Empty lattice approximation: Difference between revisions

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The '''Empty Lattice Approximation''' is a theoretical [[electronic band structure]] model in which the periodic potential of the crystal lattice is defined not more precisely than '''"periodic"''' and it is assumed that the potential is '''weak'''. The Empty Lattice Approximation is a description of the properties of electrons in an [[Fermi gas|electron gas]] of non-interacting [[Free electron model|free electrons]] that move through a weak periodic potential of a [[crystal structure]]. The model mainly serves to illustrate a number of concepts which are fundamental to all electronic band structure phenomena.

==IntroductionScattering==

[[Image:Empty-Lattice-Approximation-FCC-bands.svg|thumb|300px|Free electron bands in a FCC crystal structure]]

[[Image:Empty-Lattice-Approximation-BCC-bands.svg|thumb|300px|Free electron bands in a BCC crystal structure]]

[[Image:Empty-Lattice-Approximation-HCP-bands.svg|thumb|500px|Free electron bands in a HCP crystal structure]]

The periodic potential of the lattice must be weak because otherwise the electronelectrons wouldn't be free,. butThe itstrength is just strong enough to '''scatter'''of the electrons. How strong must a potential be to be able to [[Scattering theory|scatter]] an electron? The answer is thatscattering itmainly depends on the topology of the system. how large topologicallyTopologically defined parameters, like [[Scattering cross-section|scattering]] [[Cross section (physics)|cross sections]], depend on the magnitude of the potential and the size of the [[potential well]]. One thing is clear for currently known 1, 2 and 3-dimensional spaces: '''potential wells do always scatter waves''' no matter how small their potentials are or what their sign is and how limited their sizes are. For a [[Particle in a one-dimensional lattice (periodic potential)|particle in a one-dimensional lattice]], like the Kronig-Penney model, it is easy to substitute the values for the potential and the size of the potential well.<ref name=Kittel>

{{cite book |author=C. Kittel |title=Introduction to Solid State Physics |year= 1953-1976 |publisher=Wiley & Sons |isbn=0-471-49024-5 }}

</ref>