Analysis of crystallographic texture information by the hyperspherical harmonic expansion

The field of texture analysis is fundamentally concerned with measuring and analyzing the distribution of crystalline orientations in a given polycrystalline material. Traditionally, the orientation distribution function describing crystallographic orientation information is written as a linear combination of the generalized spherical harmonics. Since the use of generalized spherical harmonics requires that orientations be described by sets of Euler angles, the field of texture analysis suffers from the inherent limitations of Euler angles. These include difficulty of presentation and interpretation, discontinuous changes in the description of a changing orientation, and singularities in many equations of Euler angles. An alternative expansion of the orientation distribution function as a linear combination of the hyperspherical harmonics is therefore proposed, with the advantage that this expansion allows rotations to be described by angles that directly relate to the axis and angle of a rotation. Apart from the straightforward and intuitive presentation of orientation statistics that this allows, the utility of the hyperspherical harmonic expansion rests on the fact that the orientation distribution function inherits the useful mathematical properties of the hyperspherical harmonics. The relationship of the hyperspherical harmonics to the three- and four-dimensional rotation groups is investigated, and expressions for the matrix elements of the irreducible representatives of these rotation groups as linear combinations of the hyperspherical harmonics are found.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Materials Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Mason, Jeremy K. (Jeremy Kyle)

Advisor dc:contributor.advisor

• Christopher Schuh.

• Materials Science and Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/53251

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/53251