Bragg contrast

Fig. 17. Group of metadislocations in 28-Al-Pd-Mn. (a) At lower magnification in two-beam Bragg contrast using the (006) reflection for imaging close to the (120) axis and (b) close to the (010) zone axis, (c) Imaged under bright-held Laue conditions at the (010) zone axis, (d) Boxed area in (c) at higher magnihcation. Scale bars. 100 nm (a, b, c) and 10 nm (d).

First characterizations of the Burgers vector of metadislocations were carried out by means of Bragg-contrast analysis [39]. Their Burgers vector direction was determined as parallel to the [001] direction. Since the line direction is parallel to the [010] direction, metadislocations are pure edge dislocations. 

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

The Bragg scattering of X-rays by a periodic lattice in contrast to a Mossbauer transition is a collective event which is short in time as compared to the typical lattice vibration frequencies. Therefore, the mean-square displacement (x ) in the Debye-Waller factor is obtained from the average over the ensemble, whereas (r4) in the Lamb-Mossbauer factor describes a time average. The results are equivalent. 

TRXRD detects the propagation of coherent acoustic phonons as a transient change in the diffraction angles. In contrast, the atomic motions associated with coherent optical phonons modify only the Bragg peak intensity, because they do not change the barycentric positions of the crystal lattice. The Bragg peak intensity is proportional to the squared modulus of the structure factor [1,3,4] ... 

The Bragg confinement mechanism allows great flexibility in engineering the radial mode profile. For example, it is possible to design a resonator in which the light is confined within a defect composed of low refractive index material or even air. By contrast, this would be impossible in the case of conventional TIR-based resonators. Such configuration is useful for sensing applications as discussed later. 

There are established criteria for obtaining b by using diffraction contrast (23). Briefly, the dislocation intensity (contrast) is mapped in several Bragg reflections (denoted by vector, g) by tilting the crystal to different reflections and determining the dot product of the vectors g and b (called the g b product analysis). 

We should first correct the wavevector inside the crystal for the mean refractive index, by multiplying the wavevectors by the mean refractive index (1 + IT). This expression is derived from classical dispersion theory. Equation (4. 18) shows us that is negative, so the wavevector inside the crystal is shorter than that in vacuum (by a few parts in 10 ), in contrast to the behaviom of electrons or optical light. The locus of wavevectors that have this corrected value of k lie on spheres centred on the origin of the reciprocal lattice and at the end of the vector h, as shown in Figure 4.11 (only the circular sections of the spheres are seen in two dimensions). The spheres are in effect the kinematic dispersion surface, and indeed are perfectly correct when the wavevectors are far from the Bragg condition, since if D 0 then the deviation parameter y, 0 from... 

The width of the image can be deduced using this simple idea of contrast being formed when the misorientation around the defect exceeds the perfect crystal reflecting range. We consider the case of a screw dislocation nmning normal to the Bragg planes, where the line direction / coincides with the diffraction vector g. The effective misorientation at distance r from the core is =bH r (8.41)... 

On a finer level, spherical grains that have an average diameter of 11 A are seen. A section analysis, which consisted of a plot of image contrast intensity versus distance, indicated that there is a mean periodicity of around 49 A, which is close to the values of the SAXS Bragg spacing usually associated with intercluster distances. This, as well as other microscopic studies, favors the model of phase separation as opposed to the core—shell model as applied to the interpretation of scattering data. The hydrated... 

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