Soft phonon dispersion in $ BaTiO_{3} $
Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enh...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hüller, Alfred [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1969 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1969 |
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| Übergeordnetes Werk: |
Enthalten in: Zeitschrift für Physik A Hadrons and nuclei - Springer Berlin Heidelberg, 1967, 220(1969), 2 vom: 01. Apr., Seite 145-158 |
|---|---|
| Übergeordnetes Werk: |
volume:220 ; year:1969 ; number:2 ; day:01 ; month:04 ; pages:145-158 |
| Links: |
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| DOI / URN: |
10.1007/BF01394744 |
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| 520 | |a Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. | ||
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| 650 | 4 | |a Ionic Polarizability |7 (dpeaa)DE-He213 | |
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10.1007/BF01394744 doi (DE-627)SPR002105128 (SPR)BF01394744-e DE-627 ger DE-627 rakwb eng Hüller, Alfred verfasserin aut Soft phonon dispersion in $ BaTiO_{3} $ 1969 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 1969 Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. Phase Transition Temperature (dpeaa)DE-He213 Critical Mode (dpeaa)DE-He213 Soft Mode (dpeaa)DE-He213 Electronic Polarizability (dpeaa)DE-He213 Ionic Polarizability (dpeaa)DE-He213 Enthalten in Zeitschrift für Physik A Hadrons and nuclei Springer Berlin Heidelberg, 1967 220(1969), 2 vom: 01. Apr., Seite 145-158 (DE-627)SPR002100037 nnns volume:220 year:1969 number:2 day:01 month:04 pages:145-158 https://dx.doi.org/10.1007/BF01394744 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 220 1969 2 01 04 145-158 |
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10.1007/BF01394744 doi (DE-627)SPR002105128 (SPR)BF01394744-e DE-627 ger DE-627 rakwb eng Hüller, Alfred verfasserin aut Soft phonon dispersion in $ BaTiO_{3} $ 1969 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 1969 Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. Phase Transition Temperature (dpeaa)DE-He213 Critical Mode (dpeaa)DE-He213 Soft Mode (dpeaa)DE-He213 Electronic Polarizability (dpeaa)DE-He213 Ionic Polarizability (dpeaa)DE-He213 Enthalten in Zeitschrift für Physik A Hadrons and nuclei Springer Berlin Heidelberg, 1967 220(1969), 2 vom: 01. Apr., Seite 145-158 (DE-627)SPR002100037 nnns volume:220 year:1969 number:2 day:01 month:04 pages:145-158 https://dx.doi.org/10.1007/BF01394744 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 220 1969 2 01 04 145-158 |
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10.1007/BF01394744 doi (DE-627)SPR002105128 (SPR)BF01394744-e DE-627 ger DE-627 rakwb eng Hüller, Alfred verfasserin aut Soft phonon dispersion in $ BaTiO_{3} $ 1969 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 1969 Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. Phase Transition Temperature (dpeaa)DE-He213 Critical Mode (dpeaa)DE-He213 Soft Mode (dpeaa)DE-He213 Electronic Polarizability (dpeaa)DE-He213 Ionic Polarizability (dpeaa)DE-He213 Enthalten in Zeitschrift für Physik A Hadrons and nuclei Springer Berlin Heidelberg, 1967 220(1969), 2 vom: 01. Apr., Seite 145-158 (DE-627)SPR002100037 nnns volume:220 year:1969 number:2 day:01 month:04 pages:145-158 https://dx.doi.org/10.1007/BF01394744 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 220 1969 2 01 04 145-158 |
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10.1007/BF01394744 doi (DE-627)SPR002105128 (SPR)BF01394744-e DE-627 ger DE-627 rakwb eng Hüller, Alfred verfasserin aut Soft phonon dispersion in $ BaTiO_{3} $ 1969 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 1969 Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. Phase Transition Temperature (dpeaa)DE-He213 Critical Mode (dpeaa)DE-He213 Soft Mode (dpeaa)DE-He213 Electronic Polarizability (dpeaa)DE-He213 Ionic Polarizability (dpeaa)DE-He213 Enthalten in Zeitschrift für Physik A Hadrons and nuclei Springer Berlin Heidelberg, 1967 220(1969), 2 vom: 01. Apr., Seite 145-158 (DE-627)SPR002100037 nnns volume:220 year:1969 number:2 day:01 month:04 pages:145-158 https://dx.doi.org/10.1007/BF01394744 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 220 1969 2 01 04 145-158 |
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10.1007/BF01394744 doi (DE-627)SPR002105128 (SPR)BF01394744-e DE-627 ger DE-627 rakwb eng Hüller, Alfred verfasserin aut Soft phonon dispersion in $ BaTiO_{3} $ 1969 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 1969 Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. Phase Transition Temperature (dpeaa)DE-He213 Critical Mode (dpeaa)DE-He213 Soft Mode (dpeaa)DE-He213 Electronic Polarizability (dpeaa)DE-He213 Ionic Polarizability (dpeaa)DE-He213 Enthalten in Zeitschrift für Physik A Hadrons and nuclei Springer Berlin Heidelberg, 1967 220(1969), 2 vom: 01. Apr., Seite 145-158 (DE-627)SPR002100037 nnns volume:220 year:1969 number:2 day:01 month:04 pages:145-158 https://dx.doi.org/10.1007/BF01394744 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 220 1969 2 01 04 145-158 |
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Soft phonon dispersion in $ BaTiO_{3} $ |
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Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. © Springer-Verlag 1969 |
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Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. © Springer-Verlag 1969 |
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Abstract We treat a simple lattice dynamical model for the critical modes in $ BaTiO_{3} $. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally. © Springer-Verlag 1969 |
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The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase Transition Temperature</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Critical Mode</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Soft Mode</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Electronic Polarizability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ionic Polarizability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Zeitschrift für Physik A Hadrons and nuclei</subfield><subfield code="d">Springer Berlin Heidelberg, 1967</subfield><subfield code="g">220(1969), 2 vom: 01. Apr., Seite 145-158</subfield><subfield code="w">(DE-627)SPR002100037</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:220</subfield><subfield code="g">year:1969</subfield><subfield code="g">number:2</subfield><subfield code="g">day:01</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:145-158</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/BF01394744</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">220</subfield><subfield code="j">1969</subfield><subfield code="e">2</subfield><subfield code="b">01</subfield><subfield code="c">04</subfield><subfield code="h">145-158</subfield></datafield></record></collection>
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