X-rayed perovskites: Probably

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  • Published: Nov 1, 2017
  • Author: David Bradley
  • Channels: X-ray Spectrometry
thumbnail image: X-rayed perovskites: Probably

Statistical assistance

Schematic of perovskite oxide interface (credit: Osaka University)

Researchers in Japan have used Bayesian statistical analysis to help them work out the structure of a perovskite surface from its X-ray data.

Perovskites have become the focus of intense research in recent years. They are a class of mineral with huge potential in solar energy conversion and other areas. They have well-ordered structures and show many interesting properties that could be useful in other areas of electronics. When compared to their crystalline, silicon-based counterparts, these materials offer several advantages including, flexibility, low cost, and ease of manufacture. The wide variety of characteristics present in perovskites with the same structural backbone but different functionality means they can be fine-tuned for specific applications without interfering with their general crystal lattice. The examination of their structures at the interface between such concatenated perovskites will be vital for their development if they are to augment and perhaps ultimately usurp conventional semiconductor materials. Unfortunately, at the moment, current techniques do not have sufficiently high resolution to probe such materials in detail and the data obtained from X-ray crystallographic studies is difficult to analyze.


Now, a team at Osaka University, Japan, has used an extension of the probabilistic statistics devised by eighteenth century statistician and philosopher Thomas Bayes to help them to model perovskite oxide interfaces with great precision and accuracy. The computerized application of Bayesian statistics to X-ray data allows them to pick out the correct structure from a range of possibilities. The team reports details in the Journal of Applied Crystallography.

“Using typical scanning transmission electron microscopy on perovskite oxides requires samples to be cut, which can damage the surface and affect the resolution,” explains team member and lead author Masato Anada. Surface X-ray diffraction approaches, on the other hand, avoid these effects. "But, analyzing the data is complex, so few people are using this method," he adds. The approach taken by the Osaka team, is a Monte Carlo-based refinement method that provides a rapid resolution of the search by hunting down the most probable structure from the X-ray data. "It is versatile enough to be applied to more variable interfaces," Anada adds.

Perovskites are no gamble

Monte Carlo methods allow the team to predict how the structure of an interface will most likely appear. By tweaking model with small increments in a random manner but under certain restrictions it is possible to reveal many possible structures through simulation and to home in on the most likely, the most realistic, in other words. The team applied this approach to the interface between perovskites and compared simulated X-ray data with experimental data to rapidly identify the most likely perovskite structures.

"Features of perovskite interfaces are ideal for testing out certain theories in condensed matter physics and for making new types of electronic materials system,” team member Yusuke Wakabayashi explains. “Our approach makes analyzing the complex structural data of these interfaces much easier, and it’s also robust for uneven interfacial structures. This approach should be useful for anyone currently investigating these structures.” In this particular case, the team demonstrated proof of principle with a five-unit-cell-thick lanthanum aluminate film fabricated on top of a strontium titanate substrate. "The software successfully found the global optima from an initial model prepared by a small grid search calculation. The standard deviations of the atomic positions derived from a dataset taken at a second-generation synchrotron are ±0.02 Å for metal sites and ±0.03 Å for oxygen sites," the team reports.

The team describes the advantages of their Monte Carlo approach as follows. First, "It is applicable to multi-domain structures. Secondly, "It provides the posterior probability of structures through Bayes' theorem, which allows one to evaluate the uncertainty of estimated structural parameters. And, finally, "One can involve any information provided by other experiments and theories."

Related Links

J Appl Crystallogr 2017, 50, online: "Bayesian inference of metal oxide ultrathin film structure based on crystal truncation rod measurements"

Article by David Bradley

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

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