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Vegard's Law

Vegard's Law states that the composition of a solid solution remains constant regardless of temperature, assuming ideal mixing.
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The statement of the theorem

Consider a solid solution AxB1x\mathrm{A}_x\mathrm{B}_{1-x} where xx is the atomic fraction of element A. If the solid solution exhibits ideal mixing and follows Vegard's Law, the lattice parameter a(x)a(x) is a linear interpolation of the pure component lattice parameters aAa_A and aBa_B:\na(x)=xaA+(1x)aBa(x) = x a_A + (1-x) a_B