Multigrain indexing of unknown multiphase materials

Abstract

A multigrain indexing algorithm for use with samples comprising an arbitrary number of known or unknown phases is presented. No a priori crystallographic knowledge is required. The algorithm applies to data acquired with a monochromatic beam and a conventional two-dimensional detector for diffraction. Initially, candidate grains are found by searching for crystallographic planes, using a Dirac comb convoluted with a box function as a filter. Next, candidate grains are validated and the unit cell is optimized. The algorithm is validated by simulations. Simulations of 500 cementite grains and $100 reflections per grain resulted in 99.2% of all grains being indexed correctly and 99.5% of the reflections becoming associated with the right grain. Simulations with 200 grains associated with four mineral phases and 50-700 reflections per grain resulted in 99.9% of all grains being indexed correctly and 99.9% of the reflections becoming associated with the right grain. The main limitation is in terms of overlap of diffraction spots and computing time. Potential areas of use include three-dimensional grain mapping, structural solution and refinement studies of complex samples, and studies of dilute phases.

Domain Auto Finder (DAFi) program: the analysis of single-crystal X-ray diffraction data from polycrystalline samples

“…To our knowledge, there have only been a few proposals for dealing with unknown phases, based on a fast Fourier transform approach (Sørensen et al, 2012) or on pattern recognition (Sørensen et al, 2012), or involving a search of reflections and subsequent unit-cell optimization in 3D space (Wejdemann & Poulsen, 2016). Testing of these programs was performed on data sets artificially created by randomly rotating 'grains' with exactly defined unit-cell parameters, and there is no information on how well these programs would work with real data sets where one may need to consider statistical and instrumental errors in the positions of reflections in the reciprocal space, or deal with 'junk' reflections characteristic of the XRD data sets originating from highpressure experiments in DACs.…”

“…Another important problem is the long program running time; e.g. according to Wejdemann & Poulsen (2016), indexing of 500 cementite grains takes 5 days.…”

Non-destructive determination of phase, size, and strain of individual grains in polycrystalline photovoltaic materials

“…However, the application of standard 3DXRD software to thin-film solar cells is hampered by the complication of phase identification. In principle, a standard single crystal crystallographic analysis can be applied to each grain, a method known as multigrain crystallography [29], [36].…”

“…However, brute force procedures are too slow to be operational. A general-purpose method involving searching only in 3D has been suggested [36], but this algorithm still lacks a sufficiently robust software implementation. In this work, phase identification from a database search could provide sufficiently accurate for the unit cell parameters of the phases in the sample.…”

DATAD: a Python-based X-ray diffraction simulation code for arbitrary texture and arbitrary deformation

“…However, actual polycrystalline specimens can be nonideal in different ways (Krivoglaz, 2012): the crystallites in a specimen may have preferred orientations (texture) (Bunge & Morris, 1982;Wenk, 2016); they may be under nonhydrostatic strain (Birch, 1947); and there may be only a very limited number of grains sampled by X-rays (Pakala et al, 2000). Texture induces nonuniform or segmented intensity distribution on a Debye-Scherrer ring (Bunge, 1970), a small number of grains also renders incomplete diffraction rings (Sørensen et al, 2012;Wejdemann & Poulsen, 2016), and nonhydrostatic strain distorts the shape of diffraction rings (Singh, 1993;Higginbotham & McGonegle, 2014).…”