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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 InPxAs1-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} + (1-\mathit{x})\mathit{a}_{InAs}
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, \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}+(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. |
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