Characterization of mono- and divacancy in fcc and hcp hard-sphere crystals

We determine and compare the thermodynamic properties of mono- and divacancies in the face-centered-cubic and hexagonal-close-packed hard-sphere crystals via a modified grand canonical ensemble. Widom-type particle insertion was employed to estimate the free energy of formation of mono- and divacancies, and the results are supported by an alternative approach, which quantifies the entropy gain of the neighbor particles. In hcp crystal, we found a strong anisotropy in the orientational distribution of vacancies and observe an eightfold increase in the number of divacancies in the hexagonal plane compared to the one in the out of plane at highest density of interest. This phenomenon is induced by the different arrangement and behavior of the shared nearest neighbor particles, which are located at the same distance from each vacant site in divacancy. The effect of divacancies on the free energy is to reduce that of the hcp crystal relative to the fcc by around 7 x 10(-6)kBT at melting.