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 (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
Solving for we obtain
where is the particle density of free electrons.
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 are listed below[2] :
Element | |
---|---|
Li | 3.25 |
Na | 3.93 |
K | 4.86 |
Rb | 5.20 |
Cs | 5.62 |
- This is an excerpt of Table 1.1 of the cited book.
See also
References