Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 5.3, pp. 659-660   | 1 | 2 |

Section 5.3.6. Experimental tests of the dynamical theory of neutron scattering

M. Schlenkera* and J.-P. Guigayb

aLaboratoire Louis Néel du CNRS, BP 166, F-38042 Grenoble Cedex 9, France, and  bEuropean Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France
Correspondence e-mail:

5.3.6. Experimental tests of the dynamical theory of neutron scattering

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These experiments are less extensive for neutron scattering than for X-rays. The two most striking effects of dynamical theory for nonmagnetic nearly perfect crystals, Pendellösung behaviour and anomalous absorption, have been demonstrated in the neutron case too. Pendellösung measurement is described below (Section[link]) because it is useful in the determination of scattering lengths. The anomalous transmission effect occurring when a perfect absorbing crystal is exactly at Bragg setting, i.e. the Borrmann effect, is often referred to in the neutron case as the suppression of the inelastic channel in resonance scattering, after Kagan & Afanas'ev (1966)[link], who worked out the theory. A small decrease in absorption was detected in pioneering experiments on calcite by Knowles (1956)[link] using the corresponding decrease in the emission of γ-rays and by Sippel et al. (1962)[link], Shil'shtein et al. (1971)[link] and Hastings et al. (1990[link]) directly. Rocking curves of perfect crystals were measured by Sippel et al. (1964)[link] in transmission, and by Kikuta et al. (1975)[link]. Integrated intensities were measured by Lambert & Malgrange (1982)[link]. The large angular amplification associated with the curvature of the dispersion surfaces near the exact Bragg setting was demonstrated by Kikuta et al. (1975)[link] and by Zeilinger & Shull (1979)[link].

In magnetic crystals, the investigations have been restricted to the simpler geometry where the scattering vector is perpendicular to the magnetization, and to few materials. Pendellösung behaviour was evidenced through the variation with wavelength of the flipping ratio for polarized neutrons by Baruchel et al. (1982)[link] on an yttrium iron garnet sample, with the geometry selected so that the defects would not affect the Bragg reflection used. The inclination method was used successfully by Zelepukhin et al. (1989)[link], Kvardakov & Somenkov (1990)[link] and Kvardakov et al. (1990a)[link] for the weak ferromagnet FeBO3, and in the room-temperature weak-ferromagnetic phase of hematite, α-Fe2O3, by Kvardakov et al. (1990b)[link] and Kvardakov & Somenkov (1992)[link].

Experiments on the influence of defects in nearly perfect crystals have been performed by several groups. The effect on the rocking curve was investigated by Eichhorn et al. (1967)[link], the intensities were measured by Lambert & Malgrange (1982)[link] and by Albertini, Boeuf, Cesini et al. (1976)[link], and the influence on the Pendellösung behaviour was discussed by Kvardakov & Somen­kov (1992)[link]. Boeuf & Rustichelli (1974)[link] and Albertini et al. (1977)[link] investigated silicon crystals curved by a thin surface silicon nitride layer.

Many experiments have been performed on vibrating crystals; reviews are given by Michalec et al. (1988)[link] and by Kulda et al. (1988[link]). Because the velocity of neutrons is of the same order of magnitude as the velocity of acoustic phonons in crystals, the effect of ultrasonic excitation on dynamical diffraction takes on some original features compared to the X-ray case (Iolin & Entin, 1983[link]); they could to some extent be evidenced experimentally (Iolin et al., 1986[link]; Chalupa et al., 1986[link]). References to experimental work on neutron scattering by imperfect crystals under ultrasonic excitation are included in Zolotoyabko & Sander (1995)[link].

Some experiments with no equivalent in the X-ray case could be performed. The very strong incoherent scattering of neutrons by protons, very different physically but similar in its effect to absorption, was also shown to lead to anomalous transmission effects by Sippel & Eichhorn (1968)[link]. Because the velocity of thermal neutrons in a vacuum is five orders of magnitude smaller than the velocity of light, the flight time for neutrons undergoing Bragg scattering in Laue geometry in a perfect crystal could be measured directly (Shull et al., 1980[link]). The effect of externally applied fields was measured experimentally for magnetic fields by Zeilinger & Shull (1979)[link] and Zeilinger et al. (1986)[link]. Slight rotation of the crystal, introducing a Coriolis force, was used by Raum et al. (1995)[link], and gravity was tested recently, with the spectacular result that some states are accelerated upwards (Zeilinger, 1995[link]).


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Albertini, G., Boeuf, A., Klar, B., Lagomarsino, S., Mazkedian, S., Melone, S., Puliti, P. & Rustichelli, F. (1977). Dynamical neutron diffraction by curved crystals in the Laue geometry. Phys. Status Solidi A, 44, 127–136.
Baruchel, J., Guigay, J. P., Mazuré-Espejo, C., Schlenker, M. & Schweizer, J. (1982). Observation of Pendellösung effect in polarized neutron scattering from a magnetic crystal. J. Phys. 43, C7, 101–106.
Boeuf, A. & Rustichelli, F. (1974). Some neutron diffraction experiments on curved silicon crystals. Acta Cryst. A30, 798–805.
Chalupa, B., Michalec, R., Horalik, L. & Mikula, P. (1986). The study of neutron acoustic effect by neutron diffraction on InSb single crystal. Phys. Status Solidi A, 97, 403–409.
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Raum, K., Koellner, M., Zeilinger, A., Arif, M. & Gähler, R. (1995). Effective-mass enhanced deflection of neutrons in noninertial frames. Phys. Rev. Lett. 74, 2859–2862.
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