Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity
Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classif...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Evarestov, R. A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Physics of the solid state - Pleiades Publishing, 1993, 61(2019), 6 vom: Juni, Seite 994-1006 |
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| Übergeordnetes Werk: |
volume:61 ; year:2019 ; number:6 ; month:06 ; pages:994-1006 |
| Links: |
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| DOI / URN: |
10.1134/S1063783419060040 |
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OLC2040755527 |
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| 520 | |a Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. | ||
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10.1134/S1063783419060040 doi (DE-627)OLC2040755527 (DE-He213)S1063783419060040-p DE-627 ger DE-627 rakwb eng 530 VZ Evarestov, R. A. verfasserin aut Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2019 Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. Lukyanov, S. I. aut Enthalten in Physics of the solid state Pleiades Publishing, 1993 61(2019), 6 vom: Juni, Seite 994-1006 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:61 year:2019 number:6 month:06 pages:994-1006 https://doi.org/10.1134/S1063783419060040 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 61 2019 6 06 994-1006 |
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10.1134/S1063783419060040 doi (DE-627)OLC2040755527 (DE-He213)S1063783419060040-p DE-627 ger DE-627 rakwb eng 530 VZ Evarestov, R. A. verfasserin aut Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2019 Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. Lukyanov, S. I. aut Enthalten in Physics of the solid state Pleiades Publishing, 1993 61(2019), 6 vom: Juni, Seite 994-1006 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:61 year:2019 number:6 month:06 pages:994-1006 https://doi.org/10.1134/S1063783419060040 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 61 2019 6 06 994-1006 |
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10.1134/S1063783419060040 doi (DE-627)OLC2040755527 (DE-He213)S1063783419060040-p DE-627 ger DE-627 rakwb eng 530 VZ Evarestov, R. A. verfasserin aut Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2019 Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. Lukyanov, S. I. aut Enthalten in Physics of the solid state Pleiades Publishing, 1993 61(2019), 6 vom: Juni, Seite 994-1006 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:61 year:2019 number:6 month:06 pages:994-1006 https://doi.org/10.1134/S1063783419060040 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 61 2019 6 06 994-1006 |
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10.1134/S1063783419060040 doi (DE-627)OLC2040755527 (DE-He213)S1063783419060040-p DE-627 ger DE-627 rakwb eng 530 VZ Evarestov, R. A. verfasserin aut Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2019 Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. Lukyanov, S. I. aut Enthalten in Physics of the solid state Pleiades Publishing, 1993 61(2019), 6 vom: Juni, Seite 994-1006 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:61 year:2019 number:6 month:06 pages:994-1006 https://doi.org/10.1134/S1063783419060040 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 61 2019 6 06 994-1006 |
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10.1134/S1063783419060040 doi (DE-627)OLC2040755527 (DE-He213)S1063783419060040-p DE-627 ger DE-627 rakwb eng 530 VZ Evarestov, R. A. verfasserin aut Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2019 Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. Lukyanov, S. I. aut Enthalten in Physics of the solid state Pleiades Publishing, 1993 61(2019), 6 vom: Juni, Seite 994-1006 (DE-627)16567332X (DE-600)1159011-7 (DE-576)038490706 1063-7834 nnns volume:61 year:2019 number:6 month:06 pages:994-1006 https://doi.org/10.1134/S1063783419060040 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_70 AR 61 2019 6 06 994-1006 |
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Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity |
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Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. © Pleiades Publishing, Ltd. 2019 |
| abstractGer |
Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. © Pleiades Publishing, Ltd. 2019 |
| abstract_unstemmed |
Abstract Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a $ SrTiO_{3} $ crystal lowers the symmetry to tetragonal; and the H site in the $ CsPbI_{3} $ crystal is characterized by the complete removal of point symmetry with the formation of an $${\text{I}}_{2}^{ - }$$ ion. © Pleiades Publishing, Ltd. 2019 |
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Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity |
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