Predicting the solid solubility limit in high-entropy alloys using the molecular orbital approach

High-entropy alloys (HEAs) are currently at the research frontier of metallic materials. Understanding the solid solubility limit in HEAs, such a highly concentrated multicomponent alloy system, is scientifically intriguing. It is also technically important to achieve desirable mechanical properties by controlling the formation of topologically or geometrically closed packed phases. Previous approaches to describe the solid solubilities in HEAs could not accurately locate the solubility limit and have to utilize at least two parameters. Here, we propose to use a single parameter, the average energy of d-orbital levels, Md, to predict the solid solubility limit in HEAs. It is found that Md can satisfactorily describe the solid solubilities in fcc structured HEAs containing 3 d transition metals, and also in bcc structured HEAs. This finding will greatly simplify the alloys design and lends more flexibility to control the mechanical properties of HEAs. When 4 d transition metals are alloyed, Md alone cannot describe the solid solubility limit in fcc structured HEAs, due to the large increase of the bond strength that can be gauged by the bond order, Bo. The potential opportunities and challenges with applying the molecular orbital approach to HEAs are discussed.