International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 2.5, p. 87
|
In traditional neutron-diffraction experiments, using a continuous source of neutrons from a nuclear reactor, a narrow wavelength band is selected from the wide spectrum of neutrons emerging from a moderator within the reactor. This monochromatization process is extremely inefficient in the utilization of the available neutron flux. If the requirement of discriminating between different orders of reflection is relaxed, then the entire white beam can be employed to contribute to the diffraction pattern and the count-rate may increase by several orders of magnitude. Further, by recording the scattered neutrons on photographic film or with a position-sensitive detector, it is possible to probe simultaneously many points in reciprocal space.
If the experiment is performed using a pulsed neutron beam, the different orders of a given reflection may be separated from one another by time-of-flight analysis. Consider a short polychromatic burst of neutrons produced within a moderator. The subsequent times-of-flight, t, of neutrons with differing wavelengths, λ, measured over a total flight path, L, may be discriminated one from another through the de Broglie relationship: where mn is the neutron mass and h is Planck's constant. Expressing t in microseconds, L in metres and λ in Å, equation (2.5.2.1)
becomes
Inserting Bragg's law,
, for the nth order of a fundamental reflection with spacing d in Å gives
Different orders may be measured simply by recording the time taken, following the release of the initial pulse from the moderator, for the neutron to travel to the sample and then to the detector.
The origins of pulsed neutron diffraction can be traced back to the work of Lowde (1956) and of Buras, Mikke, Lebech & Leciejewicz (1965
). Later developments are described by Turberfield (1970
) and Windsor (1981
). Although a pulsed beam may be produced at a nuclear reactor using a chopper, the major developments in pulsed neutron diffraction have been associated with pulsed sources derived from particle accelerators. Spallation neutron sources, which are based on proton synchrotrons, allow optimal use of the Laue method because the pulse duration and pulse repetition rate can be matched to the experimental requirements. The neutron Laue method is particularly useful for examining crystals in special environments, where the incident and scattered radiations must penetrate heat shields or other window materials. [A good example is the study of the incommensurate structure of α-uranium at low temperature (Marmeggi & Delapalme, 1980
).]
A typical time-of-flight single-crystal instrument has a large area detector. For a given setting of detector and sample, a three-dimensional region is viewed in reciprocal space, as shown in Fig. 2.5.2.1. Thus, many Bragg reflections can be measured at the same time. For an ideally imperfect crystal, with volume Vs and unit-cell volume vc, the number of neutrons of wavelength λ reflected at Bragg angle
by the planes with structure factor F is given by
where
is the number of incident neutrons per unit wavelength interval. In practice, the intensity in equation (2.5.2.3)
must be corrected for wavelength-dependent factors, such as detector efficiency, sample absorption and extinction, and the contribution of thermal diffuse scattering. Jauch, Schultz & Schneider (1988
) have shown that accurate structural data can be obtained using the single-crystal time-of-flight method despite the complexity of these wavelength-dependent corrections.
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