Violation of the Cauchy–Born rule in multi-principal element alloys

Abstract

Multi-principal element alloys are a novel class of materials that are formed by combining multiple elements in high concentrations and show exceptional properties compared to conventional alloys. These alloys have high configurational entropy due to inherent atomic disorder. The Cauchy–Born rule is a popular homogenization method for linking atomistic to continuum length scales. In this Letter, we use ab initio density functional theory calculations to report that the Cauchy–Born rule, which holds in conventional alloys in the absence of defects, is not valid in multi-principal element alloys. The violation of the Cauchy–Born rule in these alloys is attributed to the presence of atomic disorder due to which the deformations are inhomogeneous. Our results also show the deviations in deformation are related to the magnitude of the stretch and shear by power laws.