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

Size effects and deformation mechanisms in diamond and silicon

At ambient temperature and pressure, most of the semiconductor materials are brittle. Traditionally, use of confining pressure via indentation or a hydrostatic confining medium [1, 2] has been required to study the plasticity of such brittle materials. In the case of group IV semiconductors (Diamond, Silicon, and Germanium) the situation is further complicated by pressure-induced phase transformations occurring underneath the indentations. However, previous work has demonstrated that sample miniaturization can also prevent the onset of cracking and allow plastic deformation [3]. Recent advances in in situ instrumentation have enabled micro-compression techniques to extract temperature- and time-dependent deformation parameters [5, 6]. Thus, micro-pillar compression is a promising technique for investigating the plasticity of these semiconductors in their brittle regimes. Previous work has noted a brittle-ductile transition in Silicon which is dependent on orientation, size, and temperature. This has been tied to transitions between partial and perfect dislocations in III-V semiconductors, but the extreme brittle character of silicon has prevented characterization of plastic flow in the low temperature regimes. In this work, [123]-oriented crystals are utilized to prevent the onset of cracking and allow plastic deformation. Micro-compression is shown to be capable of achieving incredibly high stresses ( \u3e100 GPa), and this is applied to investigate the behavior of the hardest natural material - diamond - and its nearest analog – silicon

Comparison between classical potentials and ab initio for silicon under large shear

The homogeneous shear of the {111} planes along the direction of bulk silicon has been investigated using ab initio techniques, to better understand the strain properties of both shuffle and glide set planes. Similar calculations have been done with three empirical potentials, Stillinger-Weber, Tersoff and EDIP, in order to find the one giving the best results under large shear strains. The generalized stacking fault energies have also been calculated with these potentials to complement this study. It turns out that the Stillinger-Weber potential better reproduces the ab initio results, for the smoothness and the amplitude of the energy variation as well as the localization of shear in the shuffle set

On some aspects of the geometry of differential equations in physics

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study of the differential equations with which they are related. Furthermore, research to be developed in these areas is also commented.Comment: 21 page

Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information

“Conjugate Channeling” Effect in Dislocation Core Diffusion: Carbon Transport in Dislocated BCC Iron

Dislocation pipe diffusion seems to be a well-established phenomenon. Here we demonstrate an unexpected effect, that the migration of interstitials such as carbon in iron may be accelerated not in the dislocation line direction [symbol], but in a conjugate diffusion direction. This accelerated random walk arises from a simple crystallographic channeling effect. [c] is a function of the Burgers vector b, but not [symbol], thus a dislocation loop possesses the same everywhere. Using molecular dynamics and accelerated dynamics simulations, we further show that such dislocation-core-coupled carbon diffusion in iron has temperature-dependent activation enthalpy like a fragile glass. The 71° mixed dislocation is the only case in which we see straightforward pipe diffusion that does not depend on dislocation mobility.National Science Foundation (U.S.) (Grant No. CMMI-0728069)National Science Foundation (U.S.) (Grant No. DMR-1008104)National Science Foundation (U.S.) (Grant No. DMR-1120901