Exact and explicit expression of the atomic pair distribution function as obtained from X-ray total scattering experiments

Olivier Masson (1) , Philippe Thomas (1)

1 SPCTS-AXE3 - Axe 3 : organisation structurale multiéchelle des matériaux

The atomic pair distribution function (PDF) as obtained from X-ray or neutron total scattering experiments has proved to be powerful in obtaining valuable structural information for many complex functional materials, be they amorphous or crystalline. In the case of measurements made with X-rays and for samples containing more than one kind of atom, the usefulness of the PDF is, however, somewhat hampered because of the lack of an exact and simple expression relating it to the structure of the materials. Only an approximate relationship exits, which is still in use today. This is particularly detrimental given the wide availability of X-ray sources and the increasing quality of PDFs obtained with laboratory sources. In this paper, the exact and explicit expression of the PDF as obtained from X-ray scattering is derived with respect to partial functions. This expression allows exact and efficient calculation of the PDF from any structure model without using approximate formulae.

Mots clés: X-ray total scattering; atomic pair distribution function (PDF); structure analysis

Domaines: Matériaux

Olivier Masson, Philippe Thomas. Exact and explicit expression of the atomic pair distribution function as obtained from X-ray total scattering experiments. Journal of Applied Crystallography, 2013, 46 (2), pp.461-465. ⟨10.1107/S0021889812051357⟩. ⟨hal-00809022⟩