In general, a pair distribution function will take a form somewhere between the sparsely packed (HC approximation) and the densely packed (delta function) models, depending on the packing density . Radial distribution function Of special practical importance is the radial distribution function, which is independent of orientation. It is a major descriptor for the atomic structure of amorphous materials (glasses, polymers) and liquids. The radial distribution function can be calculated directly from physical measurements like light scattering or x-ray powder diffraction by performing a Fourier Transform. In Statistical Mechanics the PDF is given by the expression Applications Thin Film Pair Distribution Function When thin films are disordered, as they are in electronic devices, pair distribution is used so to view the strain and structure-properties of that material or composition. They have these properties that cannot be exploited in the bulk or crystalline form. There is a method with the radial distribution that is able to view the local structure of a disordered thin film of GeSe2.But the creators of this method called a need for a better method to view the mid-range order of disordered films. The creation of thin-film Pair Distribution Function (tfPDF) uses a statistical distribution of a material’s mid-range order that enables viewing important details like the disorder. In this technique, 2D data from a scattering method is integrated and Fourier transformed into 1D data that shows the probability of bonds in that material. TfPDF works best when in conjunction with other characterization methods like transmission electron microscopy. Although a developing methodology, tfPDF can give complete structure-property relationships through a reliable characterization technique. See also classical-map hypernetted-chain method References Fischer-Colbrie, Bienenstock, Fuoss, Marcus. Phys. Rev. B (1988) 38, 12388 Jensen, K. M., Billinge, S. J. (2015). IUCrJ, 2(5), 481-489. Statistical mechanics Condensed matter physics