Planar interfaces, diffraction

In recent years, high-resolution x-ray diffraction has become a powerful method for studying layered strnctnres, films, interfaces, and surfaces. X-ray reflectivity involves the measurement of the angnlar dependence of the intensity of the x-ray beam reflected by planar interfaces. If there are multiple interfaces, interference between the reflected x-rays at the interfaces prodnces a series of minima and maxima, which allow determination of the thickness of the film. More detailed information about the film can be obtained by fitting the reflectivity curve to a model of the electron density profile. Usually, x-ray reflectivity scans are performed with a synchrotron light source. As with ellipsometry, x-ray reflectivity provides good vertical resolution [14,20] but poor lateral resolution, which is limited by the size of the probing beam, usually several tens of micrometers. 

Gevers, Landuyt, and Amelinckx (1965) have used the two-beam dynamical theory with absorption, Eqs. (5.5), to derive explicit expressions for the transmitted intensity TT and the diffracted intensity SS for a crystal containing a general boundary, from which the detailed nature of the intensity profiles of the fringe patterns due to specific types of planar interfaces can be determined. 

The study of planar interfaces by means of electron microscopy. In Modern Diffraction and Imaging Techniques in Materials Science, edited by S. Amelinckx, R. Gevers, G. Remaut, J. van Landuyt, pp. 257-94. Amsterdam North-Holland. 

Diffraction by a Crystal Containing a Planar Interface [155]. The amplitudes of the transmitted and scattered beams for a foil containing a planar interface, with displacement vector R (Fig. 29 B), can be formulated as... 

Planar Defects. The diffraction contrast images of planar interfaces that intersect the foil surfaces consist of a set of fringes parallel to the closest surface with a depth period given by la (which is equal to tgfor 5 = 0 see Section 29.2.2.4.6). If the planar interface is parallel to the foil surfaces, which is often the case in cleaved foils, the faulted area exhibits only a brightness difference. 

Figure 4 shows a SEM image of the oxide scale after 50 h of oxidation at 950 °C. revealing the platelet-shape morphology on the oxide surface. Figure 5 represents a cross-sectional TEM image of the oxide scale and the interface. A high number of planar defects was observed in the oxide scale. Electron diffraction revealed that the orienta-... 

To observe the equilibrium shape of a crystal experimentally, it is necessary to confirm that the crystal one wants to observe exhibits such a shape. Since the equilibrium shape of a crystal in a matrix is the same as the equilibrium shape of the matrix entrapped within the crystal, the equilibrium crystal shape can be determined by observing the shape of the entrapped matrix. If a number of randomly oriented grains exhibit an equilibrium shape, the shape can also be determined stereographically from the crystal plane orientations of the grains and the directions of the grain interfaces on a planar section that can be obtained by the electron backscattered diffraction technique. For metals for which the anisotropy in interfacial energy is low at their processing... 

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