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Register a new userRepresentational Analysis of Extended Disorder in Atomistic Ensembles Derived from Total Scattering Data
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With the increased availability of high intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches and necessitates reverse Monte Carlo (RMC) simulations using large supercells. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. We use representational analysis to describe displacements of atoms in RMC ensembles from an ideal crystallographic structure. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. This method enables the extraction of statistically relevant displacement modes (orientation, amplitude, and distribution) of the crystalline disorder and provides directly meaningful information in a symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics.
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Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry, J. Appl. Cryst. 25, 391 (1992)]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 100, making refinement of atomistic models to large diffuse-scattering volumes practical.
We explore data reduction and correction steps and processed data reproducibility in the emerging single crystal total scattering based technique of three-dimensional differential atomic pair distribution function (3D-$Delta$PDF) analysis. All steps from sample measurement to data-processing are outlined in detail using a CuIr$_2$S$_4$ example crystal studied in a setup equipped with a high-energy x-ray beam and a flat panel area detector. Computational overhead as it pertains to data-sampling and the associated data processing steps is also discussed. Various aspects of the final 3D-$Delta$PDF reproducibility are explicitly tested by varying data-processing order and included steps, and by carrying out a crystal-to-crystal data comparison. We identify situations in which the 3D-$Delta$PDF is robust, and caution against a few particular cases which can lead to inconsistent 3D-$Delta$PDFs. Although not all the approaches applied here-in will be valid across all systems, and a more in-depth analysis of some of the effects of the data processing steps may still needed, the methods collected here-in represent the start of a more systematic discussion about data processing and corrections in this field.
Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models. However, the fundamental limitation of machine learning methods is their correlative nature, leading to extreme susceptibility to confounding factors. Here, we implement the workflow for causal analysis of structural scanning transmission electron microscopy (STEM) data and explore the interplay between physical and chemical effects in ferroelectric perovskite across the ferroelectric-antiferroelectric phase transitions. The combinatorial library of the Sm-doped BiFeO3 is grown to cover the composition range from pure ferroelectric BFO to orthorhombic 20% Sm-doped BFO. Atomically resolved STEM images are acquired for selected compositions and are used to create a set of local compositional, structural, and polarization field descriptors. The information-geometric causal inference (IGCI) and additive noise model (ANM) analysis are used to establish the pairwise causal directions between the descriptors, ordering the data set in the causal direction. The causal chain for IGCI and ANM across the composition is compared and suggests the presence of common causal mechanisms across the composition series. Ultimately, we believe that the causal analysis of the multimodal data will allow exploring the causal links between multiple competing mechanisms that control the emergence of unique functionalities of morphotropic materials and ferroelectric relaxors.
In this paper we investigated the most important family of proton conducting oxides, i.e. cerates, by means of pair distribution function analysis (PDF) obtained from total neutron scattering data. The results clearly demonstrates that the local structure plays a fundamental role in the protonation process. Oxygen vacancy creation by acceptor doping reduces the local structure symmetry which is then restored upon water uptake. This mechanism mainly involves the Ba-O shell which flexibility seems to be at the basis of the proton conduction mechanism, thus providing a direct insight on the design of optimal proton conducting materials.
X-ray and neutron powder diffraction data as a function of temperature are analyzed for the colossal dielectric constant material CaCu3Ti4O12. The local structure is studied using atomic pair distribution function analysis. No evidence is found for enhanced oxygen displacement parameters suggesting that short-range octahedral tilt disorder is minimal. However, an unusual temperature dependence for the atomic displacement parameters of calcium and copper is observed. Temperature dependent modeling of the structure, using bond valence concepts, suggests that the calcium atoms become underbonded below approximately 260 K, which provides a rationale for the unusually high Ca displacement parameters at low temperature.
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