Bragg diffraction and surface reflection of neutrons from perfect crystals at grazing incidence

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Abstract
Bragg diffraction of neutrons incident at grazing angles on crystal surfaces has been studied both theoretically and experimentally. In the theoretical analysis, use of the complete fourth-order expression for the dispersion surface had to be made. The calculations have shown that significant modifications are expected in both the optical total reflection phenomena and in the characteristics of the Darwin diffraction plateau as compared to situations where only either process can occur. The most interesting consequences are (a) a change of the critical angle for total reflection, (b) a significant reduction of the height of the Darwin plateau and a modification of its intensity distribution, (c) pronounced shifts of the Bragg peak to angles above the critical angle, and (d) a significant reduction of the penetration depth of Bragg-diffracted radiation. An experimental study of Bragg diffraction at internal (022) planes of a large Si crystal with neutrons incident at grazing angles onto a polished external (211) surface has been performed. The wavelength distribution of that beam was characteristic of neutron-diffraction experimentation and hence broad by dynamical diffraction standards. The experimental result therefore shows features as expected from a sum of many individual reflectivity profiles and confirms both that the Bragg reflectivity is small for incidence below the critical angle and that a peak of that reflectivity occurs just above the critical angle. Practical application of the observed phenomena for the investigation of surface structures is discussed.