The configurational entropy of mixing of metastable random solid solution in complex multicomponent alloys

Since the advent of "high-entropy" alloys, the simple ideal mixing rule has been commonly used to calculate the configurational entropy of mixing for these multicomponent alloys. However, there have been increasing experimental evidence reported recently showing that the ideal mixing rule tends to overestimate the configurational entropy of mixing in the multicomponent alloys, particularly at a low temperature. In contrast to the ideal mixing rule, here we provide a formula to assess the configurational entropy of mixing in random solid-solution multicomponent alloys by considering the possible correlations among the constituent elements due to various factors, such as atomic size misfit and chemic bond misfit, which may disturb the potential energy of the system and thus reduce the configurational entropy of mixing. With our entropy formulation, the correlation is explored between the configuration entropy of mixing of different alloys and the general character of the phases formed, such as single- or multiple-phased crystalline phase versus amorphous phase. Being in good agreement with the simulation and experimental results, our work provides an analytical framework that could be further used to explore phase stability in complex multicomponent alloys.