Statistical multiple diffuse scattering in a distorted crystal system: An exact theory

Wang, Zhong Lin

doi:10.1080/01418639608241072

Cited by 5 publications

(3 citation statements)

References 35 publications

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“…In electron scattering, most of the existing dynamical theories have been developed under the first order diffuse scattering approximation; thus, they are restricted to cases where the lattice distortion is small. A formal dynamical theory is presented for calculating diffuse scattering with the inclusion of multiple diffuse scattering (Wang, 1996b). By inclusion of a complex potential in dynamical calculation, a rigorous proof is given to show that the high order diffuse scattering are fully recovered in the calculations using the equation derived under the distorted wave Born approximation, and more importantly, the statistical time and structure averages over the distorted crystal lattices are evaluated analytically prior numerical calculation.…”

Section: The Contribution From Tds Electrons Is Especiallymentioning

confidence: 99%

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Thermal diffuse scattering in sub-angstrom quantitative electron microscopy—phenomenon, effects and approaches

Wang

2003

Micron

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This paper reviews the recent progress in the following areas.(1) In quantitative high-resolution transmission electron microscopy, the theoretically calculated images usually give better contrast than the experimentally observed ones although all of the factors have been accounted for. This discrepancy is suggested due to thermal diffusely scattered (TDS) electrons, which were not included in the image calculation. The contribution from TDS electrons is especially important if the image resolution is approaching 0.1 nm and beyond with the introduction of Cs corrected microscopes. A more rigorous multislice theory has been developed to account for this effect. (2) We proved that the off-axis holography is an ideal energy filter that even filters away the contribution made by TDS electrons in the electron wave function, but conventional high-resolution microscopy do contain the contribution made by phonon scattered electrons. (3) In electron scattering, most of the existing dynamical theories have been developed under the first order diffuse scattering approximation, thus, they are restricted to cases where the lattice distortion is small. A formal dynamical theory is presented for calculating diffuse scattering with the inclusion of multiple diffuse scattering. By inclusion of a complex potential in dynamical calculation, a rigorous proof is given to show that the high order diffuse scattering are fully recovered in the calculations using the equation derived under the distorted wave Born approximation, and more importantly, the statistical time and structure averages over the distorted crystal lattices are evaluated analytically prior numerical calculation. This conclusion establishes the basis for expanding the applications of the existing theories. (4) The 'frozen lattice' model is a semi-classical approach for calculating electron diffuse scattering in crystals arisen from thermal vibration of crystal atoms. Based on a rigorous quantum mechanical phonon excitation theory, we have proved that the frozen lattice mode is an excellent approximation and no detectable error would be possible under normal experimental conditions. q

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Section: The Contribution From Tds Electrons Is Especiallymentioning

confidence: 99%

“…(20) can be applied to recover the high order diffuse scattering terms dropped when Cðr 1 ; tÞ is replaced by C 0 ðK 0 ; r 1 Þ in deriving Eq. (18) under the first order diffuse scattering approximation (Wang, 1996b). Starting from the integral form of Eq.…”

Section: High Order Diffuse Scattering Theorymentioning

confidence: 99%

Thermal diffuse scattering in sub-angstrom quantitative electron microscopy—phenomenon, effects and approaches

Wang

2003

Micron

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show abstract

“…In electron scattering, most of the existing dynamical theories have been developed under the first order diffuse scattering approximation, thus, they are restricted to cases where the lattice distortion is small. A formal dynamical theory is presented for calculating diffuse scattering with the inclusion of multiple diffuse scattering [3,4,5]. By inclusion of a complex potential in dynamical calculation, a rigorous proof is given to show that the high order diffuse scattering are fully recovered in the calculations using the equation derived under the distorted wave Born approximation, and more importantly, the statistical time and structure averages over the distorted crystal lattices are evaluated analytically prior numerical calculation.…”

mentioning

confidence: 99%

Phonon Scattering in Quantitative High-Resolution Electron Microscopy – effects, problems and approaches

Wang

2002

Microsc Microanal

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An optical potential approach to incoherent multiple thermal diffuse scattering in quantitative HRTEM

Wang

1998

Ultramicroscopy

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Statistical multiple diffuse scattering in a distorted crystal system: An exact theory

Cited by 5 publications

References 35 publications

Thermal diffuse scattering in sub-angstrom quantitative electron microscopy—phenomenon, effects and approaches

Thermal diffuse scattering in sub-angstrom quantitative electron microscopy—phenomenon, effects and approaches

Phonon Scattering in Quantitative High-Resolution Electron Microscopy – effects, problems and approaches

An optical potential approach to incoherent multiple thermal diffuse scattering in quantitative HRTEM

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