Elasticity and Vacancy Behaviour of Crystals of Hard Cubes

Abstract

In this thesis we examine the effects of vacancies on the elasticity of a simple cubic crystal with cubic particles. We calculate the elastic constants as a function of the vacancy concentration and the packing fraction. Furthermore we examine the correlation between the deformation of the crystal and the direction of the defects caused by vacancies in the crystal, for a shear and a stretch deformation. To this extent we explore two viable simulation techniques: the Monte Carlo and the Event Driven Molecular Dynamics methods. We implement two different methods of calculating the elastic constants in the two respective simulations: calculation by means of global strain fluctuations and calculation by means of the stress-strain relation. We find that for a stable crystal, the elastic constants $C_{11}$ and $C_{44}$ increase as a function of both the packing fraction and the vacancy concentration, while $C_{12}$ decreases. Furthermore we find that there is no correlation between a shear deformation and the direction of the defects. For the stretch deformation, the defects align with the compressed direction.