International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 2.7, pp. 114-115

Section 2.7.2.1. Reflection topographs

A. R. Langa

a H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, England

2.7.2.1. Reflection topographs

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Combining the simple diffraction geometry of Fig. 2.7.1.1[link] with a laboratory microfocus source of continuous radiation offers a simple yet sensitive technique for mapping misorientation textures of large single crystals (Schulz, 1954[link]). One laboratory X-ray source much used produces an apparent size of S 30 µm in the axial direction and 3 µm in the plane of incidence. Smaller source sizes can be achieved with X-ray tubes employing magnetic focusing of the electron beam. Then b/a ratios between [1\over2] and 1 can be adopted without serious loss of geometric resolution, and, with a = 0.3 m typically, misorientation angles of 10′′ can be measured on images of the type (c) in Fig. 2.7.1.3[link]. The technique is most informative when the crystal is divided into well defined subgrains separated by low-angle boundaries, as is often the case with annealed melt-grown crystals. On the other hand, when continuous lattice curvature is present, as is usually the case in all but the simplest cases of plastic deformation, it is difficult to separate the relative contributions of orientation contrast and diffraction contrast on topographs taken by this method. In principle, the separation could be effected by recording a series of exposures with a wide range of values of b, and it becomes practicable to do so when exposures can be brief, as they can be with synchrotron-radiation sources (see Section 2.7.4[link]).

For easier separation of orientation contrast and diffraction contrast, and for quicker exposures with conventional X-ray sources, collimated characteristic radiation is used, as in the Berg–Barrett method. Barrett (1945[link]) improved an arrangement earlier described by Berg (1931[link]) by using fine-grain photographic emulsion and by minimizing the ratio b/a, and achieved high topographic resolution ([\sim1] µm). The method was further developed by Newkirk (1958[link], 1959[link]). A typical Berg–Barrett arrangement is sketched in Fig. 2.7.2.1[link] . Usually, the source S is the focal spot of a standard X-ray tube, giving an apparent source 1 mm square perpendicular to the incident beam. The openings of the slits [S_1] and [S_2] are also 1 mm in the plane of incidence, and the distance [S_1][S_2] (which may be identified with the distance a) is typically 0.3 m. The specimen is oriented so as to Bragg reflect asymmetrically, as shown. Softer radiations, e.g. Cu Kα, Co Kα or Cr Kα, are employed and higher-angle Bragg reflections are chosen [(2\theta_B\simeq90]° is most convenient). Fig. 2.7.2.1[link] indicates three possible film orientations, F1F3. (These possibilities apply in most X-ray topographic arrangements.) Choice of orientation is made from the following considerations. If minimum distance b is required over the whole length CD, then position F1 is most appropriate. If a geometrically undistorted image of CD is needed, then position F2, in which the film plane is parallel to the specimen surface, satisfies this condition. If a thick emulsion is used, it should receive X-rays at normal incidence, and be in orientation F3. If high-resolution spectroscopic photographic plates are used, in which the emulsion thickness is [\sim1] µm only, then considerable obliquity of incidence of the X-rays is tolerable. But these plates have low X-ray absorption efficiency. Nuclear emulsions (particularly Ilford type L4) are much used in X-ray topographic work. Ilford L4 is a high-density emulsion (halide weight fraction 83%) and hence has high X-ray stopping power. The usual minimum emulsion thickness is 25 µm. Such emulsions should be oriented not more than about 2° off perpendicularity to the X-ray beam if resolution loss due to oblique incidence is not to exceed 1 µm (with correspondingly closer limits on obliquity for thicker emulsions). With 1 mm openings of [S_1] and [S_2], and a = 0.3 m, most of the irradiated area of CD will receive an angular range of illumination sufficient to allow both components of the [K\alpha] doublet to Bragg reflect. In these circumstances, the distance b must be everywhere less than 1–2 mm if image spreading due to superimposition of the [\alpha_1] and [\alpha_2] images is not to exceed a few micrometres. In order to eliminate this major cause of resolution loss (and, incidentally, gain sensitivity in misorientation measurements), the apertures [S_1] and [S_2] should be narrowed and/or a increased so that the angular range of incidence on the specimen is less than the difference in Bragg angle of the [\alpha_1] and [\alpha_2] components for the particular radiation and Bragg angle being used. (This condition applies equally in the transmission specimen techniques, described below.). With a narrower beam, the illuminated length of CD is reduced. This disadvantage may be overcome by mounting the specimen and film together on a linear traverse mechanism so that during the exposure all the length of CD of interest is scanned. In this way, surface-reflection X-ray topographs can be recorded for comparison with, say, etch patterns or cathodo­luminescence patterns (Lang, 1974[link]).

[Figure 2.7.2.1]

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Berg–Barrett arrangement for surface-reflection topographs.

References

First citation Barrett, C. S. (1945). A new microscopy and its potentialities. Trans. Am. Inst. Min. Metall. Pet. Eng. 161, 15–64.Google Scholar
First citation Berg, W. F. (1931). Über ein röntgenographische Methode zur Untersuchung von Gitterstörungen an Kristallen. Naturwissenschaften, 19, 391–396.Google Scholar
First citation Lang, A. R. (1974). On the growth-sectorial dependence of defects in natural diamonds. Proc. R. Soc. London Ser. A, 340, 233–248.Google Scholar
First citation Newkirk, J. B. (1958). Method for the detection of dislocations in silicon by X-ray extinction contrast. Phys. Rev. 110, 1465–1466.Google Scholar
First citation Newkirk, J. B. (1959). The observation of dislocations and other imperfections by X-ray extinction contrast. Trans. TMS–AIME, 215, 483–497.Google Scholar
First citation Schulz, L. G. (1954). Method of using a fine-focus X-ray tube for examining the surface of single crystals. J. Met: Trans. AIME, 200, 1082–1083.Google Scholar








































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