A bond-based model for accurate prediction of lattice parameters of bcc solid solution alloys

The lattice parameter is an important material feature for solid solution alloys, a class of materials which includes the emerging high-entropy alloy (HEA) family. The Vegard's law is a typical method to estimate lattice parameters of random solid solutions and thus has been widely used by the HEA community. However, in this work, we show that the Vegard's law becomes inaccurate in predicting the lattice parameters of solid solution alloys featuring a body-centered-cubic (bcc) lattice, including the refractory high-entropy alloys (RHEAs). The inaccuracy of the Vegard's law originates from its inability to account for the charge transfer that arises from heteroelement atomic bonding, which alters the volumes of the atoms from their pure-element states. To address this limitation, a new physical model based on the atomic bond lengths derived from binary ordered intermetallic structures is proposed for accurate lattice parameter prediction by effectively capturing the charge transfer effect. This new model is validated by comparing its predictions to lattice parameters calculated by first-principles calculations for 292 alloy compositions including twelve different metal elements. Notably, our new model largely outperforms the Vegard's law in terms of prediction accuracy while maintaining a similar level of simplicity, free of fitting or any empirical parameters for making predictions. Specifically, the model produces a root mean squared error (RMSE) of 0.006 Å which is less than half that of the Vegard's law (RMSE = 0.015 Å).