First principles determination of the Peierls stress of the shuffle screw dislocation in silicon

The Peierls stress of the a/2 screw dislocation belonging to the shuffle set is calculated for silicon using density functional theory. We have checked the effect of boundary conditions by using two models, the supercell method where one considers a periodic array of dislocations, and the cluster method where a single dislocation is embedded in a small cluster. The Peierls stress is underestimated with the supercell and overestimated with the cluster. These contributions have been calculated and the Peierls stress is determined in the range between 2.4 x 10-2 and 2.8 x 10-2 eV {\AA}-3. When moving, the dislocation follows the {111} plane going through a low energy metastable configuration and never follows the 100 plane, which includes a higher energy metastable core configuration

Ascoli's theorem for functions vanishing at infinity and selected applications

AbstractWe give a new form of the Ascoli theorem for functions on RN tending to some given closed subset Z of a complete metric space E at infinity. For instance, when E is a normed space and Z={0}, the usual uniform decay requirement is replaced by the assumption that the 0 function is the only continuous function produced by some limiting process. This formulation, which has significant practical value in concrete applications, is described in its general form, but with emphasis on the case when Z is totally disconnected. Variants in Sobolev spaces and the properness of nonlinear ordinary differential operators are discussed

Stability of undissociated screw dislocations in zinc-blende covalent materials from first principle simulations

The properties of perfect screw dislocations have been investigated for several zinc-blende materials such as diamond, Si, $\beta$-SiC, Ge and GaAs, by performing first principles calculations. For almost all elements, a core configuration belonging to shuffle set planes is favored, in agreement with low temperature experiments. Only for diamond, a glide configuration has the lowest defect energy, thanks to an sp$^2$ hybridization in the core

Theoretical study of dislocation nucleation from simple surface defects in semiconductors

Large-scale atomistic calculations, using empirical potentials for modeling semiconductors, have been performed on a stressed system with linear surface defects like steps. Although the elastic limits of systems with surface defects remain close to the theoretical strength, the results show that these defects weaken the atomic structure, initializing plastic deformations, in particular dislocations. The character of the dislocation nucleated can be predicted considering both the resolved shear stress related to the applied stress orientation and the Peierls stress. At low temperature, only glide events in the shuffle set planes are observed. Then they progressively disappear and are replaced by amorphization/melting zones at a temperature higher than 900 K