The flipping ratio

Schlenker, M.; Guigay, J. P.

doi:10.1107/97809553602060000571

International
Tables for
Crystallography
Volume B
Reciprocal Space
Edited by U. Shmueli

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International Tables for Crystallography (2006). Vol. B. ch. 5.3, p. 561 | 1 | 2 |

Section 5.3.3.5. The flipping ratio

M. Schlenker^a ^* and J.-P. Guigay^a,^b

^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: schlenk@polycnrs-gre.fr

5.3.3.5. The flipping ratio

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In polarized neutron diffraction by a magnetically saturated magnetic sample, it is usual to measure the ratio of the reflected intensities $[I_{+}]$ and $[I_{-}]$ measured when the incident beam is polarized parallel or antiparallel to the magnetization in the sample. This ratio is called the flipping ratio, $[R = I_{+}/I_{-}, \eqno(5.3.3.12)]$ because its measurement involves flipping the incident-beam polarization to the opposite direction. This is an experimentally well defined quantity, because it is independent of a number of parameters such as the intensity of the incident beam, the temperature factor or the coefficient of absorption. In the case of an ideally imperfect crystal, we obtain from the kinematical expressions of the integrated reflectivities $[R_{\rm kin} ({\bf h}) = (I_{+}/I_{-})_{\rm kin} = \left({|F_{N} + F_{M}| \over |F_{N} - F_{M}|}\right)^{2}. \eqno(5.3.3.13)]$ In the case of an ideally perfect thick crystal, we obtain from the dynamical expressions of the integrated reflectivities $[R_{\rm dyn} ({\bf h}) = (I_{+}/I_{-})_{\rm dyn} = {|F_{N} + F_{M}| \over |F_{N} - F_{M}|}. \eqno(5.3.3.14)]$ In general, $[R_{\rm dyn}]$ depends on the wavelength and on the crystal thickness; these dependences disappear, as seen from (5.3.3.14), if the path length in the crystal is much larger than the extinction distances for the two polarization states. It is clear that the determination of $[R_{\rm kin}]$ or $[R_{\rm dyn}]$ allows the determination of the ratio $[F_{M}/F_{N}]$ , hence of $[F_{M}]$ if $[F_{N}]$ is known. In fact, because real crystals are neither ideally imperfect nor ideally perfect, one usually introduces an extinction factor y (extinction is discussed below, in Section 5.3.4) in order to distinguish the real crystal reflectivity from the reflectivity of the ideally imperfect crystal. Different extinction coefficients $[y_{+}]$ and $[y_{-}]$ are actually expected for the two polarization states. This obviously complicates the task of the determination of $[F_{M}/F_{N}]$ .

In the kinematical approximation , the flipping ratio does not depend on the wavelength, in contrast to dynamical calculations for hypothetically perfect crystals (especially for the Laue case of diffraction). Therefore, an experimental investigation of the wavelength dependence of the flipping ratio is a convenient test for the presence of extinction. Measurements of the flipping ratio have been used by Bonnet et al. (1976) and by Kulda et al. (1991) in order to test extinction models. Baruchel et al. (1986) have compared nuclear and magnetic extinction in a crystal of MnP.

Instead of considering only the ratio of the integrated reflectivities, it is also possible to record the flipping ratio as a function of the angular position of the crystal as it is rotated across the Bragg position. Extinction is expected to be maximum at the peak and the ratio measured on the tails of the rocking curve may approach the kinematical value. It has been found experimentally that this expectation is not of general validity, as discussed by Chakravarthy & Madhav Rao (1980). It would be valid in the case of a perfect crystal, hence in the case of pure primary extinction. It would also be valid in the case of secondary extinction of type I, but not in the case of secondary extinction of type II [following Zachariasen (1967), type II corresponds to mosaic crystals such that the diffraction pattern from each block is wider than the mosaic statistical distribution].

References

Baruchel, J., Patterson, C. & Guigay, J. P. (1986). Neutron diffraction investigation of the nuclear and magnetic extinction in MnP. Acta Cryst. A42, 47–55.Google Scholar

Bonnet, M., Delapalme, A., Becker, P. & Fuess, H. (1976). Polarised neutron diffraction – a tool for testing extinction models: application to yttrium iron garnet. Acta Cryst. A32, 945–953.Google Scholar

Chakravarthy, R. & Madhav Rao, L. (1980). A simple method to correct for secondary extinction in polarised-neutron diffractometry. Acta Cryst. A36, 139–142.Google Scholar

Kulda, J., Baruchel, J., Guigay, J.-P. & Schlenker, M. (1991). Extinction effects in polarized neutron diffraction from magnetic crystals. I. Highly perfect MnP and YIG samples. Acta Cryst. A47, 770–775.Google Scholar

Zachariasen, W. H. (1967). A general theory of X-ray diffraction in crystals. Acta Cryst. 23, 558–564.Google Scholar

International Tables for Crystallography (2006). Vol. B. ch. 5.3, p. 561