Mechanical properties of crystals bent through indentations for the realization of a Laue lens for concentration of hard x-rays

A Laue lens is an optical component to focus hard x-ray photons through Bragg diffraction in Laue geometry within a properly arranged array of crystals. For a Laue lens a significantly important field of application is represented by astrophysics. Indeed, a Laue lens as space-borne focusing telescope would allow a sensitivity leap by more than an order of magnitude with respect to existing telescopes in the hard x-ray domain. Observations of many violent phenomena occurring in our Galaxy would take advantage of this kind of concentrator. As an example, the study of positron distribution in space would provide significantly important clues thanks to the concentration of 511-keV annihilation line by a Laue lens. Since in most cases a Laue lens is requested to concentrate radiation over a broad energy range, a typical component for wide-passband focusing is a mosaic crystal. However, this latter suffers a 50%-limit in diffraction efficiency. A method to overcome such a limitation is the usage of crystals with curved diffracting planes. Curved crystals exhibit a uniform energy distribution with a passband proportional to the curvature and their diffraction efficiency is not limited to 50% [1]. For fabrication of curved crystals several methods have been worked out [2]. Nevertheless, since a Laue lens application demands as light components as possible, among curved crystals special interest is given to those that are being bent due to internal forces. For this aim, within the framework of the “Laue project” as financed by the Italian Space Agency, an easy and reproducible technique to fabricate curved crystals by internal forces is presented. Indentations manufactured on the surface of a crystal by a diamond saw induce a permanent curvature within the crystal, with no need for external device. Indeed, this method is based on irreversible compression of the crystal beneath and beside the indentations. This region, being highly defected, prevents the crystalline material between the indentations from full mechanical relaxation. As a result of such a deformation, the remaining crystal below the indentations is bent to a net and uniform curvature, without the usage of any external device. Morphological curvature of indented crystals has been modeled through the theory of elasticity in an anisotropic medium and a revisitation of the Stoney equation has been worked out for determination of the radius of curvature. Si crystals bent by indentations were fabricated at Sensor and Semiconductor Laboratory (Ferrara, Italy) and characterized by synchrotron radiation at European Synchrotron Radiation Facility. Crystals proved to efficiently diffract up to 700 keV, peaking 95% at 150 keV. This method can thus combine easiness and reproducibility with high-efficiency concentration of hard x-rays.