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Electrical Conductivity in Alloys
Matthiesen's rule
Nordheim's Rule, and the Mixture rule
For low concentrations of solute, and pure metals, the low temperature dependence of resistivity on temperature is described by Matthiesen's rule: \[ \rho (T) = \rho _{defect} + \rho _{thermal}(T) \]
Adding more defects, such as solute atoms, increases ρdefect.

Change the compostion and see the effect on the resistivity.
0 Temperature Resistivity
Composition

Cu - 0.0 at% Ni

Change the temperature which the samples are quenched with the slider
For the two phase region, the rule of mixtures applies: \[ \rho = \chi_{\alpha} \rho_{\alpha} + \chi_{\beta}\rho_{\beta} \]
For the solid solution regions, ρ is described by Nordheim's rule:
\( \rho = \chi_{\alpha} \rho_{\alpha} + \chi_{\beta}\rho_{\beta} + C\chi_{\alpha}\chi_{\beta} \)
Note that resistivity actually varies with temperature as well as composition
Temperature Resistivity Composition A B Liquid L α L + α L + β β α + β ρA ρB