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discrete translational periodicity
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Figure 1: Arrangements of molecules.
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discrete translational periodicity

physics
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Figure 1: Arrangements of molecules.
Figure 1: Arrangements of molecules.

The term "discrete translational periodicity" is a concept in physics that describes the ordered arrangement of atoms in crystalline solids. In crystals, atoms are arranged in a pattern that repeats at regular intervals, meaning that if you shift the crystal by a certain distance in a specific direction, the atoms will occupy the same positions as before. This repeating unit is called a unit cell.12

This property is fundamental to understanding crystal structures and their symmetries. For example, the allowed rotational symmetries in periodic crystals are limited to twofold, threefold, fourfold, and sixfold axes because only these are compatible with translational symmetry. Structures with other rotational symmetries, such as fivefold, cannot exhibit translational periodicity. This concept is contrasted with quasicrystals, which have ordered structures but lack precise, repeating intervals.21

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  1. period
  2. quasicrystal
  3. symmetry

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