[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

One can find predictions of this effect in the

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One can find predictions of this effect in the literature [163]. The mea- sured linear gradient of Ge concentration of 0.8 at.%/cm followed a curvature of the lattice plane with a radius of 102 m. Such crystal parameters fulfil the conditions of an effective compensation of a natural synchrotron beam diver- gence at a distance of 22 m from the source. For the crystals chosen we found perfect beam collimation at the energy of about 8 keV using simultaneously a linear lattice parameter gradient and a bent lattice structure. Double-crystal diffractometer measurements of the divergence of the beam diffracted from the graded crystal at 8 keV photon energy are shown in Fig. 3.53. Here is plotted the angular variation of the diffracted beam measured with the beam directed along the concentration gradient (1) and anti-parallel to the gradient (2). The monochromatic parallel beam with a divergence of less than 1 arcsec and cross-section of 0 . 1 × 0 . 1 mm 2 was used as the input beam in this experiment. Diffraction angle variations were measured by scans over the entire crystal surface with 1 mm steps. One can see no variation of the Bragg angle for the beam coming anti-parallel to the gradient direction along the crystal surface. For energies lower than 8 keV, due to the larger Bragg angle, the dif- fracted beam becomes slightly divergent. For energies higher than 8 keV, the diffracted beam is convergent and focused at the corresponding distance. The effect of this convergence/divergence gives us an additional, very important
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X-Ray Optics 165 Crystal SiGe (220) Ge gradient 0.8 at.% /cm X-Ray beam 8 keV (2) (1) (a) 0 5 10 15 20 25 30 - 100 - 80 - 60 - 40 - 20 0 20 (b) (2) (1) Bragg angle variation (arcsec) Position (mm) Fig. 3.53. X-ray beam collimation by a graded SiGe crystal: Optical arrangement ( a ) and Bragg angle variation in parallel (1) and anti-parallel (2) incident beam directions ( b ) advantage. For a crystal with a linear parallel lattice and a parameter gradi- ent, the theory predicts a very sharp energy of maximum energy resolution, especially for the higher indices of reflection (3.101). In the case of a bent lattice this range becomes relatively broad, as is shown experimentally in this paper. The broadening of the “resonant” curve is produced by a combination of the lattice parameter gradient and bent lattice planes. Double-Crystal Monochromator Performance The graded crystals were mounted in a double-crystal monochromator at the BESSY KMC-2 beamline. Carefully polished crystals with (220) orien- tation were placed in positions according to the calculations as it is shown in Fig. 3.54. Crystal 2 SiGe (220) X-ray beam Graded crystal 1 SiGe (220) Fig. 3.54. Optical scheme of the KMC-2 monochromator with a graded SiGe crystal as the first element. The second crystal is SiGe without gradient
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166 A. Erko The first graded crystal has curved lattice planes in addition to the lat- tice parameter gradient. The gradient direction is shown in Fig. 3.54 by an arrow. Thus diffraction focusing takes place in the meridional direction and changes the beam divergence. A monochromatic beam, slightly divergent or
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