Empty lattice approximation: Difference between revisions

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Revision as of 10:22, 3 April 2020

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In three-dimensional space the Brillouin zone boundaries are planes. The dispersion relations show conics of the free-electron energy dispersion parabolas for all possible reciprocal lattice vectors. This results in a very complicated set intersecting of curves when the dispersion relations are calculated because there is a large number of possible angles between evaluation trajectories, first and higher order Brillouin zone boundaries and dispersion parabola intersection cones.

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==Second, third and higher Brillouin zones==

[[Image:Brillouin Zone (1st, FCC).svg|thumb|300px|right|FCC Brillouin zone]]

"Free electrons" that move through the lattice of a solid with wave vectors <math>\mathbf{k}</math> far outside the first Brillouin zone are still reflected back into the first Brillouin zone. See the [[#External links|external links]] section for sites with examples and figures.

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==The nearly free electron model==