Topic
Atomic form factor
About: Atomic form factor is a research topic. Over the lifetime, 129 publications have been published within this topic receiving 4981 citations. The topic is also known as: atomic form factor.
Papers published on a yearly basis
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Papers
TL;DR: In this paper, the atomic form factor and the incoherent scattering function were derived from available state-of-the-art theoretical data, including the Pirenne formulas for Z=1, configuration-into-action results by Brown using Brown‐Fontana and Weiss correlated wavefunctions for Z =2 to 6 non-relativistic Hartree‐Fock results by Cromer for Z ≥ 0.005 A−1 to 109 A− 1, for all elements A=1 to 100.
Abstract: Tabulations are presented of the atomic form factor,F (α,Z), and the incoherent scattering function, S (x,Z), for values of x (=sin ϑ/2)/λ) from 0.005 A−1 to 109 A−1, for all elements A=1 to 100. These tables are constructed from available state‐of‐the‐art theoretical data, including the Pirenne formulas for Z=1, configuration‐into action results by Brown using Brown‐Fontana and Weiss correlated wavefunctions for Z=2 to 6 non‐relativistic Hartree‐Fock results by Cromer for Z=7 to 100 and a relativistic K‐shell analytic expression for F (x,Z) by Bethe Levinger for x≳10 A−1 for all elements Z=2 to 100. These tabulated values are graphically compared with available photon scatteringangular distributionmeasurements. Tables of coherent (Rayleigh) and incoherent (Compton) total scattering cross sections obtained by numerical integration over combinations of F 2(x,Z) with the Thomson formula and S (x,Z) with the Klum‐Nishina Formual, respectively, are presented for all elements Z=1 to 100, for photon energies 100 eV (λ=124 A) to 100 MeV (0.000124 A). The incoherent scattering cross sections also include the radiative and double‐Compton corrections as given by Mork. Similar tables are presented for the special cases of terminally‐bonded hydrogen and for the H2 molecule, interpolated and extrapolated from values calculated by Stewart et al., and by Bentley and Stewart using Kolos‐Roothaan wavefunctions.
1,843 citations
TL;DR: In this article, the authors derived new theoretical results of substantially higher accuracy in near-edge soft x-ray regions, where the energy range covered is 0.1 to 10 keV and the associated figures and tabulation demonstrate the current comparison with alternate theory and with available experimental data.
Abstract: Reliable knowledge of the complex x-ray form factor [Re(f ) and f″] and the photoelectric attenuation coefficient (σPE) is required for crystallography, medical diagnosis, radiation safety, and XAFS studies. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 to 3 keV x-ray energies. The key discrepancies are due to the smoothing of edge structure, the use of nonrelativistic wave functions, and the lack of appropriate convergence of wave functions. This paper addresses these key discrepancies and derives new theoretical results of substantially higher accuracy in near-edge soft x-ray regions. The high-energy limitations of the current approach are also illustrated. The energy range covered is 0.1 to 10 keV. The associated figures and tabulation demonstrate the current comparison with alternate theory and with available experimental data. In general, experimental data are not sufficiently accurate to establish the errors and inadequacies of theory at this ...
427 citations
TL;DR: In this article, a detailed error analysis is presented showing that the over-all root-mean-square error in $a(q)$ never exceeds 2.5% for any value of the momentum transfer.
Abstract: Highly accurate x-ray diffraction measurements are presented for the static structure factor $a(q)$ for liquid Na (at 100 and 200 \ifmmode^\circ\else\textdegree\fi{}C) and liquid K (at 65 and 135 \ifmmode^\circ\else\textdegree\fi{}C). A detailed error analysis is presented showing that the over-all root-mean-square error in $a(q)$ never exceeds 2.5% for any value of the momentum transfer $q$ and the relative root-mean-square error in $a(q)$ between different temperatures is always less than 1.5%. We discuss and demonstrate the reliability of the tabulated values for the atomic form factor and the Compton-scattering correction. A brief discussion is included of the relative merits of x-ray vs neutron diffraction for obtaining the static structure factor.
289 citations
TL;DR: In this paper, the absorptive contribution of high-energy electron diffraction to the atomic form factor has been calculated using the Debye-Waller factor, which is calculated as a function of scattering vector s and temperature factor M on a grid which enables polynomial interpolation of the results to be accurate to better than 2% for much of the ranges 0 ≤ M ≤ 2 A2.
Abstract: The thermal diffuse scattering contribution to the absorptive potential in high-energy electron diffraction is calculated in the form of an absorptive contribution to the atomic form factor. To do this, the Einstein model of lattice vibrations is used, with isotropic Debye-Waller factors. The absorptive form factors are calculated as a function of scattering vector s and temperature factor M on a grid which enables polynomial interpolation of the results to be accurate to better than 2% for much of the ranges 0 ≤ Ms2 ≤ 6 and 0 ≤ M ≤ 2 A2. The computed values, together with an interpolation routine, have been incorporated into a Fortran subroutine which calculates both the real and absorptive form factors for 54 atomic species.
250 citations
TL;DR: In this paper, the relativistic Hartree-Fock-Slater modified atomic form factor (HFFS) was used to represent the atomic Rayleigh scattering amplitudes with good accuracy at energies well above the K−shell binding energies and small momentum transfers.
Abstract: Tabulations are presented of relativistic Hartree–Fock–Slater modified atomic form factors from x=0 to 100 A−1 for all elements from Z=1 to Z=100. These modified form factors represent the atomic Rayleigh scattering amplitudes with good accuracy at energies well above the K‐shell binding energies and small momentum transfers and therefore should be used instead of the normal relativistic atomic form factors in the MeV energy range.
187 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 3 |
| 2016 | 2 |
| 2015 | 8 |