TOF neutron diffraction
14 Aug 2009



TOF neutron diffraction on Rotax




At the spallation source ISIS protons are accelerated to 800 MeV and then directed onto a tantalum target. On striking the target each proton produces 25-30 fast neutrons by a spallation process. ISIS operates at 50 Hz and produces a pulse of polychromatic neutrons every 20 milliseconds. The pulse is roughly 30 microseconds wide after passage of the 95 K liquid methane moderator.

The neutrons reach ROTAX after a flight path of about 15 m and hit the sample which is mounted on a large table of about 80 cm diameter. Neutrons are diffracted according to Bragg’s law

l =2 dhkl sin Q

l : neutron-wavelength; dhkl: interplanar spacing

2q : scattering angle;

The wavelengths of the neutrons can be obtained from measurement of their flight times using the de Broglie relationship:

h/l =mn L/ t

h: Planck’s constant; mn: neutron mass

L: total flight path; t: time-of-flight

Combining above equations yields a relation between the time of flight (TOF) and interplanar d-spacing between lattice planes:

t[m sec]=505.56 L(m) d(Å) sinQ

The diffracted neutrons are registered with respect to both, time-of-flight (t) and position (2Q) using large position sensitive detectors.

Introducing zero shifts the following relation between time-of-flight and d-dpacing can be introduced: (see GSAS manual p 126) 

t =DIFC*d + DIFA*d**2 + ZERO 

DIFC=252.816 * 2* L * SinQ

and DIFA and ZERO are d-spacing-dependent and independent  zero shift parameters, respectively.

Special features of time-of-flight powder diffractometers

  • A considerable flux of long wavelengths neutrons (up to 5.2 Angstrom on ROTAX) is available to measure diffraction intensities with long-d-spacings, for example magnetic reflections. The reduction of neutron flux at long wavelengths is partly compensated for by the lambda**4 dependence of the diffraction intensity.
  • High epithermal neutron flux allows measurements to be made to very low d-spacings leading to high resolution in real space.
  • The best resolution is achieved in backscattering where the small d-spacings are measured. Another advantage of the backscattering geometry is that the resolution (i.e. the width of a diffraction peak) is nearly independent of the d-spacing.
  • Complete diffraction patterns are obtained at a single scattering angle, i.e. there is no need to move the sample or the detector.


Ref: B.T.M. Willis, Z. Krist 209 (1994) 385