Grain Size Limit of Nanocrystalline Materials Obtained by Annealing Bulk Metallic Glasses

Abstract

Polycrystalline materials with nanometer sized grains, termed nanocrystalline materials, can be formed by crystallizing completely amorphous solids under proper heat treatment conditions termed as ‘annealing’. Experimentally it is found that the smallest grain size is obtained when the glasses are annealed at a crystallization temperature which is nearly half of the melting temperature in metallic glasses. At this temperature the Gibbs free energy difference between the amorphous and crystalline state is maximum. However, in case of bulk metallic glasses (BMG), the maximum in Gibbs free energy, ΔG, is observed to fall below Tm /2, because the Kauzamann temperature (TK ), at which ΔG is maximum falls below Tm /2. Therefore, annealing BMG's at temperatures close to their TK is likely to lead to the smallest grain size. In this paper, we have calculated the minimum grain size for different metallic glasses by considering a simple thermodynamic relation that suggests a general thermodynamic lower limit of grain size of metallic nanocrystalline materials. Two different ΔG relations are used for calculations. The grain size is also calculated using the experimental values of ΔG. The results show that the values of grain size calculated by using theoretical ΔG are in reasonable agreement with those calculated using experimental ΔG.