Matthiessen Rule

Matthiessen Rule

 

a principle obeyed by the specific electric resistivity of solid conductors if the resistivity is determined by several mechanisms.

According to the Matthiessen rule, the total specific resistivity is equal to the sum of individual specific resistivities, if each of them corresponds to a separate mechanism. The rule was first formulated in 1862 by the German chemist A. Matthiessen as applied to metals, in which one component of resistivity is determined by the scattering of electrons in impurities and dislocations (residual resistivity) and does not depend on temperature, whereas the other component is associated with electron scattering by thermal lattice vibrations (ideal resistivity). It varies with temperature and becomes very small as r—*• 0°K. The Matthiessen rule is an approximation; it is not valid in cases where there is a correlation between scattering processes. Nevertheless, the rule is used for approximate estimates of the resistivity of metals.

REFERENCES

Lifshits, I. M., M. Ia. Azbel’, and M. I. Kaganov. Elektronnaia teoriia metallov. Moscow, 1971.
Ziman, J. Elektrony i fonony. Moscow, 1962. (Translated from English.)

E. M. EPSHTEIN

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For the system that contains several scattering mechanisms, the Matthiessen rule is often used to evaluate the total scattering rate,
In most cases the Matthiessen rule gives reasonable results, although it is found to be not accurate in some cases recently [58, 92,93].