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Electrical conductivity of a non-uniformly deformed metal crystal with alloying elements

Abstract

The effect is considered of non-uniform deformations satisfying the condition λ|∇u αβ |≪|u αβ |, where λ is the free path length of an electron in the undeformed crystal and, u αβ is the deformation tensor, on the electrical conductivity of a metal crystal with alloying elements. Account is taken of the local change of the dispersion law for conductivity electrons and also of the dependence on the coordinates of the alloying element of the electron scattering cross-section on the alloying element in the non-uniformly deformed crystal. An explicit expression is obtained for the tensor of the effective conductivity, first introduced by Herring and connecting the average volume density of the electrical current with the average electrical field in the crystal. The local electron scattering cross-section on the charged alloying elements is evaluated on the Thomas-Fermi model taking into account the local change of the constant shielding. Account is also taken of the possibility of redistribution of the alloying elements in the field of the deformations. The dependence is found and discussed of the conductivity on the sign of the constant, introduced in the continuous approximation, of the interaction of the alloying element with the deformation field. By way of illustration of the results obtained the simple case of unidimensional deformation is considered.

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 70–75, February, 1973.

The writers express their gratitude to Yu. V. Kornyushin for useful discussion of this work.

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Partenskii, M.B., Pershin, V.K. Electrical conductivity of a non-uniformly deformed metal crystal with alloying elements. Soviet Physics Journal 16, 196–199 (1973). https://doi.org/10.1007/BF00892673

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Keywords

  • Electrical Conductivity
  • Electrical Current
  • Free Path
  • Explicit Expression
  • Conductivity Electron