In the present study, we show that time-consuming manual tuning of parameters in the Rietveld method, one of the most frequently used crystal structure analysis methods in materials science, can be automated by considering the entire trial-and-error process as a blackbox optimisation problem. The automation is successfully achieved using Bayesian optimisation, which outperforms both a human expert and an expert-system type automation despite the absence of expertise. This approach stabilises the analysis quality by eliminating human-origin variance and bias, and can be applied to various analysis methods in other areas which also suffer from similar tiresome and unsystematic manual tuning of extrinsic parameters and human-origin variance and bias.
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The physical properties of materials are governed by their crystal structure; thus, crystal structure analysis is an indispensable element in materials science research1,2. Compared to the drastic improvement in material fabrication and measurement throughput, the throughput of crystal structure analysis has not been improved because the analysis heavily relies on manual time-consuming trial-and-error methods3,4,5,6,7,8. Rietveld refinement or the Rietveld method9,10, one of the most widely used crystal structure analysis methods for powder diffraction data, such as X-ray diffraction (XRD) and neutron diffraction, faces this problem as well.
Next, we discuss the interesting outlier at the upper left of Fig. 6. The outlier (Table 2) has good converged Rwp, but the x position of O1 atom in the refined structure is considerably different from others. The difference exceeds the uncertainty calculated by the software, and, from the structural point of view, the positional shift corresponding to 5% of the lattice parameter would be enough to affect physical properties. This implies that the outlier corresponds to a local minimum not belonging to the cluster discussed above. In such a situation, multiple crystal structure candidates can explain the experimental data sufficiently with a similar level, which may affect the conclusion of a study or evoke a new discussion. Despite that it meets the constraint in the optimisation (positive Uiso), the outlier can be rejected due to the violation of the conventional criterion for Uiso as well as the best result by BBO. We believe that imposing constraints other than universal physical requirements in BBO can result in biased optimisation of results toward human expectations. Experts can examine the list of candidates using conventional criteria and other knowledge, and can eliminate inappropriate solutions at any time. This ability to propose multiple candidates without human effort and bias is a great advantage of automation and may lead to the discovery of hitherto unnoticed new knowledge beyond the standard practices of conventional manual tuning and the expert system simulating the practices. The use of empirical constraints in a manual analysis by experts also has the purpose of bounding the search space to reach a valid solution as soon as possible. However, Rietveld refinement using BBO can evaluate a large number of parameter combinations and suggest candidate structures much more efficiently than manual approach, that is, the constraints imposed to save time are no longer essential. 2ff7e9595c
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