Empty lattice approximation: Difference between revisions

Revision as of 16:56, 28 December 2010

Revision as of 21:41, 12 January 2011

Line 36:

{{clear}}

==The nearly free electron model==

In most [[Metal|simple metals]], like [[aluminium]], the [[screening effect]] strongly reduces the electric field of the ions in the solid. The elctrostaticelectrostatic potential is expressed as

:<math>V(r) = \frac{Z e}{r} e^{-q r}</math>

Line 44:

:<math>U_{\bold{G}} = \frac{4 \pi Z e}{q^2 + \bold{G}^2}</math>

When the values of the off-diagonal elements <math>U_{\bold{G}}</math> between the reciprocal lattice vectors in the Hamiltonian almost go to zero. As a result the magnitude of the band gap <math>2|U_{\bold{G}}|</math> collapses and the Empty Lattice Approximation is optainedobtained.

==The crystal structures of metals==