An anisotropic thin crystal deformed by an inclined dislocation

International audienceThe elastic field around a dislocation piercing obliquely an anisotropic thin crystal is obtained by combining the classical solution applicable to an infinite anisotropic crystal with an analysis using the concept of continuous dislocation density. Numerical applications are presented for inclined dislocations in Ni3Al and Ni

Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches

Inclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, which assumes no dislocation core size and needs numerical double integrations. In a first stage of the work, a new and alternative approach to the integral formalism is developed using double Fourier series and the concept of a finite core size, which is often observed in high-resolution transmission electron microscopy. In a second stage, the integral formalism and the Fourier series approaches are applied to the important case of a TD piercing the basal free surface of a hexagonal crystal. For this particular geometry, easy-to-use expressions are derived and compared to a third approach previously known for a plate-like crystal. Finally, the numerical interest and the convergence of these approaches are tested using the basal free surface of the GaN compound, in particular for TDs with Burgers vectors c and (a + c)

Free surface relaxation of a semicoherent interface in an isotropic thin plate

International audienceA method leading to an explicit evaluation of the elastic field of a planar semicoherent interface placed in a thin isotropic plate is proposed. It is assumed that the interface contains a single family of straight, periodically distributed, misfit dislocations. The known properties of continuous distributions of dislocations and periodic elastic fields in an unbounded medium are used to solve the problem. Surface stresses are cancelled from the addition of appropriate fields applying to an infinite medium. Numerical applications illustrate, for a near Sigma 9{122} semicoherent grain boundary in silicon, the dependence of the deformation field on the plate thickness and on the orientation parameters of the interface. (C) 2015 Elsevier B.V. All rights reserved

A semi-coherent interface with nanoledges intersecting the free surface of an elastic half-space

International audienceThe elastic field generated by a semi-coherent interface formed by a succession of parallel terraces and nanoledges is investigated when the interface intersects the free surface of an isotropic half-space medium. The method uses the combination of semi-infinite Somigliana dislocations placed on each terrace and semi-infinite translation (or Volterra) dislocations placed at one or two corners of the nanoledges. Numerical examples depict the deformation fields nearby emerging regions of two semi-coherent interfaces; one is flat, while the other includes nanoledges

Screw heterointerfacial dislocations piercing a thin plate

A specimen observed in high-resolution transmission electron microscopy is electron transparent and its thickness is often less than about 10 nm. When it contains a linear defect like a screw dislocation, the obtained image can exhibit more or less important perturbations due to elastic relaxation nearby both free surfaces. Therefore, the theoretical interpretation of an image should include this relaxation in the calculation model. In the present work, it is evaluated for screw misfit dislocations piercing normally an elastically heterogeneous bicristalline plate (thickness 2h) from the following assumptions: there is no applied force on the thin plate and any surface stress related to a possible nanometric structure along the two free surfaces is neglected. The solution is found from an appropriate combination of known elastic fields in an infinite medium, which enables total stresses applying on two planes distant of 2h to be cancelled. This solution generalizes for the first time that of Eshelby and Stroh (1951), who consider an isolated screw dislocation normal to a homogeneous plate. (C) 2018 Academie des sciences. Public par Elsevier Masson SAS