Studies of point defects in strained solids by molecular simulation
Kwak, Sang Kyu
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Defects exert disproportionate effects on crystalline solids. To understand the behavior of defects, we must know fundamental properties such as their formation free energy and their concentration. Most dominant type of defects in crystal systems without impurities is point defects, and vacancies in particular. We investigate prevailing mono and divacancies in unstrained and strained equilibrium crystals. Model systems, which we investigate, are the unstrained Lennard-Jones crystal and the unstrained/strained hard-sphere crystal system, which could exhibit qualitative features of realistic models as well as provide quantitative measures of colloidal materials. We first investigate the free energy and the concentration of mono and divacancies in unstrained face-centered-cubic hard-sphere crystals by Monte Carlo simulation following a modified grand canonical ensemble. Over the range of densities from close-packed to melting, we quantify the driving force to fill a vacant site by inserting a particle increases as density increases so that concentrations of both vacancies decrease. The concentration of divacancies is about two orders of magnitude lower than that of monovacancies. We find that interaction between two vacancies diminishes rapidly and disappears beyond 4th nearest neighbor distance. The relative strength of association of divacancy to independent monovacancies is around 3 at melting and around 2 toward close packed structure. We extend this approach further to examine strain effects on monovacancies in face-centered-cubic hard-sphere crystals by using conventional molecular dynamics simulation. We study two distinct constant-volume strains, considering a simple shear and an orthogonal expansion and contraction. Strains are examined across the linear elastic region and include also some non-linear elastic deformations. Second-order elastic constants are calculated as a function of density. The concentration of monovacancies decreases as density increases, following similar behavior as in unstrained crystals. The effect of strain is to cause the monovacancy concentration to increase. The expansion-contraction strain exerts around 8 times more increase on the concentration of monovacancies than the shear strain does at the largest deformation studied. Efficient stacking order of hard-spheres results in two types of crystal structures, which are face-centered-cubic and hexagonal-close-packed. They exhibit almost same thermophysical properties except a certain second order elastic constants differs between them. We investigate properties of monovacancies in both phases, for which particles are packed in unstrained rhombohedral boxes. Concentrations of monovacancies in both phases are almost the same over densities in interest including melting. Based on the free energy calculation, relative stability does not change by presence of monovacancies: face-centered-cubic hard-sphere crystal is still more stable. Apart from studies described above, we also apply the integral equation theory to evaluate structural properties of the hard-sphere system. We determine coefficients of the h -bond expansion of the bridge function of the hard-sphere system up to 4th order of density, which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r) . Calculations are performed using Monte Carlo Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein-Zernike equation with a closure given by the calculated clusters. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated in this way.