Combinatorial appraisal of transition states for in situ pair distribution function analysis

Abstract

In situ total scattering measurements are increasingly utilized to follow atomic and nanoscale structural details of phase transitions and other transient processes in materials. This contribution presents an automated method and associated tool set to analyze series of diffraction and pair distribution function data with a linear combination of end‐member states. It is demonstrated that the combinatorial appraisal of transition states (CATS) software tracks phase changes, relative phase fractions and length scales of interest in experimental data series. It is further demonstrated, using a series of local structure data simulations, that the misfit of such a model can reveal details of phase aggregation and growth related to the pair distribution function's sensitivity to interphase correlations. CATS may be applied to quantitative evaluation of many transient processes, including amorphous‐to‐crystalline phase transitions, the evolution of solid‐solution behaviors, the precipitation and growth of aggregates, and other atomic to nanoscale details of crystallization and phase transformation phenomena.

Investigating temperature-induced structural changes of lead halide perovskites by in situ X-ray powder diffraction

“…A great advantage of the PDF technique is that it offers the opportunity to carry out a detailed analysis of phase transitions in the space domain. This was already pointed out by Olds et al (2017), who studied the orthorhombic-to-tetragonal phase transition of MAPbI 3 by using a linear combination of initial and final PDF profiles as a fitting model. They investigated the transition behaviour as a function of the length scale in the material, by plotting the parameter describing the combination of initial and final PDF profiles, as determined by a least-squares fit of PDF profiles considered up to a given interatomic distance (R max ).…”

“…They investigated the transition behaviour as a function of the length scale in the material, by plotting the parameter describing the combination of initial and final PDF profiles, as determined by a least-squares fit of PDF profiles considered up to a given interatomic distance (R max ). They found a clear transition for R max > 5 Å and a more complex behaviour at shorter distances, where the local structure remains distinct from the average structure (Olds et al, 2017). Here we use the same approach for the study of the tetragonal-to-cubic phase transition, but replacing the least-squares fit with PCA, with the advantage of using a blind analysis of the data matrix that avoids taking the first and last profiles as representative of the initial and final states of the system.…”

“…Rietveld (1969) and PDF refinement (Proffen & Billinge, 1999) or simultaneous fitting of the average crystal structure and local morphology by the Debye scattering equation (Bertolotti et al, 2017) are methods that belong to the first group. Principal component analysis (PCA) and the combinatorial appraisal of transition states, which highlights the occurrence of structural changes at different interatomic distances by exploiting a linear combination of the first and last profiles of the data set as fitting model (Olds et al, 2017), are examples of methods that belong to the second group. In particular, PCA has been used to analyse in situ PDF data (Chapman et al, 2015), to extract the kinetic parameters that best fit XRPD data and to identify (active) atoms in the bulk material that are responding to external in situ stimuli (Palin et al, 2015).…”

Constrained non-negative matrix factorization enabling real-time insights of $\textit{in situ}$ and high-throughput experiments

“…Automation and engineering has increased capabilities for data streaming and in situ experimentation in many settings, including university laboratories, 9 industrial research, 10 and central facilities. 11 This technological advancement opens up new opportunities for interrogating the dynamic processes of a system including phase transitions 12 and reactive processes. 7 Such opportunities bear the burden of an increased rate of data production, as well as a commensurate increase in the volume of data to process.…”

“…11 These tools have been demonstrated for classifying diffraction patterns, [21][22][23][24][25][26][27][28] or decomposing large datasets. 12,[29][30][31][32][33] Particularly, unsupervised learning is useful for offering rapid diagnostics and analysis without prior training. 13,30,34 Because unsupervised decomposition-or data reduction-algorithms do not require any prior data labeling or expected phases, they are exceptionally useful for interpreting datasets where there are potentially new or unexpected phases.…”