Improved representations of misorientation information for grain boundary science and engineering

Progress in Materials Science

Volumn 57, Issue 8, 2012, Pages 1383-1425

  Patala, Srikanth ^a,b   Mason, Jeremy K ^a,c   Schuh, Christopher A ^a  

^a USA   (United States)

^b Northwestern University   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTION FUNCTIONS; POLYCRYSTALLINE MATERIALS;

BOUNDARY MISORIENTATIONS; BOUNDARY REPRESENTATIONS; GRAIN BOUNDARY ENGINEERING; GRAIN BOUNDARY MISORIENTATION; GRAIN BOUNDARY STATISTICS; GRAPHICAL REPRESENTATIONS; HYPERSPHERICAL HARMONICS; ORIENTATION DISTRIBUTIONS;

GRAIN BOUNDARIES;

EID: 84861702412     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pmatsci.2012.04.002     Document Type: Review

References (210)

1. P.J.E. Forsyth, R. King, G.J. Metcalfe, and B. Chalmers Grain boundaries in metals Nature 158 1946 875 876
2. R. Smoluchowski Theory of grain boundary diffusion Phys Rev 87 1952 482
3. C.W. Haynes, and R. Smoluchowski Grain boundary diffusion in a body-centered cubic lattice Acta Metall 3 1955 130 134
4. J. Hirth The influence of grain boundaries on mechanical properties Metall Mater Trans B 3 1972 3047 3067
5. O. Hunderi Influence of grain boundaries and lattice defects on the optical properties of some metals Phys Rev B 7 1973 3419
6. G.A. Chadwick, and D.A. Smith Grain boundary structure and properties 1976 Academic Press Inc.
7. H. Gleiter The interaction of point defects, dislocations and two-dimensional defects with grain boundaries Prog Mater Sci 1981 125 183 [Chalmers Anniversary Volume]
8. H. Gleiter On the structure of grain boundaries in metals Mater Sci Eng 52 1982 91 131
9. 7 bicrystals Phys Rev B 41 1990 4038
10. D. Wolf, and S. Yip Materials interfaces: atomic-level structure and properties 1992 Kluwer Academic Publishers
11. G. Gottstein, and L.S. Shvindlerman Grain boundary migration in metals: thermodynamics, kinetics, applications 1999 CRC Press
12. A.P. Sutton, and R.W. Balluffi Interfaces in crystalline materials (monographs on the physics and chemistry of materials) 2007 Oxford University Press USA
13. T. Watanabe An approach to grain boundary design for strong and ductile polycrystals Res Mech 11 1984 47 84
14. T. Watanabe The impact of grain boundary character distribution on fracture in polycrystals Mater Sci Eng: A 176 1994 39 49
15. G. Palumbo, E.M. Lehockey, and P. Lin Applications for grain boundary engineered materials JOM J Miner Metals Mater Soc 50 1998 40 43
16. T. Watanabe, and S. Tsurekawa Preface to the special issue on grain boundary engineering J Mater Sci 40 2005 817
17. T. Watanabe, S. Tsurekawa, X. Zhao, and L. Zuo The coming of grain boundary engineering in the 21st century Microstruct Text Steels 2009 43 82
18. 7 on biaxially textured nickel (0 0 1): an approach to superconducting tapes with high critical current density Science 274 1996 755
19. E.M. Lehockey, and G. Palumbo On the creep behaviour of grain boundary engineered nickel Mater Sci Eng A, Struct Mater: Prop Microstruct Process 237 1997 168 172
20. E.M. Lehockey, G. Palumbo, and P. Lin Improving the weldability and service performance of nickel-and iron-based superalloys by grain boundary engineering Metall Mater Trans A 29 1998 3069 3079
21. E.M. Lehockey, D. Limoges, G. Palumbo, J. Sklarchuk, K. Tomantschger, and A. Vincze On improving the corrosion and growth resistance of positive pb-acid battery grids by grain boundary engineering J Power Sour 78 1999 79 83
22. C. Cheung, U. Erb, and G. Palumbo Application of grain boundary engineering concepts to alleviate intergranular cracking in alloys 600 and 690 Mater Sci Eng: A 185 1994 39 43
23. A.J. Schwartz The potential engineering of grain boundaries through thermomechanical processing JOM J Miner Metals Mater Soc 50 1998 50 55
24. I. Weiss, and S.L. Semiatin Thermomechanical processing of alpha titanium alloys - An overview Mater Sci Eng A 263 1999 243 256
25. T. Watanabe, and S. Tsurekawa The control of brittleness and development of desirable mechanical properties in polycrystalline systems by grain boundary engineering Acta Mater 47 1999 4171 4185
26. R. Ding, Z.X. Guo, and A. Wilson Microstructural evolution of a Ti-6Al-4V alloy during thermomechanical processing Mater Sci Eng A 327 2002 233 245
27. T. Furuhara, and T. Maki Grain boundary engineering for superplasticity in steels J Mater Sci 40 2005 919 926
28. M. Furukawa, Z. Horita, and T.G. Langdon Processing by equal-channel angular pressing: applications to grain boundary engineering J Mater Sci 40 2005 909 917
29. M. Michiuchi, H. Kokawa, Z.J. Wang, Y.S. Sato, and K. Sakai Twin-induced grain boundary engineering for 316 austenitic stainless steel Acta Mater 54 2006 5179 5184
30. L. Tan, K. Sridharan, and T.R. Allen Effect of thermomechanical processing on grain boundary character distribution of a Ni-based superalloy J Nucl Mater 371 2007 171 175
31. Y. Zhang, G. Vincent, N. Dewobroto, L. Germain, X. Zhao, and L. Zuo The effects of thermal processing in a magnetic field on grain boundary characters of ferrite in a medium carbon steel J Mater Sci 40 2005 903 908
32. T. Watanabe, S. Tsurekawa, X. Zhao, and L. Zuo Grain boundary engineering by magnetic field application Scripta Mater 54 2006 969 975
33. T. Watanabe, S. Tsurekawa, X. Zhao, L. Zuo, and C. Esling A new challenge: grain boundary engineering for advanced materials by magnetic field application J Mater Sci 41 2006 7747 7759
34. W. Bollmann Crystal defects and crystalline interfaces 1970 Springer-Verlag Berlin
35. L. Lu, R. Schwaiger, Z.W. Shan, M. Dao, K. Lu, and S. Suresh Nano-sized twins induce high rate sensitivity of flow stress in pure copper Acta Mater 53 2005 2169 2179
36. M. Dao, L. Lu, Y.F. Shen, and S. Suresh Strength, strain-rate sensitivity and ductility of copper with nanoscale twins Acta Mater 54 2006 5421 5432
37. L. Lu, X. Chen, X. Huang, and K. Lu Revealing the maximum strength in nanotwinned copper Science 323 2009 607
38. K. Lu, L. Lu, and S. Suresh Strengthening materials by engineering coherent internal boundaries at the nanoscale Science 324 2009 349
39. A. Singh, L. Tang, M. Dao, L. Lu, and S. Suresh Fracture toughness and fatigue crack growth characteristics of nanotwinned copper Acta Mater 2011
40. M. Kumar, W.E. King, and A.J. Schwartz Modifications to the microstructural topology in fcc materials through thermomechanical processing Acta Mater 48 2000 2081 2091
41. R.W. Minich, C.A. Schuh, and M. Kumar Role of topological constraints on the statistical properties of grain boundary networks Phys Rev B 66 2002 52101
42. M. Frary, and C.A. Schuh Grain boundary networks: scaling laws, preferred cluster structure, and their implications for grain boundary engineering Acta Mater 53 2005 4323 4335
43. M. Frary, and C.A. Schuh Percolation and statistical properties of low-and high-angle interface networks in polycrystalline ensembles Phys Rev B 69 2004 134115
44. C.A. Schuh, M. Kumar, and W.E. King Universal features of grain boundary networks in fcc materials J Mater Sci 40 2005 847 852
45. M. Frary, and C.A. Schuh Connectivity and percolation behaviour of grain boundary networks in three dimensions Philos Mag 85 2005 1123 1143
46. M. Li, and T. Xu Topological and atomic scale characterization of grain boundary networks in polycrystalline and nanocrystalline materials Prog Mater Sci 2011
47. X. Guo Physical origin of the intrinsic grain-boundary resistivity of stabilized-zirconia: role of the space-charge layers Solid State Ionics 81 1995 235 242
48. S.E. Babcock, and J.L. Vargas The nature of grain boundaries in the high-Tc superconductors Annu Rev Mater Sci 25 1995 193 222
49. H. Hilgenkamp, and J. Mannhart Grain boundaries in high-Tc superconductors Rev Mod Phys 74 2002 485
50. M. Frary, and C.A. Schuh Nonrandom percolation behavior of grain boundary networks in high-Tc superconductors Appl Phys Lett 83 2003 3755
51. R.W. Balluffi Grain boundary diffusion mechanisms in metals Metall Mater Trans B 13 1982 527 553
52. N.L. Peterson Grain-boundary diffusion in metals Int Met Rev 28 1983 65 91
53. Y. Chen, and C.A. Schuh Contribution of triple junctions to the diffusion anomaly in nanocrystalline materials Scripta Mater 57 2007 253 256
54. Y. Chen, and C.A. Schuh Diffusion on grain boundary networks: percolation theory and effective medium approximations Acta Mater 54 2006 4709 4720
55. Y. Chen, and C.A. Schuh Geometric considerations for diffusion in polycrystalline solids J Appl Phys 101 2007 63524
56. Y. Chen, and C.A. Schuh Percolation of diffusional creep: a new universality class Phys Rev Lett 98 2007 35701
57. G. Palumbo, and K.T. Aust Structure-dependence of intergranular corrosion in high purity nickel Acta Metall Mater 38 1990 2343 2352
58. P. Lin, G. Palumbo, U. Erb, and K.T. Aust Influence of grain boundary character distribution on sensitization and intergranular corrosion of alloy 600 Scripta Mater 33 1995 1387 1392
59. Y. Pan, B.L. Adams, T. Olson, and N. Panayotou Grain-boundary structure effects on intergranular stress corrosion cracking of alloy X-750 Acta Mater 44 1996 4685 4695
60. E.M. Lehockey, G. Palumbo, A. Brennenstuhl, and P. Lin Mitigating intergranular attack and growth in lead-acid battery electrodes for extended cycle and operating life Metall Mater Trans A 29 1998 387 396
61. H. Kokawa Weld decay-resistant austenitic stainless steel by grain boundary engineering J Mater Sci 40 2005 927 932
62. G. Gupta, P. Ampornrat, X. Ren, K. Sridharan, T.R. Allen, and G.S. Was Role of grain boundary engineering in the SCC behavior of ferritic-martensitic alloy HT-9 J Nucl Mater 361 2007 160 173
63. H. Kokawa, M. Shimada, M. Michiuchi, Z.J. Wang, and Y.S. Sato Arrest of weld-decay in 304 austenitic stainless steel by twin-induced grain boundary engineering Acta Mater 55 2007 5401 5407
64. V. Thaveeprungsriporn, and G.S. Was The role of coincidence-site-lattice boundaries in creep of Ni-16Cr-9Fe at 360 °C Metall Mater Trans A 28 1997 2101 2112
65. B. Alexandreanu, B.H. Sencer, V. Thaveeprungsriporn, and G.S. Was The effect of grain boundary character distribution on the high temperature deformation behavior of Ni-16Cr-9Fe alloys Acta Mater 51 2003 3831 3848
66. Y. Chen, and C.A. Schuh Coble creep in heterogeneous materials: the role of grain boundary engineering Phys Rev B 76 2007 64111
67. D. Bika, and C.J. McMahon Others. A model for dynamic embrittlement Acta Metall Mater 43 1995 1909 1916
68. G. Palumbo, and K.T. Aust Solute effects in grain boundary engineering Can Metall Quart 34 1995 165 173
69. T. Watanabe, and S. Tsurekawa Toughening of brittle materials by grain boundary engineering Mater Sci Eng A 387 2004 447 455
70. U. Krupp, P.E.G. Wagenhuber, W.M. Kane, and C.J. McMahon Improving resistance to dynamic embrittlement and intergranular oxidation of nickel based superalloys by grain boundary engineering type processing Mater Sci Technol 21 2005 1247 1254
71. S. Bechtle, M. Kumar, B.P. Somerday, M.E. Launey, and R.O. Ritchie Grain-boundary engineering markedly reduces susceptibility to intergranular hydrogen embrittlement in metallic materials Acta Mater 57 2009 4148 4157
72. S. Kobayashi, S. Tsurekawa, T. Watanabe, and G. Palumbo Grain boundary engineering for control of sulfur segregation-induced embrittlement in ultrafine-grained nickel Scripta Mater 62 2010 294 297
73. A.J. Schwartz, and M. Kumar Electron backscatter diffraction in materials science 2009 Springer Verlag
74. C.A. Schuh, M. Kumar, and W.E. King Analysis of grain boundary networks and their evolution during grain boundary engineering Acta Mater 51 2003 687 700
75. A.J. Schwartz, W.E. King, and M. Kumar Influence of processing method on the network of grain boundaries Scripta Mater 54 2006 963 968
76. S. Tsurekawa, S. Nakamichi, and T. Watanabe Correlation of grain boundary connectivity with grain boundary character distribution in austenitic stainless steel Acta Mater 54 2006 3617 3626
77. T. Wanner, E.R. Fuller Jr., and D.M. Saylor Homology metrics for microstructure response fields in polycrystals Acta Mater 58 2010 102 110
78. G.S. Rohrer, and H.M. Miller Topological characteristics of plane sections of polycrystals Acta Mater 58 2010 3805 3814
79. G.S. Rohrer Measuring and interpreting the structure of grain-boundary networks J Am Ceram Soc 94 2011 633 646
80. I.M. Robertson, C.A. Schuh, J.S. Vetrano, N.D. Browning, D.P. Field, and D.J. Jensen Others. Towards an integrated materials characterization toolbox J Mater Res 1 2011 1 43
81. H.F. Poulsen Three-dimensional X-ray diffraction microscopy: mapping polycrystals and their dynamics 2004 Springer Verlag
82. S. Schmidt, S.F. Nielsen, C. Gundlach, L. Margulies, X. Huang, and D.J. Jensen Watching the growth of bulk grains during recrystallization of deformed metals Science 305 2004 229 232
83. D.J. Jensen, E.M. Lauridsen, L. Margulies, H.F. Poulsen, S. Schmidt, and H.O. Sorensen X-ray microscopy in four dimensions Mater Today 9 2006 18 25
84. J.-Y. Buffière, P. Cloetens, W. Ludwig, E. Maire, and L. Salvo In situ X-ray tomography studies of microstructural evolution combined with 3d modeling MRS Bull 33 2008 611 619
85. D.J. Jensen, S.E. Offerman, and J. Sietsma 3dxrd characterization and modeling of solid-state transformation processes MRS Bull 33 2008 621 629
86. B.L. Adams, S.I. Wright, and K. Kunze Orientation imaging: the emergence of a new microscopy Metall Mater Trans A 24 1993 819 831
87. F.J. Humphreys Review grain and subgrain characterisation by electron backscatter diffraction J Mater Sci 36 2001 3833 3854
88. G.S. Rohrer, D.M. Saylor, B.S. El-Dasher, B.L. Adams, A.D. Rollett, and P. Wynblatt The distribution of internal interfaces in polycrystals Z Metall 95 2004 197 214
89. C.S. Kim, A.D. Rollett, and G.S. Rohrer Grain boundary planes: new dimensions in the grain boundary character distribution Scripta Mater 54 2006 1005 1009
90. A.C. Lewis, J.F. Bingert, D.J. Rowenhorst, A. Gupta, A.B. Geltmacher, and G. Spanos Two- and three-dimensional microstructural characterization of a super-austenitic stainless steel Mater Sci Eng A 418 2006 11 18
91. W. Xu, M. Ferry, N. Mateescu, J.M. Cairney, and F.J. Humphreys Techniques for generating 3-d ebsd microstructures by fib tomography Mater Charact 58 2007 961 967
92. S. Zaefferer, S.I. Wright, and D. Raabe Three-dimensional orientation microscopy in a focused ion beam-scanning electron microscope: a new dimension of microstructure characterization Metall Mater Trans A 39 2008 374 389
93. G. Spanos, D.J. Rowenhorst, A.C. Lewis, and A.B. Geltmacher Combining serial sectioning, ebsd analysis, and image-based finite element modeling MRS Bull 33 2008 597 602
94. G.S. Rohrer, J. Li, S. Lee, A.D. Rollett, and M. Groeber Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional ebsd data Mater Sci Technol 2009
95. D.J. Rowenhorst, and A.C. Lewis Image processing and analysis of 3-d microscopy data JOM 63 2011 53 57
96. V. Randle Overview no. 127 the role of the grain boundary plane in cubic polycrystals Acta Mater 46 1998 1459 1480
97. P. Davies, and V. Randle Grain boundary engineering and the role of the interfacial plane Mater Sci Technol 17 2001 615 626
98. V. Randle 'Special' boundaries and grain boundary plane engineering Scripta Mater 54 2006 1011 1015
99. G.S. Rohrer The distribution of grain boundary planes in polycrystals JOM J Miner Met Mater Soc 59 2007 38 42
100. V. Randle Grain boundary engineering: an overview after 25 years Mater Sci Technol 26 2010 253 261
101. D.M. Saylor, A. Morawiec, B.L. Adams, and G.S. Rohrer Misorientation dependence of the grain boundary energy in magnesia Interface Sci 8 2000 131 140
102. D.M. Saylor, B.S. El Dasher, A.D. Rollett, and G.S. Rohrer Distribution of grain boundaries in aluminum as a function of five macroscopic parameters Acta Mater 52 2004 3649 3655
103. D.M. Saylor, B. El Dasher, T. Sano, and G.S. Rohrer Distribution of grain boundaries in srtio3 as a function of five macroscopic parameters J Am Ceram Soc 87 2004 670 676
104. G.S. Rohrer, V. Randle, C.S. Kim, and Y. Hu Changes in the five-parameter grain boundary character distribution in [alpha]-brass brought about by iterative thermomechanical processing Acta Mater 54 2006 4489 4502
105. V. Randle, G.S. Rohrer, and Y. Hu Five-parameter grain boundary analysis of a titanium alloy before and after low-temperature annealing Scripta Mater 58 2008 183 186
106. V. Randle, G.S. Rohrer, H.M. Miller, M. Coleman, and G.T. Owen Five-parameter grain boundary distribution of commercially grain boundary engineered nickel and copper Acta Mater 56 2008 2363 2373
107. D.L. Olmsted, S.M. Foiles, and E.A. Holm Survey of computed grain boundary properties in face-centered cubic metals - I: Grain boundary energy Acta Mater 57 2009 3694 3703
108. D.L. Olmsted, E.A. Holm, and S.M. Foiles Survey of computed grain boundary properties in face-centered cubic metals - II: Grain boundary mobility Acta Mater 57 2009 3704 3713
109. G.S. Rohrer, J. Li, S. Lee, A.D. Rollett, M. Groeber, and M.D. Uchic Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional ebsd data Mater Sci Technol 26 2010 661 669
110. J.W. Cahn, and J.E. Taylor Metrics, measures, and parametrizations for grain boundaries: a dialog J Mater Sci 41 2006 7669 7674
111. D.L. Olmsted A new class of metrics for the macroscopic crystallographic space of grain boundaries Acta Mater 57 2009 2793 2799
112. A. Morawiec Models of uniformity for grain boundary distributions J Appl Crystallogr 42 2009 783 792
113. A. Morawiec On the frequency of occurrence of tilt and twist grain boundaries Scripta Mater 61 2009 438 440
114. Sutton AP, Balluffi RW. The geometry of interfaces. In: Interfaces in crystalline materials. Clarendon Press; 1995. pp. 3-68.
115. S. Patala, and C.A. Schuh Topology of homophase grain boundaries in two-dimensional crystals: the role of grain exchange symmetry CMC: Comput Mater Conti 17 2010 1 18
116. J. Stuelpnagel On the parametrization of the three-dimensional rotation group SIAM Rev 6 1964 422 430
117. V. Randle Application of electron backscatter diffraction to grain boundary characterisation Int Mater Rev 49 2004 1 11
118. A.C. Lewis, K.A. Jordan, and A.B. Geltmacher Determination of critical microstructural features in an austenitic stainless steel using image-based finite element modeling Metall Mater Trans A 39 2008 1109 1117
119. B.W. Reed, M. Kumar, R.W. Minich, and R.E. Rudd Fracture roughness scaling and its correlation with grain boundary network structure Acta Mater 56 2008 3278 3289
120. A. Garbacz, and M.W. Grabski The relationship between texture and csl boundaries distribution in polycrystalline materials - I: The grain boundary misorientation distribution in random polycrystal Acta Metall Mater 41 1993 469 473
121. V.Y. Gertsman, K. Tangri, and R.Z. Valiev Overview no 116: on the grain boundary statistics in metals and alloys susceptible to annealing twinning Acta Metall Mater 42 1994 1785 1804
122. A. Morawiec Misorientation-angle distribution of randomly oriented symmetric objects J Appl Crystallogr 28 1995 289 293
123. A. Morawiec Distributions of rotation axes for randomly oriented symmetric objects J Appl Crystallogr 29 1996 164 169
124. O.V. Mishin, V.Y. Gertsman, R.Z. Valiev, and G. Gottstein Grain boundary distribution and texture in ultrafine-grained copper produced by severe plastic deformation Scripta Mater 35 1996 873 878
125. A. Morawiec Distributions of misorientation angles and misorientation axes for crystallites with different symmetries Acta Crystallogr Sect A: Found Crystallogr 53 1997 273 285
126. D.P. Field, J.E. Sanchez Jr., P.R. Besser, and D.J. Dingley Analysis of grain-boundary structure in Al-Cu interconnects J Appl Phys 82 1997 2383
127. V. Randle, H. Davies, and I. Cross Grain boundary misorientation distributions Curr Opin Solid State Mater Sci 5 2001 3 8
128. W.B. Hutchinson, L. Ryde, P.S. Bate, and B. Bacroix On the description of misorientations and interpretation of recrystallization textures Scripta Mater 1996 35
129. B. Bacroix, J. Tarasiuk, K. Wierzbanowski, and K. Zhu Misorientations in rolled and recrystallized zirconium compared with random distribution: a new scheme of misorientation analysis J Appl Crystallogr 43 2009 134 139
130. C.M. Sargent Texture transformations Scripta Metall 1974 8
131. J.S. Kallend, P.P. Morris, and G.J. Davies Texture transformations - the misorientation distribution function Acta Metall 24 1976 361 370
132. J. Pospiech, K. Sztwiertnia, and F. Haessner The misorientation function Text Microstruct 6 1986 201 215
133. B.L. Adams Description of the intercrystalline structure distribution in polycrystalline materials Metall Mater Trans A 17 1986 2199 2207
134. B.L. Adams, P.R. Morris, T.T. Wang, K.S. Willden, and S.I. Wright Description of orientation coherence in polycrystalline materials Acta Metall 35 1987 2935 2946
135. J. Pospiech, K. Lucke, and K. Sztwiertnia Orientation distribution and orientation correlation functions for description of microstructures Acta Metall Mater 41 1993 305 321
136. J.K. Mason, and C.A. Schuh Hyperspherical harmonics for the representation of crystallographic texture Acta Mater 56 2008 6141 6155
137. Euler L. Formulae generales pro translatione quacunque corporum rigidorum. Novi Acad. Sci. Petrop 1775;20:189-207.
138. H.J. Bunge, and P.R. Morris Texture analysis in materials science: mathematical methods 1982 Butterworths London
139. U.F. Kocks, C.N. Tomé, and H.-R. Wenk Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties 2000 Cambridge University Press
140. B.T.M. Willis Use of a three-circle goniometer for diffraction measurements Br J Appl Phys 13 1962 548
141. R.J. Roe Description of crystallite orientation in polycrystalline materials - III: General solution to pole figure inversion J Appl Phys 36 1965 2024 2031
142. R.J. Roe Inversion of pole figures for materials having cubic crystal symmetry J Appl Phys 37 1966 2069 2072
143. A. Morawiec The rotation rate field and geometry of orientation space J Appl Crystallogr 23 1990 374 377
144. F.C. Frank Orientation mapping Metall Mater Trans A 19 1988 403 408
145. R. Becker, and S. Panchanadeeswaran Crystal rotations represented as rodrigues vectors Text Microstruct 10 1989 167 194
146. V. Randle, and A. Day Use of rodrigues-frank space for representation of microtexture and grain boundary parameters Mater Sci Technol 9 1993 1069 1078
147. A. Morawiec, and D.P. Field Rodrigues parameterization for orientation and misorientation distributions Philos Mag A 73 1996 1113 1130
148. P. Neumann Representation of orientations of symmetrical objects by rodrigues vectors Text Microstruct 14 1991 53 58
149. Y. Takahashi, K. Miyazawa, M. Mori, and Y. Ishida Quaternion representation of the orientation relationship and its application to grain boundary problems Trans Jpn Inst Met 27 1985 345 352
150. A. Morawiec, and J. Pospiech Some information on ouaternions useful in texture Text Microstruct 10 1989 211 216
151. L. Meister, and H. Schaeben A concise quaternion geometry of rotations Math Methods Appl Sci 28 2005 101 126
152. A.P. Sutton Statistical representation and analysis of orientational data Philos Mag Lett 74 1996 389 394
153. K. Kunze, and H. Schaeben The Bingham distribution of quaternions and its spherical radon transform in texture analysis Math Geol 36 2004 917 943
154. H. Grimmer Disorientations and coincidence rotations for cubic lattices Acta Crystallogr Sect A: Crystal Phys Diffract Theor Gen Crystallogr 30 1974 685 688
155. H. Grimmer Coincidence rotations for cubic lattices Scripta Metall 7 1973 1295 1300
156. H. Grimmer The generating function for coincidence site lattices in the cubic system Acta Crystallogr Sect A: Found Crystallogr 40 1984 108 112
157. S.L. Altmann Rotations, quaternions, and double groups 1986 Clarendon Press Oxford England
158. R. Gilmore Lie groups, lie algebras, and some of their applications 2006 Dover Publications
159. J.K. Mason, and C.A. Schuh The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures Acta Mater 57 2009 4186 4197
160. Adams BL, Kumar M, Schwartz AJ. Representations of texture in orientation space. In: Electron backscatter diffraction in materials science. Kluwer Acad./Plenum Publ; 2000. pp. 31-8.
161. A. Kumar, and P.R. Dawson Dynamics of texture evolution in face-centered cubic polycrystals J Mech Phys Solids 57 2009 422 445
162. A. Kumar, and P.R. Dawson Polycrystal plasticity modeling of bulk forming with finite elements over orientation space Comput Mech 17 1995 10 25
163. A. Kumar, and P.R. Dawson The simulation of texture evolution with finite elements over orientation space - I: Development Comput Methods Appl Mech Eng 130 1996 227 246
164. A. Kumar, and P.R. Dawson The simulation of texture evolution with finite elements over orientation space - II: Application to planar crystals Comput Methods Appl Mech Eng 130 1996 247 261
165. A. Kumar, and P.R. Dawson Modeling crystallographic texture evolution with finite elements over neo-eulerian orientation spaces Comput Methods Appl Mech Eng 153 1998 259 302
166. A. Heinz, and P. Neumann Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals Acta Crystallogr Sect A: Found Crystallogr 47 1991 780 789
167. B.L. Adams, and T. Olson The mesostructure: properties linkage in polycrystals Prog Mater Sci 43 1998 1 87
168. Morawiec A. Symmetry. In: Orientations and rotations: computations in crystallographic textures. Springer Verlag; 2004. p. 93-114.
169. Randle V, Engler O. Descriptors of orientation. In: Introduction to texture analysis: macrotexture, microtexture and orientation mapping; 2000. p. 15-50.
170. D.M. Saylor, A. Morawiec, and G.S. Rohrer Distribution of grain boundaries in magnesia as a function of five macroscopic parameters Acta Mater 51 2003 3663 3674
171. S. Ranganathan On the geometry of coincidence-site lattices Acta Crystallogr 21 1966 197 199
172. H. Grimmer, W. Bollmann, and D.H. Warrington Coincidence-site lattices and complete pattern-shift in cubic crystals Acta Crystallogr Sect A: Crystal Phys Diffract Theor Gen Crystallogr 30 1974 197 207
173. R.W. Balluffi, A. Brokman, and A.H. King Csl/dsc lattice model for general crystal-crystal boundaries and their line defects Acta Metall 30 1982 1453 1470
174. H. Grimmer Systematic determination of coincidence orientations for all hexagonal lattices with axial ratio c/a in a given interval Acta Crystallogr Sect A: Found Crystallogr 45 1989 320 325
175. H. Grimmer Coincidence orientations of grains in rhombohedral materials Acta Crystallogr Sect A: Found Crystallogr 45 1989 505 523
176. V. Randle The coincidence site lattice and the 'sigma enigma' Mater Charact 47 2001 411 416
177. M. Frary, and C.A. Schuh Combination rule for deviant csl grain boundaries at triple junctions Acta Mater 51 2003 3731 3743
178. D.G. Brandon The structure of high-angle grain boundaries Acta Metall 14 1966 1479 1484
179. H. Kokawa, T. Watanabe, and S. Karashima Reexamination of deviation angles from exact csl misorientations in early work on grain boundary characterization Scripta Metall 21 1987 839 842
180. M. Dechamps, F. Baribier, and A. Marrouche Grain-boundaries: criteria of specialness and deviation from csl misorientation Acta Metall 35 1987 101 107
181. G. Palumbo, K.T. Aust, E.M. Lehockey, U. Erb, and P. Lin On a more restrictive geometric criterion for 'special' csl grain boundaries Scripta Mater 38 1998 1685 1690
182. B.L. Adams, A. Henrie, B. Henrie, M. Lyon, S.R. Kalidindi, and H. Garmestani Microstructure-sensitive design of a compliant beam J Mech Phys Solids 49 2001 1639 1663
183. G. Saheli, H. Garmestani, and B.L. Adams Microstructure design of a two phase composite using two-point correlation functions J Comput-Aided Mater Des 11 2004 103 115
184. A.M. Gokhale, A. Tewari, and H. Garmestani Constraints on microstructural two-point correlation functions Scripta Mater 53 2005 989 993
185. J. Zeman, and M. Sejnoha From random microstructures to representative volume elements Model Simulat Mater Sci Eng 15 2007 S325
186. D.T. Fullwood, S.R. Niezgoda, B.L. Adams, and S.R. Kalidindi Microstructure sensitive design for performance optimization Prog Mater Sci 55 2010 477 562
187. B.L. Hansen, B.L. Adams, M.E. Lyon, and A.J. Henrie On the reconstruction of polycrystalline microstructures from two-point correlation statistics J Comput-Aided Mater Des 10 2005 163 173
188. A. Brahme, M.H. Alvi, D. Saylor, J. Fridy, and A.D. Rollett 3d reconstruction of microstructure in a commercial purity aluminum Scripta Mater 55 2006 75 80
189. A.D. Rollett, S.B. Lee, R. Campman, and G.S. Rohrer Three-dimensional characterization of microstructure by electron back-scatter diffraction Annu Rev Mater Res 37 2007 627 658
190. M.A. Groeber, M.D. Uchic, D.M. Dimiduk, Y. Bhandari, and S. Ghosh A framework for automated 3d microstructure analysis & representation J Comput-Aided Mater Des 14 2007 63 74
191. M. Groeber, S. Ghosh, M.D. Uchic, and D.M. Dimiduk A framework for automated analysis and simulation of 3d polycrystalline microstructures - Part 1: Statistical characterization Acta Mater 56 2008 1257 1273
192. M. Groeber, S. Ghosh, M.D. Uchic, and D.M. Dimiduk A framework for automated analysis and simulation of 3d polycrystalline microstructures - Part 2: Synthetic structure generation Acta Mater 56 2008 1274 1287
193. Schwartz AJ, Kumar M. 3D reconstruction of digital microstructures. In: Electron backscatter diffraction in materials science. Springer; 2009. p. 139-53.
194. M. Miodownik, A.W. Godfrey, E.A. Holm, and D.A. Hughes On boundary misorientation distribution functions and how to incorporate them into three-dimensional models of microstructural evolution Acta Mater 47 1999 2661 2668
195. E.A. Holm, G.N. Hassold, and M.A. Miodownik On misorientation distribution evolution during anisotropic grain growth Acta Mater 49 2001 2981 2991
196. J. Gruber, H.M. Miller, T.D. Hoffmann, G.S. Rohrer, and A.D. Rollett Misorientation texture development during grain growth - Part I: Simulation and experiment Acta Mater 57 2009 6102 6112
197. J. Gruber, A.D. Rollett, and G.S. Rohrer Misorientation texture development during grain growth - Part II: Theory Acta Mater 58 2010 14 19
198. R. Kohn Irreversibility and the statistics of grain boundaries Physics 4 2011 33
199. C. Muller Spherical harmonics 1966 Springer
200. M. Bander, and C. Itzykson Group theory and the hydrogen atom (i) Rev Mod Phys 38 1966 330 345
201. J. Avery, and Z.Y. Wen Angular integrations in m-dimensional spaces and hyperspherical harmonics Int J Quantum Chem 22 1982 717 738
202. Arfken GB, Weber HJ. Mathematical methods for physicists. Elsevier Academic Press; 2005.
203. J.K. Mason The relationship of the hyperspherical harmonics to so (3), so (4) and orientation distribution functions Acta Crystallogr Sect A: Found Crystallogr 65 2009 259 266
204. J.K. Mason, and C.A. Schuh Expressing crystallographic textures through the orientation distribution function: conversion between generalized spherical harmonic and hyperspherical harmonic expansions Metall Mater Trans A 40 2009 2590 2602
205. J.R. Munkres Topology 2000 Prentice Hall
206. H. Hopf Systeme symmetrischer bilinearformen und euklidische modelle der projektiven raume Vjschr Naturf Ges Zurich 85 1940 165 177
207. S. Patala, and C.A. Schuh A continuous and one-to-one coloring scheme for misorientations Acta Mater 59 2011 554 562
208. S. Patala, and C.A. Schuh The topology of homophase misorientation spaces Philos Mag 91 2011 1489 1508
209. H. Grimmer A unique description of the relative orientation of neighbouring grains Acta Crystallogr Sect A: Crystal Phys Diffract Theor Gen Crystallogr 36 1980 382 389
210. R.C. Pond, and D.S. Vlachavas Bicrystallography Proc Roy Soc Lond A: Math Phys Sci 386 1983 95