A generally reliable model for composition-dependent lattice constants of substitutional solid solutions

Solid solutioning has long been employed to improve the performance of enegineering materials, the degree of improvement generally correlates closely with the resultant lattice parameters. It is therefore of great importance for materials design to describe accurately the composition-dependent lattice constants of the solid solutions (SSs). However, existing models could hardly reproduce the usually non-linear relationship between the compositions and the lattice constants. Herein, we present a new model within the framework of virtual crystal approximation by taking into account both the size factor and the electronic effect. The model takes inputs as simple as the fundamental property parameters of the elementary substances and N referential SSs for an N-component system, and can then predict the lattice constant of SS with any composition within the system. Systematical validation using datasets obtained from high-throughput first-principles calculations and available experiments confirmed the high reliability and general applicability of our model for various substitutional SSs. Applications and limitations of the model as well as outlooks were also discussed. It is expected that this model will deepen the understanding of the relationship between the composition and the properties of materials.