Momentum transfer

Résumé

In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the simplest example of scattering of two colliding particles with initial momenta \vec{p}{i1},\vec{p}{i2}, resulting in final momenta \vec{p}{f1},\vec{p}{f2}, the momentum transfer is given by : \vec q = \vec{p}{i1} - \vec{p}{f1} = \vec{p}{f2} - \vec{p}{i2} where the last identity expresses momentum conservation. Momentum transfer is an important quantity because \Delta x = \hbar / |q| is a better measure for the typical distance resolution of the reaction than the momenta themselves. Wave mechanics and optics A wave has a momentum p = \hbar k and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called moment

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https://en.wikipedia.org/wiki/Momentum_transfer

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Electron Energy Loss Spectrometry (EELS) in Transmission Electron Microscopy (TEM) is a powerful tool for the investigation of the electronic structure of materials. In the low loss regime, one can access the optical properties which are governed by the dielectric function ε(ω), which may be retrieved thanks to the so-called "loss function". The energy range covered by EELS goes from the infrared (less than 1 eV) to the hard X-rays (about 3 keV), each region having its own interest. The low loss region (0–100 eV) serves to investigate the valence electron structure and the inter-band transition behavior. Using angular resolved EELS gives further information about the dispersion behavior of the investigated material. This work is a part of a large project aiming a closer agreement between theory and experiment in angular resolved EELS by improving the state of the art in both fields. The purpose of this work is to set up a reliable experimental technique to retrieve the momentum transfer resolved single scattering distribution at very low energy with good accuracy and resolutions. One of the main challenges was to use the newly installed JEOL 2200 FS transmission electron microscope that is equipped with an in-column Ω filter for retrieval of the loss function in diffraction energy filtered TEM. Issues such as the angular resolution, contamination, image-coupling in diffraction mode and plural scattering have been solved. Several optical alignments and operational modes of the JEOL 2200 FS have been tested, and finally nano-beam diffraction was found to be the optimal running mode. This work provides for the first time a full 3D energy loss data cube in diffraction mode with energy and angular resolutions of 1 eV and 0.5 nm−1 respectively. After processing, the energy and angular relevant data span an energy loss range from 2.75 eV to 40.25 eV and the angular momentum transfer up to 12.5 nm−1. Although theoretically, without CCD camera binning and the maximum available camera length of the JEOL (250 cm), a momentum transfer resolution of 0.04 nm−1 would have been possible, the effective angular resolution was limited by the smallest obtainable beam convergence as well as by the remaining aberrations of the microscope. The presented technique can be reproduced on any transmission electron microscope equipped with an in-column energy filter. Furthermore, it is demonstrated that the proposed method provides working ranges in energy, spatial and angular resolutions limited only by the perfor- mance of the microscope. Previous techniques did not provide experimental results showing an energy resolution independent of the spatial and angular resolutions.

EPFL2013

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Experimental study on tsunamis generated by landslides

Christophe Ancey, Ivan Maeder, Zhenzhu Meng

Tsunami generated by landslides is one of the major threats to populations in coastal areas. A recent example is the 2017 Nuugaatsiaq tsunami. The village in Greenland was partially swept by a tsunami created by a landslide that fell into the Karrat Fjord. We carried out laboratory experiments to understand how the wave characteristics are related to the landslide features. Emphasis was put on slide-water interactions and efficiency of momentum transfers between the two media. We manufactured granular slides made of differently sized particles using plasticine clay, whose density is close to that of real-world materials. The granular mixture could be shaped, which made it possible to study how the leading edge’s shape affected momentum transfer. The mixture was initially placed in a reservoir upstream of a chute, which entered into a water basin. The angle of chute and water depth were kept constant in all our experiments, whereas the material properties and volume were varied systematically. Wave amplitudes and heights were determined from the free-surface variations, which were recorded using a high-speed camera. The velocity field within the water basin was measured using Particle image velocimetry (PIV). To compare the waves generated by slides exhibiting different properties, empirical equations for prediction of wave characteristics were used. We discuss the differences between experimental results and predictions based on empirical equations. Among other things, we found that the lower the material’s permeability, the larger the wave amplitude.

2020

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Theoretical analysis of the momentum-dependent loss function of bulk Ag

Audrius Alkauskas, Cécile Hébert, Simon Schneider

We analyze the momentum-dependent loss function of bulk silver, calculated via the random-phase approximation and based on the band structure from semi-local density functional theory calculations. In the energy range of 0-55 eV the spectrum reveals the existence of seven well-pronounced peaks, in accordance with experiment. The two lowest of these are collective plasmon excitations, while the higher ones originate from inter-band transitions. Due to the different nature of those peaks, they display a different dependence on the momentum transfer q. While the plasmon peaks show an approximately quadratic q-dependence, the peaks caused by inter-band transitions are characterized by a much less pronounced dispersion. (C) 2009 Elsevier B.V. All rights reserved.

Elsevier2010

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EPFL2013