Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $
Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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...
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Gespeichert in:
| Autor*in: |
Zinenko, V. I. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2001 |
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| Schlagwörter: |
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| Anmerkung: |
© MAIK "Nauka/Interperiodica" 2001 |
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| Übergeordnetes Werk: |
Enthalten in: Physics of the solid state - Nauka/Interperiodica, 1993, 43(2001), 12 vom: Dez., Seite 2290-2300 |
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| Übergeordnetes Werk: |
volume:43 ; year:2001 ; number:12 ; month:12 ; pages:2290-2300 |
| Links: |
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| DOI / URN: |
10.1134/1.1427959 |
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OLC2040688587 |
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| 245 | 1 | 0 | |a Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ |
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| 520 | |a Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. | ||
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10.1134/1.1427959 doi (DE-627)OLC2040688587 (DE-He213)1.1427959-p DE-627 ger DE-627 rakwb eng 530 VZ Zinenko, V. I. verfasserin aut Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK "Nauka/Interperiodica" 2001 Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter Zamkova, N. G. aut Enthalten in Physics of the solid state Nauka/Interperiodica, 1993 43(2001), 12 vom: Dez., Seite 2290-2300 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:43 year:2001 number:12 month:12 pages:2290-2300 https://doi.org/10.1134/1.1427959 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_40 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_4116 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4700 AR 43 2001 12 12 2290-2300 |
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10.1134/1.1427959 doi (DE-627)OLC2040688587 (DE-He213)1.1427959-p DE-627 ger DE-627 rakwb eng 530 VZ Zinenko, V. I. verfasserin aut Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK "Nauka/Interperiodica" 2001 Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter Zamkova, N. G. aut Enthalten in Physics of the solid state Nauka/Interperiodica, 1993 43(2001), 12 vom: Dez., Seite 2290-2300 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:43 year:2001 number:12 month:12 pages:2290-2300 https://doi.org/10.1134/1.1427959 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_40 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_4116 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4700 AR 43 2001 12 12 2290-2300 |
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10.1134/1.1427959 doi (DE-627)OLC2040688587 (DE-He213)1.1427959-p DE-627 ger DE-627 rakwb eng 530 VZ Zinenko, V. I. verfasserin aut Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK "Nauka/Interperiodica" 2001 Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter Zamkova, N. G. aut Enthalten in Physics of the solid state Nauka/Interperiodica, 1993 43(2001), 12 vom: Dez., Seite 2290-2300 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:43 year:2001 number:12 month:12 pages:2290-2300 https://doi.org/10.1134/1.1427959 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_40 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_4116 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4700 AR 43 2001 12 12 2290-2300 |
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10.1134/1.1427959 doi (DE-627)OLC2040688587 (DE-He213)1.1427959-p DE-627 ger DE-627 rakwb eng 530 VZ Zinenko, V. I. verfasserin aut Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK "Nauka/Interperiodica" 2001 Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter Zamkova, N. G. aut Enthalten in Physics of the solid state Nauka/Interperiodica, 1993 43(2001), 12 vom: Dez., Seite 2290-2300 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:43 year:2001 number:12 month:12 pages:2290-2300 https://doi.org/10.1134/1.1427959 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_40 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_4116 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4700 AR 43 2001 12 12 2290-2300 |
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10.1134/1.1427959 doi (DE-627)OLC2040688587 (DE-He213)1.1427959-p DE-627 ger DE-627 rakwb eng 530 VZ Zinenko, V. I. verfasserin aut Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © MAIK "Nauka/Interperiodica" 2001 Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter Zamkova, N. G. aut Enthalten in Physics of the solid state Nauka/Interperiodica, 1993 43(2001), 12 vom: Dez., Seite 2290-2300 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:43 year:2001 number:12 month:12 pages:2290-2300 https://doi.org/10.1134/1.1427959 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_40 GBV_ILN_70 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_4116 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4700 AR 43 2001 12 12 2290-2300 |
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Enthalten in Physics of the solid state 43(2001), 12 vom: Dez., Seite 2290-2300 volume:43 year:2001 number:12 month:12 pages:2290-2300 |
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Enthalten in Physics of the solid state 43(2001), 12 vom: Dez., Seite 2290-2300 volume:43 year:2001 number:12 month:12 pages:2290-2300 |
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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 $ InF_{6} $ 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. 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Zinenko, V. I. ddc 530 misc Phase Transition misc Brillouin Zone misc Phase Transition Temperature misc Tetragonal Phase misc Deformation Parameter Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ |
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530 VZ Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ Phase Transition Brillouin Zone Phase Transition Temperature Tetragonal Phase Deformation Parameter |
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Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ |
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Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ |
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lattice dynamics and statistical mechanics of the fm3m → i4/m structural phase transition in $ rb_{2} $$ kinf_{6} $ |
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Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in $ Rb_{2} $$ KInF_{6} $ |
| abstract |
Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. © MAIK "Nauka/Interperiodica" 2001 |
| abstractGer |
Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. © MAIK "Nauka/Interperiodica" 2001 |
| abstract_unstemmed |
Abstract The static and dynamic properties of cubic $ Rb_{2} $$ KInF_{6} $ 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 $ InF_{6} $ 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. © MAIK "Nauka/Interperiodica" 2001 |
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