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.