Dirac–Fock calculations of X-ray scattering factors and contributions to the mean inner potential for electron scattering

Rez, David; Rez, Peter; Grant, I P

doi:10.1107/s0108767393013200

Cited by 200 publications

(189 citation statements)

References 8 publications

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“…Hence, bonding lengths and charge densities are expected to be different in both cases, and likewise the potential well depths. Since the scattering factor of Se is larger than that of Cu and Ga [37,38], one would expect a smaller potential well depth at a core with a higher density of Se atoms, i.e., the anion core, as found in the present study. cation GB cores after a tilt of 1.5 • , and the measured potential profile from Fig.…”

supporting

confidence: 61%

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Electrostatic Potentials at Cu(In,Ga)Se2Grain Boundaries: Experiment and Simulations

et al. 2012

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In the present Letter, we report on a combined ab-initio density functional theory calculation, multislice simulation, and electron holography study, performed on a Σ9 grain boundary (GB) in a CuGaSe 2 bicrystal, which exhibits a lower symmetry compared with highly symmetric Σ3 GBs.We find an electrostatic potential well at the Σ9 GB of 0.8 V in depth and 1.3 nm in width, which in comparison with results from Σ3 and random GBs exhibits the trend of increasing potential-well depths with lower symmetry. The presence of this potential well at the Σ9 GB can be explained conclusively by a reduced density of atoms at the GB. Considering experimental limitations in resolution, we demonstrate quantitative agreement of experiment and theory.

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supporting

confidence: 61%

“…Scattering factors of neutral atoms (since that for Se 2− is not given in the literature) according to Refs. [37,38] were employed.…”

mentioning

confidence: 99%

Electrostatic Potentials at Cu(In,Ga)Se2Grain Boundaries: Experiment and Simulations

et al. 2012

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“…Furthermore, scattering factors have been parameterized for a large number of elements as the sum of a number of Gaussian distributions (Smith & Burge, 1962;Doyle & Turner, 1968;Rez & Rez, 1994). In this paper we will use the parameterization as given by Doyle & Turner (1968), which is:…”

Section: Intensity Distributionmentioning

confidence: 99%

How to optimize the design of a quantitative HREM experiment so as to attain the highest precision

1999

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SummaryUsing parameter estimation theory, an expression is derived for the maximum precision with which the position of a single atom can be estimated from high resolution transmission electron microscopy images. This expression, being a complicated function of the object as well as of the microscope parameters and the electron dose, can be used to optimize the design of an HREM experiment so as to attain the highest precision.

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“…The Fourier coefficients of the atomic potential in (1) are approximated by those calculated for spherical neutral atoms (Rez, Rez & Grant, 1994). This is only an approximation since bonding effects are completely ignored.…”

Section: Temperature Factorsmentioning

confidence: 99%

“…A complete set of Fourier transformed atomic potentials for neutral atoms fs(q) has been computed by Rez, Rez & Grant (1994) using a self-consistent Dirac-FockSlater code. These data are very close to the most commonly used Doyle & Turner (1968) tables, which represent the output of various programs.…”

Section: Jgmentioning

confidence: 99%

High-Precision Measurement of Temperature Factors for NiAl by Convergent-Beam Electron Diffraction

Nüchter¹,

Weickenmeier²

1998

Acta Cryst Sect A

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Convergent-beam electron diffraction is applied to measure the temperature factors of the intermetallic phase NiA1 with high accuracy. The patterns are recorded in an energy-filtering transmission electron microscope at zero energy loss using a slow-scan CCD camera. The specimens were tilted in systematic row orientation. In this new approach, data are extracted from the brightfield disc as well as from several high-order dark-field discs along line scans. The temperature factors are determined by fitting Bloch-wave simulations to the intensity profiles. The harmonic approximation for temperature factors is used. For B2-phase NiA1, mean thermal displacements u(Ni) -5.5 + 0.1 and u(A1) = 5.7 4-0.1 pm are obtained at 100 K. Avery detailed error analysis is given, and stochastic and systematic errors are discussed and quantified.

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Dirac–Fock calculations of X-ray scattering factors and contributions to the mean inner potential for electron scattering

Cited by 200 publications

References 8 publications

Electrostatic Potentials at Cu(In,Ga)Se2Grain Boundaries: Experiment and Simulations

Electrostatic Potentials at Cu(In,Ga)Se2Grain Boundaries: Experiment and Simulations

How to optimize the design of a quantitative HREM experiment so as to attain the highest precision

High-Precision Measurement of Temperature Factors for NiAl by Convergent-Beam Electron Diffraction

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