Origin of quasi-mosaic effect for symmetric skew planes in a silicon or germanium plate

Bent silicon and germanium crystals are used for several modern physics applications, above all for focusing of hard X-rays and for steering of charged particle beams by means of channeling and related coherent phenomena. In particular, anisotropic deformations are effectively exploited for these applications. A typical anisotropic deformation that is used is the quasi-mosaic (QM) curvature. It involves the bending of crystallographic planes that would be otherwise flat in the case of an isotropic medium. Here, the curvature the {110} planes was obtained through the quasi-mosaic effect in the symmetric configuration for the first time. This achievement is important because the {110} family of planes is highly efficient for both the applications mentioned above. Until now, the curvature of {110} planes in the QM configuration has not been used because it vanishes if the direction of the planes is aligned with the applied moment that bends the crystal plate. Indeed, to obtain the curvature of this particular family of crystallographic planes, the 〈110〉 direction has not to be aligned with respect to the imparted moment that bends the plate, i.e. the {110} planes have to be skew planes. Experimental verification of the quasi-mosaic curvature for the {110} planes was provided through hard X-ray diffraction at beamline ID15A of the European Synchrotron Radiation Facility in Grenoble, France, showing good agreement with the theoretical expectation.