X-ray diffraction topography is a well-established method for the visualisation and analysis of crystal defects in high-quality single crystals. Distortions of the crystal lattice, such as those provoked by individual dislocations, give rise, in the low absorption case, to locally enhanced X-ray reflectivity. They can be observed as line-shaped contrasts (so-called "direct image" contrast [1]). However, in a single diffraction topograph, the 3D dislocation structure is projected into two dimensions. Therefore, more refined methods are required to determine the spatial arrangement of the dislocations in the bulk of the crystal.

Provided the direct image is the dominant contrast mechanism, the intensity distribution in the diffraction image is a good approximation to a 2D projection of the local reflectivity along the direction of the diffracted beam. Consequently, if one succeeds in measuring a large number of such projections while turning the sample around a fixed rotation axis, the principles of computed tomography can be applied in order to reconstruct the unknown 3D distribution of the local reflectivity. However, compared to conventional absorption tomography, there is the additional constraint that the crystal, during its turn around the rotation axis, has to stay in diffraction for a given reflection. This can be achieved by an experimental setup as depicted in Figure 143, which allows precise alignment of the rotation axis a and the reciprocal lattice vector g associated with the chosen sample reflection.


Fig. 143: Experimental setup used for topo-tomographic data acquisition. During the tomographic scan, the crystal is turned around the rotation axis a (angle ). The crystal has to be aligned such that the diffraction vector g is parallel to a.

Figure 144a shows one of the 500 diffraction topographs recorded from a 7 x 7 x 2 mm3 sized synthetic diamond sample. As can be seen from this diffraction image, the crystal contains a large number of individual dislocations, which superpose in this single projection. Figure 144b shows the result of the tomographic reconstruction: the depicted slice corresponds to a virtual section of the crystal at the position of the dashed line AA', indicated in Figure 144a. One can clearly distinguish the trapezoidal outline of the sample cross-section and a number of isolated point-like contrasts. These contrasts correspond to the positions where the dislocations thread through the layer. Applying a simple intensity threshold to the 3D data set, one can easily visualise the 3D arrangement of the dislocation lines with standard volume rendering software. Such a 3D rendition of a small part of the crystal (indicated by the box in Figure 144a) is finally shown in Figure 144c. One can observe different families of line-shaped contrasts, which correspond to dislocations with preferential orientations in the crystal lattice.


Fig. 144: (a) Integrated, monochromatic beam X-ray diffraction topograph (2D) of diamond sample (white corresponds to higher diffracted intensity). (b) 2D tomographic slice (plane AA' in (a)), reconstructed from a series of 500 diffraction topographs. (c) 3D rendition of the small part of the crystal, indicated in (a).

To summarise, "topo-tomography" may be regarded as a new three-dimensional crystal characterisation technique, based on the combination of X-ray diffraction topography and computed microtomography. The approach is applicable to high-quality single crystals and yields an approximation of the three-dimensional distribution of the local Bragg reflectivity in the bulk of the crystal.

Reference
[1] B.K. Tanner, X-ray Diffraction Topography, Pergamon Press, Oxford (1976).

Principal Publication and Authors
W. Ludwig (a), P. Cloetens (a), J. Härtwig (a), J. Baruchel (a), B. Hamelin (b) and P. Bastie (c), J. Appl. Cryst., 34, 602-607 (2001).
(a) ESRF
(b) ILL
(c) Laboratoire de Spectrométrie Physique, UMR UJF-CNRS Grenoble (France)