An Empirical Potential of Interatomic Interaction

A potential of interatomic interaction for simulating complex structural states of solids (grain boundaries and heterogeneous equilibrium states) is put forward. In simulating heterogeneous states of systems, the potential must simultaneously provide for stability conditions for several phases in equilibrium and correct values of a number of macroscopic parameters such as lattice constants, elastic moduli, internal energy, heat capacity, and stability parameters. The existing empirical potentials of interatomic interaction fail to provide agreement of the calculated and experimentally obtained parameters determining the structure of the system and structural transformations due to changes in the external parameters. The potential under discussion is a polynomial representing a solution to the problem of interpolation of functions and their derivatives to the nth order prescribed on a finite system of points (Hermit interpolation problem). The relation for a general solution to the foregoing problem is so complicated that it is virtually inapplicable. A new polynomial is constructed on the basis of the Lagrangian interpolation polynomial. The interpolation of the known interatomic potentials with allowance for the fourth-order derivatives by the polynomial is achieved with high accuracy where three to four interpolation nodes are specified. Local changes can easily be introduced to the polynomial. In doing so, the values of the potential and its derivatives in other regions of space are retained. This allows mechanical stability for stable and metastable phases to be ensured.