Monte Carlo Simulation of Diffusion Processes in Three-Component Alloys

Abstract

The methods of molecular dynamics applied to a representative volume of a substance make it possible to calculate atomic trajectories within the time intervals on the order of 1 ns, which ensures an investigation of such slow processes as diffusion. This problem can be solved using the Monte Carlo method successfully applied to investigation of such diffusion-controlled processes as order – disorder transitions in the alloys or diffusion welding of heterogeneous metals through a backing plate. The majority of studies have been made for binary alloys, while the alloys in practical use contain a larger number of components. A theoretical model is presented, which allows investigating diffusion processes in three-component alloys via the vacancy mechanism in a solid-sphere approximation. A relation is derived for calculating the potential energy of an alloy, which is specified for the case of a completely disordered alloy. The difference between these energies is expressed via the ordering energies and order parameter. The proposed model is applicable to crystal lattices of any dimensionality. An example of its use for a three-component alloy of the A2BC stoichiometry is given, whose atoms occupy the sites of a two-dimensional square lattice is given.