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Statistical mechanics and free energy calculations of solids with repulsive and attractive potentials by a Monte Carlo integration algorithm
Abstract
Using an adaptive, importance sampling Monte Carlo algorithm, the configuration integral, and subsequently all relevant thermodynamic properties, is computed for various solids with different intermolecular potential energy functions. Three types of potential functions are studied: the inverse twelfth power (soft-sphere) repulsive potential, the inverse power potential for softness parameter equal to 6, 7 and 8, and the HFD-B potential function developed by Aziz$\sp1$. Calculations on the face-centered cubic (fcc) soft-sphere solid serve as a general means of testing the validity of the algorithm by comparing its results to those obtained by Monte Carlo experiments and thermodynamic integration. Excess free energy and the compressibility factor are computed and compared to thermodynamic integration results of Hoover el al.$\sp2$ A favorable agreement was observed between the results of the two methods at densities approaching close-packing density. The fcc to body-centered cubic (bcc) phase transition was investigated by using the Monte Carlo integration method on inverse power potential solids with sixth, seventh, and eighth power repulsive potentials. In all cases the fcc structure is the one with the lowest free energy, except for the sixth power function at high density. The solid comprised of particles interacting via the HFD-B function with parameters for argon serves as a model of a realistic solid, with both attractive and repulsive interactions present in the lattice. Results of the computations on the HFD solid are compared to those obtained for the Lennard-Jones solid as well as experimental data on the rare gas solids. ftn$\sp1$R. A. Aziz and M. J. Slaman, Mol. Phys. 58, 679 (1986). $\sp2$W. G. Hoover, M. Ross, K. W. Johnson, D. Henderson, J. A. Barker and B. C. Brown, J. Chem. Phys. 52, 4931 (1970).
Subject Area
Chemistry
Recommended Citation
Kulver, Robert, "Statistical mechanics and free energy calculations of solids with repulsive and attractive potentials by a Monte Carlo integration algorithm" (1990). ETD collection for University of Nebraska-Lincoln. AAI9034277.
https://digitalcommons.unl.edu/dissertations/AAI9034277