Determination of the transition to the high entropy regime for alloys of refractory elements

Abstract

The development of high entropy alloys is currently limited to experimental work aimed at the determination of specific compositions that exhibit particular properties. The main feature of these alloys is their particular phase structure, which tends to be a continuous solid solution in spite of the large number of constituents which would otherwise form a large number of intermetallic phases. While it is known that equimolar concentrations and large number of elements are two necessary conditions for achieving high entropy behavior, not much is known regarding the transition to this regime in the presence of specific elements. Such knowledge would be useful when determining alloy compositions, as it would set boundaries for the necessary concentrations of each element in experimental situations. In this work, results of a computational modeling effort are presented, where a recently developed 5-element high entropy alloy of refractory elements is used as the foundation needed to examine such transition and determine the necessary lower bounds for the concentration of each element. Details of the phase structure of the quaternary combinations of W, Nb, Mo, Ta and V as they evolve upon the addition of a fifth element are discussed. The results are compared to the experimental case for the case of V added to W-Nb-Mo-Ta. Using these examples as a reference, the concept of critical concentrations for each element, signaling the transition to the high entropy regime, is developed, based on a simple analysis of only bulk properties of such alloys (lattice parameter, bulk modulus, and cohesive energy).