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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., Comment: Preprint, 82 pages in total (front page: 1 page, abstract: 1 page, paper: 34 pages, supporting information: 40 pages, references: 5 pages, synopsis: 1 page), 35 figures in total (frontpage: 1 figure, paper: 8 figures, supporting information: 26 figures)

We investigate a prototype application for machine-readable literature. The program is called "pyDataRecognition" and serves as an example of a data-driven literature search, where the literature search query is an experimental data-set provided by the user. The user uploads a powder pattern together with the radiation wavelength. The program compares the user data to a database of existing powder patterns associated with published papers and produces a rank ordered according to their similarity score. The program returns the digital object identifier (doi) and full reference of top ranked papers together with a stack plot of the user data alongside the top five database entries. The paper describes the approach and explores successes and challenges., Comment: 27 pages, 4 figures

Structural modelling of octahedral tilts in perovskites is typically done using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports on the development of constraints for modelling pure octahedral tilts and implemented the constraints in diffpy-CMI, a powerful package to analyse pair distribution function (PDF) data. The program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, provides an intuitive picture of the tilting, and as it has many fewer refinable variables than the unconstrained space-group fits, provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO$_3$ which has a known Glazer tilt system $\alpha^+ \beta^- \beta^-$. The Glazer model fits comparably to the corresponding space group model $Pnma$ below $r$ = 14 A and becomes progressively worse than the space group model at higher $r$ due to non-rigid distortions in the real material., Comment: 17 pages, 5 figures, 2 tables

A cloud-hosted web-based software application, nmfMapping, for carrying out a nonnegative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This app allows structure scientists to rapidly find trends in sets of related data such as from in situ and operando diffraction experiments. The application is easy to use and does not require any programming expertise. It is available at the pdfitc.org website., Comment: 19 Pages, 7 Figures, submitted to Acta Crystallographica Section A