Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.5, p. 139

Section Pole-figure interpolation and use of symmetry

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: Pole-figure interpolation and use of symmetry

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The pole figure is stored and displayed as a bitmap image. The pole-density data from the data set may not fill up all the pixels of the pole-figure image. In order to generate a smooth pole figure, the unmapped pixels are filled with values generated from the interpolation of the surrounding pixels. A linear interpolation within a defined box is sufficient to fill the unmapped pixels. The size of the box should be properly chosen. A box that is too small may not be able to fill all unmapped pixels and a box that is too big may have a smearing effect on the pole figure, especially if a sharp pole figure is processed. All the gaps between the measured pole-density points are filled after this interpolation. For a sample with sharp texture, smaller ϕ-scan steps should be used.

All pole figures possess symmetry as a consequence of the Laue symmetry of the crystallites in the sample. This symmetry can be used to fill in values for pixels in the pole figure for which data were not measured, or to smooth the pole figure. For example, orthorhombic materials exhibit mmm symmetry, thus one needs to collect only an octant or quadrant of the pole sphere to generate the entire pole figure. The pole figures of materials with higher symmetry may be treated by using lower symmetry in the processing. For instance, one can use 2/m or mmm symmetry for hexagonal materials and mmm for cubic materials. In symmetry processing, all the symmetry-equivalent pole-figure pixels are filled by the average value of the measured pixels. For the unmeasured pole-figure pixels, this symmetry processing fills in a value from the average of all the equivalent pixels. For the measured pixels, this average processing serves as a smoothing function. Fig. 2.5.22[link](b) shows the results after both interpolation and use of symmetry.

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