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Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solidPDF


Title:Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solid
Author(s):Kugler, Alfred Adam
Department / Program:Physics
Subject(s):equilibrium anharmonic properties
Abstract:A self-consistent method for determining equilibrium properties of Bravais crystals is derived from a variational principle for the free energy, first for the independent oscillator model of a solid, then for the general case of dispersion. The method leads to a set of self-consistent equations which are identical with those derived by Choquard in the "RHA," (renormalized harmonic approximation) using ring diagram summation of the cumulant expansion for the free energy. A particular approximation is shown to lead to a simpler set of equations which can properly be termed "Hartree approximation with dispersion," and which in some cases offer a suitable alternative to the harmonic approximation as a starting point in carrying out calculations. Some higher order anharmonic effects are treated on the basis of Choquard's generalized self-consistent equations; in particular, their contributions to the free energy and dynamical self-energy matrix are calculated. The above theories and methods are applied to the electron solid at T=O. The Hartree approximation is solved, and self-consistent calculations in second order are carried out. In both cases, the effects of anharmonicity on the frequencies are found to be large, and are responsible for bringing about a dynamical instability of the lattice. Various results obtained previously in the harmonic approximation and in second order perturbation theory are reviewed to facilitate comparison with the self-consistent theories.
Issue Date:1968
Dissertation / Thesis
Other Identifier(s):6079952
Rights Information:© 1968 Alfred Adam Kugler
Date Available in IDEALS:2010-07-27

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