Time-of-Flight Concepts

Course Material Index  Section Index  Previous Page  Next Page 

Concepts

So far the properties of the neutron beam have been discussed in terms of the different scattering/absorption processes. The de Broglie equation relates the wavelength, λ, of a neutron to its momentum, mv, according to the equation:

where h is Planck's constant (= 6.626×10^-34 Js) and m is the mass of the neutron (= 1.675×10^-27 kg). Thus the velocity, v, of the neutron is inversely proportional to its wavelength.

The important point to understand here is that in 1 ms a neutron will travel only a couple of metres. Since times of ns to µs are readily measured with modern electronics, by timing a neutron over a fixed path length, its velocity, and consequently its wavelength, can be measured. This technique is generally referred to as the time-of-flight (TOF) method. Combining the above equation with the Bragg equation yields the key equation for TOF, which is:

where L is the path length and t is the time-of-flight. Since d spacing is proportional to time, TOF powder diffraction patterns are normally displayed with the ordinate axis going from small to large d spacing, in contrast to both angle-dispersive and energy-dispersive methods (which in effect have a reverse scale in terms of d spacing).

You may immediately wonder how this technique can be carried out in practice. The solution is relatively simple in that if the start time of the neutron is fixed, then all we need to measure is the arrival time at its destination, i.e. in the detector. The start time of the neutron can be fixed by two methods: At a reactor source, the constant flux of neutrons is simply time sliced by a mechanical chopper, which in its simplest form is a high-frequency rotating disk with two transparent windows in it. While this method is exploited in the design of neutron spectrometers, it is rarely used for diffractometers at reactor sources. The second method is for the neutron source itself to be pulsed in short well-defined intervals. Although pulsed reactors have been built, the main source of pulsed neutrons is by the spallation process.

In Europe, the most intense spallation source of pulsed neutrons is at the ISIS facility at the Rutherford-Appleton Laboratories (RAL), deep in the middle of southern England. See the external links page for references to this and other sources worldwide. The next section discusses how neutrons are produced by the spallation process with reference to ISIS as a prototype source.

Course Material Index  Section Index  Previous Page  Next Page