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.
For example, consider the semiconductor compound InPxAs1-x. A relation exists between the constituent elements and their associated lattice parameters, , such that:
One can also extend this relation to determine semiconductor band gap energies. Using InPxAs1-x as before one can find an expression that relates the band gap energies, , to the ratio of the constituents and a bowing parameter :
When variations in lattice parameter are very small across the entire composition range, Vegard's law becomes equivalent to Amagat's law.
- Vegard, L. (1921). "Die Konstitution der Mischkristalle und die Raumfüllung der Atome". Zeitschrift für Physik 5 (1): 17–26. Bibcode:1921ZPhy....5...17V. doi:10.1007/BF01349680.
- Denton, A. R.; Ashcroft, N. W. (1991). "Vegard’s law". Phys. Rev. A 43 (6): 3161–3164. Bibcode:1991PhRvA..43.3161D. doi:10.1103/PhysRevA.43.3161.
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