Rodrigues parameterization for orientation and misorientation distributions

Morawiec, Adam; Field, David P.

doi:10.1080/01418619608243708

Cited by 72 publications

(65 citation statements)

References 15 publications

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“…grids solve the covering problem in R 3 , b.c.c. grids are constructed in Rodrigues-Frank (RF) space (Frank, 1988;Morawiec & Field, 1996) in order to generate good coverings in SOð3Þ. Table 1 summarizes the properties of the different methods of generating orientation sets.…”

Section: Previous Workmentioning

confidence: 99%

Improved orientation sampling for indexing diffraction patterns of polycrystalline materials

Larsen¹,

Schmidt²

2017

J Appl Cryst

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Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as pattern indexing. A recent development in pattern indexing is the use of a bruteforce approach, whereby diffraction patterns are simulated for a large number of crystalline orientations and compared against the experimentally observed diffraction pattern in order to determine the most likely orientation. Whilst this method can robustly identify orientations in the presence of noise, it has very high computational requirements. In this article, the computational burden is reduced by developing a method for nearly optimal sampling of orientations. By using the quaternion representation of orientations, it is shown that the optimal sampling problem is equivalent to that of optimally distributing points on a fourdimensional sphere. In doing so, the number of orientation samples needed to achieve a desired indexing accuracy is significantly reduced. Orientation sets at a range of sizes are generated in this way for all Laue groups and are made available online for easy use.

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Section: Previous Workmentioning

confidence: 99%

Improved orientation sampling for indexing diffraction patterns of polycrystalline materials

Larsen¹,

Schmidt²

2017

J Appl Cryst

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“…Rodrigues vectors are an axis/angle representation of orientations, the direction of the vector is parallel to the rotation axis and the length is proportional to the rotation angle around the axis (e.g. Morawiec and Field [36]). Rodrigues representation is chosen since the crystal symmetry is easily represented by the fundamental zone consisting of a hexagonal prism for the trigonal symmetry of quartz.…”

Section: Track Particle Orientationmentioning

confidence: 99%

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

et al. 2013

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The three-dimensional x-ray diffraction (3DXRD) nondestructive technique was used to measure lattice strains within individual sand particles subjected to compressive loading. Three experiments were conducted on similar single columns of silica sand particles with particle sizes between 0.595 mm and 0.841 mm. In each experiment, three sand particles were placed inside an acrylic mold with an inner diameter of 1 mm. Multiple in situ 3DXRD scans were acquired for each sand column as compressive load was increased. The volume-averaged lattice strain tensor was calculated for each sand particle. In addition, particle orientation and volumetric strain were calculated for individual sand particles. The axial normal strain  zz exhibited a linear response in the range of 0 to 10 -3 when the applied compressive axial load (F) increased from 0 to ~30 N when one particle in the sand column fractured. Stress tensor of individual particles was calculated from the acquired lattice strain measurements and elastic constants of silica sand that were reported in the literature. To the best of our knowledge, there have been no reported experimental measurements of the lattice strain tensor measurements within individual silica sand particles. The quantitative measurements reported in this paper at the particle level are very valuable for developing, validating or calibrating micromechanics-based finite element and discrete element models to predict the constitutive behavior of granular materials. 3DXRDrepresents an exciting new non-destructive technique to directly measure constitutive behavior at the scale of individual particles.

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“…The parallelism between the two spaces is even more obvious if we think that for a fixed position in orientation-space, a point (ω, u, v) on the detector defines a projection line in real-space, and for a fixed point in real-space, a position (ω, θ, η) on the detector defines a line in orientation-space [11,12]. This means that the maximum resolution on the detector for (ω, θ, η) will define the maximum resolution in orientation-space.…”

Section: Orientation-space Resolutionmentioning

confidence: 99%

An Orientation-space Super Sampling Technique for Six-dimensional Diffraction Contrast Tomography

Viganò

Batenburg

Ludwig

2016

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Abstract. Diffraction contrast tomography (DCT) is an X-ray full-field imaging technique that allows for the non-destructive three-dimensional investigation of polycrystalline materials and the determination of the physical and morphological properties of their crystallographic domains, called grains. This task is considered more and more challenging with the increasing intra-granular deformation, also known as orientation-spread. The recent introduction of a sixdimensional reconstruction framework in DCT (6D-DCT) has proven to be able to address the intra-granular crystal orientation for moderately deformed materials. The approach used in 6D-DCT, which is an extended sampling of the six-dimensional combined position-orientation space, has a linear scaling between the number of sampled orientations, which determine the orientation-space resolution of the problem, and computer memory usage. As a result, the reconstruction of more deformed materials is limited by their high resource requirements from a memory and computational point of view, which can easily become too demanding for the currently available computer technologies. In this article we propose a super-sampling method for the orientation-space representation of the six-dimensional DCT framework that enables the reconstruction of more deformed cases by reducing the impact on system memory, at the expense of longer reconstruction times. The use of super-sampling can further improve the quality and accuracy of the reconstructions, especially in cases where memory restrictions force us to adapt to inadequate (undersampled) orientation-space sampling.

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Rodrigues parameterization for orientation and misorientation distributions

Cited by 72 publications

References 15 publications

Improved orientation sampling for indexing diffraction patterns of polycrystalline materials

Improved orientation sampling for indexing diffraction patterns of polycrystalline materials

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

An Orientation-space Super Sampling Technique for Six-dimensional Diffraction Contrast Tomography

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