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In high-entropy alloys (HEAs), the local chemical fluctuations from disordered solute solution state into segregation, precipitation and ordering configurations are complex due to the large number of elements. In this work, the cluster expansion (CE) Hamiltonian for multi-component alloy systems is developed in order to investigate the dependence of chemical ordering of HEAs as a function of temperature dependence due to derivation of configuration entropy from the ideal solute solution. Analytic expressions for Warren–Cowley short-range order (SRO) parameters are derived for a five component alloy system. The theoretical formulation is used to investigate the evolution of the ten different SRO parameters in the MoNbTaVW and the sub-quaternary systems obtained by Monte-Carlo simulations within the combined CE and first-principles formalism. The strongest chemical SRO parameter is predicted for the first nearest-neighbor Mo-Ta pair that is in consistent agreement with high value of enthalpy of mixing in the 2 structure for this binary system. The prediction of 2 phase presence for Mo-Ta pairs in the considered bcc HEAs is reinforced by the positive contribution to the average SRO from the second nearest-neighbor shell. Interestingly, it is found that the average SRO parameter for the first and second nearest-neighbor shells of V-W pairs is also strongly negative in a comparison with the Mo-Ta pairs. This finding in the HEAs can be rationalized and discussed by the presence of the ordered-like 32 phase which has been predicted as the ground-state structure in binary bcc V-W system at the equimolar composition.

Short-Range Order in High Entropy Alloys: Theoretical Formulation and Application to Mo-Nb-Ta-V-W System