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, pp. 8788

In traditional neutrondiffraction 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 countrate may increase by several orders of magnitude. Further, by recording the scattered neutrons on photographic film or with a positionsensitive 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 timeofflight analysis. Consider a short polychromatic burst of neutrons produced within a moderator. The subsequent timesofflight, 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 m_{n} 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 αuranium at low temperature (Marmeggi & Delapalme, 1980).]
A typical timeofflight singlecrystal instrument has a large area detector. For a given setting of detector and sample, a threedimensional 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 V_{s} and unitcell volume v_{c}, 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 wavelengthdependent 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 singlecrystal timeofflight method despite the complexity of these wavelengthdependent corrections.
This technique, first developed by Buras & Leciejewicz (1964), has made a unique impact in the study of powders in confined environments such as highpressure cells (Jorgensen & Worlton, 1985). As in singlecrystal Laue diffraction, the time of flight is measured as the elapsed time from the emergence of the neutron pulse at the moderator through to its scattering by the sample and to its subsequent detection. This time is given by equation (2.5.2.2). Many Bragg peaks, each separated by time of flight, can be observed at a single fixed scattering angle, since there is a wide range of wavelengths available in the incident beam.
A good approximation to the resolution function of a timeofflight powder diffractometer is given by the secondmoment relationship where , and are, respectively, the uncertainties in the d spacing, time of flight, and Bragg angle associated with a given reflection, and is the uncertainty in the total path length (Jorgensen & Rotella, 1982). Thus, the highest resolution is obtained in back scattering (large ) where cot is small. Timeofflight instruments using this concept have been described by Steichele & Arnold (1975) and by Johnson & David (1985). With pulsed neutron sources a large source aperture can be viewed, as no chopper is required of the type used on reactor sources. Hence, long flight paths can be employed and this too [see equation (2.5.2.4)] leads to high resolution. For a well designed moderator the pulse width is approximately proportional to wavelength, so that the resolution is roughly constant across the whole of the diffraction pattern. For an ideal powder sample the number of neutrons diffracted into a complete Debye–Scherrer cone is proportional to (Buras & Gerward, 1975). j is the multiplicity of the reflection and the remaining symbols in equation (2.5.2.5) are the same as those in equation (2.5.2.3).
References
Buras, B. & Gerward, L. (1975). Relations between integrated intensities in crystal diffraction methods for Xrays and neutrons. Acta Cryst. A31, 372–374.Buras, B. & Leciejewicz, J. (1964). A new method for neutron diffraction crystal structure investigations. Phys. Status Solidi, 4, 349–355.
Buras, B., Mikke, K., Lebech, B. & Leciejewicz, J. (1965). The timeofflight method for investigations of singlecrystal structures. Phys. Status Solidi, 11, 567–573.
Jauch, W., Schultz, A. J. & Schneider, J. R. (1988). Accuracy of single crystal timeofflight neutron diffraction: a comparative study of MnF_{2}. J. Appl. Cryst. 21, 975–979.
Johnson, M. W. & David, W. I. F. (1985). HPRD: the high resolution powder diffractometer at the spallation neutron source. Report RAL85112. Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK.
Jorgensen, J. D. & Rotella, F. J. (1982). Highresolution timeofflight powder diffractometer at the ZINGP′ pulsed neutron source. J. Appl. Cryst. 15, 27–34.
Jorgensen, J. D. & Worlton, T. G. (1985). Disordered structure of D_{2}O ice VII from in situ neutron powder diffraction. J. Chem. Phys. 83, 329–333.
Lowde, R. D. (1956). A new rationale of structurefactor measurement in neutrondiffraction analysis. Acta Cryst. 9, 151–155.
Marmeggi, J. C. & Delapalme, A. (1980). Neutron Laue photographs of crystallographic satellite reflections in alphauranium. Physica (Utrecht), 102B, 309–312.
Schultz, A. J., Srinivasan, K., Teller, R. G., Williams, J. M. & Lukehart, C. M. (1984). Singlecrystal timeofflight neutron diffraction structure of hydrogen cisdiacetyltetracarbonylrhenate. J. Am. Chem. Soc. 106, 999–1003.
Steichele, E. & Arnold, P. (1975). A highresolution neutron timeofflight diffractometer. Phys. Lett. A44, 165–166.
Turberfield, K. C. (1970). Timeofflight neutron diffractometry. Thermal neutron diffraction, edited by B. T. M. Willis, pp. 34–50. Oxford University Press.
Windsor, C. G. (1981). Pulsed neutron diffraction. London: Taylor & Francis.