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

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.