Fermi-Dirac distribution for metals

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Discussion Overview

The discussion centers around the application of the Fermi-Dirac distribution to metals, specifically addressing whether it applies to all electrons or only to valence (conduction) electrons. Participants explore the distinctions between core and conduction electrons in the context of the electron gas model and electrical conductivity.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the Fermi-Dirac distribution primarily describes the valence (conduction) electrons, while core electrons are bound and do not contribute to the distribution.
  • One participant explains that core electrons occupy discrete energy levels and cannot be described by the Fermi-Dirac distribution, which applies to a free electron gas model.
  • Another participant questions whether the Fermi-Dirac distribution applies to all electrons except those in the lowest energy level (E1s) or only to higher energy levels (E3s).
  • A participant clarifies that in sodium, the conduction electron is the 3s electron, and the Fermi-Dirac distribution is relevant only to this electron.
  • It is noted that the Fermi-Dirac distribution assumes weak interactions among electrons, which does not hold for core electrons due to their mutual Coulomb repulsion.
  • One participant emphasizes that the electron gas model is a simplification and that conduction electrons interact with their environment, leading to the concept of an effective electron mass.

Areas of Agreement / Disagreement

Participants generally agree that the Fermi-Dirac distribution applies to conduction electrons, specifically the 3s electrons in sodium, but there is some uncertainty regarding the treatment of core electrons and their exclusion from the distribution.

Contextual Notes

The discussion reflects varying levels of understanding regarding the application of the Fermi-Dirac distribution, particularly in distinguishing between core and conduction electrons. Assumptions about weak interactions and the simplifications inherent in the electron gas model are acknowledged but not resolved.

ilconformista
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Hello everyone!
I'm a little confused. The Fermi-Dirac distribution is about every electron in a metal or only about the valence electrons?
 

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As far as I understand it, we think of the valence (conduction) electrons as forming a free electron gas, whose states are occupied as the FD distribution describes. The core electrons are thought to be bound to the atoms they belong to, and don't even have a continuous spectrum of possible states (bound states form a discrete spectrum), so they can't be described with the FD distribution. Well, in principle even the electron gas has a discrete set of states as it is confined to a finite volume, but the spacing between energy levels is very small.
 
Thanks a a lot! I'll give you an example to see if i got it right.
The core electrons of lithium occupy the energy level E1s. All the other electrons occupy the levels E2s, E2p, E3s.
The FD distribution is about all the electrons apart from the ones in E1s? Or only about the ones in E3s?
 
A lithium atom has three electrons, and in the simple orbital model two of them occupy the 1s orbital and the remaining one occupies a 2s orbital. In the context of the electron gas model of electrical conductivity, we think of the 2s electrons getting delocalized over the entire volume of the metal object.

In deriving the FD distribution, an assumption is made that the electrons interact very weakly with each other. This is not the case for the core electrons which are rather close to each other and feel their mutual Coulomb repulsion.
 
I'm very sorry, I meant Sodium (Na), which has an atomic number 11. So the same questions but for sodium...
 
All alkali metals have only one conduction electron per atom. In the case of sodium the 3s electron becomes the conduction electron.
 
And in deriving the FD distribution we take in consideration only the 3s electrons right, not the 2s, 2p?
 
Yes, the FDD only applies to conduction electrons. Just remember that the electron gas model is just that, only a model. Even the conduction electrons are actually interacting with their environment, and we usually take this into account by introducing an effective electron mass - the conduction electrons in the lattice behave as they would be heavier than genuinely free electrons.
 
Thanks a lot! You 've been very helpful!
 

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