Multigrain indexing of unknown multiphase materials.

Current methods for indexing diffraction data often require prior knowledge of crystal structures. This limits their use in analyzing unknown or complex multiphase materials. Prior research has shown that indexing algorithms typically assume a known set of phases. That uncertainty drove the development of a new algorithm that works without any crystallographic input. No prior work had resolved the challenge of indexing unknown phases in arbitrary numbers. This gap motivated the design of a multigrain indexing algorithm. The algorithm must handle both known and unknown phases in a single sample. It must also manage overlapping diffraction patterns from multiple grains. This study aims to fill that gap by introducing a novel indexing approach.

The goal is to develop a multigrain indexing algorithm that works with unknown multiphase materials. The algorithm should not require any prior crystallographic information. It should be applicable to monochromatic beam and 2D detector data. The researchers propose to use a Dirac comb convoluted with a box function as a filter. This method allows for identifying crystallographic planes without known structures. The algorithm must validate candidate grains and optimize unit cells. Simulations are used to test the algorithm's accuracy and efficiency. The study aims to demonstrate the algorithm's potential in complex material analysis.

The algorithm begins by searching for crystallographic planes using a Dirac comb filter. This filter is convoluted with a box function to identify candidate grains. Once candidate grains are found, the algorithm validates them through unit cell optimization. Simulations are used to test the algorithm's performance on synthetic data. The simulations include 500 cementite grains with 100 reflections per grain. Another simulation includes 200 grains across four mineral phases with 50-700 reflections per grain. The algorithm's success rate is measured by indexing accuracy and reflection association. The main limitations are overlapping diffraction spots and computational time. These factors are evaluated to determine the algorithm's practicality.

The algorithm successfully indexed 99.2% of 500 cementite grains in simulations. It associated 99.5% of reflections with the correct grain in that test. In a second simulation with 200 grains across four mineral phases, 99.9% of grains were indexed correctly. Over 99.9% of reflections were matched to the right grain in that test. The algorithm's performance is robust even with high numbers of reflections per grain. The main limitation is the overlap of diffraction spots from multiple grains. Computing time increases with the number of reflections per grain. These results suggest the algorithm is highly accurate for complex samples.

The multigrain indexing algorithm achieves high accuracy in indexing unknown phases. It works without any prior crystallographic knowledge. The algorithm's success rate is over 99% in simulations with complex samples. The researchers propose that it is suitable for three-dimensional grain mapping. It may also be useful for structural solution studies of complex materials. The algorithm's performance is limited by spot overlap and computing time. These factors must be considered when applying the algorithm to real-world data. The authors suggest that the algorithm could improve the analysis of dilute phases in materials.