In crystallography, materials science and metallurgy, Vegards 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:
e.g., in the case of a mixed oxide of uranium and plutonium as used in the fabrication of MOX nuclear fuel:
Vegards law assumes that both components A and B in their pure form (i.e.', before mixing) have the same crystal structure. Here,  is the lattice parameter of the solid solution,  and  are the lattice parameters of the pure constituents, and  is the molar fraction of B in the solid solution.
Vegard's law is seldom perfectly obeyed; often deviations from the linear behavior are observed. A detailed study of such deviations was conducted by King. However, it is often used in practice to obtain rough estimates when experimental data are not available for the lattice parameter for the system of interest.
For systems known to approximately obey Vegard's law, the approximation may also be used to estimate the composition of a solution from knowledge of its lattice parameters, which are easily obtained from diffraction data. For example, consider the semiconductor compound . A relation exists between the constituent elements and their associated lattice parameters, , such that:
When variations in lattice parameter are very small across the entire composition range, Vegards law becomes equivalent to Amagats law.