# Vegard's law

## Description

In materials science and metallurgy, Vegard’s law is the empirical heuristic that the lattice parameter of a solid solution of two constituents is approximately equal to a rule of mixtures of the two constituents’ lattice parameters at the same temperature.

Vegard’s law assumes that both components A and B in their pure form (i.e. before mixing) have the same crystal structure. Here, aAxB(1-x) is the lattice parameter of the solution, aA and aB are the lattice parameters of the pure constituents, and x is the molar fraction of B in the 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.

Related formulas## Variables

a_{AB} | lattice parameter (dimensionless) |

x | x, parameter (dimensionless) |

a_{A} | lattice of constituent A (dimensionless) |

a_{B} | lattice of constituent B (dimensionless) |