Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core field to the dislocation interaction energy with an external stress, thus showing that dislocation can interact with a pressure. The additional force that derives from this core field contribution is proportional to the gradient of the applied stress. Such a supplementary force on dislocations may be important in high stress gradient regions, such as close to a crack tip or in a dislocation pile-up

Stress induced dislocation roughening -- phase transition in 1d at finite temperature

We present an example of a generically forbidden phase transition in 1d at finite temperature -- stress induced and thermally assisted roughening of a superclimbing dislocation in a Peierls potential. We also argue that such roughening is behind the strong suppression of the superflow through solid \he4 in a narrow temperature range recently observed by Ray and Hallock (Phys.Rev. Lett. {\bf 105}, 145301 (2010)).Comment: 4 revtex pages, 5 figures. Replaced with the published versio

Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in FCC Metals

We develop a finite element based dislocation dynamics model to simulate the structure and strength of dislocation junctions in FCC crystals. The model is based on anisotropic elasticity theory supplemented by the explicit inclusion of the separation of perfect dislocations into partial dislocations bounding a stacking fault. We demonstrate that the model reproduces in precise detail the structure of the Lomer-Cottrell lock already obtained from atomistic simulations. In light of this success, we also examine the strength of junctions culminating in a stress-strength diagram which is the locus of points in stress space corresponding to dissolution of the junction.Comment: 9 Pages + 4 Figure

1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Lattice Resistance and Peierls Stress in Finite-size Atomistic Dislocation Simulations

Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bcc metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals. One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size independent results are to be obtained. One of the approaches that has been developed for treating such boundary forces is by computing them directly and subsequently subtracting their effects, as developed by V. B. Shenoy and R. Phillips [Phil. Mag. A, 76 (1997) 367]. That work was primarily analytic, and limited to screw dislocations and special symmetric geometries. We extend that work to edge and mixed dislocations, and to arbitrary two-dimensional geometries, through a numerical finite element computation. We also describe a method for estimating the boundary forces directly on the basis of atomistic calculations. We apply these methods to the numerical measurement of the Peierls stress and lattice resistance curves for a model aluminum (fcc) system using an embedded-atom potential.Comment: LaTeX 47 pages including 20 figure

The role of Helium-3 impurities in the stress induced roughening of superclimbing dislocations in solid Helium-4

We analyze the stress induced and thermally assisted roughening of a forest of superclimbing dislocations in a Peierls potential in the presence of Helium-3 impurities and randomly frozen in static stresses. It is shown that the temperature of the dip $T_d$ in the flow rate observed by Ray and Hallock (Phys.Rev. Lett. {\bf 105}, 145301 (2010)) is determined by the energy of the impurity activation from dislocation core. However, it is suppressed by, essentially, the logarithm of the impurity fraction. The width of the dip is determined by inhomogeneous fluctuations of the stresses and is shown to be much smaller than $T_d$.Comment: Submitted to the LT26-conference proceeding

Buried dislocation networks designed to organize the growth of III-V semiconductor nanostructures

We first report a detailed transmission electron microscopy study of dislocation networks (DNs) formed at shallowly buried interfaces obtained by bonding two GaAs crystals between which we establish in a controlled manner a twist and a tilt around a k110l direction. For large enough twists, the DN consists of a twodimensional network of screw dislocations accommodating mainly the twist and of a one-dimensional network of mixed dislocations accommodating mainly the tilt. We show that in addition the mixed dislocations accommodate part of the twist and we observe and explain slight unexpected disorientations of the screw dislocations with respect to the k110l directions. By performing a quantitative analysis of the whole DN, we propose a coherent interpretation of these observations which also provides data inaccessible by direct experiments. When the twist is small enough, one screw subnetwork vanishes. The surface strain field induced by such DNs has been used to pilot the lateral ordering of GaAs and InGaAs nanostructures during metal-organic vapor phase epitaxy. We prove that the dimensions and orientations of the nanostructures are correlated with those of the cells of the underlying DN and explain how the interface dislocation structure governs the formation of the nanostructures

Slip energy barriers in aluminum and implications for ductile versus brittle behavior

We conisder the brittle versus ductile behavior of aluminum in the framework of the Peierls-model analysis of dislocation emission from a crack tip. To this end, we perform first-principles quantum mechanical calculations for the unstable stacking energy $\gamma_{us}$ of aluminum along the Shockley partial slip route. Our calculations are based on density functional theory and the local density approximation and include full atomic and volume relaxation. We find that in aluminum $\gamma_{us} = 0.224$ J/m$^2$. Within the Peierls-model analysis, this value would predict a brittle solid which poses an interesting problem since aluminum is typically considered ductile. The resolution may be given by one of three possibilites: (a) Aluminum is indeed brittle at zero temperature, and becomes ductile at a finite temperature due to motion of pre-existing dislocations which relax the stress concentration at the crack tip. (b) Dislocation emission at the crack tip is itself a thermally activated process. (c) Aluminum is actually ductile at all temperatures and the theoretical model employed needs to be significantly improved in order to resolve the apparent contradiction.Comment: 4 figures (not included; send requests to [email protected]

Modified embedded-atom method interatomic potentials for the Mg-Al alloy system

We developed new modified embedded-atom method (MEAM) interatomic potentials for the Mg-Al alloy system using a first-principles method based on density functional theory (DFT). The materials parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, were used to determine the MEAM parameters. Face-centered cubic, hexagonal close packed, and cubic rock salt structures were used as the reference structures for Al, Mg, and MgAl, respectively. The applicability of the new MEAM potentials to atomistic simulations for investigating Mg-Al alloys was demonstrated by performing simulations on Mg and Al atoms in a variety of geometries. The new MEAM potentials were used to calculate the adsorption energies of Al and Mg atoms on Al (111) and Mg (0001) surfaces. The formation energies and geometries of various point defects, such as vacancies, interstitial defects and substitutional defects, were also calculated. We found that the new MEAM potentials give a better overall agreement with DFT calculations and experiments when compared against the previously published MEAM potentials.Comment: Fixed a referenc

Damping in high-frequency metallic nanomechanical resonators

We have studied damping in polycrystalline Al nanomechanical resonators by measuring the temperature dependence of their resonance frequency and quality factor over a temperature range of 0.1 - 4 K. Two regimes are clearly distinguished with a crossover temperature of 1 K. Below 1 K we observe a logarithmic temperature dependence of the frequency and linear dependence of damping that cannot be explained by the existing standard models. We attribute these phenomena to the effect of the two-level systems characterized by the unexpectedly long (at least two orders of magnitude longer) relaxation times and discuss possible microscopic models for such systems. We conclude that the dynamics of the two-level systems is dominated by their interaction with one-dimensional phonon modes of the resonators.Comment: 5 pages, 3 figure