Vegard's law
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: a A ( 1 − x ) B x = ( 1 − x ) a A + x a B {\displaystyle a_{\mathrm {A} _{(1-x)}\mathrm {B} _{x}}=(1-x)\ a_{\mathrm {A} }+x\ a_{\mathrm {B} }} e.g., in the case of a mixed oxide of uranium and plutonium as used in the fabrication of MOX nuclear fuel: a U 0.93 P u 0.07 O 2 = 0.93 a U O 2 + 0.07 a P u O 2 {\displaystyle a_{\mathrm {U_{0.93}Pu_{0.07}O_{2}} }=0.93\ a_{\mathrm {UO_{2}} }+0.07\ a_{\mathrm {PuO_{2}} }} Vegard's law assumes that both components A and B in their pure form (i.e., before mixing) have the same crystal structure.