Avoiding broadened and negative peaks in non-negative matrix factorization: Thermal expansion and background corrections for in-situ diffraction data

Here it is demonstrated with both simulated and experimental in situ X-ray diffraction data that a “correction” of the peak shift due to thermal expansion and an unmodeled, global background subtraction improve the results of non-negative matrix factorization (NMF). NMF is one of a group of matrix decomposition algorithms which has seen increasing use in the automatization of the processing and interpretation of large sets of experimental data. This is due mostly to its non-negativity constraint, which causes it to have a higher likelihood of returning physically meaningful information compared to other decomposition algorithms. The nature of in situ diffraction experiments does not lend itself perfectly to the use of NMF though, as any changes in the constituent phases of the experiment that result in horizontal peak shift – that is, almost any change that would be induced in an in situ experiment – is poorly handled by NMF, hence the motivation for removing thermal peak shift prior to calling NMF. Performing both added steps – thermal correction and unmodeled background subtraction – are computationally inexpensive, completely automatic, and totally general – they can be applied to any set of in situ data. These measures are particularly relevant for high-energy synchrotron data, where the thermal peak shift relative to the peak widths is large – an especially challenging but very common use case for NMF. In all examples studied here it is found that thermal correction and background subtraction aid the NMF algorithm in returning phase components that better represent the underlying data quality and in affording superior phase fraction evolution information. In particular, without temperature correction, NMF returns phase components that have wider peaks than those of the raw data. This is especially egregious for high resolution data, where, as is demonstrated with a simulated experiment, NMF peaks can be up to 75 times wider than the original data.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Materials Science & Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Coppedge, Michael

Contributors dc:contributor

• Shoemaker, Daniel P

• X-ray Diffraction
• Non-negative Matrix Factorization
• Machine Learning
• Temperature Correction

Statement dc:rights

• Copyright 2022 Michael Coppedge

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120324

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120324