Design of high-entropy alloys with a single solid-solution phase: Average properties vs. their variances

The empirical thermo-physical parameters for designing of high-entropy alloys (HEAs) with a single solid-solution phase (SSP) are based on the average properties of constituent elements, significant derivation from which might make them out of work. In the current work, both the important roles of average properties and their variances were studied. After an introduction of the variance of dimensionless enthalpy of mixing to characterize the chemical bond mismatch and a comparative study between two typical collections of HEAs to show the validity of previous designing rules, it was found that all the previous parameters to some extent fail to predict the formation of HEAs with a single SSP whereas the variance of dimensionless enthalpy of mixing is able to separate the regions of HEAs with a single SSP, with multi-phases and with an amorphous phase. Application to three typical HEA systems proved further that the lower value of the variance of dimensionless enthalpy of mixing corresponds to the higher possibility to form HEAs with a single SSP. The current work provides some necessary conditions for designing of HEAs, based on which preparation of potential HEAs with a single SSP could be accelerated.