The free electron model vs. nearly free electron model.

In summary, the conversation discusses the occurrence of energy gaps in the nearly free electron model when plotting ε(k) against k. It also addresses the concept of Bragg reflection and its relationship with the free electron model. The participants conclude that while Bragg reflection does not occur in a completely free electron model, it can be observed in materials such as alkali and noble metals due to their deviation from the first approximation of the model. The example of De Haas-Van Alphen measurements is also mentioned.
  • #1
Brammo
7
0
Ok so If I plot ε(k) against k for the nearly free electron model there will be an energy gap. Bragg refelction leads to these energy gaps and standing waves. So does Bragg reflection not ocurr in the free electron model? What materials have the property of the free electron model and what materials the nearly free electron model?

Thank you for your help.
 
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  • #2
Of course Bragg reflection does not occur in a 100% free electron model: the electrons are independent and "live" in a box with 0 potential (there are no positive ions).

No materials satisfy that, because that is the first approximation. But there are materials where this approximation may be really good: alkali metals, for example (noble metals also: Cu, Ag, Au). This happens because a free electron Fermi sphere for the only conduction electron -they are monovalent- is far away from the limits of the first Brillouin zone. So it deviates very little from the free electron behavior. Na and K, for example, produce De Haas-Van Alphen measurements (you know? this shows the Fermi surface structure) which deviate only a part in thousands from those expected from the free electron measurements (cf. Ashcroft- Mermin)
 

1. What is the difference between the free electron model and the nearly free electron model?

The free electron model assumes that electrons in a solid are completely free to move and are not influenced by the atoms in the crystal lattice. On the other hand, the nearly free electron model takes into account the influence of the lattice on the electrons, but still treats them as relatively free to move.

2. Which model is more accurate in describing the behavior of electrons in a solid?

Neither model is entirely accurate, as they both make simplifying assumptions. However, the nearly free electron model is generally considered to be more accurate as it takes into account the effects of the crystal lattice on the electrons.

3. How do the two models explain the phenomenon of electrical conductivity in solids?

The free electron model explains electrical conductivity by stating that the delocalized electrons are able to move freely and carry an electric current. The nearly free electron model adds to this by considering the influence of the lattice on the movement of the electrons, which can lead to a decrease in conductivity in certain materials.

4. Can the free electron model and the nearly free electron model be applied to all types of solids?

No, these models are most applicable to metals, which have a high number of delocalized electrons. They are less accurate in describing the behavior of electrons in insulators and semiconductors, which have a different electronic structure.

5. What are some of the limitations of the free electron model and the nearly free electron model?

The free electron model does not account for the interactions between electrons, which can have a significant impact on the behavior of electrons in a solid. The nearly free electron model still makes simplifying assumptions about the crystal lattice, and does not take into account the effects of impurities or defects in the solid.

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