Derivation of unit cell volume, and lattice parameter of cubic high entropy alloys from volume size factors

An equation has been derived to predict unit cell volume of high entropy alloys, HEA's, by two different methods. In the first method, a HEA is considered as a mixture of solid solutions. Based on an equation previously reported to calculate unit cell volume of intermetallic compounds, an expression to calculate unit cell volume of HEA's was obtained. In the second method, a HEA is modeled as a mixture of solute element atoms surrounded by different environments. Using the effective volume of solute atoms in these environments, the unit cell volume of a HEA was derived. Both treatments led to the same equation. For cubic HEA's lattice parameters were calculated. The predicted lattice parameters were compared with those reported for 79 HEA's. Lattice parameters were also calculated using the equivalent of Vegard's law for these alloys. Average errors were 0.64%, and 0.53% when Vegard's law, and the equation derived in this work were used, respectively. Although these average errors seem acceptable, they were as high as 4.27%, and 4.70% when Vegard's law, and the equation proposed are applied, respectively. The roles on error, of method to determine chemical composition, method to measure lattice parameter, and type of elements present on the alloy were examined.

Automated summary

An equation has been derived to predict the unit cell volume of high entropy alloys using two different methods. The study found that both methods led to the same equation, and accurate lattice parameters were calculated for cubic HEA's.