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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.
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