Orientations and rotations: computations in crystallographic textures
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Engineering online library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 200 S. graph. Darst. |
| ISBN: | 3540407340 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804130227035570176 |
|---|---|
| adam_text | Titel: Orientations and rotations
Autor: Morawiec, Adam
Jahr: 2004
Contents
1 Preliminaries ............................................. 1
1.1 Rotations as Displacements .............................. 1
1.2 Composition of Rotations ................................ 5
1.3 Improper Rotations ..................................... 7
1.4 Matrix Representation................................... 8
1.5 Formal Approach to Orthogonal Transformations............ 10
2 Parameterizations......................................... 19
2.1 Half-turns ............................................. 19
2.2 Cayley Transformation and Rodrigues Parameters .......... 20
2.3 Axis and Angle Parameters .............................. 23
2.4 Euler Angles ........................................... 27
2.5 Cayley-Klein Parameters ................................ 30
2.6 Quaternions............................................ 35
2.7 Rotation Vector ........................................ 41
2.8 Rotation Matrix in Non-Cartesian Coordinate Systems ...... 44
2.9 Miller Indices .......................................... 46
2.10 Computational Properties of Parameterizations ............. 49
3 Geometry of the Rotation Space .......................... 51
3.1 SO(3) as a Riemannian Manifold ......................... 52
3.2 Exponential Mapping ................................... 61
3.3 SO(3) as a Lie Group ................................... 64
3.4 Integration on SO(3) .................................... 70
4 More on Small Orientation Changes ...................... 73
4.1 Vector of Infinitesimal Rotation........................... 73
4.2 Rotation Rate Field and Continuity Equation .............. 76
4.3 Short Excursion into Mechanics.......................... 77
5 Some Statistical Issues .................................... 81
5.1 Mean Orientation ....................................... 81
5.2 Distributions on the Rotation Manifold .................... 86
5.3 Generation of Orientations ............................... 90
X Contents
5.4 Comparing Smooth Orientation Functions ................. 92
6 Symmetry ................................................ 93
6.1 Finite Point Groups..................................... 93
6.2 Crystallographic Point Groups............................ 95
6.3 Asymmetric Domains ................................... 97
6.4 Asymmetric Domains in Rodrigues Space ..................104
7 Misorientation Angle and Axis Distributions ..............115
7.1 Misorientation Angle Distributions ........................116
7.2 Distributions of Rotation Axes ...........................124
8 Crystalline Interfaces and Symmetry......................129
8.1 Symmetrically Equivalent Boundaries .....................129
8.2 Boundary Distributions..................................131
9 Crystallographic Textures .................................135
9.1 Texture Components in Cubic-Orthorhombic Case ..........136
9.2 Rational Orientation Relationships ........................138
9.3 Coincident Sublattices...................................142
10 Diffraction Geometry .....................................151
10.1 Elementary Relations ...................................152
10.2 Orientations of Individual Crystallites .....................152
10.3 Orientation Distributions from Pole Figures ................159
11 Effective Elastic Properties of Polycrystals ................165
11.1 Definitions and Simplest Principles........................165
11.2 Perturbation Methods ...................................173
11.3 Related Issues ..........................................187
References.....................................................189
Index..........................................................197
|
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| discipline | Chemie / Pharmazie Physik |
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| id | DE-604.BV017410890 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:17:40Z |
| institution | BVB |
| isbn | 3540407340 |
| language | English |
| lccn | 2003061087 |
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| publisher | Springer |
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| spelling | Morawiec, Adam Verfasser aut Orientations and rotations computations in crystallographic textures Adam Morawiec Berlin [u.a.] Springer 2004 X, 200 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering online library Crystals Materials science Texture (Crystallography) Texturanalyse (DE-588)4184965-6 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Kristallorientierung (DE-588)4623755-0 gnd rswk-swf Rotation (DE-588)4178485-6 gnd rswk-swf Kristallorientierung (DE-588)4623755-0 s DE-604 Rotation (DE-588)4178485-6 s Texturanalyse (DE-588)4184965-6 s Numerisches Verfahren (DE-588)4128130-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010490299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morawiec, Adam Orientations and rotations computations in crystallographic textures Crystals Materials science Texture (Crystallography) Texturanalyse (DE-588)4184965-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Kristallorientierung (DE-588)4623755-0 gnd Rotation (DE-588)4178485-6 gnd |
| subject_GND | (DE-588)4184965-6 (DE-588)4128130-5 (DE-588)4623755-0 (DE-588)4178485-6 |
| title | Orientations and rotations computations in crystallographic textures |
| title_auth | Orientations and rotations computations in crystallographic textures |
| title_exact_search | Orientations and rotations computations in crystallographic textures |
| title_full | Orientations and rotations computations in crystallographic textures Adam Morawiec |
| title_fullStr | Orientations and rotations computations in crystallographic textures Adam Morawiec |
| title_full_unstemmed | Orientations and rotations computations in crystallographic textures Adam Morawiec |
| title_short | Orientations and rotations |
| title_sort | orientations and rotations computations in crystallographic textures |
| title_sub | computations in crystallographic textures |
| topic | Crystals Materials science Texture (Crystallography) Texturanalyse (DE-588)4184965-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Kristallorientierung (DE-588)4623755-0 gnd Rotation (DE-588)4178485-6 gnd |
| topic_facet | Crystals Materials science Texture (Crystallography) Texturanalyse Numerisches Verfahren Kristallorientierung Rotation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010490299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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