Computing the resistivity due to electron collision with 1BZ

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SUMMARY

The discussion focuses on estimating the resistivity due to electron collisions with the first Brillouin zone (1BZ) as a function of the number of valence electrons in metals. Marius inquires about the impact of increasing valence electrons, starting with sodium (Na) and adding materials with two valence electrons. The resistivity is confirmed to be a complex calculation influenced by temperature and impurity concentration, especially in pure samples at low temperatures.

PREREQUISITES
  • Understanding of electron collisions in solid-state physics
  • Familiarity with the concept of the Brillouin zone
  • Knowledge of resistivity and its dependence on temperature
  • Basic principles of valence electrons in metals
NEXT STEPS
  • Research the relationship between valence electron count and resistivity in metals
  • Study the effects of temperature on resistivity in pure materials
  • Explore the role of impurities in electrical conductivity
  • Learn about the Fermi wavevector and its implications in solid-state physics
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Physicists, materials scientists, and electrical engineers interested in the behavior of metals and their resistivity characteristics in relation to electron interactions and temperature effects.

Jonsson
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Hello there,

Id like to estimate how the resistivity due to electron 'collision' with 1st Brillouin zone changes as a function of number of valence electrons in a metal.

Say you start with Na, then add some other material with 2 valence electrons instead of 1, then the fermi wavevector will eventually get so long that it there will be electrons interacting with the Brillouin zone boundary.

How does the resistivity change as a function of number of valence electrons in such a solid?

Thank you for your time.

Kind regards,
Marius
 
The calculation of the resistivity is a highly non-trivial task. Also, resistivity depends very strongly on temperature (especially in very pure samples and at low temperatures) and on the concentration of impurities.
 

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