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Structural modelling of $operando$ pair distribution function (PDF) data offunctional materials can be highly complex. To aid the understanding of complexoperando PDF data, we here demonstrate a toolbox for PDF analysis. The toolsinclude the structureMining, similarityMapping, nmfMapping apps availablethrough the online service 'PDF in the cloud' (PDFitc, www.pdfitc.org), as wellas noise-filtering using principal component analysis (PCA). The tools areapplied to both ex situ and operando PDF data for 3 nm$\mathrm{TiO_{2}}$-bronze nanocrystals, which function as the active electrodematerial in a Li-ion battery. The tools enable structural modelling of the exsitu and operando PDF data, revealing two pristine $\mathrm{TiO_{2}}$ phases(bronze and anatase) and two lithiated $\mathrm{Li_{x}TiO_{2}}$ phases(lithiated versions of bronze and anatase), and the phase evolution duringGalvanostatic cycling is characterized.

Operando pair distribution function analysis of nanocrystalline  functional materials: the case of $\mathrm{TiO_{2}}$-bronze nanocrystals in  Li-ion battery electrodes