Is Free-electron model := Drude Model (of metals) ?

In summary, the free electron model is a combination of the quantum behaviour of electrons (Pauli principle) and the classical Drude model.
  • #1
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Is the free-electron model synonymous with Drude model? or is Drude model a special subset of the free-electron model?

I have seen texts that refer to a "free-electron model" and do not mention Drude's name. and i have also seen texts use these two terms interchangeably.

Sorry, i have no specific examples. I'm just looking for a generalization.

Thanks guys.

also as a small side question: whenever a text refers to energy bands, fermi levels, or potential wells, is this necessarily a "quantum approach"? or is this why the Drude model is considered "semi-classical"?
 
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  • #2
As far as I know, Free electron model is a combination of the quantum behaviour of electrons (Pauli principle) and the classical Drude model.

Thus the difference between Free Electron model and Drude, is that FEM takes into account that electrons are fermions, hence we get a fermi surface in k-space even at temperature of 0K.

Yes those are quantum approaches, since one has wave functions and quantum statistics (Pauli principle).

I don't know exactly how to explain that the Drude Model is considered to be Semiclassical, but Iam sure that someone else here know it and will explain it to you ;-)
 
  • #3
Usually the "free electron approximation" means your model ignores the background potential seen by the electrons. For example, one of the simplest ways to calculate band structure is called the "nearly free electron approximation" in which you simply compute perturbative corrections to the energy levels of the free electron gas due to the nuclear lattice.

Another important approximation is the "independent electron approximation" which means your model neglects electron-electron interactions. The Sommerfeld model of electrons assumes both free and independent electrons and retains only their basic quantum character via the Pauli principle.

The Drude model is completely classical because it contains classical particles obeying Netwon's laws. The Drude model is also a mean field description because it includes scattering only in an average way via the relaxation time. Because of the relation between dissipation and fluctuation, there should be an additional fluctuating force which the Drude model effectively averages over. I'm not sure if you would say the Drude model assumes free electrons because I think Drude originally thought the relaxation time came from the nuclei (it doesn't, of course, because of Bloch's theorem). One should simply imagine some unspecified scatterers (impurities, phonons, etc) leading to an effective relaxation time.

On the other hand, the Sommerfeld model of electrons is a quantum model but of free and independent electrons. One can incorporate a description of transport using, for example, a classical Boltzmann equation. However, when using such an equation one is implicitly assuming a description in terms of wavepackets with reasonably sharp momentum and position which approximately obey Newton's laws. This makes the description semi-classical.

Hope this helps.
 

1. What is the Free-electron model?

The Free-electron model, also known as the Drude Model, is a simplified theoretical model used to describe the behavior of electrons in metals. It assumes that the electrons in a metal are free to move throughout the entire material, and that they are not bound to any specific atoms.

2. How does the Free-electron model explain the properties of metals?

The Free-electron model explains the properties of metals by considering the behavior of the free electrons. These electrons are able to move throughout the material, which allows metals to conduct electricity and heat, and also gives them their characteristic luster, malleability, and ductility.

3. What are the limitations of the Free-electron model?

While the Free-electron model is a useful tool for understanding the properties of metals, it has some limitations. For example, it does not take into account the interactions between the electrons and the metal ions, which can affect the behavior of electrons in real metals. It also cannot explain certain phenomena, such as the specific heat of metals at low temperatures.

4. How does the Free-electron model relate to the behavior of electrons in other materials?

The Free-electron model is specific to metals, as it assumes that the electrons in a metal are unbound and free to move throughout the material. However, similar models have been developed to describe the behavior of electrons in other materials, such as semiconductors and insulators.

5. Is the Free-electron model an accurate representation of the behavior of electrons in metals?

The Free-electron model is a simplified theoretical model and does not fully capture all aspects of the behavior of electrons in metals. However, it provides a good framework for understanding the basic properties of metals and has been used successfully in many applications, such as in the development of electronic devices.

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