Defects in Hard-Sphere Colloidal Crystals

Abstract

Colloidal crystals of \(1.55 \mu m\) diameter silica particles were grown on {100} and flat templates by sedimentation and centrifugation. The particles interact as hard spheres. The vacancies and divacancies in these crystals are not in equilibrium, since no movement of single vacancies is observed. The lack of mobility is consistent with the extrapolation of earlier simulations at lower densities. The volume of relaxation of the vacancy has a plausible value for these densities as the volume of formation is approaching the volume in a close-packed crystal. The volume of relaxation for the divacancy is smaller than that of two vacancies, so that the association of two vacancies into a divacancy requires extra volume, and hence extra entropy. The mean square displacement of the nearest neighbors of the vacancies is an order of magnitude larger than that of the nearest neighbors of particles. The mobility of the divacancies is consistent with the extrapolation of older simulations and is similar to that associated with the annihilation of the vacancy-interstitial pair. The volume of motion of the divacancies is \(\Delta V_m = 0.19V_o (V_o\): close-packed volume) and the entropy of motion is \(\Delta S_m = 0.49k_BT\). Dislocation-twin boundary interactions can be observed by introducing strain via a misfit template. The dislocations formed are Shockley partials. When a dislocation goes through the boundary, two more dislocations are created: a reflected dislocation and one left at the boundary, both with the same magnitude Burgers vector. The dislocations relieve a total of about a third of the misfit strain. The remaining strain is sufficiently large to move the dislocation up to the boundary and close to sufficient to move the dislocation through the boundary. A small amount to extra strain energy is needed to cause nucleation of the two additional dislocations after a waiting time.