Prediction of chemical ordering in refractory high-entropy superalloys

Refractory high-entropy superalloys (RHESs) exhibit impressive nanostructure-property relationships and have promise in next-generation high-temperature structural applications, which has motivated extensive research into these materials. The design space, however, is compositionally vast and complex due to the presence of multiple phases that differ in the composition and chemical order. To address these obstacles in a computationally efficient manner, an advanced approach combining the mean-field density functional theory with parameters determined using machine learning tools has been developed. This approach was implemented here to investigate AlMo0.5NbTa0.5TiZr, which exhibits a nanostructure consisting of cuboidal BCC precipitates coherently embedded within the B2 matrix. It was found that Al and Zr were responsible for the formation of the B2 matrix. In addition, the matrix and the precipitate were found to have very different elastic characteristics. The matrix has a small elastic moduli and large anisotropy while the precipitate is elastically stiff and nearly isotropic. Beyond the current findings, the parameters for the mean field approach are given in the supplementary material and these can be used in future efforts to predict chemical orders, phase partitioning, and elastic properties of RHESs as a function of chemical composition.