Wigner–Seitz radius
The Wigner-Seitz 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. 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. 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:
| Element | |
| Li | 3.25 |
| Na | 3.93 |
| K | 4.86 |
| Rb | 5.20 |
| Cs | 5.62 |
