The thermodynamics of multicomponent high-entropy materials

Abstract Human development has been based for millennia on manufacturing materials using a conventional alloying strategy of selecting a principal component for the primary property requirement of the material and then adding one or two minor alloying components at relatively low concentrations, either to enhance the primary property or to provide additional secondary properties. We have discovered relatively recently that, with sufficiently large numbers of alloying elements added in sufficiently large concentrations, the configurational entropy of mixing can often become large enough to suppress the formation of brittle compound phases, leading instead to the formation of multicomponent high-entropy solid solutions. In fact, there are literally billions of multicomponent high-entropy single-phase solid-solution materials, with a wide range of exciting new properties, in most cases relatively straightforward to manufacture by conventional processing methods. There seems, however, to be an upper limit to these effects, so that, beyond about ten or twelve alloying components, the inevitable increase in chemical diversity prevents the configurational entropy of mixing from suppressing the increasingly strong chemical reactions between them. This paper discusses in more detail the thermodynamic balance between: (1) increasing configurational entropy and promoting high-entropy solid solutions; and (2) increasing chemical diversity and promoting the formation of brittle compound phases. This is discussed on the basis of regular solution thermodynamics, without the need for more complex, semi-empirical Calphad calculations that can sometimes obscure the underlying key physical and chemical principles. The results show: (1) why large single-phase solid-solution regions are relatively common in multicomponent phase space; (2) why single-phase solid solutions are often favoured over stoichiometric compounds for large numbers of chemically similar components, in concentrated rather than dilute proportions, at high temperatures, and after quenching to room temperature; and (3) the difficulty of detailed thermodynamic analysis in multicomponent materials because of the large numbers of thermodynamic parameters that need to be known and the corresponding lack of underlying thermodynamic measurements.