Brian H. Toby

The author recaps software development over the course of his career and how George Sheldrick inspired and improved this. He concludes that software development is more accepted at present as a role for research scientists, but that more consideration is needed for long-scale project development.

Physical properties and functionalities of materials are dictated by global crystal structures and local defects. To establish a structure–property relationship, we require not only the crystallographic symmetry but also quantitative knowledge about defects. Here, we present a hybrid machine learning (ML) framework that integrates a physically constrained variational autoencoder (pc-VAE) with different Bayesian optimization (BO) methods to systematically accelerate and improve crystal structure refinement with resolution of defects. We chose the pyrochlore-structured Ho2Ti2O7 as a model system and employed the GSAS-II package for benchmarking crystallographic parameters from traditional refinement based on the least-square algorithm and for training data generation. However, the function space of these material systems is highly non-linear, which limits optimizers, such as in traditional least-square refinement, into trapping fits at local minima. In addition, these naïve methods do not provide an extensive learning about the overall function space, which is essential for large space, large time consuming explorations to identify various potential regions of interest. Thus, we present the approach of exploring the high-dimensional structure parameters of defect-sensitive systems via pretrained pc-VAE-assisted Bayesian optimization and Sparse Axis-Aligned Bayesian Optimization. The pc-VAE, designed and trained on physically plausible Ho2Ti2O7 structure models, projects high-dimensional diffraction data consisting of thousands of independently measured diffraction orders into a low-D latent space while enforcing scaling invariance and physical relevance of the latent space. In this proposed design of closed-loop autonomous exploration, we aim to minimize the χ2 errors, also known as L2 norm, in the real and latent spaces separately between experimental and simulated diffraction patterns, thereby steering the refinement toward potential optimum in the parameter space of crystal structures. We investigated and compared the results among different methods, such as pc-VAE-assisted BO, non pc-VAE-assisted BO, and Rietveld least-square refinement. The result shows that the methodology can be generalized to other complex materials where ultra-precise determination of structural defects is needed to reveal subtle structure–property relationships, highlighting a new paradigm for integrating crystallography with ML to accelerate discoveries and characterizations of magnetic materials.

Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

A methodology is developed where a fundamental parameters approach (FPA) description of a laboratory powder diffraction instrument (configured in divergent-beam Bragg–Brentano geometry) is used to determine GSAS-II profile parameters for peak asymmetry and instrumental peak widths. This allows the instrumental contribution to peak shapes to be robustly determined directly from a physical description of the instrument, even though GSAS-II does not directly implement FPA for peak shape computation. The FPA-derived parameters can be used as the starting point for instrument characterization, or to characterize sample broadening without the use of a standard to determine the instrument profile function. This new method can facilitate generation of training sets for machine learning. A plot is generated that shows the differences between the two approaches, demonstrating upper bounds for the accuracy of the GSAS-II profile model for a particular instrumental configuration.

In a detailed powder diffraction study of the structural forms of psilocybin, Sherwood et al. [Acta Cryst. C78, 36–55] cast doubt that any other anhydrous polymorphs could exist.

A recent article by Von Dreele, Clarke & Walsh [J. Appl. Cryst. (2021), 54, https://doi.org/10.1107/S1600576720014624] introduces an entirely new paradigm in structure determination, where a complete structural measurement is made in a tenth of a nanosecond.

Titanium dioxide is an inexpensive wide-gap highly ionic semiconductor with striking photocatalytic capabilities in several heterogeneous photoredox reactions. A small crystal size is desirable to maximize the surface area, since photocatalytic reactions occur at the surface of a photocatalyst. Presented here are the synthesis and microstructural characterization of 4 at.% Sc-doped TiO₂(4SDT) prepared by water-based co-precipitation. The crystal structure of 4SDT was examined viain situhigh-temperature powder X-ray diffraction experiments from 25 to 1200°C. Rietveld analysis revealed single-phase anatase up to 875°C, while at 900°C the anatase-to-rutile phase transformation occurred and at higher temperatures additional reflections of Sc-rich phases (Sc₂TiO₅from 975°C and Ti₃Sc₄O₁₂or Sc₂O₃at 1200°C) were observed. Debye function analysis (DFA) was applied to model the total scattering pattern directly in reciprocal space, allowing the reconstruction of Ti vacancies. Both Rietveld and DFA methods were applied to estimate the nanocrystallite size and shape with consistent growth in crystallite size with temperature: an ellipsoid shape with equatorial ∼4.7 nm / axial (001) ∼6.9 nm at 25°C to equatorial ∼27.9 nm / axial (001) ∼39.6 nm at 900°C refined by Rietveld analysis,versusa cylinder shape withD_a,b= 4.3 nm and size dispersion σ_ab= 1.5 nm,L_c= 4.9 nm and σ_c= 2.3 nm at 25°C toD_a,b= 21.4 nm, σ_ab= 8.3 nm,L_c= 23.9 and σ_c= 10.9 nm at 900°C estimated by DFA. The microstructural changes obtained by Rietveld and DFA methods were supported by high-resolution transmission electron microscopy image analysis, as well as by the less direct nitrogen sorption techniques that provide information on the size of non-agglomerated and dense particles. The Ti site-occupancy factor showed a linear increase from 0.6–0.8 at 25°C to unity at 900°C for anatase, and from ∼0.7 at 900°C to unity at 1200°C for rutile, via Rietveld analysis and DFA.

Calibration of area detectors from powder diffraction standards is widely used at synchrotron beamlines. From a single diffraction image, it is not possible to determine both the sample-to-detector distance and the wavelength, but, with images taken from multiple positions along the beam direction and where the relative displacement is known, the sample-to-detector distance and wavelength can both be determined with good precision. An example calibration using the GSAS-II software package is presented.

The General Structure Analysis System (GSAS-II) package provides materials and crystallographic analysis for all types of diffraction data. It was initially made available with very limited capabilities, but over much of the last decade the features have been expanded, so that GSAS-II is now a comprehensive tool for nearly all types of structural and materials characterization studies. The need to provide materials to teach use of GSAS-II, while the software has been undergoing constant revision and expansion, has required new approaches for documentation. This has included providing tutorials, as each major new capability has been added, and context-sensitive help for each section of the program. Comments in the code are also expanded into a software reference guide. Most recently, video versions of more than half of the tutorials were created and others were provided with animated graphics. All GSAS-II documentation is web-based.