Vegard's law

In metallurgy, Vegard's law is an approximate empirical rule which holds that a linear relation exists, at constant temperature, between the crystal lattice parameter of an alloy and the concentrations of the constituent elements. ^[1] ^[2]

For example, consider the semiconductor compound InP_xAs_1-x. A relation exists between the constituent elements and their associated lattice parameters, $\mathit{a}$ , such that:

$\mathit{a}_{InPAs} = \mathit{x}\mathit{a}_{InP} %2B (1-\mathit{x})\mathit{a}_{InAs}$

One can also extend this relation to determine semiconductor band gap energies. Using InP_xAs_1-x as before one can find an expression that relates the band gap energies, $\mathit{E_g}$ , to the ratio of the constituents and a bowing parameter $\mathit{b}$ :

$\mathit{E_g}_{InPAs} = \mathit{x}\mathit{E_g}_{InP}%2B(1-\mathit{x})\mathit{E_g}_{InAs}-\mathit{bx}(1-\mathit{x})$

When variations in lattice parameter are very small across the entire composition range, Vegard's law becomes equivalent to Amagat's law.

References

^ L. Vegard. Die Konstitution der Mischkristalle und die Raumfüllung der Atome. Zeitschrift für Physik, 5:17, 1921.
^ Harvard.edu A. R. Denton and N. W. Ashcroft. Vegard’s law. Phys. Rev. A, 43:3161–3164, March 1991.