Z and Z'

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Definitions

In the description of a crystal structure, the letter Z characterises the number of (chemical) formula units contained in the unit cell. For 3D-periodic structures, this number is always an integer which is at least 1.

When dealing with molecular structures, it is also convenient to define Z'. Z' indicates the number of formula units in the asymmetric unit. In other words, Z' is the value of Z divided by the multiplicity of the general position of the corresponding space group. Z' can be a fraction or a positive integer.

Examples

The cubic structure of NaCl belongs to space group [math]Fm\overline{3}m[/math]. The unit cell contains 4 Na and 4 Cl atoms. Consequently Z=4. for inorganic structures, Z' might be a fraction. For NaCl, Z' would be 4/196 or 1/48 indicating that each atom lies on highly symmetric special positions with site symmetry [math]m\overline{3}m[/math].

In molecular structures, Z' is very often equal to one. However, when Z' is an integer larger than 1 this gives some interesting information about the stereochemistry of the molecular compound.

See also

• Unit cell
• Asymmetric unit
• What is Z'? http://zprime.co.uk
• Looking deeper into molecular structures with Z' > 1, Chapuis,G., Acta Cryst. (2020). B76, 510–511