Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-07T15:14:14.551Z Has data issue: false hasContentIssue false
  • English
  • Français

Elaboration on the hexagonal grid and spiral trace schemes for pole figure data collection

Published online by Cambridge University Press:  29 February 2012

Anthony C. Rizzie ,
Thomas R. Watkins  and
E. Andrew Payzant
Anthony C. Rizzie
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306
Thomas R. Watkins
Affiliation:
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
E. Andrew Payzant
Affiliation:
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Get access Rights & Permissions [Opens in a new window]

Abstract

A practical description of the mathematics required to implement the hexagonal grid and spiral trace pole figure data collection schemes is presented. Applying the concepts of stereographic and equal area projections with geometry, spreadsheets were created to calculate the angular settings of the goniometer. Using the generated settings, the hexagonal grid and spiral trace schemes were programmed into the existing X-ray software and employed to collect data for a sample of aluminum foil. The resulting (111) pole figures were similar to those collected with the conventional 5°χ×5°ϕ grid. The hexagonal grid has been shown by others to reduce the number of data points and time needed to complete a pole figure, while providing equal area sampling. Although not optimized, the spiral method was also investigated as another alternative to the 5°χ×5°ϕ grid.

Keywords

pole figuremathematicshexagonal gridspiral tracecrystallographic texture
Type
X-Ray Diffraction
Information
Powder Diffraction , Volume 23 , Issue 2 , June 2008 , pp. 87 - 91
Copyright
Copyright © Cambridge University Press 2008

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.)

References

Cullity, B. D. and Stock, S. R. (2001). Elements of X-Ray Diffraction (Prentice–Hall, New York), 3rd ed., pp. 416–423.Google Scholar
Eichhorn, R. M. (1965). “Automatic pole figure plotter,” Rev. Sci. Instrum. RSINAK 10.1063/1.1719805 36, 997–1000.CrossRefGoogle Scholar
Kocks, U. F., Tomé, C. N., and Wenk, H.-R. (1998). Texture and Anisotropy: Preferred Orientation in Polycrystals and their Effect on Materials Properties (Cambridge, U.P., New York), pp. 52–54, 137–139.Google Scholar
Krause, H. and Haase, A. (1986). Experimental Techniques of Texture Analysis, edited by Bunge, H. J. (DGM Informationsgesellschaft-Verlag, Oberursel, Germany), pp. 405–408.Google Scholar
Matthies, S. and Wenk, H.-R. (1992). “Optimization of texture measurements by pole figure coverage with hexagonal grids,” Phys. Status Solidi A PSSABA 133, 253–257.CrossRefGoogle Scholar
Tarkowski, L., Laskosz, L., and Bonarski, J. T. (2004). “Optimization of x-ray pole figure measurement,” Mater. Sci. Forum MSFOEP 443–444, 137–140.CrossRefGoogle Scholar