Indexing of diffraction patterns for determination of crystal orientations

Scanning precession electron diffraction data analysis approaches for phase mapping of precipitates in aluminium alloys

Mapping the spatial distribution of crystal phases with nm-scale spatial resolution is an important characterisation task in studies of multi-phase materials. One popular approach is to use scanning precession electron diffraction which enables semi-automatic phase mapping at the nanoscale by collecting a single precession electron diffraction pattern at every probe position over regions spanning up to a few micrometers. For a successful phase mapping each diffraction pattern must be correctly identified. In this work four different approaches for phase mapping of embedded precipitates in an Al-Cu-Li alloy are compared on a sample containing three distinct crystal phases. These approaches are based on: non-negative matrix factorisation, vector matching, template matching and artificial neural networks. To evaluate the success of each approach a ground truth phase map was manually created from virtual images based on characteristic phase morphologies and compared with the deduced phase maps. The percentage accuracy of all methods when compared to the ground truth was satisfactory, with all approaches obtaining scores above 98%. The optimal method depends on the specific task at hand. Non-negative matrix factorisation is suitable with limited prior data knowledge but performs best with few unique diffraction patterns and requires substantial post-processing. It has the advantage of reducing the dimensionality of the dataset and handles weak diffracted intensities well given that they occur repeatedly. The current vector matching implementation is fast, simple, based only on the Bragg spot geometry and requires few parameters. It does however demand that each Bragg spot is accurately detected in each pattern and the current implementation is limited to zone axis patterns. Template matching handles a large range of orientations, including off-axis patterns. However, achieving successful and reliable results often require thorough data pre-processing and do require adequate diffraction simulations. For artificial neural networks a substantial setup effort is demanded but once trained it excels for routine tasks, offering fast predictions. The implemented codes and the data used are available open-source. These resources and the detailed assessment of the methods will allow others to make informed decisions when selecting a data analysis approach for 4D-STEM phase mapping tasks on other material systems.

Upgraded LauePt4 for rapid recognition and fitting of Laue patterns from crystals with unknown orientations

The LauePt program is a popular and easy-to-use crystallography tool for indexing and simulating X-ray Laue patterns, but its previous versions lack search functions for recognizing Laue patterns taken from crystals with unknown orientations. To overcome this obstacle, a major upgrade of the program, called LauePt4, is presented with three robust search schemes implemented: (i) crystal rotation along a single diffraction vector, (ii) a look-up method to search for reflection pairs matching the interplanar angle of two selected diffraction spots, and (iii) a more efficient look-up scheme to search for reflection triplets matching three interplanar angles. Extensive tests show that all these schemes, together with the convenient graphical user interfaces and highly optimized computing algorithms, are reliable and powerful for recognizing and fitting Laue patterns of any crystal taken under any diffraction geometry.

Indexing of superimposed Laue diffraction patterns using a dictionary-branch-bound approach

X-ray Laue diffraction is an important method for characterizing the local crystallographic orientation and elastic strain in polycrystalline materials. Existing analysis methods are designed mainly to index a single or a few Laue diffraction pattern(s) recorded in a detector image. In this work, a novel method called dictionary-branch-bound (DBB) is presented to determine the crystallographic orientations of multiple crystals simultaneously illuminated by a parallel X-ray incident beam, using only the spot positions in a detector image. DBB is validated for simulated X-ray Laue diffraction data. In the simulation, up to 100 crystals with random crystallographic orientations are simultaneously illuminated. Fake spots are randomly added to the detector image to test the robustness of DBB. Additionally, spots are randomly removed to test the resilience of DBB against true spots that are undetected due to background noise and/or spot overlap. Poisson noise is also added to test the sensitivity of DBB to less accurate positions of detected spots. In all cases except the most challenging one, a perfect indexing with a mean angular error below 0.08° is obtained. To demonstrate the potential of DBB further, it is applied to synchrotron microdiffraction data. Finally, guidelines for using DBB in experimental data are provided.