Bayesian estimation to identify crystalline phase structures for X-ray diffraction pattern analysis

ABSTRACT

Crystalline phase structure is essential for understanding the performance and properties of a material. Therefore, this study identified and quantified the crystalline phase structure of a sample based on the diffraction pattern observed when the crystalline sample was irradiated with electromagnetic waves such as X-rays. Conventional analysis necessitates experienced and knowledgeable researchers to shorten the list from many candidate crystalline phase structures. However, the Conventional diffraction pattern analysis is highly analyst-dependent and not objective. Additionally, there is no established method for discussing the confidence intervals of the analysis results. Thus, this study aimed to establish a method for automatically inferring crystalline phase structures from diffraction patterns using Bayesian inference. Our method successfully identified true crystalline phase structures with a high probability from 50 candidate crystalline phase structures. Further, the mixing ratios of selected crystalline phase structures were estimated with a high degree of accuracy. This study provided reasonable results for well-crystallized samples that clearly identified the crystalline phase structures.

GRAPHICAL ABSTRACT

IMPACT STATEMENT

We developed a method to automatically estimate crystalline phase structures from diffraction patterns using Bayesian inference. Our method successfully identified true crystalline phase structures with a high probability from 50 candidate crystalline phase structures.

KEYWORDS:

• X-ray diffraction
• Bayesian inference
• model selection
• automatic spectral analysis
• replica exchange Monte Carlo method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by MEXT/JSPS KAKENHI Grant Numbers [18K05191, and 19K12154].