Towards quantifying (meta-)stability of multi-principal element alloys: From configurational entropy to characteristic temperatures

Understanding and hence predicting the stability and metastability of multi-principal-element alloys (MPEAs) is crucial for their design and applications, but it remains a complex and time-consuming task. Descriptors based on the configurational entropy alone are often insufficient in determining the relative stability of MPEA solid solutions, since they predict, against experimental evidence, that alloys containing a large number of elements will be eventually stable. Here we introduce two characteristic temperatures, derived from the temperature dependence of the configurational entropy, which effectively act as (meta-)stability indicators. These can be further combined in a dimensionless quantity, $T_{\mathrm{d0}}$, which enables us to rank alloys according to their compositional and structural (meta-)stability across a broad composition range. In particular, we are able to map equiatomic and non-equiatomic alloys, and even regions covered by conventional alloys. Our proposed descriptors are validated against a large body of experimental results and compared to other (meta-)stability descriptors. Furthermore, they allow us to revise the alloys classification scheme into high-entropy, medium-entropy and low-entropy. Our work sheds new light into the thermodynamic origin of alloying metastability, it provides a potential tool to correlate metastability thermodynamics and kinetics, and ultimately may help in alloys design and discovery.