Highlights
- Basis profile decomposition uses matrix factorization to separate mixed powder X-ray diffraction patterns into estimated component profiles and their relative contributions.
- This approach is useful when pure reference profiles, crystal structure data, or database matches are unavailable, making conventional Rietveld analysis or standard DD method workflows difficult.
- Combining extracted basis profiles with the DD method enables quantitative analysis of mixtures without physically preparing every pure component.
- Method selection matters: amorphous regularization improves smooth amorphous profiles, semi-supervised minimization incorporates known background or reference information, and constrained alternating least squares handles components common to all samples.
- In the indomethacin examples, quantitative error improved from 10.3% RMSE with basic alternating least squares to 9.6% with amorphous regularization and 8.4% with semi-supervised minimization.
Summary
Powder X-ray diffraction is often used to identify and measure the different crystalline or amorphous materials in a mixed sample. A typical XRD pattern contains peaks from all components at once, so the challenge is separating overlapping signals and determining how much of each material is present.
Basis profile decomposition is a computational method that helps solve this problem. It takes multiple XRD profiles from related samples and looks for recurring “basis profiles,” which can be thought of as estimated patterns for the individual components. At the same time, it estimates how strongly each basis profile contributes to each measured pattern.
This is especially helpful when the pure substances are not available for measurement, when an intermediate phase cannot be isolated, or when crystal structure data are missing. In those cases, conventional phase identification or Rietveld analysis may not be practical.
Once the individual basis profiles are estimated, they can be used with the DD method to calculate approximate quantities of each component. The quality of the result depends on choosing the right decomposition method. A simple alternating least squares method is fast and useful for first-pass analysis, but more specialized methods can improve the result. For example, amorphous regularization is better when one or more amorphous materials are present because it encourages broad, smooth profiles. Semi-supervised minimization is useful when some known information, such as a background shape or reference profile, can be included. Constrained alternating least squares is useful when one component is present in the same amount in every measured sample.
Overall, basis profile decomposition expands what can be done with powder XRD data, particularly for mixtures where the usual reference-based methods are limited.
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