Z Dependence of Electron Scattering by Single Atoms into Annular Dark-Field Detectors

2011 ◽  
Vol 17 (6) ◽  
pp. 847-858 ◽  
Author(s):  
Michael M.J. Treacy
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Dark Field ◽  
Single Atom ◽  
Single Atoms ◽  
Annular Dark Field ◽  
Annular Detector ◽  
The Cross

AbstractA simple parameterization is presented for the elastic electron scattering cross sections from single atoms into the annular dark-field (ADF) detector of a scanning transmission electron microscope (STEM). The dependence on atomic number, Z, and inner reciprocal radius of the annular detector, q0, of the cross section σ(Z,q0) is expressed by the empirical relationwhere A(q0) is the cross section for hydrogen (Z = 1), and the detector is assumed to have a large outer reciprocal radius. Using electron elastic scattering factors determined from relativistic Hartree-Fock simulations of the atomic electron charge density, values of the exponent n(Z,q0) are tabulated as a function of Z and q0, for STEM probe sizes of 1.0 and 2.0 Å.Comparison with recently published experimental data for single-atom scattering [Krivanek et al. (2010). Nature464, 571–574] suggests that experimentally measured exponent values are systematically lower than the values predicted for elastic scattering from low-Z atoms. It is proposed that this discrepancy arises from the inelastic scattering contribution to the ADF signal. A simple expression is proposed that corrects the exponent n(Z,q0) for inelastic scattering into the annular detector.

Creation, destruction, and transfer of atomic multipole moments by electron scattering: relativistic treatment1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

2011 ◽  
Vol 89 (5) ◽  
pp. 521-531 ◽  
Author(s):  
G. Csanak ◽  
C.J. Fontes ◽  
D.P. Kilcrease ◽  
D.V. Fursa
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Matrix Formalism ◽  
Multipole Moments ◽  
Magnetic Sublevel ◽  
Coherence Transfer ◽  
International Colloquium

We have obtained expressions for the creation, destruction, and transfer of atomic multipole moments by electron scattering under relativistic conditions. More specifically, we have obtained separate expressions for different-level processes (inelastic scattering) and for same-level processes (elastic and inelastic scattering). The cross sections for different-level processes are expressed in terms of inelastic magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of an angular integral of a product of inelastic magnetic sublevel amplitudes. The same-level cross sections are expressed in terms of the imaginary part of the elastic forward scattering amplitude and in terms of elastic scattering magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of the (complex) forward elastic scattering amplitudes and an angular integral of a product of elastic scattering magnetic sublevel amplitudes. If the collisional model supports the optical theorem, then the same-level cross sections can be rewritten in such a form that they are broken up into two parts: an elastic scattering part and an inelastic scattering part. In carrying out this work, we have used the density matrix formalism of Fano and Blum in combination with the electron scattering formalism of Gell-Mann and Goldberger.

scholarly journals Electron scattering cross-sections for particle transport modeling in a weakly ionized air plasma

2021 ◽  
Vol 51 ◽  
pp. 96-111
Author(s):  
Vasily Sergeevich Zakharov ◽  
Mikhail Evgenievich Zhukovskiy ◽  
Sergey Vasilievich Zakharov ◽  
Mikhail Borisovich Markov
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Electron Interaction ◽  
Inelastic Electron ◽  
Neutral Atoms ◽  
Hartree Fock ◽  
Wide Range ◽  
The Cross

Data on processes of electron scattering on ions and neutral atoms are required in fundamental studies and in applied research in such fields as astro- and laser physics, low density plasma simulations, kinetic modeling etc. Experimental and computational data on elastic and inelastic electron scattering in a wide range of electron energies is available mostly for the electron interaction with neutral atoms, but are very limited for the scattering on ions, notably for elastic processes. In present work the calculational approaches for the cross-section computation of electron elastic and inelastic scattering on neutral atoms and ions are considered. The atomic and ion properties obtained in quantum-statistical Hartree-Fock-Slater model are used in the direct computation of electron elastic scattering and ionization cross-sections by a partial waves method, semiclassical and distorted-wave approximations. Calculated cross-sections for elastic scattering on nitrogen and oxygen atoms and ions, and electron ionisation cross-sections are compared with the available experimental data and widely used approximations and propose consistent results. Considering applicability of Hartree-Fock-Slater model in wide scope of temperatures and densities, such approach to the cross-section calculation can be used in a broad range of energies and ion charges.

Anchoring Copper Single Atoms on Porous Boron Nitride Nanofiber to Boost Selective Reduction of Nitroaromatics

2021 ◽  
Author(s):  
Jianli Liang ◽  
Qianqian Song ◽  
Jianghua Wu ◽  
Qi Lei ◽  
Zhongming Huang ◽  
...  
Keyword(s):  
Boron Nitride ◽  
High Performance ◽  
Selective Reduction ◽  
Dark Field ◽  
Single Atom ◽  
Single Atoms ◽  
Annular Dark Field ◽  
Cu Catalyst ◽  
Calcination Method ◽  
Turn Over Frequency

Abstract Single atom catalysts have received widespread attention for their fascinating performance in terms of metal atom efficiency as well as their unique catalysis mechanisms comparing to conventional catalysts. Here, we prepared a high-performance catalyst of single-Cu-atom-decorated boron nitride nanofibers (BNNF-Cu) via a facile calcination method for the first time. The as-prepared catalyst shows excellent catalytic activity and good stability for converting different nitro compounds into their corresponding amines both with and without photoexcitation. By combined studies using synchrotron radiation analysis, high-resolution high-angle annular dark-field transmission electron microscopy studies and DFT calculation, dispersion and coordination of Cu atoms as well as their catalytic mechanisms are explored. The BNNF-Cu catalyst is found to have a record high turn-over frequency comparing to previously reported nonprecious-metal-based catalysts. While the performance of the BNNF-Cu catalyst is only of the middle range level among the state-of-the-art precious-metal-based catalysts, due to the much lower cost of the BNNF-Cu catalyst, its cost-efficiency is the highest among these catalysts. This work provides a new choice of support material which can promote the development of single atoms catalysts.

B(E2) of the First 2+ Level of 150Sm

1971 ◽  
Vol 49 (21) ◽  
pp. 2690-2692 ◽  
Author(s):  
J. A. Cameron ◽  
Z. Zámori
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Transition Probability ◽  
The Cross ◽  
Bombarding Energy

The cross section for the inelastic scattering of 4He ions exciting the first 2+ state of 150Sm was compared with the cross section for elastic scattering. From the measured ratios at 9 and 10 MeV bombarding energy, the reduced transition probability was found to be[Formula: see text]

Elastic Scattering in Electron Microscopy

1973 ◽  
Vol 31 ◽  
pp. 252-253
Author(s):  
J. Langmore ◽  
M. Isaacson ◽  
J. Wall ◽  
A. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Elastic Scattering ◽  
Cross Section ◽  
Quantum Noise ◽  
Dark Field ◽  
Elastic Cross Section ◽  
Biological Molecules ◽  
Dark Field Microscopy ◽  
Field Systems ◽  
Effects Of Radiation

High resolution dark field microscopy is becoming an important tool for the investigation of unstained and specifically stained biological molecules. Of primary consideration to the microscopist is the interpretation of image Intensities and the effects of radiation damage to the specimen. Ignoring inelastic scattering, the image intensity is directly related to the collected elastic scattering cross section, σɳ, which is the product of the total elastic cross section, σ and the eficiency of the microscope system at imaging these electrons, η. The number of potentially bond damaging events resulting from the beam exposure required to reduce the effect of quantum noise in the image to a given level is proportional to 1/η. We wish to compare η in three dark field systems.

Atomic resolution Z-contrast imaging of bulk crystal surfaces in Scanning Reflection Electron Microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 414-415
Author(s):  
Z. L. Wang ◽  
J. Bentley
Keyword(s):  
Electron Microscopy ◽  
Elastic Scattering ◽  
Dark Field ◽  
Contrast Imaging ◽  
Crystal Lattices ◽  
Small Probe ◽  
Scanning Transmission ◽  
Annular Dark Field ◽  
Image Position ◽  
Z Contrast

The success of obtaining atomic-number-sensitive (Z-contrast) images in scanning transmission electron microscopy (STEM) has shown the feasibility of imaging composition changes at the atomic level. This type of image is formed by collecting the electrons scattered through large angles when a small probe scans across the specimen. The image contrast is determined by two scattering processes. One is the high angle elastic scattering from the nuclear sites,where ϕNe is the electron probe function centered at bp = (Xp, yp) after penetrating through the crystal; F denotes a Fourier transform operation; D is the detection function of the annular-dark-field (ADF) detector in reciprocal space u. The other process is thermal diffuse scattering (TDS), which is more important than the elastic contribution for specimens thicker than about 10 nm, and thus dominates the Z-contrast image. The TDS is an average “elastic” scattering of the electrons from crystal lattices of different thermal vibrational configurations,

Differential cross-section measurements in positron–argon collisions

1996 ◽  
Vol 74 (7-8) ◽  
pp. 505-508 ◽  
Author(s):  
R. M. Finch ◽  
Á. Kövér ◽  
M. Charlton ◽  
G. Laricchia
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Inelastic Scattering ◽  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Coupling Effect ◽  
Channel Coupling ◽  
Scattering Cross

Differential cross sections for elastic scattering and ionization in positron–argon collisions as a function of energy (40–150 eV) are reported at 60°. Of particular interest is the energy range 55–60 eV, where earlier measurements by the Detroit group found a drop in the elastic-scattering cross section of a factor of 2. This structure has been tentatively attributed to a cross channel-coupling effect with an open inelastic-scattering channel, most likely ionization. Our results indicate that ionization remains an important channel over the same energy range and only begins to decrease at an energy above 60 eV.

ICSC: a program for calculating inelastic scattering cross sections for fast electrons incident on crystals

2003 ◽  
Vol 36 (3) ◽  
pp. 940-943 ◽  
Author(s):  
M. P. Oxley ◽  
L. J. Allen
Keyword(s):  
Inelastic Scattering ◽  
Cross Sections ◽  
Dark Field ◽  
Fast Electrons ◽  
Scattering Coefficients ◽  
Einstein Model ◽  
Annular Dark Field ◽  
Inner Shell Ionization ◽  
Scattering Cross Sections ◽  
Shell Ionization

A computer program which calculates inner-shell ionization and backscattering cross sections for fast electrons incident on a crystal is presented. The program calculates the inelastic scattering coefficients for inner-shell ionization, pertinent to electron energy loss spectroscopy and energy dispersive X-ray analysis, using recently presented parameterizations of the atomic scattering factors. Orientation-dependent cross sections, suitable for atom location by channelling enhanced microanalysis, may be calculated. Inelastic scattering coefficients that allow the calculation of orientation-dependent annular dark-field and Rutherford backscattering maps are calculated using an Einstein model. In all cases, absorption due to thermal diffuse scattering, also calculated using an Einstein model, can be included.

Quantitative Annular Dark Field Electron Microscopy Using Single Electron Signals

2013 ◽  
Vol 20 (1) ◽  
pp. 99-110 ◽  
Author(s):  
Ryo Ishikawa ◽  
Andrew R. Lupini ◽  
Scott D. Findlay ◽  
Stephen J. Pennycook
Keyword(s):  
Electron Microscopy ◽  
Dynamic Range ◽  
Light Element ◽  
Dark Field ◽  
Atomic Scale ◽  
Single Electron ◽  
Single Atom ◽  
Intensity Level ◽  
Primitive Cell ◽  
Annular Dark Field

AbstractOne of the difficulties in analyzing atomic resolution electron microscope images is that the sample thickness is usually unknown or has to be fitted from parameters that are not precisely known. An accurate measure of thickness, ideally on a column-by-column basis, parameter free, and with single atom accuracy, would be of great value for many applications, such as matching to simulations. Here we propose such a quantification method for annular dark field scanning transmission electron microscopy by using the single electron intensity level of the detector. This method has the advantage that we can routinely quantify annular dark field images operating at both low and high beam currents, and under high dynamic range conditions, which is useful for the quantification of ultra-thin or light-element materials. To facilitate atom counting at the atomic scale we use the mean intensity in an annular dark field image averaged over a primitive cell, with no free parameters to be fitted. To illustrate the potential of our method, we demonstrate counting the number of Al (or N) atoms in a wurtzite-type aluminum nitride single crystal at each primitive cell over the range of 3–99 atoms.

scholarly journals Investigation of the cross section for dd elastic scattering and dd→nHe3 reactions at 160 MeV

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
I. Ciepał ◽  
J. Kuboś ◽  
K. Bodek ◽  
N. Kalantar-Nayestanaki ◽  
G. Khatri ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
The Cross
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