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Pair distribution function

The atomic pair distribution function (PDF) describes the density of interatomic distances in a material. Of special practical importance is the radial pair distribution function, which is independent of orientation. It is a major descriptor for the atomic structure of amorphic materials (glasses, polymers) and liquids. The radial PDF can be calculated directly from physical measurements like light scattering or x-ray powder diffraction.

$g_{ab}(r) = \frac{1}{N_{a} N_b}\sum\limits_{i=1}^{N_a} \sum\limits_{j=1}^{N_b} \langle \delta( \vert \mathbf{r}_{ij} \vert -r)\rangle$