Pair distribution function

The pair distribution function (PDF) describes the distribution of distances between pairs of particles 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 through the use of Fourier Transform.

In Statistical Mechanics the PDF is given by the expression:

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

The Diffpy project is used to match crystal structures with PDF data derived from X-ray or neutron diffraction data.

See also

• Radial distribution function