Luca Lanzoni

Study of anticlastic deformation in a silicon crystal for channeling experiments

Anticlastic deformation (AD) is an established mechanical property of isotropic solid bodies, which has been recently used to steer particle beams through channeling in Si crystals. An analysis of AD in an anisotropic material, such as Si, has been worked out with particular emphasis to the cases used in channeling experiments. Both a theoretical model and finite element simulations were developed and compared to experimental data achieved by optical profilometry on bent Si crystals. A quantifier of the extent of AD, namely the ratio between primary and secondary curvature radii, has been found to be orientation dependent and determined analytically. The realistic case of crystal bending by a mechanical holder has been studied for applications. We addressed the case of the holder with a crystal at the energy currently under operation in the CERN super proton synchrotron and its possible extension to higher energy cases such as for the large hadron collider. Anisotropy-driven torsion of the crystal was inv...

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.

Ion implantation for manufacturing bent and periodically bent crystals

Ion implantation is proposed to produce self-standing bent monocrystals. A Si sample 0.2 mm thick was bent to a radius of curvature of 10.5 m. The sample curvature was characterized by interferometric measurements; the crystalline quality of the bulk was tested by X-ray diffraction in transmission geometry through synchrotron light at ESRF (Grenoble, France). Dislocations induced by ion implantation affect only a very superficial layer of the sample, namely, the damaged region is confined in a layer 1 μm thick. Finally, an elective application of a deformed crystal through ion implantation is here proposed, i.e., the realization of a crystalline undulator to produce X-ray beams.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

A Wiener-Hopf System of Equations in the Steady-State Propagation of a Rectilinear Crack in an Infinite Elastic Plate

A Wiener-Hopf system of functional equations is shown to govern the steady-state propagation of a semi-infinite rectilinear crack in an infinite elastic Kirchhoff–Love plate. Solution is presented in terms of Fourier transforms via kernel factorization.

Thin film bonded to elastic orthotropic substrate under thermal loading

The problem of thin elastic films bonded on an elastic orthotropic substrate under thermal load is investigated in this work. Differently from past studies on the same topic, the effects induced by anisotropic behavior of the elastic substrate will be taken into account. Particular attention will also be paid to the determination of the displacement and stress fields induced by thermal loading. In particular, it is assumed that the thin films are deposed on the substrate at high temperature, and then the mismatch occurring during the cooling process, due to the difference between the thermal expansion coefficients of the two materials, is responsible for the permanent deformation assumed by the system. This phenomenon can be exploited for realizing a crystalline undulator. To this aim, the permanent deformation must be optimized in order to encourage the channeling phenomenon. By imposing equilibrium conditions and perfect adhesion between the film and the substrate, a singular integral equation is derived. A closed-form solution is achieved by expanding the interfacial shear stress fields in Chebyshev series. The unknown coefficients in the series expansion are then determined by transforming the integral equation into an infinite algebraic system.

Bent crystals as high-reflectivity components for a Laue lens: basic concepts and experimental techniques

For fabrication of crystals with curved diffracting planes, several techniques have been worked out. Amongst curved crystals, special interest is given to those that are being bent due to internal forces. Surface grooving is proposed as an efficient method to reproducibly obtain self-standing bent crystals. Silicon or germanium plates can be plastically deformed by grooving one of their major surfaces with very good control of the curvature. We present a systematic experimental study and a model based on the theory of elasticity. The technique enables the fabrication, in a very reproducible fashion, of curved crystals for the realization of an high-efficiency hard X-ray concentrator (Laue lens).