Towards Quantifying (Meta-)Stability of Multi-Principal Element Alloys: From Configurational Entropy to Characteristic Temperatures

Abstract Understanding the thermodynamics of multi-principal-element alloys (MPEAs), although crucial for their design, remains an elusive task. The configurational entropy, Sconf, is a critical thermodynamic quantity determining stability, but its calculation for real materials poses a hard computational challenge. Strong of a highly efficient cluster expansion, constructed on density functional theory data,and of an advanced sampling technique, we are able to compute Sconf over the huge configurational and compositional space of the prototype bcc Ti-Zr-Hf-Nb-Ta system. In particular, we explore around 200,000 atomic arrangements across more than 200 compositions. The main features of the computed Sconf-vs-temperature curves can be captured by the definition of two characteristic temperatures, which are then used to define a dimensionless descriptor. This, together with Sconf, enable us to rank alloys according to their (meta- )stability across a broad composition range, going from equiatomic to nonequiatomic, and even to the regions covered by conventional alloys. Such classification is informed and validated against hundreds of experimental results. Our analysis allows us to revise the classification scheme of alloys into high-entropy, medium-entropy and low-entropy and, in general, sheds light into the thermodynamic origin of their metastability, ultimately helping in the design and development.