Grain size limit of nanocrystalline materials obtained by annealing glasses

A lower limit for the grain size of nanocrystalline solids obtained by crystallization of the glass and its dependency on the crystallization temperature are thermodynamically considered. It is found that the nanocrystalline materials have the smallest grain size when the crystallization temperature is roughly half of the melting temperature. At this temperature, the Gibbs free energy difference between the undercooled liquid and the crystal reaches the maximum. It is found that for polymorphous crystallization the lower bound of grain size is essentially dependent on melting entropy. The results are consistent with available experimental evidence.