The phase transition point determination for materials with cubic lattice by using atomistic approach

Abstract

The computational-statistical approach to studying physical-mechanical properties for finite sized monocrystals is developed. The approach is based on combination of the high-performance computational techniques and statistical analysis of the crystal response on external thermo-mechanical actions for specimens with statistically small amount of atoms (i.e. for micro- and nanoparticles). Computation of pure mechanical properties was performed using the atomistic statics method. The heat motion of atoms is modelled in the statics approach by including independent degrees of freedom for atoms connected with their oscillations. The amplitude A of the oscillations is considered as a variable of the state, but the frequency distribution among the atoms is supposed to be constant and considered as a material function to be identified. These oscillations are simulated by applying the random displacements with amplitude A under uniform distribution of directions for such perturbations in space. Each obtained perturbed configuration of crystal is frozen for calculating its potential energy density. Equilibrium thermo-mechanical parameters have been computing by averaging of huge amount of different realizations of the perturbed crystal configurations. The dependences of potential energy densities for FCC- and BCC- crystal lattices on heat perturbations amplitude were calculated for wide interval of A. These curves have points of intersection which may correspond to the points of phase transition and hence may be used for the frequency function identification.