A geometrical parameter for the formation of disordered solid solutions in multi-component alloys

• A geometrical parameter (Λ) is developed to predict the formation of DSS.
• No knowledge of physical parameters is required (as Λ = ΔSmix/δ2).
• The power of the new parameter is shown by comparison with standard parameters.
• Ranges prescribed for Λ for the formation of: DSS/compound(s)/mixture.

One or more disordered solid solutions (DSS) are entropically stabilized in high entropy alloys (HEA), in competition with possible intermetallic compounds or phase segregation. In spite of the supreme role of Gibbs free energy, various parameters have been used to understand the formation of DSS in multi-component alloys. These include, the δ-parameter (based on atomic size differences between the elements), the enthalpy of mixing (ΔHmix) the Ω-parameter (TmΔSmix/|ΔHmix|). These parameters have had different degrees of success in the context of understanding the formation of DSS in multi-component alloys. In the current work, we develop a purely geometrical parameter (Λ = ΔSmix/δ2) to predict the formation of DSS. Ranges are prescribed for this parameter for the formation of: (a) DSS, (b) a mixture involving compounds and (c) (only) compound(s). Results from the literature are used to highlight the utility of the Λ-parameter, in the context of other standard approaches. The role of the value of the Λ-parameter in understanding the nature (complexity) and volume fraction of the compound formed is also highlighted.