International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 3.3, p. 265
Section 3.3.3.1. The experiment^{a}Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439–4814, USA |
The neutron source in a time-of-flight (TOF) powder diffraction experiment produces pulses of polychromatic neutrons; these travel over the distance from the source to the sample and then to the detectors which are placed at fixed scattering angles about the sample position; the travel times are of the order of 1–100 ms. This has been briefly described in Volume C of International Tables for Crystallography (Jorgensen et al., 1992). Because neutrons of differing velocities (v) have differing wavelengths (λ) according to the de Broglie relationship (λ = h/mv) given Planck's constant (h) and the neutron mass (m), they will sort themselves out in their time of arrival at the detector. The powder pattern appears as a function of TOF via Bragg's law (λ = 2d sin θ) in which the wavelength is varied and θ is fixed. The approximate relationship between TOF, wavelength and d-spacing observed in a particular detector can be derived from the de Broglie relationship and Bragg's law to giveThe constants are such that given λ in ångströms and the total neutron flight path length L in metres, then the TOF will be in µs. An analysis of the possible variances in these components then gives an estimate of the powder diffraction peak widths:where Δd, Δt, Δθ and ΔL are, respectively, the uncertainties in d-spacing, TOF, scattering angle θ and total flight path L (Jorgensen & Rotella, 1982). Consequently, these three terms also determine the instrumental contribution to the neutron TOF powder peak profile.
References
Jorgensen, J. D., David, W. I. F. & Willis, B. T. M. (1992). White-beam and time-of-flight neutron diffraction. In International Tables for Crystallography, Vol. C, edited by A. J. C. Wilson. Dordrecht: Kluwer.Google ScholarJorgensen, J. D. & Rotella, F. J. (1982). High-resolution time-of-flight powder diffractometer at the ZING-P′′ pulsed neutron source. J. Appl. Cryst. 15, 27–34.Google Scholar