International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 2.5, pp. 87-88

Section 2.5.2.2. Neutron time-of-flight powder diffraction

J. D. Jorgensen,c W. I. F. Davida and B. T. M. Willisd

2.5.2.2. Neutron time-of-flight powder diffraction

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This technique, first developed by Buras & Leciejewicz (1964[link]), has made a unique impact in the study of powders in confined environments such as high-pressure cells (Jorgensen & Worlton, 1985[link]). As in single-crystal 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)[link]. 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 time-of-flight powder diffractometer is given by the second-moment relationship [\Delta d/d=[(\Delta t/t)^2+(\Delta\theta\cot \theta)^2+(\Delta L/L)^2]^{1/2},\eqno (2.5.2.4)]where [\Delta d], [\Delta t] and [\Delta\theta] are, respectively, the uncertainties in the d spacing, time of flight, and Bragg angle associated with a given reflection, and [\Delta L] is the uncertainty in the total path length (Jorgensen & Rotella, 1982[link]). Thus, the highest resolution is obtained in back scattering (large [2\theta]) where cot [\theta] is small. Time-of-flight instruments using this concept have been described by Steichele & Arnold (1975[link]) and by Johnson & David (1985[link]). 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)[link]] 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 [N'=i_0(\lambda)\lambda^4V_s\,jF^2\cos \theta \Delta\theta/(4v^2_c\sin ^2 \theta)\eqno (2.5.2.5)](Buras & Gerward, 1975[link]). j is the multiplicity of the reflection and the remaining symbols in equation (2.5.2.5)[link] are the same as those in equation (2.5.2.3)[link].

References

Buras, B. & Gerward, L. (1975). Relations between integrated intensities in crystal diffraction methods for X-rays 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.
Johnson, M. W. & David, W. I. F. (1985). HPRD: the high resolution powder diffractometer at the spallation neutron source. Report RAL-85-112. Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK.
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.
Jorgensen, J. D. & Worlton, T. G. (1985). Disordered structure of D2O ice VII from in situ neutron powder diffraction. J. Chem. Phys. 83, 329–333.
Steichele, E. & Arnold, P. (1975). A high-resolution neutron time-of-flight diffractometer. Phys. Lett. A44, 165–166.








































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