  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).
