# Neutron Time of Flight

In many of the neutron experiments it is essential to know the energy or wavelength of the neutrons precisely. The velocity of the neutron is related to its energy and wavelength through the following relations:

λ=h/MnV wavelength equals the Plancks constant divided by the neutrons mass times its velocity

and

E= ½M2V2 E equals one half of the mass multiplied by the velocity squared

where λ is the wavelength, mn lambda is the wavelength, mn is the neutron mass, v is the neutron velocity, and h is Plancks constant. The neutron wavelength (and thus wavelength and velocity) cannot be directly detected but a simple and effective way to find it is by a Time of Flight (ToF) analysis which is similar to recording the results of runners in a marathon. If we know when the neutron was emitted (or passses through a chopper) at a specific place and measure the time t it takes for it to travel a certain distance L, we can calculate its wavelength (λ) (and thus velocity and energy), from the following relation:

t=αλL t equals alpha times lambda times L

where α = mn/h ≈ 252.7 μs/m/Å alpha equals proton mass divided by Plancks constant, which is close to 252.7 microseconds divided by meters divided by armstrongs , is a constant. Also like runners, if we want to make sure to be able to separate them by who is the faster we need a long-running track. Think about it; it would be hard to separate one hundred people by their running speed if the track is only 5 meters long. For the same reason, instruments that require a high precision in energy or wavelength may be placed more than 100 m away from the moderator.

Some neutron instruments will make use of time-of-flight analysis to filter out a specific wavelength (range) of neutrons before the sample. These types of instruments are called direct geometry instruments and our diffraction instrument in this simulation is an example. Other instruments will filter out specific wavelengths after the sample and they are called indirect geometry instruments. Our QENS experiment is conducted on such an instrument.

Figure 1. a; Time of Flight graph. b; Simulated ToF diffraction map as a function of wavelength calculated by arrival time of the neutron for each scattering angle.

Time of flight scattering maps By clever design of the chopper wavelength selection system and neutron detector, which can precisely record the time a neutron has arrived, it is possible to get more, or faster information about our sample. For instance in the diffraction experiment in our game we are only considering the diffraction pattern from a single incoming neutron wavelength, but we could, in principle, have several wavelengths in our beam and get a diffraction pattern for each wavelength which we would distinguish by the time each pattern arrived at the detectors. What we get from this is a scattering map which is both a function of the distances in the sample and the wavelength of the neutrons. As you see on figure 1.b such a map is rather complicated to look at, but if we instead present the data in q-space then we get a series of flat lines where we can sum the intensity of each one to get a similar diffraction pattern as if we had used a single wavelength.

So what is the advantage of this? In short: higher neutron flux. If we select only a single wavelength for our experiment then we throw away all the other neutrons. A common issue with neutron scattering is that the flux is rather low compared to that of X-ray experiments, and it can take minutes, hours, or even days to record neutron scattering data from a sample. This is no good if we want to record the structural change in a sample as it occurs, but if we can utilize most of the neutrons at our disposal we can record data more rapidly and measure faster changes.