Dislocation nucleation and vacancy formation during high-speed deformation of fcc metals

Recently, a dislocation free deformation mechanism was proposed by Kiritani et al., based on a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large density of stacking fault tetrahedra, but very low dislocation densities in the foils after deformation. This was interpreted as evidence for a new dislocation-free deformation mechanism, resulting in a very high vacancy production rate. In this paper we investigate this proposition using large-scale computer simulations of bulk and thin films of copper. To favour such a dislocation-free deformation mechanism, we have made dislocation nucleation very difficult by not introducing any potential dislocation sources in the initial configuration. Nevertheless, we observe the nucleation of dislocation loops, and the deformation is carried by dislocations. The dislocations are nucleated as single Shockley partials. The large stresses required before dislocations are nucleated result in a very high dislocation density, and therefore in many inelastic interactions between the dislocations. These interactions create vacancies, and a very large vacancy concentration is quickly reached.Comment: LaTeX2e, 8 pages, PostScript figures included. Minor modifications only. Final version, to appear in Philos. Mag. Let

Modelling of dislocation generation and interaction during high-speed deformation of metals

Recent experiments by Kiritani et al. have revealed a surprisingly high rate of vacancy production during high-speed deformation of thin foils of fcc metals. Virtually no dislocations are seen after the deformation. This is interpreted as evidence for a dislocation-free deformation mechanism at very high strain rates. We have used molecular-dynamics simulations to investigate high-speed deformation of copper crystals. Even though no pre-existing dislocation sources are present in the initial system, dislocations are quickly nucleated and a very high dislocation density is reached during the deformation. Due to the high density of dislocations, many inelastic interactions occur between dislocations, resulting in the generation of vacancies. After the deformation, a very high density of vacancies is observed, in agreement with the experimental observations. The processes responsible for the generation of vacancies are investigated. The main process is found to be incomplete annihilation of segments of edge dislocations on adjacent slip planes. The dislocations are also seen to be participating in complicated dislocation reactions, where sessile dislocation segments are constantly formed and destroyed.Comment: 8 pages, LaTeX2e + PS figures. Presented at the Third Workshop on High-speed Plastic Deformation, Hiroshima, August 200

Quantum mechanics without spacetime II : noncommutative geometry and the free point particle

In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential geometry. In the present paper we discuss this formulation for the free point particle, by introducing a commutation relation for a set of noncommuting coordinates. The sought for background independent quantum mechanics is derived from this commutation relation for the coordinates. We propose that the basic equations are invariant under automorphisms which map one set of coordinates to another- this is a natural generalization of diffeomorphism invariance when one makes a transition to noncommutative geometry. The background independent description becomes equivalent to standard quantum mechanics if a spacetime manifold exists, because of the proposed automorphism invariance. The suggested basic equations also give a quantum gravitational description of the free particle.Comment: 8 page

Phase diagram and magnetic collective excitations of the Hubbard model in graphene sheets and layers

We discuss the magnetic phases of the Hubbard model for the honeycomb lattice both in two and three spatial dimensions. A ground state phase diagram is obtained depending on the interaction strength U and electronic density n. We find a first order phase transition between ferromagnetic regions where the spin is maximally polarized (Nagaoka ferromagnetism) and regions with smaller magnetization (weak ferromagnetism). When taking into account the possibility of spiral states, we find that the lowest critical U is obtained for an ordering momentum different from zero. The evolution of the ordering momentum with doping is discussed. The magnetic excitations (spin waves) in the antiferromagnetic insulating phase are calculated from the random-phase-approximation for the spin susceptibility. We also compute the spin fluctuation correction to the mean field magnetization by virtual emission/absorpion of spin waves. In the large $U$ limit, the renormalized magnetization agrees qualitatively with the Holstein-Primakoff theory of the Heisenberg antiferromagnet, although the latter approach produces a larger renormalization

The generalized gradient approximation kernel in time-dependent density functional theory

A complete understanding of a material requires both knowledge of the excited states as well as of the ground state. In particular, the low energy excitations are of utmost importance while studying the electronic, magnetic, dynamical, and thermodynamical properties of the material. Time-Dependent Density Functional Theory (TDDFT), within the linear regime, is a successful \textit{ab-initio} method to access the electronic charge and spin excitations. However, it requires an approximation to the exchange-correlation (XC) kernel which encapsulates the effect of electron-electron interactions in the many-body system. In this work we derive and implement the spin-polarized XC kernel for semi-local approximations such as the adiabatic Generalized Gradient Approximation (AGGA). This kernel has a quadratic dependence on the wavevector, {\bf q}, of the perturbation, however the impact of this on the electron energy loss spectra (EELS) is small. Although the GGA functional is good in predicting structural properties, it generality overestimates the exchange spin-splitting. This leads to higher magnon energies, as compared to both ALDA and experiment. In addition, interaction with the Stoner spin-flip continuum is enhanced by AGGA, which strongly suppresses the intensity of spin-waves.Comment: 11 pages, 7 figure

The Mott insulator - 10th order perturbation theory extended to infinite order using QMC

We present a new method, based on the combination of analytical and numerical techniques within the framework of the dynamical mean-field theory (DMFT). Building upon numerically exact results obtained in an improved quantum Monte Carlo (QMC) scheme, 10th order strong-coupling perturbation theory for the Hubbard model on the Bethe lattice is extrapolated to infinite order. We obtain continuous estimates of energy E and double occupancy D with unprecedented precision O(10^{-5}) for the Mott insulator above its stability edge U_{c1}=4.78 as well as critical exponents. The relevance for recent experiments on Cr-doped V_2O_3 is pointed out.Comment: 4 pages, 5 figures. Significant changes in introduction and summary; experimental reference added; Figs. 1 and 3 modifie

Optimum Trajectories with Specified Transfer Angle

Inter-orbital optimum trajectories with specified transfer angle in an inverse square gravitational field have been analysed. Criterion of optimization adopted is minimum velocity increment in the entire transfer operation with one impulse each at the initial and final terminal. Particular cases of the above problem are discussed and as a numerical illustration, results are obtained for transfer trajectories between two orbits in Earth's gravitational field