Machine Learning Force Field-Aided Cluster Expansion Approach to Phase Diagram of Alloyed Materials

First-principles approaches based on density functional theory (DFT) have played important roles in the theoretical study of multicomponent alloyed materials. Considering the highly demanding computational cost of direct DFT-based sampling of the configurational space, it is crucial to build efficient and low-cost surrogate Hamiltonian models with DFT accuracy for efficient simulation of alloyed systems with configurational disorder. Recently, the machine learning force field (MLFF) method has been proposed to tackle complicated multicomponent disordered systems. However, the importance of integrating significant physical considerations, including, in particular, convex hull preservation, which is the prerequisite for the accurate prediction of phase diagrams, into the training process of the MLFF remains rarely addressed. In this work, a workflow is proposed to train a convex-hull-preserved (CHP) MLFF for binary alloy systems, based on which the order-disorder phase boundary is predicted by using the Wang-Landau Monte Carlo (WLMC) technique. The predicted values for order-disorder phase transition temperatures agree well with the experiment. The CHP-MLFF is further used to build CE models with the same accuracy as the MLFF and higher efficiency in sampling configurational space. Using the results obtained from the MLFF-based WLMC simulation as a reference, the performances of different schemes for constructing CE models were evaluated in a transparent manner, which revealed the close correlation between the prediction accuracy of ground-state configurations and that of the order-disorder phase transition temperature. This work clearly indicates the great importance of reproducing the convex hull and energetics of ground-state configurations when constructing surrogate Hamiltonians for the statistical modeling of alloyed systems.