Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-18T19:33:40.885Z Has data issue: false hasContentIssue false

On the Symmetry of Orientation Distribution in Crystal Aggregates*

Published online by Cambridge University Press:  06 March 2019

David W. Baker*
Affiliation:
University of California Los Angeles, California 90024
Get access

Abstract

In a number of laboratories data from the X-ray pole-figure goniometer are now processed numerically to obtain a suite of complete and normalized pole- figures. From these pole-figures the preferred orientat ion of the grains in a monomineralic aggregate is determined using spherical harmonic analysis and represented as a frequency distribution of the Euler angles Ψ, θ, ø, termed the “orientation distribution function” (ODF),When the frequency density of grain orientations is plotted in a Cartesian coordinate system with Ψ, θ, ø, as axes,it must have a translation periodicity Of 2π or less along each of the axes, because the Euler Angles are angles of rotation.

Type
Research Article
Copyright
Copyright © International Centre for Diffraction Data 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Publication #755, Institute of Geophysics & Planetary Physics, University of California, Los Angeles, California 90024

References

1. Azároff, L.V., Elements of X-ray Crystallography, McGraw-Hill, New York, 1968, p. 544548.Google Scholar
2. Barrett, C. S. and Massalski, T. B., Structures of Metals, 3rdEd., McGraw-Hill, New York, 1966, p. 200203.Google Scholar
3. Bunge, H. J. and Haessner, F., “Three Dimensional Orientation Distribution Function of Crystals in Cold-Rolled Copper,” Jour. Appl. Physics, 39: 55035514, (1968).Google Scholar
4. Morris, P. R. and Heckler, A. J., “Crystallite Orientation Analysis for Rolled Cubic Materials,” in J.B. Newkirk, Editor, Advances in X-ray Analysis, Vol. 11, Plenum Press, New York, 1968, p. 454472.Google Scholar
5. Adachi, T., Crystallite Orientation Distribution for Biaxiaily Stretched Polyethylene, Ph.D. Thesis, Duke University, Durham, N.C., University Microfilms, Ann Arbor, Mich., 1967, 174 p.Google Scholar
6. Baker, D. W., Wenk, H. R. and Christie, J. M., “X-ray Analysis of Preferred Orientation in Fine-Grained Quartz Aggregates,” Jour. Geology, 77:144172,(1969).Google Scholar
7. Bunge, H. J., “Die dreidimensionale Orientierungs- vertei1ungs funktion and Methoden zu ihrer Best immung,” Kristall und Technik, 3:439454, (1968).Google Scholar
8. Bunge, H. J., “Zur Darstellung aligemeiner Texturen,” Zeitschr. Metallkunde, 56:872874, (1965).Google Scholar
9. Bunge, H. J., “Einige Bemerkungen zur Symmetrie vera11 gemeinerter Kugel funktionen,” Monatsber. Deutsche Akad. Wiss., 7:351360, (1965).Google Scholar
10. Roe, R. J., “Description of Crystallite Orientation in Polycrystalline Materials. III. General Soiution to Pole Figure Inversion,” Jour. Appl. Physics, 36: 20242031, (1965).Google Scholar
11. Roe, R. J., “Inversion of Pole Figures for Materials Having Cubic Crystal Symmetry,” Jour. Appl. Physics, 37: 20692072, (1966).Google Scholar
12. Buerger, M. J., Elementary Crysta11ography, McGraw-Hill, NewYork, 1963, p. 337.Google Scholar
13. Baker, D. W. and Wenk, H. R., “Spherical Harmonic Analysis of X-ray Pole-Figure Data for Specimens With Low Symmetry,” (abs.), Am. Geophys. Union Trans., 50: 323,(1969).Google Scholar
14. Henry, N.F.M. and Lonsdale, K., International Tables for X-ray Crystallography, Vol.1, Kynoch Press, Birmingham, 1952, p. 4950.Google Scholar
15. Paterson, M. S. and Weiss, L. E., “Symmetry Concepts in the Structural Analysis of Deformed Rocks,” Geol. Soc. America Bull., 72: 865868, (1961).Google Scholar