Self-Consistent Phonon Theory of a Lennard-Jones Solid

Authors

Jing Yang, University of Nebraska-Lincoln

Date of this Version

5-1993

Document Type

Thesis

Citation

Thesis (M.S.)—University of Nebraska—Lincoln, 1993. Department of Physics and Astronomy.

Comments

Copyright 1993, the author. Used by permission.

Abstract

The purpose of this thesis is to develop self-consistent phonon theory and use it to determine the thermodynamic properties of a face centered cubic crystal with Lennard-Jones nearest neighbor interactions.The Gibbs-Bogoliubov inequality F≤F_GB ≡ F₀ + ₀ >₀ is derived.The approximate Hamiltonian H₀ is chosen to be the harmonic Hamiltonian that minimizes the free energy F_GB, which requires that H₀ be determined self-consistently.The real space integrations needed to find the harmonic canonical averages<…>₀ are formulated in terms of the pair-displacement auto correlation tensor. The translation and point group symmetries of the crystal lattice are used to obtain the transformation matrix that diagonalizes H₀ and to simplify the reciprocal space integrations needed for determining the normal mode frequencies and auto correlation tensor. Results are given for the zero pressure temperature dependence of the specific heat, bulk modulus, and thermal expansion coefficient.

Advisor: Robert J. Hardy