International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 259-429
https://doi.org/10.1107/97809553602060000593

Chapter 4.3. Electron diffraction

Contents

  • 4.3. Electron diffraction  (pp. 259-429) | html | pdf | chapter contents |
    C. Colliex, J. M. Cowley, S. L. Dudarev, M. Fink, J. Gjønnes, R. Hilderbrandt, A. Howie, D. F. Lynch, L. M. Peng, G. Ren, A. W. Ross, V. H. Smith Jr, J. C. H. Spence, J. W. Steeds, J. Wang, M. J. Whelan and B. B. Zvyagin
    • 4.3.1. Scattering factors for the diffraction of electrons by crystalline solids  (pp. 259-262) | html | pdf |
      J. M. Cowley
      • 4.3.1.1. Elastic scattering from a perfect crystal  (p. 259) | html | pdf |
      • 4.3.1.2. Atomic scattering factors  (pp. 259-260) | html | pdf |
      • 4.3.1.3. Approximations of restricted validity  (p. 260) | html | pdf |
      • 4.3.1.4. Relativistic effects  (pp. 260-261) | html | pdf |
      • 4.3.1.5. Absorption effects  (p. 261) | html | pdf |
      • 4.3.1.6. Tables of atomic scattering amplitudes for electrons  (p. 261) | html | pdf |
      • 4.3.1.7. Use of Tables 4.3.1.1 and 4.3.1.2  (pp. 261-262) | html | pdf |
    • 4.3.2. Parameterizations of electron atomic scattering factors  (p. 262) | html | pdf |
      J. M. Cowley, L. M. Peng, G. Ren, S. L. Dudarev and M. J. Whelan
    • 4.3.3. Complex scattering factors for the diffraction of electrons by gases  (pp. 262-391) | html | pdf |
      A. W. Ross, M. Fink, R. Hilderbrandt, J. Wang and V. H. Smith Jr
      • 4.3.3.1. Introduction  (p. 262) | html | pdf |
      • 4.3.3.2. Complex atomic scattering factors for electrons  (pp. 262-390) | html | pdf |
        • 4.3.3.2.1. Elastic scattering factors for atoms  (pp. 262-389) | html | pdf |
        • 4.3.3.2.2. Total inelastic scattering factors  (pp. 389-390) | html | pdf |
        • 4.3.3.2.3. Corrections for defects in the theory of atomic scattering  (p. 390) | html | pdf |
      • 4.3.3.3. Molecular scattering factors for electrons  (pp. 390-391) | html | pdf |
    • 4.3.4. Electron energy-loss spectroscopy on solids  (pp. 391-412) | html | pdf |
      C. Colliex
      • 4.3.4.1. Definitions  (pp. 391-394) | html | pdf |
        • 4.3.4.1.1. Use of electron beams  (pp. 391-392) | html | pdf |
        • 4.3.4.1.2. Parameters involved in the description of a single inelastic scattering event  (p. 392) | html | pdf |
        • 4.3.4.1.3. Problems associated with multiple scattering  (pp. 392-393) | html | pdf |
        • 4.3.4.1.4. Classification of the different types of excitations contained in an electron energy-loss spectrum  (pp. 393-394) | html | pdf |
      • 4.3.4.2. Instrumentation  (pp. 394-397) | html | pdf |
        • 4.3.4.2.1. General instrumental considerations  (pp. 394-395) | html | pdf |
        • 4.3.4.2.2. Spectrometers  (pp. 395-397) | html | pdf |
        • 4.3.4.2.3. Detection systems  (p. 397) | html | pdf |
      • 4.3.4.3. Excitation spectrum of valence electrons  (pp. 397-404) | html | pdf |
        • 4.3.4.3.1. Volume plasmons  (pp. 397-399) | html | pdf |
        • 4.3.4.3.2. Dielectric description  (pp. 399-401) | html | pdf |
        • 4.3.4.3.3. Real solids  (pp. 401-403) | html | pdf |
        • 4.3.4.3.4. Surface plasmons  (pp. 403-404) | html | pdf |
      • 4.3.4.4. Excitation spectrum of core electrons  (pp. 404-411) | html | pdf |
        • 4.3.4.4.1. Definition and classification of core edges  (pp. 404-406) | html | pdf |
        • 4.3.4.4.2. Bethe theory for inelastic scattering by an isolated atom (Bethe, 1930; Inokuti, 1971; Inokuti, Itikawa & Turner, 1978, 1979)  (pp. 406-408) | html | pdf |
        • 4.3.4.4.3. Solid-state effects  (pp. 408-410) | html | pdf |
        • 4.3.4.4.4. Applications for core-loss spectroscopy  (pp. 410-411) | html | pdf |
      • 4.3.4.5. Conclusions  (pp. 411-412) | html | pdf |
    • 4.3.5. Oriented texture patterns  (pp. 412-414) | html | pdf |
      B. B. Zvyagin
      • 4.3.5.1. Texture patterns  (p. 412) | html | pdf |
      • 4.3.5.2. Lattice plane oriented perpendicular to a direction (lamellar texture)  (pp. 412-413) | html | pdf |
      • 4.3.5.3. Lattice direction oriented parallel to a direction (fibre texture)  (pp. 413-414) | html | pdf |
      • 4.3.5.4. Applications to metals and organic materials  (p. 414) | html | pdf |
    • 4.3.6. Computation of dynamical wave amplitudes  (pp. 414-416) | html | pdf |
    • 4.3.7. Measurement of structure factors and determination of crystal thickness by electron diffraction  (pp. 416-419) | html | pdf |
      J. Gjønnes and J. W. Steeds
    • 4.3.8. Crystal structure determination by high-resolution electron microscopy  (pp. 419-429) | html | pdf |
      J. C. H. Spence and J. M. Cowley
      • 4.3.8.1. Introduction  (pp. 419-421) | html | pdf |
      • 4.3.8.2. Lattice-fringe images  (pp. 421-422) | html | pdf |
      • 4.3.8.3. Crystal structure images  (pp. 422-424) | html | pdf |
      • 4.3.8.4. Parameters affecting HREM images  (pp. 424-425) | html | pdf |
      • 4.3.8.5. Computing methods  (pp. 425-427) | html | pdf |
      • 4.3.8.6. Resolution and hyper-resolution  (p. 427) | html | pdf |
      • 4.3.8.7. Alternative methods  (pp. 427-428) | html | pdf |
      • 4.3.8.8. Combined use of HREM and electron diffraction  (pp. 428-429) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 4.3.4.1. Definition of the regions in ( E, q ) space that can be investigated with the different primary sources of particles available at present  (p. 392) | html | pdf |
      • Fig. 4.3.4.2. A primary electron of energy E 0 and wavevector k is inelastically scattered into a state of energy E 0 − ΔE and wavevector k ′  (p. 392) | html | pdf |
      • Fig. 4.3.4.3. Excitation spectrum of aluminium from 1 to 250 eV, investigated by EELS on 300 keV primary electrons  (p. 393) | html | pdf |
      • Fig. 4.3.4.4. Complete electron energy-loss spectrum of a thin rhodizite crystal (thickness ~60 nm)  (p. 393) | html | pdf |
      • Fig. 4.3.4.5. Schematic energy-level representation of the origin of a core-loss excitation (from a core level C at energy E c to an unoccupied state U above the Fermi level E f ) and its general shape in EELS, as superimposed on a continuously decreasing background  (p. 393) | html | pdf |
      • Fig. 4.3.4.6. Energy-loss spectrum, in the meV region, of an evaporated germanium film (thickness [\simeq] 25 nm)  (p. 394) | html | pdf |
      • Fig. 4.3.4.7. Schematic drawing of a uniform magnetic sector spectrometer with induction B normal to the plane of the figure  (p. 395) | html | pdf |
      • Fig. 4.3.4.8. Different factors contributing to the energy resolution in the dispersion plane  (p. 395) | html | pdf |
      • Fig. 4.3.4.9. Optical coupling of a magnetic sector spectrometer on a STEM column  (p. 396) | html | pdf |
      • Fig. 4.3.4.10. Principle of the Wien filter used as an EELS spectrometer: the trajectories are shown in the two principal (dispersive and focusing) sections  (p. 396) | html | pdf |
      • Fig. 4.3.4.11. Principle of the Castaing & Henry filter made from a magnetic prism and an electrostatic mirror  (p. 396) | html | pdf |
      • Fig. 4.3.4.12. A commercial EELS spectrometer designed for parallel detection on a photodiode array  (p. 397) | html | pdf |
      • Fig. 4.3.4.13. The dispersion curve for the excitation of a plasmon (curve 1) merges into the continuum of individual electron–hole excitations (between curves 2 and 4) for a critical wavevector q c   (p. 398) | html | pdf |
      • Fig. 4.3.4.14. Measured angular dependence of the differential cross section d σ /d Ω for the 15 eV plasmon loss in Al (dots) compared with a calculated curve by Ferrell (solid curve) and with a sharp cut-off approximation at θ c (dashed curved)  (p. 399) | html | pdf |
      • Fig. 4.3.4.15. Variation of plasmon excitation mean free path Λ p as a function of accelerating voltage V in the case of carbon and aluminium  (p. 399) | html | pdf |
      • Fig. 4.3.4.16. Dielectric and optical functions calculated in the Drude model of a free-electron gas with ħω p = 16 eV and τ = 1.64 × 10 −16  s  (p. 400) | html | pdf |
      • Fig. 4.3.4.17. Same as previous figure, but for a Lorentz model with an oscillator of eigenfrequency ħω 0 = 10 eV and relaxation time τ 0 = 6.6 × 10 −16  s superposed on the free-electron term  (p. 401) | html | pdf |
      • Fig. 4.3.4.18. Dielectric coefficients [\varepsilon_1], [\varepsilon_2] and [{\rm Im}(-1/\varepsilon)] from a collection of typical real solids  (p. 402) | html | pdf |
      • Fig. 4.3.4.19. Dielectric functions in graphite derived from energy losses for E ⊥ c ( i.e. the electric field vector being in the layer plane) and for E || c   (p. 403) | html | pdf |
      • Fig. 4.3.4.20. Geometric conditions for investigating the anisotropic energy-loss function  (p. 404) | html | pdf |
      • Fig. 4.3.4.21. Definition of electron shells and transitions involved in core-loss spectroscopy  (p. 404) | html | pdf |
      • Fig. 4.3.4.22. Chart of edges encountered in the 50 eV up to 3 keV energy-loss range with symbols identifying the types of shapes  (p. 405) | html | pdf |
      • Fig. 4.3.4.23. A selection of typical profiles ( K, L 2,3 , M 4,5 , and N 2,3 ) illustrating the most important behaviours encountered on major edges through the Periodic Table  (p. 406) | html | pdf |
      • Fig. 4.3.4.24. Bethe surface for K -shell ionization, calculated using a hydrogenic model  (p. 407) | html | pdf |
      • Fig. 4.3.4.25. A novel technique for simulating an energy-loss spectrum with two distinct edges as a superposition of theoretical contributions (hydrogenic saw-tooth for O K , Lorentzian white lines and delayed continuum for Fe L 2,3 calculated with the Hartree–Slater description)  (p. 407) | html | pdf |
      • Fig. 4.3.4.26. Definition of the different fine structures visible on a core-loss edge  (p. 408) | html | pdf |
      • Fig. 4.3.4.27. High-energy resolution spectra on the L 2,3 titanium edge from two phases (rutile and anatase) of TiO 2   (p. 408) | html | pdf |
      • Fig. 4.3.4.28. The dramatic change in near-edge fine structures on the L 3 and L 2 lines of Cu, from Cu metal to CuO  (p. 409) | html | pdf |
      • Fig. 4.3.4.29. Illustration of the single and multiple scattering effects used to describe the final wavefunction on the excited site  (p. 409) | html | pdf |
      • Fig. 4.3.4.30. Comparison of the experimental O K edge (solid line) with calculated profiles in the multiple scattering approach  (p. 409) | html | pdf |
      • Fig. 4.3.4.31. The conventional method of background subtraction for the evaluation of the characteristic signals S O K and S Fe L 2,3 used for quantitative elemental analysis  (p. 410) | html | pdf |
      • Fig. 4.3.4.32. Values of n eff for metallic aluminium based on composite optical data  (p. 411) | html | pdf |
      • Fig. 4.3.5.1. The relative orientations of the direct and the reciprocal axes and their projections on the plane ab , with indication of the distances B hk and D hkl that define the positions of reflections in lamellar texture patterns  (p. 412) | html | pdf |
      • Fig. 4.3.5.2. ( a ) Part of the OTED pattern of the clay mineral kaolinite and ( b ) the intensity profile of a characteristic quadruplet of reflections recorded with the electron diffractometry system  (p. 413) | html | pdf |
      • Fig. 4.3.5.3. The projections of the reciprocal axes on the plane ab of the direct lattice, with indications of the distances B and D of the hk rows from the fibre-texture axes a or [ hk ]  (p. 413) | html | pdf |
      • Fig. 4.3.7.1. ( a ) Dispersion-surface section for the symmetric four-beam case (0, g, g + h, m ), γ k is a function of k x , referred to ( b ), where k x = k y = 0 corresponds to the exact Bragg condition for all three reflections  (p. 418) | html | pdf |
      • Fig. 4.3.8.1. Atomic resolution image of a tantalum-doped tungsten trioxide crystal (pseudo-cubic structure) showing extended crystallographic shear-plane defects (C), pentagonal-column hexagonal-tunnel (PCHT) defects (T), and metallization of the surface due to oxygen desorption (JEOL 4000EX, crystal thickness less than 200 Å, 400 kV, C s = 1 mm)  (p. 419) | html | pdf |
      • Fig. 4.3.8.2. Imaging conditions for few-beam lattice images  (p. 420) | html | pdf |
      • Fig. 4.3.8.3. A summary of three- (or five-) beam axial imaging conditions  (p. 422) | html | pdf |
      • Fig. 4.3.8.4. The contrast of few-beam lattice images as a function of focus in the neighbourhood of the stationary-phase focus  (p. 422) | html | pdf |
      • Fig. 4.3.8.5. ( a ) The transfer function for a 400 kV electron microscope with a point resolution of 1.7 Å at the Scherzer focus; the curve is based on equation (4.3.8.17)  (p. 424) | html | pdf |
      • Fig. 4.3.8.6. Structure image of a thin lamella of the 6 H polytype of SiC projected along [110] and recorded at 1.2 MeV  (p. 426) | html | pdf |
    • Tables
      • Table 4.3.1.1. Atomic scattering amplitudes (Å) for electrons for neutral atoms  (pp. 263-271) | html | pdf |
      • Table 4.3.1.2. Atomic scattering amplitudes (Å) for electrons for ionized atoms  (pp. 272-281) | html | pdf |
      • Table 4.3.2.1. Parameters useful in electron diffraction as a function of accelerating voltage  (p. 281) | html | pdf |
      • Table 4.3.2.2. Elastic atomic scattering factors of electrons for neutral atoms and s up to 2.0 Å −1   (pp. 282-283) | html | pdf |
      • Table 4.3.2.3. Elastic atomic scattering factors of electrons for neutral atoms and s up to 6.0 Å −1   (pp. 284-285) | html | pdf |
      • Table 4.3.3.1. Partial wave elastic scattering factors for neutral atoms interactive version   (pp. 286-377) | html | pdf |
      • Table 4.3.3.2. Inelastic scattering factors  (pp. 378-388) | html | pdf |
      • Table 4.3.4.1. Different possibilities for using EELS information as a function of the different accessible parameters ( r , [\boldtheta], Δ E )  (p. 394) | html | pdf |
      • Table 4.3.4.2. Plasmon energies measured (and calculated) for a few simple metals  (p. 397) | html | pdf |
      • Table 4.3.4.3. Experimental and theoretical values for the coefficient α in the plasmon dispersion curve together with estimates of the cut-off wavevector  (p. 398) | html | pdf |
      • Table 4.3.4.4. Comparison of measured and calculated values for the halfwidth Δ E 1/2 (0) of the plasmon line  (p. 398) | html | pdf |