A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. II. Volume, centre-of-mass position, crystallographic orientation and strain state of grains

Abstract

This second part of the paper on an analysis strategy for data acquired using three-dimensional X-ray diffraction (3DXRD) describes the procedure for the determination of the grain characteristics for thousands of grains. The approach developed here is orders of magnitude faster than those presently available for indexing thousands of grains. Using information obtained from the steps described in Part I [Sharma, Huizenga & Offerman (2012).J. Appl. Cryst.45, 693–704], the volume, crystallographic orientation, centre-of-mass position and strain state of grains in the sample can be determined. The algorithms dealing with the determination of the orientation, centre-of-mass position and strain state of the grains are divided into two parts. The first deals with indexing,i.e.it assigns diffraction spots to individual grains assuming an unstrained lattice, and the second deals with the refinement of the crystallographic orientation, centre-of-mass position and strain state of the grains using the diffraction spots assigned during indexing. The different approaches to indexing that exist in the literature are presented and compared with the novel approach developed here. Indexing can be run in two modes depending on the number of grains. For large numbers of grains, the approach employs a novel sample `surface' scanning technique, in combination with a reduced number of search orientations, to achieve high robustness and computation efficiency. For small numbers of grains, the approach neglects the position of the diffracting grains in the sample in order to improve the computation efficiency. For unstrained samples, both modes of indexing and the subsequent process of refinement are validated using simulated data for 60 and 3000 grains. In both cases, the centre-of-mass position of the grains was determined with a mean error of 0.7 µm and the orientation was determined with a mean error of 0.0003°. Furthermore, an experiment was `mimicked' by introducing experimental errors into the simulation for 3000 grains. The resulting mean errors in the centre-of-mass position (2.1 µm) and orientation (0.008°) of the grains are higher than those for the ideal simulations, and the errors in an experiment will depend on the `true' experimental errors. The algorithms dealing with strained samples are validated using a simulation for 3000 grains with mimicked experimental errors. The centre-of-mass position, crystallographic orientation, normal strain tensor components and shear strain tensor components of the grains were determined with mean errors of 8 µm, 0.006°, 5.2 × 10−5and 2.8 × 10−5, respectively. The possibility of obtaining grain-level information for thousands of grains with a high speed of acquisition makes the technique very attractive forin situstudies of thermomechanical processes in polycrystalline materials.