In crystallography, materials science and metallurgy, Vegard's law is an empirical finding (heuristic approach) resembling the rule of mixtures.
In 1921, Lars Vegard discovered that the lattice parameter of a solid solution of two constituents is approximately a weighted mean of the two constituents' lattice parameters at the same temperature:[1][2] e.g., in the case of a mixed oxide of uranium and plutonium as used in the fabrication of MOX nuclear fuel: Vegard's law assumes that both components A and B in their pure form (i.e., before mixing) have the same crystal structure.
Therefore, if the lattice parameter of a semiconducting system follows Vegard's law, one can also write a linear relationship between the band gap and composition.
This curvature correction is characterized by the bowing parameter, b: The following excerpt from Takashi Fujii (1960)[5] summarises well the limits of the Vegard’s law in the context of mineralogy and also makes the link with the Gladstone–Dale equation: In mineralogy, the tacit assumption for the linear correlation of the density and the chemical composition of a solid solution is twofold: one is an ideal solid solution and the other identical or nearly identical molar volumes of the components.
If the concept of the volume fraction is introduced, density, coefficient of thermal expansion, compressibility and refractive index can be correlated linearly with the volume fraction in an ideal system.“[6]When considering the empirical correlation of some physical properties and the chemical composition of solid compounds, other relationships, rules, or laws, also closely resembles the Vegard's law, and in fact the more general rule of mixtures: