Further Considerations on the Symmetry Properties of the Normal Vibrations of a Crystal

Warren, J.L.

doi:10.1103/revmodphys.40.38

Cited by 135 publications

(43 citation statements)

References 27 publications

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“…The characteristic property of crystals is periodicity. The crystal structure is fully described 5 by a basis and the three primitive vectors a i (i = 1, 2, 3). The primitive vectors define the full set of lattice translations…”

Section: Periodicity In Crystalsmentioning

confidence: 99%

“…For s j > 1 subsets of symmetry coordinates for a given irreducible transformation would transform into each other. As the projection formalism can be fully programmed there exist computer codes [5,15], e.g. incorporated in the program package UNISOFT [16], that automatically determine the symmetry coordinates as well as the block-diagonal form of the dynamical matrix.…”

Section: Symmetry Coordinatesmentioning

confidence: 99%

“…It is our intention to make the reader familiar with the principal concepts. For a more rigorous and fully exhaustive treatment of symmetry applied to the study of electronic states and lattice excitations in molecules and crystals the reader is referred to the literature [1][2][3][4][5]. Basic introductions are given in most text books on solid sate physics [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Symmetry characterization of electrons and lattice excitations

Schober

2012

EPJ Web of Conferences

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Abstract. Symmetry concerns all aspects of a physical system from the electronic orbitals to structural and magnetic excitations. In this article we will try to elaborate the fundamental connection between symmetry and excitations. As excitations are manyfold in physical systems it is impossible to treat them exhaustively. We thus concentrate on the two topics of Bloch electrons and phonons. These two examples are complementary in the sense that Bloch electrons describe single particles in an external periodic potential while phonons exemplify a decoupled system of interacting particles. The way we develop the argument gives as by-product a short account of molecular orbitals and molecular vibrations.

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Section: Periodicity In Crystalsmentioning

confidence: 99%

Section: Symmetry Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry characterization of electrons and lattice excitations

Schober

2012

EPJ Web of Conferences

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“…5, а), що узго-джується з експериментом. Також частоти в K-точці задовольняють правилу сум для частот ( 5 1 3 2 2 2 2 k k k      ) [136], що вказує на те, що не-центральні сили взаємодії у випадку -Ti не такі сильні, як у бери-лію, який досліджувався в [137].…”

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Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

2011

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В огляді розглянуто основні методи опису енергетичного спектру електро-нів та спектру частот коливань атомів кристалічної ґратниці. Зроблено огляд основних метод дослідження впливу ефектів ангармонізму на фізич-ні властивості матеріялів та спектер частот коливань кристалічної ґратни-ці. Описано самоузгоджене гармонічне наближення, що базується на мето-ді двочасових Ґрінових функцій. В рамках цього наближення записано рі-внання руху для Ґрінових функцій «зміщення-зміщення», яке схоже на рівнання руху в гармонічному наближенні, але силові постійні будуть пе-ренормованими і визначаться термодинамічним усередненням других по-хідних потенціялу, а не їх рівноважним значенням. Досліджено вплив ефектів ангармонізму та електронної підсистеми на спектер частот криста-лічної ґратниці гексагонального щільнопакованого кристалу Ti 0,93 Al 0,07 .In a given review, the basic methods for description of the energy spectrum of electrons and the frequency spectrum of atomic vibrations of the crystal lattice are considered. The basic methods for investigation of influence of the anharmonicity effects on the physical properties of materials and a frequency spectrum of vibrations of the crystal lattice are reviewed. The self-consistent harmonic approximation, which is based on the method of double-time Green's functions, are described. Within the scope of this approximation, the equation of motion for the 'displacements-displacements' Green's functions, which is similar to the equation of motion in the harmonic approximation, is derived, but the force constants are renormalized and are determined by the thermodynamical averaging of second derivatives of potential rather than their equilibrium values. Appearances of the anharmonicity effects in the vibrational spectrum of the Ti 0.93 Al 0.07 hexagonal close-packed crystal lattice Успехи физ. мет. / Usp. Fiz. Met. 2011, т. 12, сс. 389-450 Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî â ñîîòâåòñòâèè ñ ëèöåíçèåé 2011 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû) Íàïå÷àòàíî â Óêðàèíå.

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“…First of all it has the CsCl structure which offers a very high degree of symmetry (4,5).Second, both Y and Zn have very good neutron scattering properties as summarized in Table 1. Third, since 3-brass also has the CsCl structure a comparison with that experiment (2) is possible.…”

Section: Sample Descriptionmentioning

confidence: 99%

Lattice dynamics of YZn

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Further Considerations on the Symmetry Properties of the Normal Vibrations of a Crystal

Cited by 135 publications

References 27 publications

Symmetry characterization of electrons and lattice excitations

Symmetry characterization of electrons and lattice excitations

Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

Lattice dynamics of YZn

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