Wigner–Seitz radius

The WignerSeitz radius , named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals).[1] In the more general case of metals having more valence electrons, is the radius of a sphere whose volume is equal to the volume per a free electron.[2] This parameter is used frequently in condensed matter physics to describe the density of a system. Worth to mention, is calculated for bulk materials.

Formula

In a 3-D system with free electrons in a volume , the Wigner–Seitz radius is defined by

where is the particle density of free electrons. Solving for we obtain

The radius can also be calculated as

where is molar mass, is amount of free electrons per atom, is mass density, and is the Avogadro number.

This parameter is normally reported in atomic units, i.e., in units of the Bohr radius.

Values of for the first group metals:[2]

Element
Li3.25
Na3.93
K4.86
Rb5.20
Cs5.62

See also

References

  1. Girifalco, Louis A. (2003). Statistical mechanics of solids. Oxford: Oxford University Press. p. 125. ISBN 978-0-19-516717-7.


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