On the optimisation of the composition of high-entropy alloys

Abstract The aim of this work is to find a simple and fast way to fix the composition of a multi-component alloy that maximises the probability that it will have a solid-solution single-phase microstructure. The search begins with a detailed analysis of the well-known parameter Ω, which has already been the subject of studies aimed at maximising it. In line with these theoretical efforts, this paper proposes: (i) a new optimisation strategy, in accordance with the classical definition of a multi-principal-components alloy, (ii) improvements in the calculation of the Ω parameter (through the enthalpy of mixing) and (iii) the definition of a new indicator, which we will call the Λ parameter, which also can be optimised. This new parameter not only takes into account the enthalpy of mixing, but also adds an additional term, the elastic lattice distortion enthalpy, caused by the distortion of the crystal lattice. Both the new maximisation strategy and the new parameter aim to ensure that the high precision of the composition at the maximum does not make it impossible to implement. As a novelty, this paper uses the Excel spreadsheet and its Solver tool for the task of maximisation with constraints, using the evolutionary algorithm. The paper applies the optimisation methods discussed to two multi-component systems that have been widely analysed in the specialised scientific literature, in order to compare all the techniques described. Finally, the article points to the possibility that optimisation of the indicator parameters Ω and Λ could provide the two most stable compositions into which an initially single-phase alloy subjected to high temperature would segregate. Graphical abstract