  Structural modelling of $operando$ pair distribution function (PDF) data of
functional materials can be highly complex. To aid the understanding of complex
operando PDF data, we here demonstrate a toolbox for PDF analysis. The tools
include the structureMining, similarityMapping, nmfMapping apps available
through the online service 'PDF in the cloud' (PDFitc, www.pdfitc.org), as well
as noise-filtering using principal component analysis (PCA). The tools are
applied to both ex situ and operando PDF data for 3 nm
$\mathrm{TiO_{2}}$-bronze nanocrystals, which function as the active electrode
material in a Li-ion battery. The tools enable structural modelling of the ex
situ 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 during
Galvanostatic cycling is characterized.
