Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals

Heinz, A.; Neumann, Peter M.

doi:10.1107/s0108767391006864

Cited by 125 publications

(82 citation statements)

References 4 publications

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“…Once the grain positions and orientations have been identified, the locations of all other diffraction spots belonging to each grain can be predicted and, hence, other unpaired, diffraction spots added to the sets. As previously, 3 the orientation of each grain is inferred from the point in the fundamental zone of Rodriguez space, 5 where all projection lines for pole figure inversion of the corresponding grain cross ͑each of the observed scattering vectors defines one of these projection lines in Rodriguez's space͒.…”

Section: Indexing From Friedel Pairsmentioning

confidence: 99%

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

Ludwig

Reischig²,

King³

et al. 2009

Review of Scientific Instruments

233

157

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X-ray diffraction contrast tomography ͑DCT͒ is a technique for mapping grain shape and orientation in plastically undeformed polycrystals. In this paper, we describe a modified DCT data acquisition strategy which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data. Diffraction spots are acquired during a 360°rotation of the sample and are analyzed in terms of the Friedel pairs ͑͑hkl͒ and ͑hkl͒ reflections, observed 180°apart in rotation͒. The resulting increase in the accuracy with which the diffraction vectors are determined allows the use of improved algorithms for grain indexing ͑assigning diffraction spots to the grains from which they arise͒ and reconstruction. The accuracy of the resulting grain maps is quantified with reference to synchrotron microtomography data for a specimen made from a beta titanium system in which a second phase can be precipitated at grain boundaries, thereby revealing the grain shapes. The simple changes introduced to the DCT methodology are equally applicable to other variants of grain mapping.

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Section: Indexing From Friedel Pairsmentioning

confidence: 99%

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

Ludwig

Reischig²,

King³

et al. 2009

Review of Scientific Instruments

233

157

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“…(Hamilton, 1844;Tait, 1890;du Val, 1964;Altmann, 1966, Conway, Smith, 1992etc.). The application of quaternions to the description of reorientations of a cubic lattice and the associated equivalence classes of rotations was introduced by Grimmer (1974a) and extended to other lattice types by Grimmer (1980) and Heinz and Neumann (1991).…”

Section: Quaternion Methodsmentioning

confidence: 99%

“…This 'reduced' equivalence class may contain as many as 2g 2 rotations, where g is the order of the group of rotational symmetries of L. An important problem is the selection of a unique rotation as a definitive representative of its equivalence class. The convention usually adopted is to select the rotation with the smallest rotation angle q and with axis n corresponding to a point in a chosen fundamental region of the stereogram associated with the point symmetry group of L (Grimmer, 1980;Heinz, Neumann, 1991). Clarification of this latter concept is provided by Fig.…”

Section: Equivalence Classes Of Rotationsmentioning

confidence: 99%

“…Zeiner (2005) has developed a quaternion approach to the problem of identifying the Bravais classes to which CSLs arising from cubic lattices belong and has presented the the results, up to S ¼ 59, and in a recent paper has dealt with the CSLs of four-dimensional hypercubic lattices (Zeiner 2006). The quaternion approach can be applied also in the case of non-cubic lattices (Grimmer, 1980;Heinz, Neumann, 1991). The rhombohedral case exhibits some special features (Grimmer, 1989 a, b).…”

Section: Introductionmentioning

confidence: 99%

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Coincidence sites for rational lattices

Lord¹

2006

Zeitschrift Für Kristallographie - Crystalline Materials

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Abstract. The problem of identifying the coincidence site lattices produced by the disorientations of any rational lattice is investigated. A very simple new procedure for computing the CSLs is presented, based on Grimmer's reciprocity theorem and application of the reduction algorithm introduced by Buerger for finding reduced cells. The point symmetries of a lattice imply that any orientation relationship that produces a CSL can be alternatively expressed by a variety of different rotations. Two simple numerical methods (one based on integral matrix operations and one based on quaternions) are demonstrated for finding all the equivalent rotations that produce the same CSL and for obtaining a single 'canonical' rotation as a representative of an equivalence class.

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“…The lattice strain pole figures for a diffraction volume contain sufficient data to determine a strain orientation distribution function for that volume. Here, we define that distribution over the fundamental region of Rodrigues space using finite element (FE) interpolation [16] [25]. From the strain distribution, a crystal stress distribution is readily computed using Hooke's law.…”

Section: Introductionmentioning

confidence: 99%

Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

et al. 2013

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Residual stress can play a significant role in the processing and performance of an engineered metallic component. The stress state within a polycrystalline part can vary significantly between its surface and its interior. To measure three-dimensional (3D) residual stress fields, a synchrotron x-ray diffraction-based experimental technique capable of non-destructively measuring a set of lattice strain pole figures (SPFs) at various surface and internal points within a component was developed. The resulting SPFs were used as input for a recently developed bi-scale optimization scheme [31] that combines crystal-scale measurements and continuum-scale constraints to determine the 3D residual stress field in the component. To demonstrate this methodology, the 3D residual stress distribution was evaluated for an interference-fit sample fabricated from a low solvus high refractory (LSHR) polycrystalline Ni-base superalloy.

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Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals

Cited by 125 publications

References 4 publications

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

Coincidence sites for rational lattices

Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

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