The generalized thermodynamic rule for phase selection in multicomponent alloys

The design of modern multicomponent alloys (MCAs) appears complicated, which usually entails mixing multiple elements that have a variety of sizes and heat of mixing. As a result, different phases, such as single- and multi-phased solid-solution, intermetallic compounds and even metallic glasses, can be formed upon solidification of the corresponding metallic melts. To understand such diversities in the phase selection in MCAs, tremendous research efforts have been dedicated over the past decades, which, however, are empirically or semi-empirically based. In contrast, here we show that a simple thermodynamic rule can be derived from the hard sphere model, which predicts that the phases formed in cast MCAs only depend on two dimensionless thermodynamic parameters: one is related to the entropic departure of the alloy from the ideal solution and the other to the average heat of mixing scaled by the 'ideal' configurational entropy of mixing. Using this simple rule, we are able to unfold a general trend that guides phase selection in MCAs, including super-alloys, bulk metallic-glasses, high entropy alloys and many other engineering materials. The outcome of our current research sheds an important insight into the thermodynamic origin for phase stability and alloy design of MCAs