Top Rated Structure Of Materials De Graef Mchenry Solution Manual High Quality
Top Rated Structure Of Materials De Graef Mchenry Solution Manual
as shown in fig. 3, rietveld refinement was carried out for all 180 pairs of the 14 essential materials and 14 existing materials. here, the crystal structure of 60 of the 14 essential materials is fixed as that in cifs on the github repository of autofp. 47 the remaining 90 pairs were used for the benchmark data.
the initial crystal structure models were selected from a wide space of the crystallographic data sets. the search spaces for each parameter are shown in table 1. the parameter spaces can be automatically calculated based on the density of the crystallographic data sets using autofp api 47 .
for each refinement run, the optimiser iteratively evaluated 200 configurations including the initial 20 random configurations and returned the best one with the minimum rwp. we applied the optimiser 10 times for each of the 90 pairs of the benchmark data for comparative purposes. as shown in table 2, the optimised average and rwp values were 50.89 and 50.92 for y2o3 and 59.54 and 53.81 for dsmo.
when using the rietveld method for a powder diffraction analysis, especially for a single-crystal data set, one may intuitively hypothesize that the intensities obtained from both e – s and – s reflections should be equal to each other. this is because, if the crystal structure, including the space group and miller indices, is correct, the e – s and – s reflections have identical intensities.
in this study, we first show that refining a vast number of extrinsic parameters with rietveld refinement automatically using bayesian optimisation, rather than through trial and error, does not cause the rietveld analysis to deviate significantly from the manual procedure. next, we show that the rietveld analysis, which includes the broadening parameter (b), in the refinement process shown in fig. 3 also becomes stable even when a vast number of extrinsic parameters are refined with bayesian optimisation. we have recently introduced a novel algorithm for rietveld refinement 45 and have shown that it is broadly applicable. in this algorithm, it is not necessary to evaluate the entire search space of the refinement. our aim is to realise a method that automatically adjusts the scope of the refinement to guarantee the uniqueness of the refinement. for this aim, we introduced the parzen window estimation (pwe) method and provided its algorithm in the rietveld repository. 45 instead of evaluating the entire search space of the refinement, the pwe method considers a narrowed scope containing most of the information of the entire search space; in other words, the scope information is treated as a latent variable to be learned from the data. we expect that this approach will be useful for reducing human-origin variance and bias in any kind of trial-and-error experiments, and achieving automation of crystal structure analysis.
we developed a new approach, termed bbo-rietveld, where the trial-and-error phase of a manual rietveld refinement is automated by bayesian optimisation. the method is successful in adjusting the reference value of analysis quality for any materials to be analysed, completely eliminating human-origin variance and bias, and is expected to contribute to the increase of crystal structure analysis throughput and narrowing of materials science research gap.
to evaluate the proposed bbo-rietveld approach, we optimised parameter configurations of rietveld refinement for xrd patterns of y2o3, dy0.5sr0.5mno3 (dsmo) and licoo2 which are chosen as benchmark materials. the tree-structured parzen estimator (tpe) 17, 20 , one of the variants of bayesian optimisation, is used as the optimiser. the details of our optimisation system are provided in the methods section. here we discuss the results of y2o3 and dsmo. readers who are interested in the result of licoo2 should refer to the supplementary resources provided in the bbo-rietveld repository (see code availability). for each optimisation run, the optimiser iteratively evaluated 200 configurations including the initial 20 random configurations and returned the best one with the minimum rwp. the search spaces for each parameter are shown in table 1. the initial crystal structure models were taken from crystallographic information files (cifs) on the github repository of autofp 47 , presumably those used in ref. 43 . to evaluate statistical property and reproducibility, optimisations have been performed 100 times with different random seeds each for y2o3 and dsmo. histograms of 100 rwp values for both materials are shown in fig. 2. reference values for a human expert and autofp are also shown for comparison. the latter ones are taken from the previous study 43 .