Peculiarities of the Helium-Beam Scattering on Metal Surfaces

1974 ◽  
Vol 29 (2) ◽  
pp. 189-193 ◽  
Author(s):  
George Comsa ◽  
Gerda H. Comsa ◽  
J. K. Fremerey
Keyword(s):  
Metal Surfaces ◽  
Finite Size ◽  
Waller Factor ◽  
Scattering Data ◽  
Attractive Potential ◽  
Potential Surfaces ◽  
Smooth Potential ◽  
Atom Scattering ◽  
Debye Waller Factor ◽  
Beam Scattering

Some of the peculiarities of the atom scattering on metal surfaces are discussed in connection with the applicability of the Debye-Waller factor (DWF). The influence of the attractive potential well and of the finite size of the incident particles upon the scattering is commented. By comparing calculated DWF-values with experimental He scattering data it is concluded that the existence of diffraction is a necessary but not a sufficient condition for the applicability of the DWF. It is finally shown that the smooth potential surfaces which characterize the interaction between atoms and metal surfaces explain the apparently reduced thermal roughening observed experimentally.

die Streuung von Rontgen-Strahlen an Kristallen mit statistisch verteilten Defekten / On the Scattering of X-rays from Crystals Containing a Random Distribution of Defects

1973 ◽  
Vol 28 (6) ◽  
pp. 980-994
Author(s):  
Helmut Trinkaus
Keyword(s):  
Correlation Function ◽  
Random Distribution ◽  
Waller Factor ◽  
Scattering Data ◽  
X Rays ◽  
Single Defect ◽  
Debye Waller Factor ◽  
Variable Factor ◽  
Individual Contributions ◽  
The Individual

The static correlation function governing elastic scattering of X-rays or neutrons by a defective crystal is discussed for three degrees of imperfections, that is for slight, severe, and medium distortions of the scattering crystal. In the exponent of this correlation function the main term, which is linear in the defect concentration, is shown to be fairly independent of the particular type of statistics describing the random distribution of the defects. One condition for a successful analysis of defect structures using diffuse scattering data is that the scattering function can be split into the individual contributions of all single defects. For two regions, that is for the immediate vicinity of Bragg reflections (Huang scattering) and for the asymptotic regions of distortion scattering, this "single-defect approximation" is shown to be useful even for higher concentrations. In this case the correlations due to a single defect have to be corrected by a factor which takes into account the average correlation reduction by all other defects (static Debye-Waller factor in the Huang regions and a similar but variable factor in the asymptotic regions). The formulas given in this paper are applied to the sacttering by isotropic crystals containing point defects of spherical symmetry.

scholarly journals The electron–phonon coupling constant for single-layer graphene on metal substrates determined from He atom scattering

2021 ◽  
Author(s):  
Giorgio Benedek ◽  
Joseph R. Manson ◽  
Salvador Miret-Artés
Keyword(s):  
Single Layer ◽  
Waller Factor ◽  
Single Layer Graphene ◽  
Coupling Constant ◽  
Phonon Coupling ◽  
Metal Substrates ◽  
Layer Graphene ◽  
Atom Scattering ◽  
Debye Waller Factor ◽  
Electron Phonon Coupling

A theory, previously formulated for conducting surfaces, is extended to extract the electron-phonon coupling strength λ for graphene supported on metal substrates from the thermal attenuation (Debye–Waller factor) of helium scattering reflectivity.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

scholarly journals Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Zhengwen Liu ◽  
Rafael A. Porto ◽  
Zixin Yang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Scattering Problem ◽  
Finite Size ◽  
Effective Field ◽  
Compact Objects ◽  
Scattering Data ◽  
Theory Approach ◽  
Spin Effects ◽  
Radial Action

Abstract Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

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