The other way that neutrons can be produced at great enough levels to allow powder diffraction is through spallation, which is the term initially used for sand-blasting, where material is machined by impacting it with small abrasive particles. In the case of neutron spallation, protons are accelerated into a target. The target is made from a high-Z metal, where the nuclei are rich with neutrons. The collision between the proton beam and the metal nucleus displaces protons from the atoms, but these neutrons are of very high energy and must be moderated before they can be used for scattering experiments.
It is much easier to design and build an electron accelerator than a proton accelerator, and indeed early work in neutron spallation was done with electron beams, but protons are much more effective due to their greater mass. A proton accelerator could be designed to produce an almost continuous stream of protons, which would provide a nearly steady-state source of neutrons, but spallation sources are designed where large packets of protons are brought into impact the target at periodic intervals, on the order of ten times per second. Each packet of protons causes a nearly instantaneous pulse of fast neutrons when impact occurs, but most of the proton packet’s energy is transmitted to the target in the form of heat, which must be removed by cooling so that the target does not melt. The generated neutrons must be moderated, by allowing them to partially equilibrate with a material (usually hydrogenous or deuterated). However, as will be made clear, one does not want to overly degrade the time width of pulse of neutrons, so moderator design is an art with compromises between efficiency, energy spectrum and the pulse duration. Also, since different types of neutron scattering instruments typically share a moderator, where each type of instrument may be optimized by different moderator characteristics, there may also be a compromise by instrument needs. Powder diffractometers rarely are equals in these design compromise discussions.
As the fast neutron pulse hits the moderator, some will be transmitted very quickly with very little moderation. Usually a spinning drum, called a chopper, placed between the moderator and the sample will prevent these neutrons from hitting the sample. The chopper will open to allow partially moderated neutrons to escape and will close before the lowest energy neutrons can escape. The duration that the chopper is open will be short and as the neutrons travel towards the sample, they spread out in time, with the highest energy (shortest wavelength) arriving first. Thus, by synchronizing the counting electronics with the neutron pulse emission and knowing the distance between the moderator and where the detector is located, one can determine the velocity of the neutron. From the de Broglie equation, \(\lambda = h/{mv}\), the neutron wavelength is be determined. While a single neutron pulse may produce only a small number of observed diffraction events, with many neutron pulses each second, the intensities in the pattern build up with data collection time. Since the neutron pulse has finite width and the will be some uncertainty in time measurement for when a neutron is detected, this translates to a peak width. Peaks tend to be sharper on the high energy side, as few neutrons will arrive earlier than the mean arrival time, but it is the behavior of moderators that neutrons continue to leave well after the most of the pulse has left, leading to asymmetric peak shapes with a tail at longer times (shorter Q).
Since neutron data collection time is precious, large numbers of detectors are placed around the sample. The detectors do not move, since each detector sees a spectrum of neutrons and thus a section of the full diffraction pattern. The pattern shifts to higher Q for detectors at higher Bragg angles. Also, while each detector sees the same wavelength band, the higher angle detectors offer much better resolution in terms of \(\Delta \rm Q/\rm Q\) .
One would not want to deal with, say 100 diffraction patterns from an instrument with 100 detectors, so early TOF instruments had electronics that would shift the timing for neighboring detectors so that the patterns could be superimposed for a single detector in the middle of the detector group. The detector groups were known as banks. This process was known as time-focusing, but is not actually a focusing effect, merely a form of binning. One might expect problems from time-focusing, in that detectors at different angles have differing resolution and that adding higher resolution data to lower resolution data creates, well, lower resolution data with better counting statistics, but in practice in these instruments there was a small range of angles so that the resolution was about the same and resolution degradation was imperceptible. Problems could also arise because there are corrections that are sometimes wave-length dependent corrections applied in fitting (e.g. for absorption, neutron scattering edge resonances and extinction), but since the wavelength shifts are small and the shifts are clustered around the mean, these also did not introduce any significant problems.
Time-shifting is now done in an instrument’s control software and may be done over wider angular ranges. This is not such a good idea. It is convenient to have data from few banks, but degrades the highest resolution data and makes it impossible to perform wavelength-dependent computations. It is possible to apply the absorption correction as part of the data reduction process, but this requires accurate knowledge of the composition of the sample and its density. When these are not known well, it is better to have the option to refine the absorption correction as part of fitting. The other corrections become impossible. Data should be mixed only over narrow angular ranges.
An alternate approach is to create pseudo-CW data from TOF data, by binning in Q or \(2\theta \) for relatively narrow wavelength bands. These data will appear similar to CW data, but will have the asymmetric peak shape seen with TOF. This is supported in GSAS-II.
There are not very many TOF neutron diffractometers in the world, since there are only a few spallation neutron sources, but each one is unique, as each was designed with a different set of goals. The flight path length, meaning how far the instrument is placed from the neutron source, is perhaps the most important parameter, as that dictates the resolution of the instrument, but as the path becomes longer either the wavelength range must be decreased or the number of pulses per second accepted by the instrument must be dropped. Design variables include the type and number of detectors and how far they are placed from the sample, as well as how they are distributed with respect to Bragg and azimuthal angle.