Skip to main content
SpringerLink
Log in

Peculiarities of Laue Diffraction of Neutrons in Strongly Absorbing Crystals

  • ATOMS, MOLECULES, OPTICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Well-known Kato’s theory of the Laue diffraction of spherical X-ray waves is generalized to the case of the neutron diffraction in strongly absorbing crystals, taking into consideration both the potential and the resonant scattering of neutrons by nuclei as well as a realistic angular dispersion of incident neutrons. The saddle-point method is applied for estimation of the angular integrals, being more adequate in the case of strongly absorbing crystals than the commonly used stationary-phase approximation. It is found that the intensity distribution of the diffracted and refracted beams along the basis of the Borrmann triangle significantly depends on the deviation of the neutron energy from the nuclear resonant level. When comparing our calculations with the Shull’s experimental data on neutron diffraction in silicon, we also regard the role of finite width of the collimating and scanning slits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. I. I. Gurevich and L. V. Tarasov, Low Energy Neutron Physics (Nauka, Moscow, 1965; North-Holland, Amsterdam, 1968).

  2. Dynamics of Solids and Liquids by Neutron Scattering, Ed. by S. W. Lovesey and T. Springer (Springer, Berlin, 1977).

    Google Scholar 

  3. H. Rauch and D. Petrachek, in Neutron Diffraction, Ed. by H. Duchs (Springer, Berlin, 1978), p. 303.

    Google Scholar 

  4. V. F. Sears, Phys. Rep. 82, 1 (1982).

    Article  ADS  Google Scholar 

  5. Yu. G. Abov, N. O. Elyutin, and A. N. Tyulyusov, Phys. At. Nucl. 65, 1933 (2002).

    Article  Google Scholar 

  6. Yu. G. Abov and N. O. Elyutin, Coherent Scattering of Neutrons (Mosk. Inzh.-Fiz. Inst., Moscow, 1988) [in Russian].

    Google Scholar 

  7. M. L. Goldberger and F. Seitz, Phys. Rev. 71, 294 (1947).

    Article  ADS  Google Scholar 

  8. Yu. Kagan and A. M. Afanas’ev, Sov. Phys. JETP 22, 1032 (1966).

    ADS  Google Scholar 

  9. V. F. Sears, Canad. J. Phys. 56, 1261 (1978).

    Article  ADS  Google Scholar 

  10. A. M. Afanas’ev and Yu. Kagan, Sov. Phys. JETP 21, 2151 (1965).

    Google Scholar 

  11. J. P. Hannon and G. T. Trammell, Phys. Rev. 169, 315 (1968).

    Article  ADS  Google Scholar 

  12. J. P. Hannon and G. T. Trammell, Phys. Rev. 186, 306 (1969).

    Article  ADS  Google Scholar 

  13. J. P. Hannon, N. J. Carron, and G. T. Trammell, Phys. Rev. 9, 2791 (1974).

    Article  ADS  Google Scholar 

  14. A. Ya. Dzyublik, Phys. Status Solidi B 123, 53 (1984);

    Article  ADS  Google Scholar 

  15. Phys. Status Solidi B 134, 503 (1986).

  16. A. Ya. Dzyublik, Sov. Phys. JETP 58, 965 (1983).

    Google Scholar 

  17. V. A. Belyakov, Sov. Phys. Usp. 18, 267 (1975).

    Article  ADS  Google Scholar 

  18. G. V. Smirnov, in The Rudolf Mossbauer Story, Ed. by M. Kalvius and P. Kienle (Springer, Heidelberg, 2012).

    Google Scholar 

  19. S. Sh. Shil’shtein et al., JETP Lett. 12, 56 (1970).

    ADS  Google Scholar 

  20. S. Sh. Shil’shtein, V. A. Somenkov, and V. P. Dokashenko, JETP Lett. 13, 214 (1971).

    ADS  Google Scholar 

  21. G. Borrmann, Z. Phys. 42, 157 (1941).

    Google Scholar 

  22. W. H. Zachariasen, Theory of X-ray Diffraction in Crystals (Wiley, New York, 1945).

    Google Scholar 

  23. B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681 (1964).

    Article  ADS  Google Scholar 

  24. Z. G. Pinsker, Dynamical Scattering of X-rays in Crystals (Nauka, Moscow, 1982; Springer, Heidelberg, 1978).

  25. A. Authier, Dynamical Theory of X-ray Diffraction (Oxford Univ. Press, New York, 2001).

    MATH  Google Scholar 

  26. M. K. Balyan, Acta Crystallogr. A 74, 204 (2018).

    Article  MathSciNet  Google Scholar 

  27. N. Kato, Acta Crystallogr. 13, 349 (1960).

    Article  Google Scholar 

  28. N. Kato, Acta Crystallogr. 14, 526 (1961).

    Article  Google Scholar 

  29. N. Kato, Acta Crystallogr. 14, 627 (1961).

    Article  Google Scholar 

  30. N. Kato, J. Phys. Soc. Jpn. 19, 971 (1964).

    Article  ADS  Google Scholar 

  31. C. G. Shull, Phys. Rev. Lett. 21, 1585 (1968).

    Article  ADS  Google Scholar 

  32. C. G. Shull, J. Appl. Phys. 6, 257 (1973).

    Google Scholar 

  33. C. G. Shull and W. M. Shaw, Z. Naturforsch. 28a, 657 (1973).

  34. V. V. Fedorov, V. V. Voronin, and E. G. Lapin, J. Phys. G 18, 1133 (1992).

    Article  ADS  Google Scholar 

  35. V. V. Voronin, I. A. Kuznetsov, E. G. Lapin, S. Yu. Semenikhin, and V. V. Fedorov, Phys. At. Nucl. 72, 470 (2009).

    Article  Google Scholar 

  36. V. V. Voronin, V. V. Fedorov, I. A. Kuznetsov, et al., Phys. Proc. 17, 232 (2011).

    Article  ADS  Google Scholar 

  37. E. O. Vezhlev, V. V. Voronin, I. A. Kuznetsov, S. Yu. Seminikhin, and V. V. Fedorov, JETP Lett. 96, 1 (2012).

    Article  ADS  Google Scholar 

  38. V. V. Voronin, Ya. A. Berdnikov, A. Ya. Berdnikov, Yu. P. Braginets, I. A. Kuznetsov, M. V. Lasitsa, S. Yu. Semenikhin, and V. V. Fedorov, Tech. Phys. Lett. 43, 270 (2017).

    Article  ADS  Google Scholar 

  39. A. Ya. Dzyublik, V. I. Slisenko, and V. V. Mykhaylovskyy, Ukr. J. Phys. 63, 174 (2018).

    Article  Google Scholar 

  40. A. Ya. Dzyublik and V. Yu. Spivak, Ukr. J. Phys. 61, 826 (2016).

    Article  Google Scholar 

  41. A. Akhiezer and I. Pomeranchuk, Some Problems of Nuclear Theory (GITTL, Moscow, 1950) [in Russian].

    Google Scholar 

  42. J. M. Zaiman, Principles of the Theory of Solids (Cambridge Univ. Press, Cambridge, 1972).

    Book  Google Scholar 

  43. G. Leinweber, Neutron Capture and TotalCross Section Measurements of Cadmium atthe RPI LINAC. https://accapp17.org/wpcontent/uploads/2017/09/Neutron-Capture.

  44. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964).

    MATH  Google Scholar 

  45. M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of Complex Variable (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  46. A. G. Sitenko, Scattering Theory (Vishcha Shkola, Kiev, 1975; Springer, Berli, 1999).

  47. J. T. Yardley, Silicon Basics - General Overview. https://www1.columbia.edu/sec/itc/ee/test2/pdf%20files/silicon%20basics.pdf.

Download references

Author information

Authors and Affiliations

  1. Institute for Nuclear Research, National Academy of Sciences of Ukraine, 03680, Kiev, Ukraine

    A. Ya. Dzyublik, V. V. Mykhaylovskyy & V. Yu. Spivak

Authors
  1. A. Ya. Dzyublik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Mykhaylovskyy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Yu. Spivak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Ya. Dzyublik.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dzyublik, A.Y., Mykhaylovskyy, V.V. & Spivak, V.Y. Peculiarities of Laue Diffraction of Neutrons in Strongly Absorbing Crystals. J. Exp. Theor. Phys. 128, 355–365 (2019). https://doi.org/10.1134/S1063776119020183

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776119020183

Search

Navigation