Thermal vacancies in close-packing solids

Based on Stillinger's version of cell cluster theory, we derive an expression for the equilibrium concentration of thermal monovacancies in solids which allows for a transparent interpretation of the vacancy volume and the energetic/entropic part in the corresponding Gibbs energy of vacancy formation $\Delta G_{\rm v}$. For the close--packing crystals of the hard sphere and Lennard--Jones model systems very good agreement with simulation data is found. Application to metals through the embedded--atom method (EAM) reveals a strong sensitivity of the variation of $\Delta G_{\rm v}$ with temperature to details of the EAM potential. Our truncation of the cell cluster series allows for an approximate, but direct measurement of crystal free energies and vacancy concentration in colloidal model systems using laser tweezers.