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International audienceA number of unsolved issues in materials physics suggest there is a need for an improved quantitative understanding of the interaction between acoustic (more generally, elastic) waves and dislocations. In this paper we study the coherent propagation of elastic waves through a two dimensional solid filled with randomly placed dislocations, both edge and screw, in a multiple scattering formalism. Wavelengths are supposed to be large compared to a Burgers vector and dislocation density is supposed to be small, in a sense made precise in the body of the paper. Consequently, the basic mechanism for the scattering of an elastic wave by a line defect is quite simple ("fluttering"): An elastic wave will hit each individual dislocation, causing it to oscillate in response. The ensuing oscillatory motion will generate outgoing (from the dislocation position) elastic waves. When many dislocations are present, the resulting wave behavior can be quite involved because of multiple scattering. However, under some circumstances, there may exist a coherent wave propagating with an effective wave velocity, its amplitude being attenuated because of the energy scattered away from the direction of propagation. The present study concerns the determination of the coherent wavenumber of an elastic wave propagating through an elastic medium filled with randomly placed dislocations. The real part of the coherent wavenumber gives the effective wave velocity and its imaginary part gives the attenuation length (or elastic mean free path). The calculation is performed perturbatively, using a wave equation for the particle velocity with a right hand side term, valid both in two and three dimensions, that accounts for the dislocation motion when forced by an external stress. In two dimensions, the motion of a dislocation is that of a massive particle driven by the incident wave; both screw and edge dislocations are considered. The effective velocity of the coherent wave appears at first order in perturbation theory, while the attenuation length appears at second order

The mechanism of a simple S(N)2 reaction, viz; OH(-) + CH(3)F = CH(3)OH + F(-) has been studied within the framework of reaction force and reaction electronic flux. We have computationally investigated three different types of reaction mechanisms with two different types of transition states, leading to two different products. The electronic transfer contribution of the reaction electronic flux was found to play a crucial role in this reaction. Natural bond order analysis and dual descriptor provide additional support for elucidating the mechanism of this reaction.

A quantitative theory of the elastic wave damping and velocity change due to interaction with dislocations is presented. It provides a firm theoretical basis and a generalization of the Granato and Lücke model ͓J. Appl. Phys. 27, 583 ͑1956͔͒. This is done considering the interaction of transverse ͑T͒ and longitudinal ͑L͒ elastic waves with an ensemble of dislocation segments randomly placed and randomly oriented in an elastic solid. In order to characterize the coherent wave propagation using multiple scattering theory, a perturbation approach is used, which is based on a wave equation that takes into account the dislocation motion when forced by an external stress. In our calculations, the effective velocities of the coherent waves appear at first order in perturbation theory while the attenuations have a part at first order due to the internal viscosity and a part at second order due to the energy that is taken away from the incident direction. This leads to a frequency dependence law for longitudinal and transverse attenuations that is a combination of quadratic and quartic terms instead of the usual quadratic term alone. Comparison with resonant ultrasound spectroscopy ͑RUS͒ and electromagnetic acoustic resonance ͑EMAR͒ experiments is proposed. The present theory explains the difference experimentally observed between longitudinal and transverse attenuations ͓Ledbetter, J. Mater. Res. 10, 1352 ͑1995͔͒.