Diffraction planes

The parallelization of crystallites, occurring as a result of fiber drawing, which consists in assuming by crystallite axes-positions more or less mutually parallel, leads to the development of texture within the fiber. In the case of PET fibers, this is a specific texture, different from that of other kinds of chemical fibers. It is called axial-tilted texture. The occurrence of such a texture is proved by the displacement of x-ray reflexes of paratropic lattice planes in relation to the equator of the texture dif-fractogram and by the deviation from the rectilinear arrangement of oblique diffraction planes. With the preservation of the principle of rotational symmetry, the inclination of all the crystallites axes in relation to the fiber axis is a characteristic of such a type of texture. The angle formed by the axes of particular crystallites (the translation direction of space lattice [c]) and the... 

The first term is related to the (surface weighted) average size, whereas the second is a function of the microstrains. The first term is the same for all peaks, whereas the second depends on the interplanar spacing, "d", of the diffraction planes, and is proportional to 1/d. The... 

The diffraction pattern provides us with intensity and geometric information. The equation for intensity of each diffracting plane, is given by... 

Finally we remark that proper alignment of all diffractive-optic beam corrditioners normally reqrrires that they be adjusted with a common dispersion plane. This is defirred as the plane corrtaining the incident and diffracted beam (and therefore also the rrormals of the diffracting plane) for any given reflection. If the dispersion planes are rrot parallel then some intensity will be lost from the restriction this causes to the angular acceptance in the plane perpendicular to the dispersion plane. 

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...

Figure 2.23 A 360° -scan of a sample with a single epilayer, indicating the value of that gives perfect alignment of the diffracting planes...

Gerchberg, R. W. and Saxton, W. O. (1972). A practiced algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237-46. [128]... 

X Ray Diffraction (XRD) The XRD pattern of AISBA parent material after calcination is shown in Figures 2-a. It exhibits one very intense line and two weak lines, which can be indexed to (100), (110) and (200) diffraction planes characteristic of the SBA-15 hexagonal structure [11]. This indicates that no significant changes happen in the mesoporous structure after Al incorporation and that AISBA presents a regular hexagonal array of cylindrical mesopores with dioo spacing equal to 10.8 nm, very close to that of SBA (Table 1). 

Table 6. Diffracting planes in the hydroxyapatite crystal lattice demonstrated by electron microscopy362 ...

The X-ray diffraction pattern for the electrolyte of the anode-supported cell is measured and the residual stresses were estimated by the sin2 sustaining stresses, the inter-planar spacing d between the specified diffracting planes of a crystallite in a microscopic grain can be expressed as... 

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