Feature extraction and spatial imaging of synchrotron radiation X-ray diffraction patterns using unsupervised machine learning

ABSTRACT

We analyzed a number of complicated X-ray diffraction patterns using feature patterns obtained through unsupervised machine learning. A crystalline SiGe film on a Si substrate with a spatial fluctuation in both composition and crystal orientation was tested as a model sample having complicated X-ray diffraction patterns with multipeaks. Non-negative matrix factorization (NMF), an unsupervised machine learning method, was performed on 961 patterns obtained by spatial mapping of micro-beam X-ray diffraction measurements. Among the tested number of the feature patterns from 1 to 10, four feature patterns were the most useful for extracting the information about the composition and crystal orientation because they correspond to the diffraction patterns of typical SiGe films with high and low Si fraction, and right- and left-tilted orientation. Reasonable spatial maps of composition and crystal orientation were visualized using coefficients of the four feature patterns. Furthermore, the spatial constraint was tested for NMF using 225 diffraction patterns which were down-sized from 33 × 33 to 16 × 16 pixels due to the high computational cost of simple implementation without techniques to reduce the cost. Four feature patterns similar to those of the simple NMF without the constraints and the more reasonable distribution reflecting the SiGe spatial domain structure were obtained. The feature pattern extraction by NMF and interpretation by experts demonstrated in this study will be useful for quick analysis of a number of X-ray diffraction patterns with large and complicated fluctuations.

IMPACT STATEMENT

We apply non-negative-matrix factorization to two-dimensional XRD pattern analysis.

We illustrate the spatial fluctuation of composition and orientation of SiGe film with a small computational cost.

KEYWORDS:

• X-ray diffraction pattern
• machine learning
• non-negative matrix factorization
• micro beam mapping
• synchrotron radiation

Acknowledgements

The authors acknowledge Mr. Fukami, Prof. Usami and Prof. Ujihara of Nagoya University and Mr. Nakahara and Dr. Marwan of Toyo Aluminium K.K. for their sample provision and fruitful discussions.

Disclosure statement

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

Author contributions

K.K. designed this project and performed the machine learning. S.T., S.F. and M.T. conducted the XRD measurements. I.T. and K.M. contributed to the theoretical discussion. K.K., T.K., T.S., S.T., S.F. and M.T. discussed the results of machine learning modeling. K.K. and K.M. wrote the paper. All the authors discussed the results and commented on the paper.

Data availability statement

The data and the code that support the findings of this study can be found at https://github.com/KentaroKutsukake/NMF-for-XRD.git.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/27660400.2024.2336402.

Additional information

Funding

The synchrotron radiation experiments were performed at the 11XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2016A3553, 2017A3553, 2017B3553, 2018A3553, 2018A3585, 2018B3553, 2018B3587, 2019A3587, 2019B3586, and 2020A3586). This study was supported by QST microstructural characterization platform as a program of “Nanotechnology Platform” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, and Center for Advanced Intelligence Project, RIKEN.