Defect-free nanocrystals are at thermodynamic equilibrium at room   temperature
  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. 
Faramarz Hossein-Babaei and Hamid Reza Sefidi Shirkoohi
cond-mat.mtrl-sci