  Crystal defect statistics is developed by minimizing the Gibbs free energy of
defect formation, which is commonly converted to a crystallite size-independent
equation by applying Stirling's approximation. Solutions of this equation
forecast Arrhenius-like temperature dependence for the concentrations of all
defect types, and higher defect populations for nanocrystals due to the smaller
formation free energies involved. Here, we improve the accuracy in the
mathematical processing of the equation describing the defect population at
thermodynamic equilibrium and show that this equation is intrinsically
size-dependent. The new model predicts lower defect concentrations for smaller
crystallites, and shows that vacancy-free crystallites smaller than a
determinable critical size are thermodynamically stable at elevated
temperatures. Our findings describe the previously reported data on the
mechanical properties of a number of nanocrystals and lead to a revised and
deeper understanding of many morphological occurrences in micro- and
nanocrystals.
