Riccardo Camattari

High diffraction efficiency at hard X-ray energy in a silicon crystal bent by indentation

The diffraction properties of a crystalline silicon plate of which one face was mechanically indented have been studied. This treatment induced a permanent curvature in the sample, which allowed a diffraction efficiency of 88% for 150 keV photons, i.e. a reflectivity of 64% including the absorption. This efficiency is constant over 14 arcseconds and is very close to the theoretical expectation, meaning that the curvature is highly homogeneous. The technique enables the fabrication, in a very reproducible fashion, of crystals for the realization of an astronomical hard X-ray concentrator (Laue lens).

Proposal for a Laue lens with quasi-mosaic crystalline tiles

Quasi-mosaicity is an effect of secondary bending within a crystal driven by crystalline anisotropy. This effect can be used to fabricate a series of curved crystals for the realization of a Laue lens. It is highlighted that crystals bent by the quasi-mosaic effect allow very high resolution focusing with respect to mosaic crystals. Under the same conditions for energy passband, crystal size and flux of incident photons, a Laue lens based on quasi-mosaic crystals would increase the signal-to-noise ratio by about an order of magnitude compared to the same lens with mosaic crystals. Moreover, no mosaic defocusing occurs for quasi-mosaic crystals.

Proposal for a Laue lens relying on hybrid quasi-mosaic curved crystals

A promising method of concentrating X- and soft γ-rays from celestial sources is a Laue lens. A new scheme for this lens, relying on diffraction in curved Si and Ge crystals, is introduced here. The proposed Laue lens is based on high-efficiency diffraction of curved (111) or (224) crystalline planes, which are bent through quasi-mosaic effect. While diffraction in curved (111) quasi-mosaic crystals is well known and has recently been proposed for a Laue lens, diffraction by quasi-mosaic (224) planes is suggested and demonstrated here through experimental work carried out at the Institut Laue-Langevin (ILL, Grenoble, France) at DIGRA, a facility specifically built for characterizing instrumentation in Astrophysics. Results show that the diffraction efficiency in the (224) quasimosaic sample is amplified by more than one order of magnitude with respect to an equivalent crystal without quasi-mosaic effect. The lens has been designed in such a way as to maximize and smoothen its sensitivity, thanks to a custom-made code based on a genetic algorithm.

Ordered stacking of crystals with adjustable curvatures for hard X- and γ-ray broadband focusing

A stack of plate-like curved crystals is proposed as an optical element for X- and γ-ray focusing. Si mono-crystal plates have been bent by surface grooving and positioned one over the other to form a stack. The relative alignment of the curved diffracting planes in the stack has been tested by hard X-ray diffractometry using a polychromatic and divergent beam. The stack exhibited a single and well defined spot under X-ray diffraction, highlighting that the plates are sufficiently aligned to behave as a single crystal. The curvature of the plates in the stack can be precisely set by tightly controlling the experimental parameters of grooving. Once set, the curvature is self-standing, i.e. it is maintained without any need for an external bender. Thanks to the stacking, it would be possible to realize optical elements with arbitrarily large size. This achievement has important implications for the realization of satellite-borne experiments in astrophysics and instruments for nuclear medicine with superior resolution.

Design study of a Laue lens for nuclear medicine

A Laue lens is an ensemble of crystals capable of focusing, through diffraction in transmission geometry, a fraction of the photons emitted by an X- or γ-ray source onto a small area of a detector. The present study facilitates a thorough understanding of the effect of each system parameter on the efficiency, the resolution and the field of view of the lens. In this way, the structure and the size of the crystals can be set to achieve a compact lens capable of providing a high-resolution image of the radioactivity distribution lying inside a restricted region of a patients body. As an application, a Laue lens optimized at 140.5 keV, the γ-line emitted by 99mTc, has been designed. The lens is composed of ten rings of Ge crystals with curved diffracting planes and focuses the photons onto a detector 50 cm apart from the source with 1.16 × 10−5 efficiency and 0.2 mm resolution. The combination of these two important figures of merit makes the proposed device better performing than pinhole single photon emission computed tomography, which is the technique employed for top-resolution images in nuclear medicine. Finally, the imaging capability of the designed lens has been tested through simulations performed with a custom-made Monte Carlo code.

High-efficiency focusing of hard X-rays exploiting the quasi-mosaic effect in a bent germanium crystal

A germanium crystal was bent through a grid of superficial grooves, manufactured on the sample surface. The resulting diffraction planes were bent thanks to quasi-mosaicity, which is an effect of mechanical anisotropy in crystals. High integrated diffraction efficiency was achieved in symmetric Laue geometry with a monochromatic X-ray beam set at 150 and 300 keV. It is demonstrated that the sample is capable of efficiently focusing X-rays. Such crystals can be used as optical components to focalize X- and γ-rays in a high-resolution Laue lens.

Quasi-mosaic crystals for high-resolution focusing of hard x-rays through a Laue lens

Quasi-mosaicity is an effect of secondary bending within a crystal driven by crystalline anisotropy. This effect can be used to fabricate a series of curved crystals for the realization of a Laue lens. We highlight that crystals bent by quasi-mosaic effect envisage very high resolution focusing with respect to mosaic crystals. Under same conditions for energy passband and flux of incident photons, a Laue lens based on quasi-mosaic crystals would increase the signal-to-noise ratio by more than one order of magnitude as for the same lens with mosaic crystals. A proposal for the realization of a self-standing quasi-mosaic crystal is given. Here permanent bending of a crystal is achieved as a result of superficial indentations.

AniCryDe: calculation of elastic properties in silicon and germanium crystals

A code to calculate the anisotropic elastic properties in a silicon or germanium crystal is introduced. The program, named AniCryDe, allows the user to select the crystallographic configuration of interest. For the selected crystallographic orientation, AniCryDe calculates several key mechanical parameters, such as Youngs modulus, Poissons ratio and the shear modulus. Furthermore, the program displays both the compliance and the stiffness tensors concerning the crystallographic orientation of interest. The code enables the user to set several parameters through a user-friendly control stage. As a result, the user obtains the complete displacement field of a deformed crystal and the curvature of any crystallographic plane. Manufacturing wafer defects such as miscut and misflat angle are also taken into account.

Calculation of diffraction efficiency for curved crystals with arbitrary curvature radius

A model is proposed to calculate the diffraction efficiency of X-rays in Laue geometry for curved crystals with an arbitrary value of the curvature radius. The model generalizes the results based on the dynamical theory of diffraction, which are valid only for crystals with a radius of curvature lower than the critical curvature. The model is proposed for any kind of crystal, and its efficiency tends to one-half in the limit of a thick flat crystal. On the basis of this model, it was possible to reconsider the results of recently observed diffraction efficiency for curved crystals. Finally, the model sets an upper limit for diffraction efficiency of low-curvature curved crystals, this latter being useful in applications such as the construction of a hard X-ray Laue lens.

Fabrication of quasi-mosaic Ge crystals for the LAUE project

A series of quasi-mosaic curved crystals has been fabricated for the Laue project to build up a prototype of a Laue lens. Curvature has been imparted to the samples thanks to the grooving method, which makes it possible to realize self-standing curved plates. Samples are 10 × 30 × 2 mm3 Ge crystals characterized by two curvatures of different crystallographic planes. The primary curvature allows the focalization of the diffracted X-rays on a focal spot smaller than the crystal dimension. The secondary curvature, i.e. quasi-mosaic curvature, amplifies the diffraction efficiency by more than one order of magnitude with respect to an equivalent crystal without quasi-mosaic curvature.