Understanding the effect of grain size distribution on the stability of nanocrystalline materials: An analytical approach

The grain boundary curvature and difference in internal energy between adjoining grains is the fundamental cause of grain growth in materials. The grain boundary curvature is reflected in the grain boundary energy with higher curvatures leading to higher grain boundary energies. Every microstructure would have a distribution of curvatures and hence distribution of grain boundary energies. Till recently the distribution of grain boundary energy was not accounted for in the development of the thermodynamic approaches for thermal stability of nanocrystalline materials. This aspect was addressed by Wagih and Schuh who demonstrated the importance of considering the distribution of grain boundary energies in a microstructure for improving thermal stability. While every microstructure would have a distribution of grain boundary energy, it is also true that there would be a distribution of grain size which could influence the thermal stability of nanocrystalline materials. This aspect has not been addressed in literature before and hence is the focus of the current work. By assuming a single grain boundary energy representative of all grain boundaries and by varying the grain size distribution, represented by S-n, we studied the total grain boundary energy of both nanocrystalline pure metals and binary alloys. It was found that S-n is influencing the contribution of the grain boundaries to the total energy of the system by way of controlling the grain boundary fraction and the amount of solute segregating to the grain boundaries. Consequently the grain size distribution becomes an important design parameter for nanocrystalline materials.