Date of this Version
Thesis (M.S.)—University of Nebraska—Lincoln, 1993. Department of Physics and Astronomy.
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≤FGB ≡ F0 + 0 >0 is derived.The approximate Hamiltonian H0 is chosen to be the harmonic Hamiltonian that minimizes the free energy FGB, 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