Influence of the crystal-surface unevenness on the angular spread of an x-ray diffracted beam

Abstract

One of the factors influencing the focus size in diffractive–refractive optics is the quality of diffracting surface. If the surface is uneven, as it is when the silicon crystal surface is only etched, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown theoretically that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam such that it causes a significant broadening of the focus. In this case a mechanical–chemical polishing is necessary. This has been verified by us earlier in a preliminary experiment with synchrotron radiation. In this work the new experiment with the same crystals is performed using double crystal (+, −) arrangement and a laboratory x-ray source (CuKα radiation). We compared two samples; one of them is mechanically–chemically (MC) polished and thus the diffracting surface is almost perfect; the other is only etched. This experiment allows a better comparison of the result with the theory. The difference between the measured rocking curve widths for the etched and MC polished crystals (10″) roughly agrees with theory (7″), which supports the correctness of the theoretical approach.

Elastic Variation of Quasi-One-Dimensional Cubic-Phase GaN at Nanoscale

“…At ϕ′ = 0 and 180°, h -GaN­(000 m ) ( m = 2, 4, 6) is also observable. It has been reported that the surface roughness can affect the fwhm of a peak in a low-angle incident X-ray beam to the surface . In Figure b, the surface is relatively rough at the sub-micrometer scale.…”

“…It has been reported that the surface roughness can affect the fwhm of a peak in a low-angle incident X-ray beam to the surface. 21 In Figure 1b, the surface is relatively rough at the sub-micrometer scale. For the accuracy in fwhm, as seen in Figure 4, n = 3 for c-GaN and m = 6 for h-GaN were chosen.…”

Diffractive–refractive optics: low-aberration Bragg-case focusing by precise parabolic surfaces

“…We used two Si(111) crystals in an asymmetric arrangement, with an asymmetry angle of = 15 ; with a beam energy of 7.31 keV, then  B = 15.7 . The impinging radiation formed an incident angle of 0.7 with the surface which meant that this arrangement is surface-sensitive (Hrdá et al, 2003(Hrdá et al, , 2005. The cut-off edge (creating an L-shape crystal) of the crystal (Fig.…”

Aberrations of diffractive–refractive optics: Bragg-case sagittal focusing of multiple parabolic elements

“…Consequently, the position of the diffraction events on the optical path also somewhat depends on x. As the sagittal deviation δ after diffraction from the wall of the groove is [2] |δ| = |K dy/dx|, (9) which is of the order of 10 −4 rad or less, these displacements are of the order of 10 −2 -10 −3 mm or less for dy/dx < 1 and this effect on the focus size may be obviously neglected. Only for a very steep wall of the groove might this play a role.…”

“…As in any focusing device, there is a need to determine the minimal focus size achievable by the method. The quality of the diffracting surface may play a significant role when highly asymmetric diffraction is used; this influence is discussed elsewhere [8,9] . Apart from the focus distortion caused by the crystal surface quality, we will try to discuss the theoretical aberration which limits the achievable focus size in this method.…”