UC Berkeley

This thesis discusses a general method for constructing interatomic potentials for crystal lattices based on a truncated Taylor series expansion. Such an interatomic potential may be constructed analytically, as in the case of a Lennard-Jones solid, or using ab initio methods such as Density Functional Theory. Specifically, it addresses the scope of application of the method, and demonstrates its practical importance in capturing anharmonicity for a Lennard-Jones solid. In particular, the third-order terms in the truncated potential are shown to accurately approximate the thermal conductivity of the standard interaction Lennard-Jones potential. The thesis also describes an efficient algorithm for locating the equilibrium lattice site of an atom in a three-dimensional crystal lattice displaced from its equilibrium position.

In addition, a procedure is outlined to compute the coefficients in the truncated Taylor series expansion using Density Functional Theory, which is an ab initio method. The procedure is applied to germanium, a material for which, an exact analytical interatomic potential is not known. The computed coefficients may then be used to construct an interatomic potential for germanium of ab initio accuracy. This interatomic potential is then used in MD simulations to estimate various thermophysical properties of a germanium crystal lattice within the range of applicability of this method.