where the transition to the tetragonal phase is associated with "rotation" of the ScF6 octahedron. An effective Hamiltonian is constructed to describe the Fm3m -- I4/m transition using the approximation of a local mode for which we selected a "soft mode" whose eigenvector corresponds to the rotation of the octahedron. The effective Hamiltonian also includes the relationship between the local mode and the homogeneous elastic strains. The parameters of the effective Hamiltonian were determined using the generalized Gordon-Kim model of an ionic crystal which allows for the deformability and polarizability of the ions. The thermodynamic properties of a system with this model Hamiltonian were investigated using the Monte Carlo method. The calculated phase transition temperature of 250 K is almost the same as the experimental value (252 K). The tetragonal phase remains stable as far as T = 0 K and a second transition (to the monoclinic phase) cannot be obtained using this effective Hamiltonian. This suggests that if the transition to the tetragonal phase is mainly associated with "rotations" of the octahedrons, in order to describe the phase transition to the monoclinic phase the effective Hamiltonian must allow for additional degrees of freedom mainly associated with the motion of rubidium ions. (C) 2000 MAIK "Nauka/Interperiodica".
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12.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Flerov I. N., Gorev M. V., Sciau P.
Заглавие : Heat capacity and p-T phase diagrams of the ordered perovskites Pb2MgWO6 and Pb2CoWO6
Место публикации : J. Phys.: Condens. Matter: IOP PUBLISHING LTD, 2000. - Vol. 12, Is. 5. - P.559-567. - ISSN 0953-8984, DOI 10.1088/0953-8984/12/5/304
Примечания : Cited References: 25
Предметные рубрики: CRYSTAL-STRUCTURE
X-RAY
TRANSITIONS
PRESSURE
Аннотация: The heat capacities of Pb2MgWO6 and Pb2CoWO6 and the effect of hydrostatic pressure on the phase transitions have been studied on powdered samples by means of an adiabatic calorimeter and DTA performed under pressure, respectively. Thermodynamic parameters, such as change of total excess entropy, latent hear and hysteresis of the phase transition temperature were determined. Entropies and p-T phase diagrams are discussed in connection with structural data.
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13.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S., Bartolome J., Gorev M. V., Flerov I. N.
Заглавие : Hydrostatic pressure effect on phase transitions in perovskites with ammonium cations
Место публикации : Phys. Status Solidi B. - 2000. - Vol. 217, Is. 2. - P.785-791. - ISSN 0370-1972, DOI 10.1002/(SICI)1521-3951(200002)217:2785::AID-PSSB7853.0.CO;2-Y
Примечания : Cited References: 36
Предметные рубрики: XMF3 CUBIC PEROVSKITES
THERMAL-PROPERTIES
HEAT-CAPACITY
TEMPERATURE DEPENDENCE
DIELECTRIC PROPERTIES
X-RAY
NH4ZNF3
NH4MNCL3
NH4COF3
NH4CDF3
Аннотация: The pressure dependence of the structural phase transition temperature has been measured for the powder samples of NH4MgF3, NH4ZnF3, NH4MnF3, NH4CoF3, NH4CdF3, and NH4MnCl3 perovskites in the pressure range 0 to 600 MPa. It was found that the values of dT(0)/dP are negative for the Mg, Zn. Co. Mn trifluorides and positive for NH4CdF3 and NH4MnCl3. Comparison with the known data for other halide and oxide perovskites allowed to conclude that the sign of dT(0)/dP is correlated with the value of the Goldschmidt tolerance factor of the perovskite, and its value is closely related to the temperature and mechanism of the transition.
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14.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Aleksandrov K. S., Bartolome J.
Заглавие : Structural distortions in families of perovskite-like crystals
Место публикации : Phase Transit.: TAYLOR & FRANCIS LTD, 2001. - Vol. 74, Is. 3. - P.255-335. - ISSN 0141-1594, DOI 10.1080/01411590108228754
Примечания : Cited References: 262
Предметные рубрики: LOW-TEMPERATURE PHASE
INELASTIC-NEUTRON-SCATTERING
POWDER PROFILE REFINEMENT
MII = CO
X-RAY
RAMAN-SCATTERING
ORDERED PEROVSKITE
RHOMBOHEDRAL PEROVSKITES
RB2KMIIIF6 ELPASOLITES
MAGNETIC-PROPERTIES
Ключевые слова (''Своб.индексиров.''): structural phase transitions--perovskites--perovskite-like crystals--group theoretical classification
Аннотация: The crystallographic and group theoretical analysis of the structural phase transitions in perovskite and perovskite-like crystals is reviewed. We include ABX(3) perovskites and their relative crystals of ReO3 type (G(0) = O-h(1)), elpasolites, cryolites and their relatives (G(0) = O-h(5)) layered crystals of TIAIF(4) series (G(0) = D-4h(1)), Aurivillius and Ruddlesden-Popper series (G(0) = D-4h(17)). The structures in their initial phase G(0) often contain n layers (n = 1, 2,3) of vertex linked octahedra. The distorted phases produced by one kind of tilt and by superposition of tilts in the slabs are enumerated. Most of the tilts correspond to symmetry changes, which can be associated to definite librational lattice modes irreducible representations of the G(0) group. The softening of modes associated to the PT has been found experimentally in many perovskites, elpasolites and layered crystals with n = 1. In contrast, no such soft modes have been found yet for even-layered (n = 2) crystals. Examples of successive phase transitions due to the superposition of tilts in these types of crystals have been collected.
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15.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zinenko V. I., Zamkova N. G.
Заглавие : Lattice dynamics and statistical mechanics of the Fm3m - I4/m structural phase transition in Rb2KInF6
Разночтения заглавия :авие SCOPUS: Lattice dynamics and statistical mechanics of the Fm3m I4/m structural phase transition in Rb2KInF6
Место публикации : Phys. Solid State: AMER INST PHYSICS, 2001. - Vol. 43, Is. 12. - P2290-2300. - ISSN 1063-7834, DOI 10.1134/1.1427959
Примечания : Cited References: 18
Предметные рубрики: FIRST-PRINCIPLES THEORY
RB2KSCF6 CRYSTAL
ELPASOLITES
PEROVSKITES
Аннотация: The static and dynamic properties of cubic Rb2KInF6 crystals with elpasolite structure are calculated using a nonempirical method. Calculations are performed within a microscopic ionic-crystal model taking into account the deformation and polarization of ions. The deformation parameters of ions are determined by minimizing the total energy of the crystal. The calculated equilibrium lattice parameters agree satisfactorily with the experimental data. It is found that in the cubic phase there are vibrational modes that are unstable everywhere in the Brillouin zone. The eigenvectors of the unstablest mode at the center of the Brillouin zone of the cubic phase are associated with the displacements of F ions and correspond to rotations of InF6 octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In order to describe the Fm3m -- I4/m phase transition, an effective Hamiltonian is constructed under the assumption that the soft mode whose eigenvector corresponds to octahedron rotation is local and coupled with homogeneous elastic strains. The parameters of the effective Hamiltonian are determined using the calculated crystal energy for the distorted structures due to soft-mode condensation. The thermodynamic properties of the system with this model Hamiltonian are investigated using the Monte Carlo method. The phase transition temperature is calculated to be 550 K, which is twice its experimental value (283 K). The tetragonal phase remains stable down to T = 0 K; the effective Hamiltonian used in this paper thus fails to describe the second phase transition (to the monoclinic phase). Thus, the transition to the tetragonal phase occurs for the most part through octahedron rotations; however, additional degrees of freedom, first of all, the displacements of Rb ions, should be included into the effective Hamiltonian in order to describe the transition to the monoclinic phase. (C) 2001 MAIK "Nauka/ Interperiodica".
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16.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Flerov I. N., Gorev M. V.
Заглавие : Entropy and the mechanism of phase transitions in elpasolites
Место публикации : Phys. Solid State: AMER INST PHYSICS, 2001. - Vol. 43, Is. 1. - P127-136. - ISSN 1063-7834, DOI 10.1134/1.1340198
Примечания : Cited References: 33
Предметные рубрики: ORDERED PEROVSKITE PB2MGTEO6
ELASTIC NEUTRON-DIFFRACTION
THERMODYNAMIC PROPERTIES
CUBIC PEROVSKITES
CRYSTAL-STRUCTURE
HIGH-RESOLUTION
PB2MGWO6
CSPBCL3
Аннотация: The phase transitions in series of crystals with the general formulas A(2)BB'X-6 (X = F, Cl, Br, or CN) and Pb2BB'O-6 that belong to the elpasolite family (space group Fm(3) over bar m) are analyzed. The influence of the size and the shape of cations and anions on the entropy and the mechanism of structural distortions is discussed. (C) 2001 MAIK "Nauka/Interperiodica".
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17.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Gorev M. V., Flerov I. N., Bondarev V. S., Sciau P.
Заглавие : Studies of the thermodynamic properties of the ordered perovskites Pb2CdWO6 and Pb2YbTaO6 within a broad temperature range
Место публикации : Phys. Solid State: AMER INST PHYSICS, 2002. - Vol. 44, Is. 2. - P353-357. - ISSN 1063-7834, DOI 10.1134/1.1451027
Примечания : Cited References: 18
Предметные рубрики: CRYSTAL-STRUCTURE
PB2COWO6
PB2MGWO6
PHASE
HEAT
Аннотация: This paper reports on measurements of the specific heat of Pb2CdWO6 made at temperatures ranging from 80 to 750 K and of Pb2YbTaO6 within the 350- to 700-K temperature range. First-order phase transitions from the cubic phase at 677.3 and 581 K, respectively, were observed, and their thermodynamic characteristics were determined. The entropy change on the phase transitions is close to Rln4 for both compounds. The results obtained are discussed in terms of the model of position disordering of the lead ions. It was established that below 350 K, Pb2CdWO6 can exist in two states, stable and metastable, depending on the sample thermal prehistory. (C) 2002 MAIK "Nauka/Interperiodica".
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18.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Flerov I. N., Gorev M. V., Aleksandrov K. S., Tressaud A., Fokina V. D.
Заглавие : Ferroelastic phase transitions in fluorides with cryolite and elpasolite structures
Место публикации : Crystallogr. Rep. - 2004. - Vol. 49, Is. 1. - P.100-107. - ISSN 1063-7745, DOI 10.1134/1.1643969
Примечания : Cited References: 43
Предметные рубрики: NUCLEAR MAGNETIC-RESONANCE
THERMODYNAMIC PROPERTIES
RB2KMIIIF6 ELPASOLITES
NEUTRON-DIFFRACTION
CRYSTALS
PEROVSKITES
DIAGRAM
SC
RB2KGAXSC1-XF6
SCATTERING
Аннотация: The ferroelastic phase transitions are investigated in several series of fluoride crystals belonging to the elpasolite and cryolite families (space group Fm (3) over barm) with the general formula A(2)BB'F-6. The influence of the size and shape of cations and anions on the entropy and the mechanism of structural distortions is discussed. (C) 2004 MAIK "Nauka/Interperiodica".
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19.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Gorev M. V., Flerov I. N., Bondarev V. S., Sciau P., Savariault J. M.
Заглавие : Heat capacity and thermal expansion study of relaxor-ferroelectric Ba0.92Ca0.08Ti0.76Zr0.24O3
Разночтения заглавия :авие SCOPUS: Heat capacity and thermal expansion study of relaxor-ferroelectric Ba 0.92Ca0.08Ti0.76Zr0.24O3
Место публикации : J. Phys.: Condens. Matter. - 2004. - Vol. 16, Is. 39. - P.7143-7150. - ISSN 0953-8984, DOI 10.1088/0953-8984/16/39/045
Примечания : Cited References: 18
Предметные рубрики: CERAMICS
BA(TI1-XZRX)O-3
PEROVSKITES
Ключевые слова (''Своб.индексиров.''): calorimetry--dielectric properties--ferroelectric materials--perovskite--phase transitions--solid solutions--specific heat--thermal expansion--adiabatic calorimetry--frequency dispersion--polar domains--relaxor ferroelectrics--barium compounds
Аннотация: Heat capacity and thermal expansion of the Ba0.92Ca0.08Ti0.76Zr0.24O3 compound is measured using the methods of adiabatic calorimetry and optic-mechanical dilatometry in the temperature range 100-370 K. Three blurred anomalies on the C-p(T) and alpha(T) dependencies are observed in the temperature range 200-360 K. The results of the studies are discussed together with data on the structure and dielectric properties in the framework of spherical random bond-random field model.
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20.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zinenko V. I., Pavlovskii M. S.
Заглавие : Lattice dynamics and the phase transition from the cubic phase to the tetragonal phase in the LaMnO3 crystal within the polarizable-ion model
Место публикации : Phys. Solid State: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2007. - Vol. 49, Is. 9. - P1749-1758. - ISSN 1063-7834, DOI 10.1134/S1063783407090235
Примечания : Cited References: 23
Предметные рубрики: NEUTRON-DIFFRACTION
PEROVSKITES
MANGANITES
PHONONS
Аннотация: The paper reports on the results of ab initio calculations of the static and dynamic properties of the LaMnO3 crystal with a perovskite structure in the cubic, rhombohedral, and orthorhombic phases. The calculations are performed within the ionic crystal model, which takes into account the deformability and polarizability of the ions. It is revealed that the spectrum of lattice vibrations in the cubic phase contains unstable vibrational modes, which occupy the phase space in the entire Brillouin zone. The eigenvectors of the softest mode at the boundary point R of the Brillouin zone are associated with the displacements of the oxygen ions and correspond to the "rotation" of the MnO6 octahedron. The condensation of one, two, and three components of this mode leads to the tetragonal, orthorhombic, and rhombohedral distortions of the structure. The structural phase transition is described in terms of the local mode approximation with the use of the double perovskite unit cell, in which the MnO6 octahedron is explicitly separated. The parameters of the model Hamiltonian are determined. The static properties are investigated by the Monte Carlo method. The calculated temperature of the phase transition from the cubic phase (9800 K) is considerably higher than the melting temperature of the crystal under investigation. The calculated frequencies of long-wavelength lattice vibrations in the experimentally observed orthorhombic and rhombohedral phases are in reasonable agreement with experimental data.
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