Handbook of Modern Coating Technologies

X-ray diffraction methods

Broadly speaking, the XRD measurements can be made either on transmitted or back- scattered radiation, or both. The diffraction procedure to be followed in a given case depends on specimen, type of analysis, and equipment available. Fundamental diffraction procedures are briefly explained in following subsections.

• Laue method

As said earlier, Max von Laue was the first to perform diffraction experiments using X-rays. He irradiated a single crystal using white X-rays, so that individual sets of hkl planes dif­fracted a particular wavelength that satisfied the Bragg condition for the given interplanar d-

spacing and orientation. As explained in previous sections, the set of planes, which are paral­lel to a line, are called planes of a zone. The diffracted beams originating from the planes of a particular zone emerge in the form a cone. The axis of the cone thus formed coincides with the zone axis, while its semiapex angle equals the angle between zone axis and beam direction (refer Fig. 3—21). Accordingly the spots on photographic plate can be seen to lie along conic sections—namely, on elliptical curves for transmitted radiation and parabolic curves for back-scattered radiation.

• Rotating crystal method

This method involves rotation of a single crystal placed in the path of a collimated beam of monochromatic X-rays. As shown in Fig. 3—22, a photographic film is so placed, as to form a cylinder around the crystal's rotation axis. The beams diffracted by individual sets of hkl planes each form cones, which are coaxial with the crystal's axis of rotation. The intersection of these cones with the coaxially placed cylindrical film occurs along circular trajectories, which open-up as lines on straightening the film.

FIGURE 3-21 Lauemethod.

FIGURE 3-22 Rotating crystal method.

• Hull/Debye-Scherrer powder method

Powder method is one of the most widely used procedures in materials science, as most metals and alloys have polycrystalline grain structure, which is more or less similar to an assemblage of randomly oriented powder particles. Owing to very large number of crystallites and their random orientation, when a powder specimen is placed in the path of a collimated beam of monochromatic X-rays, all such sets of hkl planes, which can produce diffraction by satisfying the Bragg's condition, will do so, with each set forming its own cone of diffracted

FIGURE 3-23 Hull/Debye-Scherrer powder method.

beams, all cones being coaxial with the axis of incident beam and having semiapex angle 2в corresponding to the Bragg condition (refer Fig. 3-23).

A flat photographic plate placed normal to the incident beam on either side of the speci­men would intersect these cones to form Debye—Scherrer rings. Another approach is to place the photographic film wrapped in cylindrical fashion around the specimen, with the film axis being orthogonal to that of the incident beam (refer Fig. 3—23). If the number of crystallites is large, their cumulative effect is similar to that of rotation of a single crystal and the resulting arcs on the film are formed as continuous curves. However, their appearance becomes grainy for lesser number of crystallites in the specimen, which might necessitate switching from 1D detectors to 2D detectors on modern diffraction equipment [81]. Any bias with respect to ori­entation of crystallites is termed as crystallographic texture and manifests as relative strength of the diffracted beams corresponding to directions of preferred orientation [82].

Over the course of years, the photographic film has got replaced with solid state detectors, which have not only helped improve the angular accuracy by several orders of magnitude, but also made it possible to quantify the relative peak intensities. Development of two-dimensional detectors has brought together the merits of photographic plates and solid state detectors [83]. At present, the commercially available diffraction equipment offers angular resolution (goni­ometer step-size) of 0.0001 degree or even better. All these capabilities are of prime importance in addressing characterization requirements of present-day materials scientists.