CALCULATIONS OF EQUILIBRIUM ANHARMONIC PROPERTIES IN BRAVAIS LATTICES WITH APPLICATION TO THE WIGNER ELECTRON SOLID.
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.' 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=0. 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. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1968
- Accession Number
- AD0833879
Entities
People
- Alfred Adam Kugler
Organizations
- University of Illinois Urbana–Champaign