Chapter 2.7. Topography

Combining the simple diffraction geometry of Fig. 2.7.1.1 with a laboratory microfocus source of continuous radiation offers a simple yet sensitive technique for mapping misorientation textures of large single crystals (Schulz, 1954). 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 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. 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).

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) improved an arrangement earlier described by Berg (1931) by using fine-grain photographic emulsion and by minimizing the ratio b/a, and achieved high topographic resolution ( µm). The method was further developed by Newkirk (1958, 1959). A typical Berg–Barrett arrangement is sketched in Fig. 2.7.2.1 . 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 and are also 1 mm in the plane of incidence, and the distance – (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 ° is most convenient). Fig. 2.7.2.1 indicates three possible film orientations, F₁–F₃. (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  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 and , 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 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 and 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 and 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 and 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).

Figure 2.7.2.1| top | pdf | Berg–Barrett arrangement for surface-reflection topographs.

The term `X-ray topograph' was introduced by Ramachandran (1944) who took transmission topographs of cleavage plates of diamond using essentially the arrangement shown in Fig. 2.7.1.2. (In this case, S was a 0.3 mm diameter pinhole placed in front of the window of a W-target X-ray tube so as to form a point source of diverging continuous radiation.) Ramachandran adopted a distance a = 0.3 m and ratio a/b of about 12, which produced images of about 25 µm geometrical resolution having the characteristics of Fig. 2.7.1.3(b), i.e. sensitive to diffraction contrast but not to orientation contrast. For each reflection under study, the film was inclined to the incident beam with that obliquity calculated to produce an undistorted image of the specimen plate. Guinier & Tennevin (1949) studied both diffraction contrast and orientation contrast in continuous-radiation transmission topograph images. Their minimum b/a ratio was set by the need to avoid overlap of Laue images of the crystal produced by different Bragg planes.

Collimated characteristic radiation is used in the methods of `section topographs' (Lang, 1957) and `projection topographs' (Lang, 1959a), the latter being sometimes called `traverse topographs'. Fig. 2.7.2.2 explains both techniques. When taking a section topograph, the specimen CD, usually plate shaped, is stationary (disregard the double-headed arrow in the figure). The ribbon-shaped incident beam issuing from the slit P is Bragg reflected by planes normal, or not far from normal, to the major surfaces of the specimen. As drawn, the Bragg planes make an angle α with the normal to the X-ray entrance surface of the specimen, the positive sense of α being taken in the same sense as the deviation of the Bragg-reflected rays. If the crystal is sufficiently perfect for multiple scattering to occur within it (with or without loss of coherence), then the multiply scattered rays associated with the Bragg reflection excited will fill the volume of the triangular prism whose base is ORT, the `energy-flow triangle' or `Borrmann triangle', contained between OT and OR whose directions are parallel to the incident wavevector, , and diffracted wavevector, , respectively. Both the and beams issuing from the X-ray exit surface of the crystal carry information about the lattice defects within the crystal. However, it is usual to record only the beam. This falls on the film, F, in a strip extending normal to the plane of incidence, of height equal to the illuminated height of the specimen multiplied by the axial magnification factor (a + b)/a, and forms the section topograph image. The screen, Q, prevents the beam from blackening the film but has a slot allowing the diffracted beam to fall on F. A diffraction-contrast-producing lattice defect cut by OT at I will generate supplementary rays parallel to and will produce an identifiable image on F at , the `direct image' or `kinematic image' of the defect. The depth of I within CD can be found via the measurement of . From a series of section topographs taken with a known translation of the specimen between each topograph, a three-dimensional construction of the trajectory of defect I (e.g. a dislocation line) within the crystal can be built up. To obtain good definition of the spatial width of the ribbon incident beam cutting the crystal, the distance between P and the crystal is kept small. The minimum practicable opening of P is about 10 µm. If diffraction is occurring from planes perpendicular to the X-ray entrance surface of the specimen, i.e. symmetrical Laue case diffraction, the width of the section topograph image is simply , t being the specimen thickness, and neglecting the contribution from the width of the ribbon incident beam. With asymmetric transmission, as drawn in the figure, . The distance b is made as small as is permitted by the specimen shape and the need to separate the emerging and beams. Suppose b is 10 mm. Then, with a source S having axial extension 100 µm, the distance a = SP should be not less than 0.5 m in order to keep the geometrical resolution in the axial direction better than 2 µm, and should be correspondingly longer with larger source sizes.

Figure 2.7.2.2| top | pdf | Arrangements for section topographs and projection topographs.

To take a projection topograph, the specimen CD and the cassette holding the film F are together mounted on an accurate linear traversing mechanism that oscillates back and forth during the exposure so that the whole area of interest in the specimen is scanned by the ribbon beam from P. The screen Q is stationary. If the specimen is plate shaped, the best traverse direction to choose is that parallel to the plate, as indicated by the double-headed arrow, for then the diffracted beam will have minimum side-to-side oscillation during the traverse oscillation, the opening of Q can be held to a minimum, and thereby unwanted scattering reaching F kept low. The projection topograph image is an orthographic projection parallel to of the crystal volume and its content of diffraction-contrast-producing lattice defects. If the specimen is plate-like, of length L in the plane of incidence, then, with F normal to , the magnification of the topograph image in the direction parallel to the plane of incidence is . There will generally be a small change of axial magnification (a + b)/a along L. The loss of three-dimensional information occurring through projection can be recovered by taking stereopairs of projection topographs. The first method (Lang, 1959a, b) used hkl, pairs of topographs as stereopairs. One disadvantage of this method is that the convergence angle is fixed at , which may be unsuitably large for thick specimens. The method of Haruta (1965) obtains two views of the specimen using the same reflection, by making a small rotation of the specimen about the h vector between the two exposures, and has the advantage that this rotation, and hence the stereoscopic sensitivity, can be chosen at will. When taking projection topographs, the slit P can be wider than the narrow opening needed for high-resolution section topographs, but not so wide as to cause unwanted reflection to occur. Best use of the X-ray source is made when the width of P is the same as or somewhat greater than S.

In certain investigations, the methods of -beam `limited projection topographs' (Lang, 1963) and of -beam section topographs and projection topographs are useful; Fig. 2.7.2.3 shows the arrangement of screens and diffracted-beam slits then adopted. The limited projection topograph technique can be employed with a plate-shaped specimen , as in the following examples. Suppose the surface of the plate contains abrasion damage that cannot be removed but that causes diffraction contrast obscuring the images of interior defects in the crystal. The diffracted-beam slit (equivalent to the opening in Q shown in Fig. 2.7.2.2), which is opened to the setting for a standard projection topograph, may now be closed down to setting so as to cut into the and edges of the beam, and thereby prevent direct images of near-surface defects located between and , and between and , from reaching F. As another example, it may be desired to receive direct images from a specimen surface and a limited depth below it only (e.g. when correlating surface etch pits with dislocation outcrops). Then, setting of the diffracted-beam slit is adopted and only the direct images from defects lying between depth and the surface reach F.

Figure 2.7.2.3| top | pdf | Arrangements for limited projection topographs and direct-beam topographs.

To record the beam image, either in a section topograph or a projection topograph, some interception of the beam on the side is needed to avoid intense blackening of the film G by radiation coming from the source, which will generally contain much energy in wavelengths other than those undergoing Bragg diffraction by the crystal. Screen S₄, critically adjusted, performs the required interception. Recording both -beam and -beam images is valuable in some studies of dynamical diffraction phenomena, such as the `first-fringe contrast' in stacking-fault fringe patterns (Jiang & Lang, 1983). Such recording can be done simultaneously, on separate films, normal to and , respectively, when is sufficiently large.

When collimated characteristic radiation is used, recording projection topographs of reasonably uniform density becomes difficult when the specimen is bent. To keep the ω axis oriented at the peak of the Bragg reflection while the specimen is scanned, several devices for `Bragg-angle control' have been designed, for example the servo system of Van Mellaert & Schwuttke (1972). The signal is taken from a detector registering the Bragg reflection through the film F, but this precludes use of glass-backed emulsions if X-ray wavelengths such as that of Cu K and softer are used. An alternative approach with thin, large-area transmission specimens is to revert to the geometry of Fig. 2.7.1.2 and deliberately elastically bend the crystal to such radius as will enable its whole length to Bragg diffract a single wavelength diverging from S, similar to a Cauchois focusing transmission monochromator (Wallace & Ward, 1975). No specimen traversing is then needed, but b cannot be made small if the wide and beams are to be spatially separated in the plane of F.

Quite simple experimental arrangements can be adopted for taking transmission topographs under high-absorption conditions, when only anomalously transmitted radiation can pass through the crystal. The technique has mainly been used in symmetrical transmission, as shown with the specimen in Fig. 2.7.2.4 . When the specimen perfection is sufficiently high for the Borrmann effect to be strongly manifested, and μt 10, say, the energy flow transmitted within the Borrmann triangle is constricted to a narrow fan parallel to the Bragg planes, the fan opening angle being only a small fraction of [see IT B (2005, Part 5 )]. Radiation of a given wavelength coming from a small source at S and undergoing Bragg diffraction in will take the path shown by the heavy line in Fig. 2.7.2.4, simplifying the picture to the case of extreme confinement of energy flow to parallelism with the Bragg planes. At the X-ray exit surface DD′, splitting into and beams occurs. A slit-less arrangement, as shown in the figure, may suffice. Then, when S is a point-like source of radiation, and distance a is sufficiently large, films F₁ and F₂ will each record a pair of narrow images formed by the and wavelengths, respectively. A wider area of specimen can be imaged if a line focus rather than a point focus is placed at S (Barth & Hosemann, 1958), but then the and images will overlap. Under conditions of high anomalous transmission, defects in the crystal cause a reduction in transmitted intensity, which appears similarly in the and images. Thus, it is possible to gain intensity and improve resolution by recording both images superimposed on a film F₃ placed in close proximity to the X-ray exit face DD′ (Gerold & Meier, 1959).

Figure 2.7.2.4| top | pdf | Topographic techniques using anomalous transmission.

The generation and properties of synchrotron X-rays are discussed by Arndt in Subsection 4.2.1.5 . For reference, his list of important attributes of synchrotron radiation is here repeated as follows: (1) high intensity, (2) continuous spectrum, (3) narrow angular collimation, (4) small source size, (5) polarization, (6) regularly pulsed time structure, and (7) computability of properties. All these items influence the design and scope of X-ray topographic experiments with synchrotron radiation, in some cases profoundly. The high intensity of continuous radiation delivered in comparison with the output of standard X-ray tubes, and hence the rapidity with which X-ray topographs could be produced, was the first attribute to attract attention, through the pioneer experiments of Tuomi, Naukkarinen & Rabe (1974), and of Hart (1975a). They used the simple diffraction geometry of the Ramachandran (Fig. 2.7.1.2) and Schulz (Fig. 2.7.1.1) methods, respectively. [Since in the transmission-specimen case a multiplicity of Laue images can be recorded, it is usual to regard this work as a revival of the Guinier & Tennevin (1949) technique.] Subsequent developments in synchrotron X-ray topography have been reviewed by Tanner (1977) and by Kuriyama, Boettinger & Cohen (1982), and described in several chapters in Tanner & Bowen (1980). Some developments of methods and apparatus that have been stimulated by the advent of synchrotron-radiation sources will be described in this and in the following Subsection 2.7.4.2, the division illustrating two recognizable streams of development, the first exploiting the speed and relative instrumental simplicity of white-radiation synchrotron X-ray topography, the second directed towards developing sophisticated `beam conditioners' to extract highly collimated and monochromatic beams from the continuous-wavelength output of the synchrotron source. In both monochromatic and continuous-radiation experiments, the high intensity renders it more practicable than with conventional sources to apply electronic `real-time' imaging systems (discussed in Sections 7.1.6 and 7.1.7 , and Subsection 2.7.5.2).

At the experimental stations where synchrotron X-ray topography is performed, the distance a from the source (the tangent point on the electron orbit) is never less than some tens of metres, e.g. 40 m at the Deutsches Elektronen-Synchrotron, Hamburg (DESY), a maximum of 80 m at the Synchrotron Radiation Source, Daresbury (SRS), and 140 m at the European Synchrotron Radiation Facility (ESRF). The dimensions of the X-ray source (given by the cross section of the electron beam at the tangent point) vary widely between different installations (see Table 4.2.1.7 ), but the dimension in the plane of the electron orbit is usually several times that normal to it. If W_x and W_z are the corresponding full widths at half-maximum intensity of the source, then with the simple X-ray optics of a white-radiation topograph the geometrical resolution will be W_xb/a and W_zb/a in the orbit-plane (horizontal) and normal to the orbit-plane (vertical) directions, respectively, independent of the orientation of the plane of incidence of the Bragg reflection concerned. Representative dimensions might be W_x= 2 mm, W_z = 0.5 mm, and a = 50 m. With b = 100 mm, the horizontal and vertical resolutions of the topograph image would then be 4 and 1 µm, respectively, comparable with those on a conventional source, but with b = 10 mm only. Thus, even under synchrotron-source conditions, it is desirable that b should not exceed some centimetres in order to avoid geometrical factors causing a severer limitation of resolution (at least in one dimension) than other factors [such as photo-electron track lengths in the emulsion and point-by-point statistical fluctuations in absorbed photon dose (Lang, 1978)]. Since synchrotron X-rays are generated at all points along a curved electron trajectory, they spread out in a sheet parallel to the orbit plane. So there is in principle no limit to the specimen dimension in that plane that can be illuminated in a white-radiation topograph. However, increased background due to scattering from air and other sources imposes a practical limit of around 100 mm on the beam width. With electrons circulating in a planar orbit, the divergence of radiation normal to the orbit plane is strongly constricted, significant intensity being contained only within a fan of opening angle , e.g. = 0.25 mrad with electron energy E = 2 GeV, equivalent to a vertical distance ∼12 mm with a = 50 m. This does impose a significant restriction on the area of specimen that can be imaged in a transmission topograph unless recourse be had to beam expansion by an asymmetrically reflecting monochromator crystal.

For analysis of the three-dimensional configuration of defects within crystals, it is a useful feature of white-radiation transmission topography that different views of the specimen are presented simultaneously by the assemblage of Laue images, and that when studying reflection from a given Bragg plane there is freedom to vary the glancing angle upon it. When interpreting the diffraction contrast effects observed, the relative contributions of all the diffraction orders superimposed must be considered. However, after taking into account source spectral distribution, specimen structure factors, absorption losses and film efficiency, it is often found that a particular order of reflection is dominant in each Laue image (Tuomi, Naukkarinen & Rabe, 1974; Hart, 1975a). The variation of diffraction contrast with wavelength follows different trends for different types of defect (Lang, Makepeace, Moore & Machado, 1983), so the ability to vary the wavelength with which a given order of reflection is studied can help in identifying the type of defect.

If the orbiting electrons are confined to a plane, then the radiation emitted in that plane is completely linearly polarized with the E vector in that plane. It follows that diffraction with the plane of incidence normal to the orbit plane is in pure σ-polarization mode (polarization factor P = 1), and with plane of incidence parallel to the orbit plane in pure π-polarization mode . The former, vertical plane of incidence is often chosen to avoid vanishing of reflections in the region of °. The ability to record patterns with either pure σ-mode or pure π-mode polarization is very helpful in the study of several dynamical diffraction phenomena. To facilitate switching of polarization mode, some diffractometers and cameras built for use with synchrotron sources are rotatable bodily about the incident-beam axis (Bonse & Fischer, 1981; Bowen, Clark, Davies, Nicholson, Roberts, Sherwood & Tanner, 1982; Bowen & Davies, 1983). From the diffraction-theoretical standpoint, it is the section topograph that provides the image of fundamental importance. High-resolution section-topograph patterns have been recorded with synchrotron radiation using a portable assembly combining crystal mount and narrow incident-beam slit. With the help of optical methods of alignment, this can be transferred between topograph cameras set up at a conventional source and at the synchrotron source (Lang, 1983).

The regularly pulsed time structure of synchrotron radiation can be exploited in stroboscopic X-ray topography. The wavefronts of travelling surface acoustic waves (SAW) on lithium niobate crystals have been imaged, and their perturbation by lattice defects disclosed (Whatmore, Goddard, Tanner & Clark, 1982; Cerva & Graeff, 1984, 1985). The latter workers made detailed studies of the relative contributions to the image made by orientation contrast and by `wavefield deviation contrast' (i.e. contrast arising from deviation of the energy-flow vector in the elastically strained crystal).

In order to achieve extremely small beam divergences and wavelength pass bands (dλ/λ), and, in particular, to suppress transmission of harmonic wavelengths, arrangements much more complicated than the double-crystal systems shown in Figs. 2.7.3.1 and 2.7.3.3 have been applied in synchrotron-radiation topography. The properties of monochromator crystals are discussed in Section 4.2.5 . In synchrotron-radiation topographic applications, the majority of monochromators are constructed from perfect silicon, with occasional use of germanium. Damage-free surfaces of optical quality can be prepared in any orientation on silicon, and smooth-walled channels can be milled into silicon monoliths to produce multireflection devices. First, for simpler monochromatization systems, one possibility is to set up a monochromator crystal oriented for Bragg reflection with asymmetry (i.e. giving to produce a narrow monochromatic beam with which section topographs can be taken (Mai, Mardix & Lang, 1980). The standard double-crystal topography arrangement is frequently used with synchrotron sources, the experimental procedure being as described in Section 2.7.3 and benefiting from the small divergence of the incident beam due to remoteness of the source. An example of a more refined angular probe is that obtainable by employing a pair of silicon crystals in setting to prepare the beam incident on the specimen crystal, the three crystals together forming a arrangement (Ishikawa, Kitano & Matsui, 1985). The first mono­chromator is oriented for asymmetric 111 Bragg reflection, the second for highly asymmetric reflection ( at λ = 0.12 nm), resulting in a divergence of only in the beam impinging on the specimen.

Multireflection systems, some of which were proposed by Du Mond (1937) but not at that time realizable, have become a practicality through the advent of perfect silicon and germanium. When multiple reflection occurs between the walls of a channel cut in a perfect crystal, the tails of the curve of angular dependence of reflection intensity can be greatly attenuated without much loss of reflectivity at the peak of the curve (Bonse & Hart, 1965a). Beaumont & Hart (1974) described combinations of such `channel-cut' monochromators that were suitable for use with synchrotron sources. One combination, consisting of a pair of contra-rotating channel-cut crystals, with each channel acting as a pair of reflecting surfaces in symmetrical setting, has found much favour as a monochromatizing device producing neither angular deviation nor spatial displacement of the final beam, whatever the wavelength it is set to pass. The properties of monoliths with one or more channels and employing two or more asymmetric reflections in succession have been analysed by Kikuta & Kohra (1970), Kikuta (1971), and Matsushita, Kikuta & Kohra (1971).

Symmetric channel-cut monochromators in perfect undistorted crystals transmit harmonic reflections. Several approaches to the problem of harmonic elimination may be taken, such as one of the following procedures (or possibly more than one in combination).

For X-ray topographic applications, it is very desirable to have a spatially wide beam issuing from the multiply reflecting device. This is achieved, together with small angular divergence and spectral window, and without need of mechanical bending, in a monolith design by Hashizume, though it lacks wavelength tunability (Petroff, Sauvage, Riglet & Hashizume, 1980). The configuration of reflecting surfaces of this monolith is shown in Fig. 2.7.4.1. Reflection occurs in succession at surfaces 1, 2, and 3. The monochromator characteristics are listed in Table 2.7.4.1. The wavelength is very suitable in many topographic applications, and this design has proved to be an effective beam conditioner for use in synchrotron-radiation `plane-wave' topography.

Table 2.7.4.1| top | pdf | Monolithic monochromator for plane-wave synchrotron-radiation topography Reflection 1 333 Reflection 2 Reflection 3 Output wavelength 0.12378 nm Spectral pass band, dλ/λ Angular divergence of exit beam Size of exit beam  mm

Figure 2.7.4.1 | top | pdf | Monolithic multiply reflecting monochromator for plane-wave topography.

In X-ray optics, the same basic geometrical interpretation of moiré patterns applies as in light and electron optics. Suppose radiation passes successively through two periodic media, (1) and (2), whose reciprocal vectors are and , so as to form a moiré pattern. Then, the reciprocal vector of the moiré fringes will be . The magnitude, D, of the moiré fringe spacing is and may typically lie in the range 0.1 to 1 mm in the case of X-ray moiré patterns. Simple special cases are the `rotation' moiré pattern in which , but makes a small angle α with . Then, the spacing of the moiré fringes is d/α and the fringes run parallel to the bisector of the small angle α. The other special case is the `compression' moiré pattern. Here, and are parallel but there is a small difference between their corresponding spacings, and . The spacing D of compression moiré fringes is given by D = d₁d₂/(d₁ − d₂) and the fringes lie parallel to the grating rulings or Bragg planes in (1) and (2). X-ray moiré topographs achieve sensitivities of to in measuring orientation differences or relative differences in interplanar spacing. Moreover, if either periodic medium contains a lattice dislocation, Burgers vector b, for which , then a magnified image of the dislocation will appear in the moiré pattern, as one or more fringes terminating at the position of the dislocation, the number of terminating fringes being , which is necessarily integral (Hashimoto & Uyeda, 1957).

X-ray moiré topography has been performed with two quite different arrangements, the Bonse & Hart interferometer, and by superposition of separate crystals (Brádler & Lang, 1968). For accounts of the principles and applications of the interferometer, see, for example, Bonse & Hart (1965b, 1966), Hart (1968, 1975b), Bonse & Graeff (1977), Section 4.2.6 and §4.2.6.3.1 . Fig. 2.7.5.1 shows the arrangement (Hart, 1968, 1972) for obtaining large-area moiré topographs by traversing the interferometer relative to a ribbon incident beam in similar fashion to taking a normal projection topograph (Fig. 2.7.2.2); P is the incident-beam slit, Q is a stationary slit selecting the beam that it is desired to record, and film, F, and interferometer, SMA, together traverse to and fro as indicated by the double-headed arrow. In Fig. 2.7.5.1, S, M, and A are the three equally thick wafers of the interferometer that remain upstanding above the base of the monolithic interferometer after the gaps between S and M, and M and A, have been milled away. The elements S, M and A are called the splitter, mirror, and analyser, respectively. The moiré pattern is formed between the Bragg planes of A and the standing-wave pattern in the overlapping and beams entering it. Maximum fringe visibility occurs in the emerging beam that the slit Q is shown selecting. A dislocation will appear in the moiré pattern whether the lattice dislocation lies in S, M, or A, provided . Moiré patterns formed in a number of Bragg reflections whose normals lie in, or not greatly inclined to, the plane of the wafers, can be recorded by appropriate orientation of the monolith. By this means, it is easily discovered in which wafer the dislocation lies, and its Burgers vector can be completely determined, including its sense, the latter being found by a deliberate slight elastic deformation of the interferometer (Hart, 1972). Satisfactory moiré topographs have been obtained with an interferometer in a synchrotron beam, despite thermal gradients due to the local intense irradiation (Hart, Sauvage & Siddons, 1980).

Figure 2.7.5.1| top | pdf | Scanning arrangement for moiré topography with the Bonse–Hart interferometer.

Fig. 2.7.5.2 shows crystal slices (1), ABCD, and (2), EFGH, superposed and simultaneously Bragg reflecting in the Brádler–Lang (1968) method of X-ray moiré topography. The slices could have been cut from separate crystals. In the case when the Bragg planes of (1) and (2) are in identical orientation but have a translational mismatch across CD and EF with a component parallel to h, strong scattering occurs towards Z as focus, producing extra intensity at in the beam and at in the beam . It is usual to record the moiré pattern using the beam. Projection moiré topographs are obtained by the standard procedure of traversing the crystal pair and film together with respect to the incident beam SO. The special procedure devised for mutually aligning the two crystals so that and coincide within their angular range of reflection is explained by Brádler & Lang (1968). This method has been applied to silicon and to natural (Lang, 1968) and synthetic quartz (Lang, 1978).

Figure 2.7.5.2| top | pdf | Superposition of crystals (1) and (2) for production of moiré topographs. [Reproduced from Diffraction and Imaging Techniques in Material Science, Vol. II. Imaging and Diffraction Techniques, edited by S. Amelinckx, R. Gevers & J. Van Landuyt (1978), Fig. 21, p. 695. Amsterdam, New York, Oxford: North-Holland.]

Position-sensitive detectors involving the production of electrons are described in Chapter 7.1 , Sections 7.1.6 and 7.1.7 , and Arndt (1986, 1990). Those descriptions cover all the image-forming devices that form the core of systems set up for `live' X-ray topography. Here, discussion is limited to remarks on the historical development of techniques designed for making X-ray topographic images directly visible, and on the leading systems that are now sufficiently developed to be acceptable for routine use, in particular on topograph cameras set up at synchrotron X-ray sources. Two types of system became practicalities about the same time, that using direct conversion of X-rays to electronic signals by means of an X-ray-sensitive vidicon television camera tube (Chikawa & Fujimoto, 1968), and the indirect method using an external X-ray phosphor coupled to a multistage electronic image-intensifier tube (Reifsnider & Green, 1968; Lang & Reifsnider, 1969) or to a television-camera tube incorporating an image-intensifier stage (Meieran, Landre & O'Hara, 1969). These two approaches, the direct and the indirect, remain in competition. Developments up to the middle 1970's have been comprehensively reviewed by Hartmann (1977). Since that time, Si-based, two-dimensional CCD (charge-coupled device) arrays have come into prominence as radiation detectors. They can be used for direct conversion of low-energy X-rays into electronic charges as well as for recording images of phosphor screens. As illustrated by Allinson (1994), four configurations employing CCD arrays for X-ray imaging can be considered: (i) direct detection by the `naked' device; (ii) detection by phosphor coated directly on the CCD array; (iii) phosphor separate, and optically coupled to the CCD by lens or fibre-optics; and (iv) the addition to (iii) of an image intensifier or microchannel plate coupled to the phosphor screen. Consider first configuration (i). X-ray absorption efficiency in the active layer of silicon is near unity for radiations such as Cu Kα, and is not less than about 20% for Mo Kα or Ag Kα. Since about one-third of the absorbed energy goes into electron–hole pair production, an absorbed 8 keV X-ray photon creates about 2000 pairs, a large number compared with a combined dark-current plus read-out noise level per photosite of a few tens of electrons r.m.s. Thus, single-photon counting is possible. Moreover, a cooled CCD can integrate the charge accumulated in each pixel for up to  s. With pixel sizes in the range 10 to 30 µm square, and 1024 × 1024 (or 2048 × 2048) arrays in production, sensitive areas of 50 mm square, or greater, are available, sufficient for the majority of topographic applications.

For X-ray-sensitive TV-camera tubes, some major improvements in resolution and sensitivity have taken place since the first applications to X-ray topography of Be-windowed vidicons. Using the more sensitive `Saticon' tube with incorporation of a 20 µm-thick Se–As target that provides good X-ray absorption efficiency, Chikawa, Sato & Fujimoto (1984) achieved a resolution as good as 6 µm at a modulation transfer function (MTF) of 5%. This betters that achieved with indirect systems or with standard-pixel-size CCD arrays used as direct detectors. The newer `Harp' tube, which employs avalanche multiplication produced by a high field ( V m⁻¹) applied across a 2 µm Se target to increase light sensitivity at least ten fold compared with the Saticon tube, has also been modified into a direct X-ray detector. Increasing the target thickness to 8 µm and adding an X-ray-transparent window provides satisfactory detector efficiency over a useful wavelength range (and the Se Kα-absorption edge at 0.098 nm causes absorption efficiencies for Cu Kα and Mo Kα to be similar, about 25%). The gain is sufficient for detection of single Cu Kα photon-absorption events (at least for photons absorbed close to the target front, giving the maximum path for avalanche formation). A limiting resolution of about 25 µm (at MTF of ∼33%) is exhibited (Sato, Maruyama, Goto, Fujimoto, Shidara, Kawamura, Hirai, Sakai & Chikawa, 1993), not yet as good as the 6 µm achieved with the Saticon tube. The rather small 6 × 9 mm sensitive areas of these camera tubes (when in standard ` in' size) restricts their range of topographic applications as direct detectors compared with CCD arrays, but their amorphous Se targets are less likely to be degraded by X-radiation damage than crystalline-silicon CCD arrays. The latter do suffer degradation, but recover after treatment (Allinson, Allsopp, Quayle & Magorrian, 1991).

In the case of indirect systems, the lens or fibre-optic plate situated between phosphor and detector automatically protects the latter from radiation damage. Somewhat better resolution can be achieved by lens coupling than by fibre-optic coupling of phosphor to detector, but at the expense of loss of light-collection efficiency generally too great to be acceptable. In principle, magnification or de-magnification of the phosphor-screen image on the detector can be selected according to whether phosphor or detector has the better resolution, in order to maximize the system resolution as a whole. Phosphor resolution can be increased by diminishing its thickness below the value that would be chosen from consideration of X-ray absorption efficiency alone. Using a phosphor screen of Gd₂O₂S(Tb) only 5 µm thick, and lens-coupling it with tenfold magnification on to the target of a low-light-level television camera, Hartmann achieved a system resolution of about 10 µm (Queisser, Hartmann & Hagen, 1981), as good as any demonstrated so far with indirect systems.

The phosphors already used (or potentially usable) in real-time X-ray topography are inorganic compounds containing elements of medium or heavy atomic weight. They include ZnS(Ag), NaI(Tl), CsI(Tl), Y₂O₂S(Tb), Y₂O₂S(Eu), La₂O₂S(Eu) and Gd₂O₂S(Tb). Problems encountered are light loss by light trapping within single-crystal phosphor sheets, and resolution loss by light scattering from grain to grain in phosphor powders. Various ways of reducing lateral light-spreading within phosphor screens by imposing a columnar structure upon them have been tried. Most success has been achieved with CsI. Evaporated layers of this crystal have a natural tendency towards columnar cracking normal to the substrate. Then internal reflection within columns reduces `cross talk' between columns (Stevels & Kühl, 1974). However, a columnar structure can be very effectively imposed on CsI films evaporated on to fibre-optic plates by etching away the cladding glass surrounding each fibre core to a depth of 10 µm, say. The evaporated CsI starts growing on the protruding cores, and continues as pillars physically separated and hence to a large degree optically separated from their neighbours (Ito, Yamaguchi & Oba, 1987; Allinson, 1994; Castelli, Allinson, Moon & Watson, 1994).

The drive to develop systems for 2D imaging of single-crystal or fibre diffraction patterns produced by synchrotron radiation that offer spatial resolution better than that within the grasp of position-sensitive multiwire gas proportional counters (say 100–200 µm) has produced several phosphor/fibre-optic/CCD combinations that with some modifications would be useful for real-time X-ray topography. Diffraction-pattern recording requires a sensitive area not less than about 50 mm in diameter, so most systems incorporate a fibre-optic taper to couple a larger phosphor screen with a small CCD array. Spatial resolution in the X-ray image cannot then be better than CCD pixel size multiplied by the taper ratio. In one system that has been fully described, this product is 20.5 µm × 2.6, and a point-spread FWHM of 80 µm on a 51 × 51 mm input area was realised without benefit from a columnar-structure phosphor (Tate, Eikenberry, Barna, Wall, Lawrance & Gruner, 1995). More appropriate for X-ray topography would be unit-magnification optical coupling of phosphor with a CCD array of not less than 1024 × 1024 elements and not more than 20 µm square pixel size. With such a combination, a system resolution of ∼25 µm should be achievable; and at a synchrotron X-ray topography station at least one device offering resolution no worse than this should be available. There is a scope for both high-resolution, small-sensitive-area and lower-resolution, large-sensitive-area imaging systems in real-time X-ray topography. It has been shown possible to incorporate both types in a single topography camera for use with synchrotron radiation (Suzuki, Ando, Hayakawa, Nittono, Hashizume, Kishino & Kohra, 1984).