Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.3, p. 265

Section The experiment

R. B. Von Dreelea*

aAdvanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439–4814, USA
Correspondence e-mail: The experiment

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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[link]). 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 give[{\rm TOF} = 252.7784 L\lambda = 505.5568 Ld \sin\theta.\eqno(3.3.16)]The 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:[\Delta d/d =[(\Delta t/t)^2 +(\Delta \theta \cot\theta)^2 +(\Delta L/L)^2]^{1/2},\eqno(3.3.17)]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[link]). Consequently, these three terms also determine the instrumental contribution to the neutron TOF powder peak profile.


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 Scholar
Jorgensen, 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

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