, 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.
is calculated for bulk materials.
free valence electrons in a volume
we obtain The radius can also be calculated as where
is count of free valence electrons per particle,
This parameter is normally reported in atomic units, i.e., in units of the Bohr radius.
Assuming that each atom in a simple metal cluster occupies the same volume as in a solid, the radius of the cluster is given by
for the first group metals:[2] Wigner–Seitz radius is related to the electronic density by the formula
where, ρ can be regarded as the average electronic density in the outer portion of the Wigner-Seitz cell.
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