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Calculation of the atomic scattering factors of fast electrons at zero angle of incidence of an electron beam and mean inner crystal potentials

  • Diffraction and Scattering of Ionizing Radiations
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Abstract

The atomic scattering factors of fast electrons at zero angle of incidence of an electron beam, f el(0), are calculated for neutral atoms with Z = 1−54, using the mean-square radii of electron-density distributions in atoms and ions, derived on the basis of the Hartree-Fock wave functions. The values of f el(0) have been calculated for the first time for some positive and negative ions. The obtained values of f el(0) were used to determine the mean inner potentials V0 of metallic, covalent, and ionic crystals. The calculated values of V0 are compared with the experimental data in the literature. The values of V0 calculated for III–V and II–VI compounds are reported.

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References

  1. Z. G. Pinsker, Electron Diffraction (Akad. Nauk SSSR, Moscow, 1949) [in Russian].

    Google Scholar 

  2. A. Sandlez and M. A. Ochando, J. Phys. C: Solid State Phys. 18, 33 (1985).

    Article  ADS  Google Scholar 

  3. H. A. Bethe, Ann. Phys. (Lpz.) 87, 55 (1928).

    Article  ADS  Google Scholar 

  4. B. K. Vaĭnshteĭn, Structural Electron Diffraction (Akad. Nauk SSSR, Moscow, 1956) [in Russian].

    Google Scholar 

  5. J. A. Ibers, Acta Crystallogr. 11, 178 (1958).

    Article  Google Scholar 

  6. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Fizmatgiz, Moscow, 1963; Pergamon, New York, 1977).

    Google Scholar 

  7. J. H. Van Vleek, Theory of Electronic and Magnetic Susceptibilities (Oxford: Clarendon, 1935).

    Google Scholar 

  8. R. J. Boyd, Can. J. Phys. 55, 452 (1977).

    ADS  Google Scholar 

  9. V. F. Brattsev, Tables of Atomic Wave Functions (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  10. G. Malli and S. Fraga, Teor. Chim. Acta 5, 284 (1966).

    Article  Google Scholar 

  11. C. L. Pekeris, Phys. Rev. 126, 143 (1962).

    Article  ADS  Google Scholar 

  12. K. E. Banyard and C. C. Baker, J. Chem. Phys. 51, 2680 (1969).

    Article  ADS  Google Scholar 

  13. A. J. Thakkar and V. H. Smith, J. Phys. B: At. Mol. Opt. Phys. 11, 3803 (1978).

    Article  ADS  Google Scholar 

  14. W. A. Goddard, J. Chem. Phys. 48, 1008 (1968).

    Article  ADS  Google Scholar 

  15. T. Sidwell and R. P. Hurst, J. Chem. Phys. 37, 203 (1962).

    Article  ADS  Google Scholar 

  16. C. L. Pekeris, Phys. Rev. 112, 1643 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  17. G. Buch and R. Kern, Helv. Phys. Acta 27, 201 (1954).

    Google Scholar 

  18. P. W. Selwood, Magnetochemistry (Interscience, New York, 1943).

    Google Scholar 

  19. C. Valdemoro and S. Fraga, Can. J. Phys. 45, 2483 (1967).

    ADS  Google Scholar 

  20. J. Heindrichs, J. Chem. Phys. 52, 6316 (1970).

    Article  ADS  Google Scholar 

  21. C. L. Pekeris, Phys. Rev. 126, 1470 (1962).

    Article  ADS  Google Scholar 

  22. O. Goscincki and P. Linder, J. Chem. Phys. 52, 2539 (1970).

    Article  ADS  Google Scholar 

  23. H. H. Landolt and R. Börnstein, Magnetische Eigenschaften. I, II (Springer-Verlag, Berlin, 1967).

    Google Scholar 

  24. L. Marton, J. A. Simpson, and J. A. Suddeth, Rev. Sci. Instrum. 25, 1099 (1954).

    Article  ADS  Google Scholar 

  25. G. Möllenstadt and H. Dücker, Naturwissenschaft 42, 41 (1955).

    Article  ADS  Google Scholar 

  26. C. Jönsson, H. Hoffmann, and G. Möllenstadt, Phys. Kondens. Mater. 3, 193 (1965).

    Article  ADS  Google Scholar 

  27. M. Keller, Z. Phys. 164, 274 (1961).

    Article  ADS  Google Scholar 

  28. M. J. Goringe and M. J. Whelan, in Electron Microscopy, Ed. by R. Uyeda (Maruzen, Tokyo, 1966), Vol. 1.

    Google Scholar 

  29. R. Buhl, Z. Phys. 155, 395 (1959).

    Article  ADS  Google Scholar 

  30. V. F. Tull, Proc. R. Soc. A 206, 219 (1951).

    Article  ADS  Google Scholar 

  31. A. Gaswami and N. D. Lisgarten, J. Phys. C: Solid State Phys. 15, 4217 (1982).

    Article  ADS  Google Scholar 

  32. R. D. Heidenreich, Fundamentals of Transmission Electron Microscopy (Interscience Publishers, New York, 1964).

    Google Scholar 

  33. V. E. Lashkarev and A. S. Chaban, Phys. Z. Sowjetunion 8, 240 (1935).

    MATH  Google Scholar 

  34. R. Beeching, Philos. Mag. 20, 841 (1935).

    Google Scholar 

  35. K. H. Gankler and R. Schwarzer, Optik 33, 215 (1971).

    Google Scholar 

  36. H. Hoffmann and C. Jönsson, Z. Phys. 182, 360 (1965).

    Article  ADS  Google Scholar 

  37. P. K. Larsen, J. F. van der Veen, A. Mazur, et al., Solid State Commun. 40, 453 (1981).

    Article  Google Scholar 

  38. P. K. Larsen, P. J. Dobson, J. H. Neave, et al., Surf. Sci. 169, 176 (1986).

    Article  ADS  Google Scholar 

  39. S. Miyake, Proc. Phys. Math. Soc. Jpn. 20, 280 (1938).

    Google Scholar 

  40. I. R. Tillman, Philos. Mag. 18, 656 (1934).

    Google Scholar 

  41. T. Yamaguti, Proc. Phys. Soc. Jpn. 23, 433 (1940).

    Google Scholar 

  42. S. Steel and H. F. Bühner, Z. Naturforsch. 22a, 1990 (1967).

    ADS  Google Scholar 

  43. S. Miyake, Proc. Phys. Math. Soc. Jpn. 22, 666 (1940).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Radio Engineering and Electronics (Fryazino Branch), Russian Academy of Sciences, pl. Vvedenskogo 1, Fryazino, Moscow oblast, 141190, Russia

    G. G. Dvoryankina, V. F. Dvoryankin & A. G. Petrov

Authors
  1. G. G. Dvoryankina
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  2. V. F. Dvoryankin
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  3. A. G. Petrov
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Correspondence to V. F. Dvoryankin.

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Original Russian Text © G.G. Dvoryankina, V.F. Dvoryankin, A.G. Petrov, 2008, published in Kristallografiya, 2008, Vol. 53, No. 2, pp. 219–225.

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Dvoryankina, G.G., Dvoryankin, V.F. & Petrov, A.G. Calculation of the atomic scattering factors of fast electrons at zero angle of incidence of an electron beam and mean inner crystal potentials. Crystallogr. Rep. 53, 187–191 (2008). https://doi.org/10.1134/S1063774508020041

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  • DOI: https://doi.org/10.1134/S1063774508020041

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