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Quantitative Determinations and Descriptions of Preferred Orientation*

  • J. R. Holland (a1)


The problems associated with quantitative determinations and descriptions of preferred orientation are discussed and a method proposed to yield quantitative descriptions. A means of obtaining representative quantitative data using reflection techniques is described. The position of intensity minima in quantitative pole figure descriptions of preferred orientation is equal in importance to intensity maxima. Hence, rate-meter counting of diffracted intensity as the sample is continuously or semicontinuously rotated in a given spatial relationship is not satisfactory. Instead, sealer counting by fixed counts at a given spatial position yields more meaningful results; however, fixed-time sealer counting is used to reduce the time for data collection. The data are plotted in the form of normalized pole figures and analyzed.

To determine the relative volume of material associated with a given-texture component and an index of preferred orientation, the data are integrated. This is done by numerical integration or, alternatively, by graphical means. Integrating over the interval from ϕ = 0 to ϕ = π/2 and α = 0 to α = n/2 (where ϕ and α are spherical coordinates) will give the pole concentration per unit area for an ideally randomly oriented specimen for an octant of the sphere of projection. The relative volume of material associated with a given set of intensity maxima can be determined by integrating the intensity over the area of the maxima, summing these values, and dividing by the multiplicity to obtain the total intensity, It . The relative volume can be expressed as a ratio of It divided by random intensity. The texture strength can be expressed as the standard deviation from the random condition. Such information is vital to quantitative predictions of the anisotropy of properties



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This work was performed under the auspices of the U.S. Atomic Energy Commission.



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1. Schulz, L. G., “A Direct Method of Determining Preferred Orientation of a Flat Reflector Sample Using a Geiger Counter X-Ray Spectrometer,” J. Appl. Phys. 20: 1030, 1949.
2. Mueller, M. H. and Knott, H. W., “Quantitative Pole Figure for Sheet Material by the Reflection Method,” Rev. Sci. Instr. 24: 925, 1953.
3. Holland, J. R., Engler, N., and Powers, W., “The Use of Computer Techniques to Plot Pole Figures,” Advances in X-Ray Analysis, Vol. 4, Plenum Press, New York, 1961, p. 74.
4. Meieran, E. S., “Use of the Reciprocal Lattice for the Development of a New Pole Figure Technique,” Rev. Sci. Instr. 33: 319, 1962.
5. Lopata, S. L. and Kula, E. B., “A Reflection Method for Pole-Figure Determination,” Trans. Am. Inst. Mining, Met., Petrol. Engrs, 224: 865, 1962.
6. Geisler, A. H., “Spurious Areas in Pole Figures,” J. Appl. Phys. 25: 1245, 1954.
7. Chernock, W. P., and Beck, P. A., “Analysis of Certain Errors in the X-Ray Reflection Method for the Quantitative Determination of Preferred Orientation,“J. Appl. Phys. 23: 341, 1952.
8. American Society for Testing Materials Specification E81-54T, Preparing Quantitative Pole Figures of Metals, Pt. 3, p. 780.

Quantitative Determinations and Descriptions of Preferred Orientation*

  • J. R. Holland (a1)


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