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application/pdf 1968_kugler.pdf (5MB)  Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solid 
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Title:  Calculations of equilibrium anharmonic properties in bravais with application to the Wigner electron solid 
Author(s):  Kugler, Alfred Adam 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  equilibrium anharmonic properties 
Abstract:  A selfconsistent 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 selfconsistent 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 selfconsistent equations; in particular, their contributions to the free energy and dynamical selfenergy matrix are calculated. The above theories and methods are applied to the electron solid at T=O. The Hartree approximation is solved, and selfconsistent 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 selfconsistent theories. 
Issue Date:  1968 
Genre:  Data Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/16593 
Other Identifier(s):  6079952 
Rights Information:  © 1968 Alfred Adam Kugler 
Date Available in IDEALS:  20100727 
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Dissertations and Theses  Physics
Dissertations in Physics