- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Electronic charge distribution in silicon

Moshe Deutsch and Michael Hart

  • Wheatstone Laboratory, King’s College, Strand, London WC2R 2LS, England

PDF

Phys. Rev. B 31, 3846 – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevB.31.3846

Abstract

The structure factors Fh of eight high-order [0.64≤(sinθ)/λ≤1.56 Å−1] reflections were measured for a number of wavelengths to an accuracy of a few thousandths of an electron per atom. Most of these have never been measured before to this level of accuracy. A monolithic double-crystal diffractometer of novel design was employed in measuring thin-crystal Laue-case rocking curves which exhibit fine structure strongly dependent on Fh. Computer fitting of the theoretical curve to the measured one yields Fh. An energy-dispersive mode of operation allowed simultaneous measurements of the rocking curves of a whole family of planes to be carried out. The Fh values obtained, while in excellent agreement with previously measured and theoretical ones for (sinθ)/λ<1 Å−1, are consistently and increasingly lower than the theoretical relativistic Hartree-Fock Fh values for (sinθ)/λ>1 Å−1. This systematic trend most probably reflects the inadequacy of the Debye parameter B calculated from medium- and low-order Fh’s for high-order reflections. Assuming different vibrational amplitudes for intermediate- and inner-shell electrons, our data yield Blow=0.4632±0.0041 Å2 for reflections up to 880 [(sinθ)/λ=1.04 Å−1], in excellent agreement with previous measurements, and Bhigh=0.5085±0.0035 Å2 for reflections higher than 10 10 0 [(sinθ)/λ≥1.30 Å−1]. We also find no anharmonic contribution to the temperature factor of Fh within the limit of accuracy of the experiment, in good agreement with previous x-ray measurements and some neutron measurements, but in contradiction to some of the neutron forbidden-222-reflection results.

View figure in article

References (50)

  1. H. Hattori, H. Kuriyama, T. Kateyawa and N. Kato, J. Phys. Soc. Jpn. 20, 1047 (1965); S. Kikuta, Phys. Status Solidi B 45, 333 (1971); M. Hart and A. D. Milne, Acta Crystallogr. Sect. A 26, 223 (1970); J. B. Roberto and B. W. Battermann, Phys. Rev. B 2, 3220 (1970); M. Fehlmann and I. Fujimoto, J. Phys. Soc. Jpn. 38, 208 (1975); R. W. Alkire and W. B. Yelon, J. Appl. Crystallogr. 14, 362 (1981); R. W. Alkire, W. B. Yelon and J. R. Schneider, Phys. Rev. B 26, 3097 (1982).
  2. J. J. De Marco and R. J. Weiss, Phys. Rev. 137, A1869 (1965).
  3. N. Kato and S. Tanemura, Phys. Rev. Lett. 19, 22 (1967); S. Tanemura and N. Kato, Acta Crystallogr. Sect. A 28, 69 (1972).
  4. P. J. E. Aldred and M. Hart, Proc. R. Soc. London, Ser. A 332, 223 (1973); 332, 239 (1973).
  5. J. B. Roberto, B. W. Batterman and D. T. Keating, Phys. Rev. B 9, 2590 (1974).
  6. I. Fujimoto, Phys. Rev. B 9, 591 (1974).
  7. C. Cusatis, M. Hart and D. P. Siddens, Acta Crystallogr. Sect. A 39, 199 (1983).
  8. U. Bonse and R. Teworte, J. Appl. Crystallogr. 13, 410 (1980).
  9. M. Deutsch and M. Hart, Acta Crystallogr. Sect. A (to be published).
  10. B. Dawson, Proc. R. Soc. London, Ser. A 298, 255 (1967); 298, 379 (1967); in Advances in Structure Research by Diffraction Methods, edited by W. Hoppe and R. Mason (Pergamon, London, 1975), Vol. 6.
  11. U. Pietsch, Phys. Status Solidi B 102, 127 (1980); J. P. Walter and M. L. Cohen, Phys. Rev. B 4, 1877 (1971).
  12. D. J. Stukel and R. N. Euwema, Phys. Rev. B 1, 1635 (1970).
  13. M. Fehlmann, J. Phys. Soc. Jpn. 47, 225 (1979).
  14. P. F. Price, E. N. Maslen and S. L. Mair, Acta Crystallogr. Sect. A 34, 183 (1978).
  15. J. R. Chelikowsky and M. L. Cohen, Phys. Rev. Lett. 33, 1339 (1974).
  16. B. F. Robertson and J. S. Reid, Acta Crystallogr. Sect. A 35, 785 (1979); W. Weber, Phys. Rev. B 15, 4789 (1977); G. Nilson and G. Nelin, ibid. 6, 3777 (1972); W. J. L. Buyers, J. D. Pirie and T. Smith, Phys. Rev. 165, 999 (1968).
  17. J. S. Reid and J. D. Price, Acta Crystallogr. Sect. A 36, 957 (1980).
  18. W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965); R. Gaspar, Acta Phys. Acad. Sci. Hung. 3, 263 (1954).
  19. J. C. Slater, Phys. Rev. 81, 385 (1951).
  20. N. Kato and A. R. Lang, Acta Crystallogr. 12, 787 (1959); N. Kato, Z. Naturforsch. 15 a, 369 (1960); Acta Crystallogr. 14, 526 (1961); ibid. 14, 627 (1961); J. Appl. Phys. 39, 2225 (1968).
  21. U. Bonse, W. Graeff, R. Teworte and H. Rauch, Phys. Status Solidi A 43, 487 (1977).
  22. R. Teworte and U. Bonse, Phys. Rev. B 29, 2102 (1984).
  23. M. Lefeld-Sosnowska and C. Malgrange, Phys. Status Solidi 34, 636 (1968).
  24. U. Bonse and W. Graeff, in X-ray Optics, edited by H. J. Queisser (Springer, Berlin, 1979).
  25. Z. G. Pinsker Dynamical Scattering of X-rays in Crystals (Springer, Berlin, 1978), Chap. 4.
  26. Routine size 8 E04FCF, NAG Subroutine Library, Mark 8 (Oxford, United Kingdom); P. E. Gill and W. Murray, SIAM J. Numer. Anal. 15, 977 (1978).
  27. G. Hildebrandt, J. D. Stephenson and H. Wagenfeld, Z. Naturforsch. 30 a, 697 (1975).
  28. International Tables for X-ray Crystallography (Kynoch, Bir- mingham, England, 1968), Vol. III, Chap. 3.2.2.
  29. G. Hildebrandt, J. D. Stephenson and H. Wagenfeld, Z. Naturforsch 28 a, 588 (1973).
  30. D. P. Siddons, Ph.D. thesis, King's College, London, 1979.
  31. A. R. D. Rodrigues and D. P. Siddons, J. Phys. E 12, 403 (1979).
  32. M. Hart and D. P. Siddons, Proc. R. Soc. London, Ser. A 376, 465 (1981).
  33. F. C. Von der Lugt and H. A. Bethe, Phys. Rev. 71, 612 (1947).
  34. B. Dawson and B. T. M. Willis, Proc. R. Soc. London, Ser. A 298, 307 (1967).
  35. B. W. Batterman and D. R. Chipman, Phys. Rev. 127, 690 (1962).
  36. A. C. Nunes, Acta Crystallogr. Sect. A 27, 219 (1971).
  37. M. Abramowitz and I. A. Stegun Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 10.
  38. See Ref. 37, Chap. 13.
  39. For example, Routine C235, Centre d'Etudes Recherche Nucleaires Subroutine Library (Geneva, Switzerland).
  40. International Tables for X-ray Crystallography (Kynoch, Birmingham, England, 1974), Vol. IV, Chap. 2.2.
  41. C. Cusatis and M. Hart, in Anomalous Scattering, edited by S. Ramaseshan and S. C. Abrahams (Munksgaard, Copenhagen, 1975).
  42. M. Deutsch and M. Hart, Phys. Rev. B 30, 647 (1984).
  43. D. T. Cromer and D. Liberman, J. Chem. Phys. 53, 1981 (1970); Acta Crystallogr. Sect. A 37, 267 (1981) M. Hart and D. P. Siddons, in Neutron Interferometry, edited by U. Bonse and H. Rauch (Oxford University Press, Oxford, England, 1978).
  44. T. Takeda and N. Kato, Acta Crystallogr. Sect. A 34, 43 (1978).
  45. M. Hart, N. KatoZ. Phys. 189, 269 (1966). , J. Phys. Soc. Jpn. 19, 971 (1964).
  46. P. A. Doyle and P. S. Turner, Acta Crystallogr. Sect. A 24, 390 (1968).
  47. B. D. Singh and B. Dayal, Phys. Status Solidi 38, 141 (1970); A. W. Solbrig, J. Phys. Chem. Solids 32, 1761 (1971); R. Tubino, L. Piseri and G. Zerbi, J. Chem. Phys. 56, 1022 (1972).
  48. A. D. Zdetsis and C. S. Wang, Phys. Rev. B 19, 2999 (1979).
  49. D. O. Welch, as reported in Ref. 5.
  50. N. H. March and S. W. Wilkins, Acta Crystallogr. Sect. A 34, 19 (1978).

Outline

Information

Phys. Rev. B 31, 3846– Published 15 March, 1985
  • Received 29 August 1984

© 1985 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation