Grain Boundary Segregation Models for High-Entropy Alloys: Theoretical Formulation and Derived Analytical Expressions to Elucidate High-Entropy Grain Boundaries

Grain boundary (GB) segregation models are derived for multi-principal element and high-entropy alloys (MPEAs and HEAs). Differing from classical models where one component is taken as solvent and others are considered solutes, these models are referenced to the bulk composition to enable improved treatments of MPEAs and HEAs with no principal components. An ideal solution model is first formulated and solved to obtain analytical expressions that predict GB segregation and GB energy in MPEAs and HEAs. A regular solution model is further derived. The GB composition calculated using the simple analytical expression derived in this study and data from the Materials Project agree well with a prior sphosipcated atomistic simulation for NbMoTaW. The simplicity of the derived analytical expressions makes them useful for not only conveniently predicting GB segregation trends in HEAs, but also analyzing nascent interfacial phenomena in composionally complex GBs. As an application example, the derived models are used to further formulate a set of useful equations to elucidate an emergent concept of high-entropy grain boundaries (HEGBs).