Report: Phase stability prediction using databases and cluster expansion methods

The problem of phase stability calculation (and crystal structure prediction) is a fundamental problem in materials research and development, and it is typically addressed with highly accurate quantum mechanical computations on a large set of candidate structures, but has limited predictive power. To allow fast prediction of crystal structures, two concepts, usual suspect structure database and cluster expansions are used for crystal structure prediction. Significant contributions in the use of structure database calculations with data mining include [1,2,4,8] where tools as varied as principal component analysis, genetic algorithms and regression techniques are used in conjunction with DFT and cluster expansion technique to improve efficiency in the computation of crystal structures. There is significant opportunity for extension of such techniques for computation of phase diagrams at higher temperatures (T > 0 where entropies play a role), but at present this work is restricted to evaluation of stable structures at 0K. In the computational work presented here, cohesive energies predicted by DFT calculations for Si and published data from databases [6] are compared. Then, for the CuCa alloy, formation energies are calculated within the framework of the Density Functional Theory (DFT) to predict the low temperature phases. Next, the concept of cluster expansion [9] is applied for prediction of phase structures of Au-Cu alloy. Cluster expansions have a disadvantage that only structures that fall within the superstructures of the parent lattices can be tested for stability. Ideas are presented here that would allow prediction of structures using a combination of cluster expansion and statistical learning over phase structure databases.