Empirical atom model of Vegard's law

Vegard's law seldom holds true for most binary continuous solid solutions. When two components form a solid solution, the atom radii of component elements will change to satisfy the continuity requirement of electron density at the interface between component atom A and atom B so that the atom with larger electron density will expand and the atom with the smaller one will contract. If the expansion and contraction of the atomic radii of A and B respectively are equal in magnitude, Vegard's law will hold true. However, the expansion and contraction of two component atoms are not equal in most situations. The magnitude of the variation will depend on the cohesive energy of corresponding element crystals. An empirical atom model of Vegard's law has been proposed to account for signs of deviations according to the electron density at Wigner-Seitz cell from Thomas-Fermi-Dirac-Cheng model.