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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
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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

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