Rodrigues parameterization for orientation and misorientation distributions

Abstract The Rodrigues parameterization of rotations offers an intuitively simple space which enables visualization of the geometric configuration of orientations and misorientations. Recent efforts have concentrated on promoting the use of Rodrigues vectors for orientation parameterization. In the present work a procedure for determining the boundaries of the asymmetric domains for orientations and misorientations in Rodrigues space is given for all crystal symmetries, and the complete description of these zones is presented. The geometric properties of the Rodrigues space are described in detail and important relations useful in crystallographic texture analysis are derived. It is demonstrated that the special properties and geometry of the Rodrigues space facilitate analysis of texture function reproduction from pole figures and of texture evolution in plastic deformation of polycrystals.

[1]  K. Wlerzbanowski,et al.  Relation between mobile dislocation parameters and orientation distribution function , 1985 .

[2]  Anil K. Jain,et al.  Texture Analysis , 2018, Handbook of Image Processing and Computer Vision.

[3]  K. Kunze,et al.  Orientation imaging: The emergence of a new microscopy , 1993 .

[4]  D. Field.  On the asymmetric domain of cubic misorientations , 1995 .

[5]  P. Neumann,et al.  REPRESENTATION OF ORIENTATIONS OF SYMMETRICAL OBJECTS BY RODRIGUES VECTORS , 1991 .

[6]  G. Tyrrell.  Textures and Microstructures , 1978 .

[7]  J. Pośpiech,et al.  Some Information on Quaternions Useful in Texture Calculations , 1989 .

[8]  S. Panchanadeeswaran,et al.  Crystal Rotations Represented as Rodrigues Vectors , 1989 .

[9]  H. Bunge.  Texture Analysis in Materials Science , 1982 .

[10]  B. Adams,et al.  Definition of an asymmetric domain for intercrystalline misorientation in cubic materials in the space of Euler angles , 1988 .

[11]  A. Morawiec.  Misorientation‐Angle Distribution of Randomly Oriented Symmetric Objects , 1995 .

[12]  T. Yeates.  The asymmetric regions of rotation functions between Patterson functions of arbitrarily high symmetry. , 1993, Acta crystallographica. Section A, Foundations of crystallography.

[13]  H. J. Bunge,et al.  Some applications of the Taylor theory of polycrystal plasticity , 1970 .

[14]  A. Clément.  Prediction of deformation texture using a physical principle of conservatiol , 1982 .

[15]  B. Adams,et al.  Heterogeneity of intergranular damage , 1992, Metallurgical and Materials Transactions A.

[16]  V. Randlè.  Representation of grain misorientations (mesotexture) in Rodrigues-Frank space , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[17]  J. Pośpiech.  The reproduction of the orientation distribution function (ODF) of a polycrystalline material from pole figures , 1980 .