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

International Tables for Crystallography (2018). Vol. H, ch. 2.4, pp. 110-111

Section 2.4.5. Texture analysis

J. L. Lábára

2.4.5. Texture analysis

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The orientation distribution in a polycrystalline (nanocrystalline) TEM sample (used for powder electron diffraction) can either be random or a large fraction of grains can favour a special direction, i.e. the sample is textured. The texture can originate from the non-spherical shape of the particles (as in sedimentation geology or drop-drying of a suspension of nanoparticles on a TEM grid) or from energetic and/or kinetic conditions during nucleation and growth of grains in the formation of polycrystalline thin films on a substrate or, alternatively, the texture can be a result of mechanical deformation (as in drawing wires or rolling sheets of metals). Although the distribution of the preferred orientations can be very different, a few general types are frequently observed.

In the simplest case only one preferred-orientation vector characterizes the sample and the orientations of the grains are distributed arbitrarily around that direction. This situation is called fibre texture (single-axis texture). The most typical representatives of this texture class are sedimentation platy particles on a flat surface where the preferred-orientation vector is normal to the flat face of the particles, or a drawn metal wire where the preferred-orientation vector is directed along the wire axis. Another texture type frequently observed in the sedimentation of rod-shaped particles is described by the preferred-orientation vector being confined within a plane, but being arbitrarily oriented within this plane. Rolling of metal sheets results in other, more complex, but well characterized texture types: `copper-type', `brass-type' and `S-type' (Mecking, 1985[link]).

There are different ways to handle texture with electron diffraction. One approach is to collect the orientation information from individual nanograins in an automated area scan and reconstruct pole figures and inverse pole figures on a medium-sized population of grains (Rauch et al., 2008[link]). In principle, this is a single-crystal method analysing the information from an assembly of crystals. The Russian crystallography group developed the theory of arcs in oblique texture and used such textured patterns in structure analysis (Vainshtein, 1964[link]; Vainshtein & Zvyagin, 1992[link]). The TexPat software (Oleynikov & Hovmoller, 2004[link]) was designed and effectively applied to determining unit-cell parameters and refining structure from oblique textured electron diffraction patterns. Tang et al. (1996[link]) developed a method to determine the axis of texture and distribution of directions around that axis. The March–Dollase model (Dollase, 1986[link]) for the description of pole densities was adapted for electron diffraction and used for the simulation of ring patterns (Li, 2010[link]); however, no attempt was made to determine the phase fractions or textured fractions automatically.

A simplified automatic treatment of texture was implemented in the ProcessDiffraction software (Lábár, 2008[link], 2009[link]). Partial texture is approximated by a linear combination of an ideally sharp fibre texture and a random distribution of components. Both the textured and the random components are treated as separately determined volume fractions during quantitative phase analysis (see Section 2.4.4[link]). The advantage of the method is that the determination of the textured fraction is combined with simultaneous handling of a quasi-kinematic scattering by the Blackman approximation, and these two effects, which both modify the relative intensities, are treated simultaneously on a unified platform.

The application of the most general method for determining texture from powder electron diffraction patterns is restricted to the thinnest samples where kinematic scattering holds (Gemmi, Voltolini et al., 2011[link]). The method consists of recording a set of powder electron diffraction patterns at defined tilt steps of the two-axis goniometer, covering a considerable part of the solid-angle range usually used for recording pole figures. Azimuthal sections are integrated separately in 10° steps. The resulting large three-dimensional data set is fed into a variant of the Rietveld method called MAUD (Lutterotti et al., 1997[link]), which has built-in scattering factors for electrons. The orientation density function (ODF) is determined from the measured data by discretization of the orientation space. For texture fitting the EWIMV algorithm is used (Lutterotti et al., 2004[link]), which can be applied with irregular pole figure coverage and includes smoothing methods based on a concept of the tube projection. Pole figures from the smoothed ODF were obtained for both sediment aggregates and evaporated thin films (Gemmi, Voltolini et al., 2011[link]).

References

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