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NEW METHODS FOR DETERMINING THE PROPERTIES OF ANHARMONIC SOLIDS
Abstract
Two new methods for obtaining accurate values for the properties of anharmonic solids are developed and tested. In the first part of the dissertation, the correlated Einstein model (CEM) is developed for classical solids. The CEM is based on the correlated particles expansion (CPE). The CPE is an expansion for harmonic averages of products of one- and two-particle functions. A diagrammatic representation of the CPE is given An exact expression in terms of a harmonic average of a product is obtained for the free energy F. The average is formed with a potential energy (PHI)(,0) of the Einstein type. The CEM is obtained by keeping the zeroth order term in the CPE of the average and by choosing the parameters in (PHI)(,0) so first and second order terms vanish. Thermodynamic properties are obtained by differentiating F. Also, a CEM approximation for canonical averages of phase functions is developed. The CEM is tested on a Lennard-Jones crystal and a 1/r('12) crystal. The CEM predictions are compared with Monte Carlo results. The predictions are accurate and at least equally competitive with the uncorrelated pairs approximation, the cell-cluster method, the correlated-cell approximation, the simple cell model, and self-consistent phonon theory. In the second part of the dissertation, a method using linear correction terms is developed for estimating the ground state energies of quantum solids. The method is based on the correlated pairs expansion which is an expansion for harmonic averages of products of pair functions. An estimate for the ground state energy is obtained by using the variational principle and Jastrow type wave functions. This estimate involves a harmonic average of a product that is approximated by keeping the zeroth order term in the correlated pairs expansion. Linear correction terms are introduced so first order terms vanish. The method is tested on models for solid helium comparing predictions with Monte Carlo results. Including linear correction terms significantly improves the accuracy of the estimates for the kinetic and potential energies, but has little effect on the total energy.
Subject Area
Condensation
Recommended Citation
DAY, MICHAEL ALAN, "NEW METHODS FOR DETERMINING THE PROPERTIES OF ANHARMONIC SOLIDS" (1983). ETD collection for University of Nebraska-Lincoln. AAI8328162.
https://digitalcommons.unl.edu/dissertations/AAI8328162