scholarly journals A low-energy decomposition theorem

2016 ◽  
Author(s):  
Antal Balog ◽  
Trevor D. Wooley
Keyword(s):  
Decomposition Theorem ◽  
Low Energy ◽  
Energy Decomposition

scholarly journals Sparse + low-energy decomposition for viscous conservation laws

2015 ◽  
Vol 288 ◽  
pp. 150-166 ◽  
Author(s):  
Thomas Y. Hou ◽  
Qin Li ◽  
Hayden Schaeffer
Keyword(s):  
Conservation Laws ◽  
Low Energy ◽  
Energy Decomposition ◽  
Viscous Conservation Laws

scholarly journals Effect of Unwanted Guest Molecules on the Stacking Configuration of Covalent Organic Frameworks: A Periodic Energy Decomposition Analysis

2020 ◽  
Author(s):  
A.D. Dinga Wonanke ◽  
Mathew Addicoat
Keyword(s):  
Guest Molecule ◽  
Dispersion Model ◽  
Critical Role ◽  
Decomposition Analysis ◽  
Empirical Method ◽  
Low Energy ◽  
Energy Decomposition Analysis ◽  
Energy Decomposition ◽  
Guest Molecules ◽  
Semi Empirical

Elucidating the precise stacking configuration of a covalent organic framework, COF, is critical to fully understand their various applications. Unfortunately, most COFs form powder crystals whose atomic characterisations are possible only through powder X-ray diffraction (PXRD) analysis. However, this analysis has to be coupled with computational simulations, wherein computed PXRD patterns for different stacking configurations are compared with experimental patterns to predict the precise stacking configuration. This task is often computationally challenging firstly because, computation of these systems mostly rely on the use of semi-empirical methods that need to be adequately parametrised for the system being studied and secondly because some of these compounds possess guest molecules, which are not often taken into account during computation. COF-1 is an extreme case in which the presence of the guest molecule plays a critical role in predicting the precise stacking configuration. Using this as a case study, we mapped out a full PES for the stacking configuration in the guest free and guest containing system using the GFN-xTB semi-empirical method followed by a periodic energy decomposition analysis using first principle DFT. Our results showed that the presence of the guest molecule leads to multiple low energy stacking configurations with significantly different lateral offsets. Also, the semi-empirical method does not precisely predict DFT low energy configurations, however, it accurately accounts for dispersion. Finally, our quantum-mechanical analysis demonstrates that electrostatic-dispersion model suggested Hunter and Sanders accurately describe the stacking in 2D COFs as oppose to the newly suggested Pauli-dispersion model.

scholarly journals Effect of Unwanted Guest Molecules on the Stacking Configuration of Covalent Organic Frameworks: A Periodic Energy Decomposition Analysis

2020 ◽  
Author(s):  
A.D. Dinga Wonanke ◽  
Mathew Addicoat
Keyword(s):  
Guest Molecule ◽  
Dispersion Model ◽  
Critical Role ◽  
Decomposition Analysis ◽  
Empirical Method ◽  
Low Energy ◽  
Energy Decomposition Analysis ◽  
Energy Decomposition ◽  
Guest Molecules ◽  
Semi Empirical

Elucidating the precise stacking configuration of a covalent organic framework, COF, is critical to fully understand their various applications. Unfortunately, most COFs form powder crystals whose atomic characterisations are possible only through powder X-ray diffraction (PXRD) analysis. However, this analysis has to be coupled with computational simulations, wherein computed PXRD patterns for different stacking configurations are compared with experimental patterns to predict the precise stacking configuration. This task is often computationally challenging firstly because, computation of these systems mostly rely on the use of semi-empirical methods that need to be adequately parametrised for the system being studied and secondly because some of these compounds possess guest molecules, which are not often taken into account during computation. COF-1 is an extreme case in which the presence of the guest molecule plays a critical role in predicting the precise stacking configuration. Using this as a case study, we mapped out a full PES for the stacking configuration in the guest free and guest containing system using the GFN-xTB semi-empirical method followed by a periodic energy decomposition analysis using first principle DFT. Our results showed that the presence of the guest molecule leads to multiple low energy stacking configurations with significantly different lateral offsets. Also, the semi-empirical method does not precisely predict DFT low energy configurations, however, it accurately accounts for dispersion. Finally, our quantum-mechanical analysis demonstrates that electrostatic-dispersion model suggested Hunter and Sanders accurately describe the stacking in 2D COFs as oppose to the newly suggested Pauli-dispersion model.

On why some low-energy decomposition pathways of simple ketone molecular ions do not give rise to metastable peaks. A reappraisal

1986 ◽  
Vol 64 (10) ◽  
pp. 1957-1959 ◽  
Author(s):  
Peter J. Derrick ◽  
Steen Hammerum
Keyword(s):  
Rate Constants ◽  
Molecular Ions ◽  
Equilibrium Theory ◽  
Low Energy ◽  
Quasi Equilibrium ◽  
Energy Decomposition ◽  
Minimum Rate ◽  
Process Loss ◽  
Energy Reaction

The concept of minimum rate constants, k(E)min, for unimolecular decompositions does not, according to the quasi equilibrium theory (QET), provide a rationalisation of the occurrence of the higher energy reaction, loss of methyl, rather than the more favorable process, loss of methane, from metastable butanone and 3-methylbutanone molecular ions.

Dissociated Σ=27 boundaries in silicon

1988 ◽  
Vol 46 ◽  
pp. 624-625
Author(s):  
A. Garg ◽  
W.A.T. Clark ◽  
J.P. Hirth
Keyword(s):  
Electron Diffraction ◽  
Local Minimum ◽  
Boundary Energy ◽  
Coincidence Site Lattice ◽  
Boundary Plane ◽  
Low Energy ◽  
Theoretical Understanding ◽  
Site Lattice ◽  
Kikuchi Pattern ◽  
Analysis Techniques

In the last twenty years, a significant amount of work has been done in the theoretical understanding of grain boundaries. The various proposed grain boundary models suggest the existence of coincidence site lattice (CSL) boundaries at specific misorientations where a periodic structure representing a local minimum of energy exists between the two crystals. In general, the boundary energy depends not only upon the density of CSL sites but also upon the boundary plane, so that different facets of the same boundary have different energy. Here we describe TEM observations of the dissociation of a Σ=27 boundary in silicon in order to reduce its surface energy and attain a low energy configuration.The boundary was identified as near CSL Σ=27 {255} having a misorientation of (38.7±0.2)°/[011] by standard Kikuchi pattern, electron diffraction and trace analysis techniques. Although the boundary appeared planar, in the TEM it was found to be dissociated in some regions into a Σ=3 {111} and a Σ=9 {122} boundary, as shown in Fig. 1.

Transfer optics for high spatial resolution electron spectroscopy

1988 ◽  
Vol 46 ◽  
pp. 666-667
Author(s):  
G. G. Hembree ◽  
Luo Chuan Hong ◽  
P.A. Bennett ◽  
J.A. Venables
Keyword(s):  
Magnetic Field ◽  
Scanning Transmission Electron Microscope ◽  
Low Energy ◽  
Objective Lens ◽  
State University ◽  
Arizona State University ◽  
Initial Field ◽  
Resolution Electron ◽  
Scanning Transmission ◽  
Low Energy Electrons

A new field emission scanning transmission electron microscope has been constructed for the NSF HREM facility at Arizona State University. The microscope is to be used for studies of surfaces, and incorporates several surface-related features, including provision for analysis of secondary and Auger electrons; these electrons are collected through the objective lens from either side of the sample, using the parallelizing action of the magnetic field. This collimates all the low energy electrons, which spiral in the high magnetic field. Given an initial field Bi∼1T, and a final (parallelizing) field Bf∼0.01T, all electrons emerge into a cone of semi-angle θf≤6°. The main practical problem in the way of using this well collimated beam of low energy (0-2keV) electrons is that it is travelling along the path of the (100keV) probing electron beam. To collect and analyze them, they must be deflected off the beam path with minimal effect on the probe position.

Performance Evaluation of a Novel Type of Low-Energy Electron Microscope

1990 ◽  
Vol 48 (1) ◽  
pp. 354-355
Author(s):  
Bertholdand Senftinger ◽  
Helmut Liebl
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Field Strength ◽  
Numerical Aperture ◽  
Low Energy ◽  
Energy Electron ◽  
High Resolution Imaging ◽  
Lens System ◽  
Resolution Imaging ◽  
Low Energy Electron

During the last few years the investigation of clean and adsorbate-covered solid surfaces as well as thin-film growth and molecular dynamics have given rise to a constant demand for high-resolution imaging microscopy with reflected and diffracted low energy electrons as well as photo-electrons. A recent successful implementation of a UHV low-energy electron microscope by Bauer and Telieps encouraged us to construct such a low energy electron microscope (LEEM) for high-resolution imaging incorporating several novel design features, which is described more detailed elsewhere.The constraint of high field strength at the surface required to keep the aberrations caused by the accelerating field small and high UV photon intensity to get an improved signal-to-noise ratio for photoemission led to the design of a tetrode emission lens system capable of also focusing the UV light at the surface through an integrated Schwarzschild-type objective. Fig. 1 shows an axial section of the emission lens in the LEEM with sample (28) and part of the sample holder (29). The integrated mirror objective (50a, 50b) is used for visual in situ microscopic observation of the sample as well as for UV illumination. The electron optical components and the sample with accelerating field followed by an einzel lens form a tetrode system. In order to keep the field strength high, the sample is separated from the first element of the einzel lens by only 1.6 mm. With a numerical aperture of 0.5 for the Schwarzschild objective the orifice in the first element of the einzel lens has to be about 3.0 mm in diameter. Considering the much smaller distance to the sample one can expect intense distortions of the accelerating field in front of the sample. Because the achievable lateral resolution depends mainly on the quality of the first imaging step, careful investigation of the aberrations caused by the emission lens system had to be done in order to avoid sacrificing high lateral resolution for larger numerical aperture.

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