Phase and vacancy behaviour of hard slanted cubes: a quantitative analysis on the influence of shape

Abstract

In this thesis, we study the phase and vacancy behaviour of hard slanted cubes (right rhombic prisms) as a function of their shape, defined through the shape parameter $\theta$ which is the slant angle of these particles. To study the phase behaviour, we use of Monte Carlo simulations in the isotension-isothermal ensemble. We find that these particles form three different crystal structures depending on the slant angle and the density: a simple cubic crystal, a sheared cubic crystal and a hexagonal random tiling crystal. We summarize these results in a phase diagram. To study the vacancy behaviour, specifically that of the simple cubic crystal, we use free energy calculations; both standard Einstein integration methods as well as a scheme which employs thermodynamic integration over the shape. This scheme will be explained in detail, as it could be useful for applications in other systems as well. We find that the vacancy concentration in this simple cubic crystal of slanted cubes does not depend on the shape of the particles, but only on the packing fraction.