Crystallization and Instabilities in Highly Anharmonic Crystals

Meissner, G.

doi:10.1103/physrevb.1.1822

Cited by 23 publications

(4 citation statements)

References 14 publications

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“…Though the frequencies (18) are by their origin the harmonic one0 they take into account all anharmonicities. And what is more, formulae (18) give us the possibility to fix the regions of the absolute stability of a crystal [40]. If upon rising the temperature the density n(woo) decreases sharply enough then, as one can see from (18), the frequency w,, is able to change its positive value to the negative one.…”

Section: Due To (16) We Have the Equation In Whichmentioning

confidence: 99%

Superharmonic Approximation for Crystal

Yukalov

1980

Annalen der Physik

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The localized approximation for a quantum crystal considered earlier by the author is taken here as the initial step of an iteration, and the higher approximations for the propagators and thermodynamic functions are calculated. This generalization is based on a new type of a double iterative procedure for the equation of motion. The method is illustrated with a three-dimensional crystal. Superharmonische Niiherung fur einen KristallInhaltsiibersicht. Die vorn Verfasser schon friiher benutzte lokale Niiherung fur einen Quantenkristall wird hier als erster Schritt fur eine Iteration genommen; ffir den Propagator und die thermodynamischen Funktionen werden die hoheren Niiherungen bereohnet. Diese Verallgemeinerung beruht auf einer neuen Art von Doppel-Iterations-Verfahren fiir die Bewegungsgleichung. Die Methode wird am Beispiel eines dreidimensionalen Kristalls gezeigt.

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Section: Due To (16) We Have the Equation In Whichmentioning

confidence: 99%

Superharmonic Approximation for Crystal

Yukalov

1980

Annalen der Physik

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“…Crystals with strong anharmonicity, large zero-point fluctuations, and unstable modes require nonperturbative and self-consistent methods (CHOQARD, 1967;WERTHAMER, 1969). A variety of special and general approaches, developed for this purpose, and an extensive body of literature can be found in the papers of NOSANOV (1966), GOTZE (1967), GOTZE and MICHEL (1968), HORNER (1967HORNER ( , 1970, , PLAKlDA and SIKLOS (1969), MEISSNER (1970aMEISSNER ( , 1970b, KERR and SJOLANDER (1970), WERTHAMER (1970), TAKENO (1970), KOEHLER and WERT-HAMER (1971), PYTTE and FEDER (1969), and FEDER and PYTTE (1970. In the following, we try to combine the perturbative and the self-consistent approaches.…”

Section: G Dynamical Theory Of Interacting Phonon Systemsmentioning

confidence: 99%

“…This quantity is obtained from the Gibbs free energy through a Legendre transformation (CALLEN, 1960;MEISSNER, 1970a), by which one changes from the sourc;e fiel9 j to the one-point function 11 as an independent variable, .…”

Section: <S)j=e1jjuimentioning

confidence: 99%

Vibrational Infrared and Raman Spectra of Non-Metals

Bilz¹,

Strauch²,

Wehner³

1984

Light and Matter Id / Licht Und Materie Id

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The vibrational properties of crystals determine the photon infrared absorption, inelastic neutron scattering and, to a large extent, inelastic photon scattering by phonons, i.e., Raman scattering. The interpretation of infrared and Raman spectra requires, therefore, an understanding of the basic features of lattice dynamics. The quantum theory of solids describes the crystal properties in terms of elementary excitations and their mutual interactions. Dynamic properties are represented by phonons (lattice vibrations) and their interactions mainly with other phonons (anharmonicity), electrons (electron-phonon coupling), and photons (interaction with radiation). This characterizes the scope of the article. Its emphasis is on the interrelation between theory and experiment, i.e., on the microscopic or model interpretation of experimental spectra.Work on infrared absorption and Raman scattering of non-metallic solids was summarized twenty years ago in two review articles in this Encyclopedia by LECOMTE (1958) and by MIZUSHIMA (1958). Since then, many important new experimental data have become available, thanks to very refined techniques for measuring spectra of pure and imperfect single crystals. Furthermore, the theory of the interactions of phonons and photons has been much improved, stimulated by the remarkable development of the theory of lattice vibrations and the mathematical techniques of many-body physics.In this article we describe the dispersion and absorption of infrared radiation and Raman scattering in non-metallic crystals, both perfect and containing point defects. At present, quantitative calculations are usually restricted to diatomic crystals, especially those with simple structures such as the alkali halides or germanium and its homologues, since our knowledge of lattice vibrations is still rather poor for polyatomic and low-symmetry crystals. The theory of lattice vibrations, as reviewed by COCHRAN and COWLEY (1967) in Vol. XXV /2a of this Encyclopedia, constitutes the background and the natural starting point for our investigations. There are other recent reviews by LUDWIG (1967), COCHRAN (1971), MARADUDIN et al. (1971), SINHA (1973), and several articles in: HORTON and MARADUDIN (eds., 1974). A summary of the developments during the last few years is given in Chap. B.An important part of the theory of lattice vibrations is the construction of models. A good example is the so-called shell model for phonons (see Sect. 4) which describes the adiabatic linear electron-ion interaction in terms of localized charges and coupling constants. This provides a natural explanation of some long-range ion-ion forces in insulators in terms of induced dipole forces. Anharmonic extensions of this shell model and its modifications seem very desirable, and first attempts in this direction are discussed.Models can often give a qualitatively and sometimes quantitatively correct description of certain processes in terms of a few parameters. They provide, therefore, an orientation for microscopic approaches. Furthermo...

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“…In order to show how the conjectured interplay depends on nonuniversal parameters of a given model we may start from a rigorous dispersion relation [8] which holds for the inverse of the order pa- …”

Section: Correlations In Low-temperature Phasesmentioning

confidence: 99%