Bragg plane tilt

Figure 2.21 Bragg plane tilt aberration, (a) Diffracting planes parallel, diffraction occurs simultaneously over the whole height of the beam, (b) Diffracting planes skewed, diffraction only takes place over a narrow band, (c) As the crystal is rotated to measure the rocking curve, the band moves up or down the crystal. The integrated intensity remains approximately the same as in case (a) but the peak intensity decreases and the width increases...

Tilt of the Bragg plane of the specimen, so that its dispersion plane is not parallel... 

The theory of this aberration was worked out in the 1920s by Schwarzchild. For simphcity we shall discuss the case of a beam conditioner comprising a single crystal and an aperture as in the classic double-crystal arrangement. If the Bragg planes are tilted about an axis contained in the incidence plane and the... 

Tilting about axis in incidence plane and Bragg plane... 

Owing to the distance between somce and specimen, the divergence of the beam normal to the dispersion plane is small and with SR it is uimecessaty to perform tilt adjustments to bring the Bragg planes of specimen and beam conditioner exactly parallel. 

Now consider how various reflection planes within the fiber might reflect the x-rays. The incident x-ray beam is in the X Y plane. Any Bragg planes that are parallel to Z, the fiber axis, would reflect the x-rays such that they remain in this plane. These are called the equatorial reflections. For the x-rays to be reflected above or below the X-Y plane, the corresponding Bragg planes must be tilted with respect to the fiber axis, and these reflections out of the X-Y plane are termed off-equatorial. There is a major distinction between... 

If, as in Fig. 108 a, the c axis of the crystal is displaced from the axis of rotation in the plane normal to the beam (for the mean position of the crystal), the zero layer (hk0) of the reciprocal lattice is tilted in this same direction, and its plane cuts the sphere of reflection in the circle AD. During the 15° oscillation a number of hkO points pass through the surface of the sphere, and thus X-rays reflected by these hkO planes of the crystal strike the film at corresponding points on the flattened-out film (Fig. 108 b) the spots fall on a curve BAD, whose distance from the equator is a maximum at a Bragg angle 0 = 45° and zero at 6 = 90°. If, on the other hand, the displacement of the c axis is in the plane containing the beam (Fig. 108 c), the spots on the film fall on a curve whose maximum distance from the equator is at 6 = 90° (Fig. 108 d). When the displacement of the c axis has components in both directions,... 

When the electrons impinge on the crystalline sample, they interact with individual lattice planes. When these interactions satisfy the Bragg condition, they exhibit backscattering diffraction and (due to the tilted sample) are directed toward a phosphor screen where the fluorescent pattern is detected by a CCD camera. The resulting pattern consists of a large number of intersecting bands, known as Kikuchi lines, which represent the unique crystallographic properties of the crystal... 

Gnki is the modulus of the vector of the reciprocal lattice associated to the (hkl) rehection, A9 is the tilt angle from the Bragg condition, and 0 is the angle between the lateral facets and the basal plane (if re-entrant angles are present, the width of the fringes is smaller [110]). If the epitaxial relationships are known, the nature of the facets is directly deduced from the 0 angles [115]. The structure of individual... 

The sample is mounted on a support that can move around three rotation axes an axis to makes it possible to choose the ineidence angle a of the beam with the film, an axis normal to the irradiated surface, makes it possible to rotate the sample in its plane, and finally an axis %, normal to the two others and belonging to the sample s plane, makes it possible to tilt the sample. The diffracted beams are measured in the n plane, since the detector can rotate aioimd the axis to shared by the sample and the part holding the detector. The incidence angle a can either be coupled or not to the detector s position if these two rotations are coupled, the measirrement is performed in the Bragg-Brentano conchtions, which should make it possible to have a constant irradiated volume if the sample is assumed to be infinite. 

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