The free electron model vs. nearly free electron model.

[Brammo]

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.

 

[Tarantinism]

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)