Applications of principal component analysis to pair distribution function data

Developments in X-ray scattering instruments have led to unprecedented access to in situ and parametric X-ray scattering data. Deriving scientific insights and understanding from these large volumes of data has become a rate-limiting step. While formerly a data-limited technique, pair distribution function (PDF) measurement capacity has expanded to the point that the method is rarely limited by access to quantitative data or material characteristics - analysis and interpretation of the data can be a more severe impediment. This paper shows that multivariate analyses offer a broadly applicable and efficient approach to help analyse series of PDF data from high-throughput and in situ experiments. Specifically, principal component analysis is used to separate features from atom-atom pairs that are correlated - changing concentration and/or distance in concert - allowing evaluation of how they vary with material composition, reaction state or environmental variable. Without requiring prior knowledge of the material structure, this can allow the PDF from constituents of a material to be isolated and its structure more readily identified and modelled; it allows one to evaluate reactions or transitions to quantify variations in species concentration and identify intermediate species; and it allows one to identify the length scale and mechanism relevant to structural transformations.