Vegard’s law

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Abstract
Vegard’s law is an approximate empirical rule which holds that a linear relation exists, at constant temperature, between the crystal lattice constant of an alloy and the concentrations of the constituent elements. Applications of a density-functional theory of nonuniform fluid mixtures to the fluid-solid transition of simple binary mixtures of hard spheres demonstrates the importance of relative atomic sizes in determining lattice constants and suggests that for sufficiently small disparities in atomic size Vegard’s law may also hold along the fluid-solid coexistence curve.