Matissen's rule

Matissen's rule - the electrical resistance of a real metal is equal to the sum of the ideal and residual resistances. The ideal resistance is the electrical resistance of an ideal crystal. The residual resistance is the electrical resistance of a real crystal at absolute zero temperature, caused by collisions of electrons with violations of the periodicity of the metal crystal lattice ^[1] .

Explanation

The probability of an electron colliding in the crystal lattice with one of the obstacles is $W=W_{ost}+W_{id}$ ${\ displaystyle W = W_ {ost} + W_ {id}}$ . Since the probability of collision is inversely proportional to the length of the free path $W={\frac {1}{L}}$ ${\ displaystyle W = {\ frac {1} {L}}}$ get ${\frac {1}{L}}={\frac {1}{L_{ost}}}+{\frac {1}{L_{id}}}$ ${\ displaystyle {\ frac {1} {L}} = {\ frac {1} {L_ {ost}}} + {\ frac {1} {L_ {id}}}}$ . Since the electrical conductivity $\sigma$ ${\ displaystyle \ sigma}$ proportional to the length of the run $L$ ${\ displaystyle L}$ and resistance $\rho ={\frac {1}{\sigma }}$ ${\ displaystyle \ rho = {\ frac {1} {\ sigma}}}$ , hence the Mathissen rule: $\rho =\rho _{ost}+\rho _{id}$ ${\ displaystyle \ rho = \ rho _ {ost} + \ rho _ {id}}$ .

Notes

↑ Kaganov, 1971 , p. 60-63.

Literature

M.I. Kaganov . Quasi-particle. What it is?. - M .: Knowledge, 1971. - 75 p.

[_3d02d04db52fdd0f-1] Kaganov, 1971 , p. 60-63.

Matissen's rule

Explanation

Notes

Literature

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