A class for containing, calculating and reading a pair distribution function (PDF).

We derive our definitions for this from the following publication: “A comparison of various commonly used correlation functions for describing total scattering” Keen, D. A. (2001). J. Appl. Cryst. 34, 172-177. DOI: https://doi.org/10.1107/S0021889800019993

We employ the following mathematical form for the total pair distribution function (PDF):

\[G(r) = \sum_{i,j}^{N_{elements}} c_ic_jb_ib_j(g_{ij}(r) - 1)\]

where \(c_i\) is the number concentration of element \(i\), \(b_i\) is the (coherent) scattering length of element \(i\). (This corresponds to equation 8 in the above publication)

The partial pair distribution, \(g_{ij}\), is:

\[g_{ij}(r) = \frac{h_{ij}(r)}{4 \pi r^2 \rho_{j} \Delta{r}}\]

where \(h_{ij}\) is the histogram of distances of \(j\) element atoms around atoms of element \(i\), with bins of size \(\Delta{r}\), and \(\rho_{j}\) is the number density of atoms of element \(j\). As \(g_{ij}(0) = 0\), it is evident that \(G(0) = -\sum_{i,j}^{N_{elements}} c_ic_jb_ib_j\). (This corresponds to equation 10 in the above publication)

The total PDF is contained in PDF and the partial pair PDFs (if calculated or imported) are contained in partial_pdfs.