X-Ray Line Profile Analysis for Single Crystals

X-Ray Line Profile Analysis for Single Crystals

Copyright: © 2014 |Pages: 29
DOI: 10.4018/978-1-4666-5852-3.ch008
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Abstract

The features of the dislocation structure in plastically deformed single crystals can be determined from diffraction line broadening. Both the measuring and the evaluation procedures of X-ray line profiles are somewhat different from the methods used for polycrystalline materials. In this chapter, these procedures are overviewed, and their effectiveness is illustrated by representative examples. It is shown that the intensity distribution in the vicinity of the reciprocal lattice points can be mapped by rocking the single crystal about appropriate axes. From the detected intensity distribution, the density, the slip systems, and the arrangement of dislocations, as well as the lattice misorientation can be determined. The average misorientation obtained from rocking curve measurement can be related to the density of geometrically necessary dislocations. It is also shown that the inhomogeneous distribution of dislocations in plastically deformed single crystals usually results in asymmetric line profiles. The evaluation of these peaks enables the determination of the long-range internal stresses besides the dislocation densities in the dislocation cell walls and interiors.
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Intensity Distribution Around The Reciprocal Lattice Points For Single Crystals

The intensity distribution in the reciprocal lattice node with the indices hkl for a single crystal is illustrated in Figure 1. The broadening along the reciprocal lattice vector (or diffraction vector) ghkl corresponds to the variation of the lattice spacing for planes (hkl) due to the strain fields of dislocations. The broadening perpendicular to ghkl represents the variation of the orientations of lattice planes (hkl) with respect to a reference orientation (Mughrabi & Obst, 2005). The former and latter broadenings are referred to as line broadening and broadening of rocking curve, respectively. The rocking curve is measured with a fixed detector position at the Bragg angle corresponding to reflection hkl, while the sample is rotated about the axis perpendicular to the plane of the incident and the diffracted beams (referred to as rocking axis). In this procedure the head of the diffraction vector scans an arc centered at the origin of the reciprocal lattice, as shown in Figure 1. During the measurement the angle between the incident beam and the sample surface, ω, changes while the Bragg angle, B, remains constant. The intensity distribution as a function of ω is referred to as rocking curve. This scan should give an unchanged intensity (except the instrumental aberrations) for random orientation distribution of crystallites (Kuzel, Cizek, & Novotny, 2012). However, for a single crystal a peak can be observed which is related to the misorientations of planes (hkl). The detection of the rocking curve should be distinguished from the other two ways of the measurement of the intensity distribution around a reciprocal lattice point. When the detector scans 2θ with a fixed sample orientation (referred to as detector scan or 2θ scan), the intensity along the Ewald sphere circumference is measured (see Figure 1). During the so-called couple scan (or 2θ-ω or θ-2θ scan) the sample is also rotated with an angular velocity as half as that for the detector, and in this case the intensity is measured along a straight line in the direction of the diffraction vector ghkl.

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