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

In situ X-ray diffraction experiments offer a unique opportunity to investigate structural dynamics at atomic resolution, by collecting several patterns in an appropriate time sequence (data matrix) while varying the applied stimulus (e.g. temperature changes). Individual measurements can be processed independently by refinement procedures that are based on prior knowledge of the average structure of each crystal phase present in the sample. If the refinement converges, parameters of the average structural model can be assessed and studied as a function of the stimulus variations. An alternative approach consists in applying a multivariate analysis to the data matrix as a whole. Methods such as principal component analysis (PCA) and phase-sensitive detection perform fast, blind and model-independent calculations that can be used for on-site analysis to identify trends in data actually related to the applied stimulus. Both classical and multivariate approaches are here applied to the in situ X-ray diffraction pair distribution function (PDF) setup on two samples of the hybrid perovskite methyl­ammonium (MA) lead iodide obtained by different synthetic routes, subjected to temperature variations. The PDF refinement allows assessing the occurrence of temperature-induced rotations of the PbI₆ octahedra and variations in the relative amount of MAPbI₃ and intermediate PbI₂–MAI–DMSO (dimethyl sulfoxide) crystal phases. A change in the orientation of the methyl­ammonium molecule with temperature is also characterized. Results of the multivariate analysis tools, which include a newly introduced space-dependent variant of PCA, are described, interpreted and validated against simulated data, and their specificity and relation to refinement results are highlighted. The interaction between nearby octahedra is identified as the driving force for the tetragonal-to-cubic phase transition, and three fundamental trends in data having different temperature behaviours are unveiled: (i) irreversible weight-fraction variations of the MAPbI₃ and PbI₂–MAI–DMSO phases; (ii) reversible structural changes related to the MAPbI₃ crystalline phase and its lattice distortion in the ab plane, having the same frequency as the temperature variations; (iii) reversible lattice distortion along the c axis, occurring at twice the frequency of the temperature changes.