Neutron flux and detectors

An optimized high neutron flux is especially important for short time measurement of evolving diffraction pattern or for inelastic experiments, where only a small part of the scattered neutrons contributes to the signal, and only in major high flux sources, a sufficient neutrons flux is available. At smaller reactors with significantly lower fluxes, one will focus, e.g., on small-angle scattering (SANS) experiments without time resolution.

A consequence of the low neutron flux is that, especially for inelastic experiments, wider resolution widths have to be tolerated than in optical spectroscopies such as IR. Due to the low relative resolution, the neutron incident energy \(_\) has to be adapted to the experiment. The resolution width of inelastic data is not only a function of \(_\), but also of the energy transfer \(E\), being worse in energy gain than in energy loss. In energy gain, the scattered neutrons have a higher velocity, which is measured with less absolute precision. In [66], the intrinsically much sharper lowest ortho–para transition in solid hydrogen at 14.7 meV had a fwhm of 0.83 meV in energy loss (J = 0 to > 1), but of 1.5 meV in energy gain (J = 1 to > 0) (IN4, incident energy 31 meV).

The number of scattered neutrons is proportional to the incident flux, which is measured by a calibrated detector with small efficiency and high transmission for the quantitative determination of scattering probabilities. Such a detector is called a monitor and gives an estimate of the total number of neutrons having reached the sample during one measurement.

In optical experiments, the intensity is often measured, and only sophisticated detectors for very low intensities apply photon-counting techniques. For the small numbers of scattered neutrons, counting techniques always have to be applied in the secondary spectrometer. Geiger tubes for radioactive β and γ radiation count single current pulses generated by gas ionization. Thermal neutrons have energies of a few meV, which is not sufficient for directly producing photons (1–2 eV) for a CCD-camera or generating a current pulse of ionized gas atoms (some 100 eV). High-energy particles have to be generated by capture of slow neutrons triggering a nuclear reaction. A standard method is to fill counter tubes with a few bars of 3He. These atoms capture neutrons with a high cross section (cf. Table 5), forming an intermediate 4He nucleus that releases ionizing particles (tritium atom and proton) with a total kinetic energy of 740 keV [21]. In contrast to the millielectronvolt neutron energies, this is largely enough to produce a detectable number of ionized particles. 3He is usually preferred to boron trifluoride (11BF3) gas, because helium has preferable chemical properties and counters have a higher efficiency. Nearly every neutron entering such a tube of, e.g., 25 mm in diameter, undergoes a nuclear reaction. This yields ionizing radiation and triggers a discharge, which is measured as in a classical proportional counter.

Since a few years, scintillator detectors started to replace gas tube devices. In this case, neutrons generate high-energy α-particles by nuclear reactions. The issue is to distinguish between neutron-induced signals and noise as produced by γ radiation. In a recent paper [67], the complex processes for obtaining efficient scintillators are laid out in detail: the traditional scintillator ZnS, which is known from many other applications, is used again, but is doped with Ag for the detection of α radiation. By producing nanoparticles and doping them with 6LiF, a material is obtained, in which first thermal neutrons are converted into high-energetic α-particles by the lithium. These particles are then generating light pulses in the ZnS:Ag, which are in turn transferred via appropriate light guides to photomultipliers, CCD-cameras and other photosensors, and finally converted into electrical signals.

Instrument design: measure the wavelength by Bragg diffraction or the velocity by time of flight

Neutrons are used for a variety of elastic and inelastic experiments in a large wavelength range. As neutrons with similar energies and wavelengths are used both for diffraction and for spectroscopy, the techniques used for diffractometers and spectrometers are similar, but very different from laboratory spectroscopy. It is characteristic that the Nobel Prize in Physics 1994 was awarded “for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter” jointly with one half to Bertram N. Brockhouse “for the development of neutron spectroscopy” and with one half to Clifford G. Shull “for the development of the neutron diffraction technique” [68].

A number of spectrometer types have been developed for different wavelength ranges of the incident beam and different precision, with which the scattered neutrons are measured. Instruments for neutron scattering may contain several tons of material including heavy shielding, choppers, detectors, and cryostats. These setups are firmly connected to the source via beam tubes and neutron guides, and thus are optimized for the spectral distribution of neutrons at the respective beam. Here, some of the characteristics of the instrumental techniques are presented for making the respective results understandable. Technical realizations differ considerably from one neutron source to another. For a profound understanding, the reader should refer to the documentation of the respective instruments [26, 47, 69].

Nearly all instruments determine the neutron wavelength at some stage, usually at least in the incident beam, which is called “direct geometry.” For elastic scattering, the scattered neutrons are counted only as a function of their direction. For inelastic scattering, the velocities or wavelengths in the scattered beam and the scattering angle are measured simultaneously. There are two important methods for determining the wavelengths or velocities of neutrons, either by diffraction at a crystal and taking out one Bragg reflection, which corresponds to a well-defined wavelength, or by measuring the time of flight (TOF) over a given distance and determining the velocity.

Monochromators using Bragg reflection at large crystals

The wavelength of the neutrons in the incident beam may be defined by Bragg scattering at a large single crystal of pyrolytic graphite, copper, silica a.o. A problem is that Bragg reflections of neutrons in crystals are often contaminated by higher order contributions. If a monochromator crystal is e.g. adjusted to admit in first order (n = 1) neutrons with 3  Å or 9.1 meV, neutrons with 1.5, 1.0, ..Å or 36.4, 81.8,.. meV also fulfill the Bragg conditon for n = 2,3,.. These “higher order contaminations” may have significant intensities. In diffraction patterns, higher order contributions may scramble the relative line intensities, which are important for the analysis of the structure. In inelastic scattering spectra as, e.g., from triple axis spectrometers (see below), higher-order reflections at the monochromator result in parasitic intensities. Previsions have to be taken to filter out the desired order, which may reduce the ranges of useful energy and momentum transfers.

DiffractionNeutron powder diffraction (NPD)

Crystals For crystalline samples, the treatment of neutron data is largely comparable to X-ray diffraction. In the case of crystalline powders, Bragg scattering at the sample is observed. For each peak, a lattice constant \(d\) is obtained from the Bragg relation discussed above, where \(p\) is the momentum of the incident neutrons:

$$p=\frac\Theta }; d=\frac\Theta }$$

(59)

The well-known Rietveld analysis [70] was first developed for neutron diffraction, since sufficient computing facilities were early available in the neutron research centers [71], and later on transferred to X-ray data. The method consists of fitting the measured data by a pattern calculated from a structure model and adjusting the corresponding structure parameters.

Amorphous solids and liquids Most textbooks focus on crystals with a long-range order, which can be described simply by intuitive concepts. In reality, systems with a short-range order such as liquids and amorphous solids play a huge role. Liquids are ubiquitous in daily life, especially water and oils. It is less obvious how important amorphous systems are. Most biomolecules such as fats, collagens, and proteins are amorphous, just think of butter, chocolate, and boiled eggs. These substances are in a soft, rubber-like state, in contrast to hard and brittle glasses for window panes or for drinking a beer.

Figure 18 (left) shows a typical elastic coherent scattering function for systems without long-range order, such as disordered glassy systems and liquids. Obviously the Q-dependence is much more smeared out than for a crystalline sample with sharp Bragg reflections. This broad intensity from coherent scattering still reflects interatomic interferences and must not be confused with incoherent contributions. Amorphous and liquid samples do not have a long-range order and cannot be described by crystallographic approaches. The short-range order around each particle is described by \(g\left(r\right)\) (Fig. 18 (right)), which is simply calculated from \(S\left(Q\right)\) by a sine Fourier transform

Fig. 18

Structure factor S(Q) (left) and pair distribution function (PDF) \(g\left(r\right)\) (right) for liquid Rubidium. Both graphs may easily be confused: S(Q) is an experimentally determined scattering function and thus plotted as a function of Q or the scattering angle. Whereas crystalline samples would show sharp Bragg peaks in this experiment from long regular columns of atoms, liquids yield a broad-intensity distribution, the maxima reflecting only the interference between few atoms. \(g\left(r\right)\) is calculated from S(Q) by Fourier transform and is plotted over the particle–particle distance r. The first sharp maximum in \(g\left(r\right)\) yields the distance between each particle and those surrounding it in a first shell (cf. Fig. 13). The corresponding value of r (here 4.9 Å) thus roughly reflects the particle diameter. Due to a lack of long-range order, further shells are strongly broadened [72, 73]. Figures were taken from Ref. [74] with kind permission of Wolf-Christian Pilgrim

The meaning of \(g\left(r\right)\) may be rationalized in two ways: if the volume element \(\mathrmV\) is large as compared with the volume of a single particle, the dimensionless quantity \(g\left(r\right)\) simply describes the ratio of the density inside the volume element to the average density. For describing the short-range order of a liquid or amorphous solid, \(\mathrmV\) (e.g., in nm3) has to be small and may only contain one or even zero particle centers. Then, the expression \(N\cdot g\left(r\right)\cdot \mathrmV\) with the particle density \(N\) (in particles per nm−3) is the average number of other particles found in a small volume \(\mathrmV\) at a distance \(r\) around any given atom. In the limit of long distances \(r\), this is just given by \(N\cdot \mathrmV\), and \(g\left(r\right)\) is normalized to \(g\left(r\to \infty \right)=1\). At very short distances below the sum \(_=_+_\) of the radii of the two particles, \(g\left(r\right)\) is close to zero, since particles cannot permeate. At \(r=_\) we find a number of particles forming a shell around the center particle, and \(g\left(r\right)\) has a pronounced maximum. Further, usually much smaller maxima indicate second and third shells, which are less pronounced. A simple shell model for \(g\left(r\right)\) and the corresponding scattering function has been introduced in [75].

A spectacular example of the merits of neutron scattering in this field is the short-range order of liquid water. Good water models have a huge importance for the understanding for processes in aqueous solution, including nearly all biochemical reactions. The intermolecular interactions including hydrogen bonding are difficult to describe and are the key issue for a consistent model of this liquid. X-ray scattering from water yields a significant signal only from oxygen. Neutrons see strong scattering from H and D [77]. By isotope substitution and varying the ratios of H and D, the coherent contribution from hydrogen atoms was separated off, and the radial distribution functions for the H–H, O–O, and O–H distances were deduced and compared with simulations (Fig. 19) [78].

Fig. 19

Measured pair distribution functions of water atoms (open circles) and comparison with force field simulations. Especially, the first peaks at about 1.8 Å (O–H), 2.5 Å (H–H), and 3 Å (O–O) reflect the hydrogen bonding and are sensitive to the modeling. Even results from simulations with a widely used sophisticated standard water force field (TIP4P/2005) (dashed line) differed significantly from the experimental data. Only after empirically modifying the force field, was a very good agreement between experiment and simulation attained (full line). Figure was reprinted from Ref. [76] by A.K. Soper under Creative Commons Attribution License

Setup A simple setup for neutron powder diffractometers has Debye–Scherrer geometry, similar to X-rays. At continuous sources, the incident wavelength \(\lambda\) is typically defined by Bragg scattering at a large monochromator single crystal from graphite, silicon, or copper. At a spallation source, the incident neutron velocity \(v\) is usually controlled by choppers. In both cases, the momentum of the incident neutrons is obtained:

$$p=\frac=_\cdot v=_\cdot \frac$$

(60)

Then, the scattering probability is measured as a function of the scattering angle at the sample, usually employing 1D-position sensitive detectors, and short measuring times below minutes are attained for high-quality diffraction patterns. The high intensity of elastic scattering permits attaining very high resolution. An example for that is the powder diffractometer HRPD at the ISIS spallation source [79, 80], where an extremely precise definition of the incident velocity is obtained by measuring the neutron flight time over a path of 100 m, and the resolution for measured lattice constants attains \(\frac=5\cdot ^\). By collimators before and after the sample, perturbation of the line shapes are reduced and, in spite of using large samples, peak quality may be at least comparable to X-ray data. By rotating the sample, texture effects are traced.

Single crystal diffraction

Similarly to X-ray scattering, diffraction of single crystals affords a four circle goniometer for orienting the sample with respect to the incident beam. Both rotating crystal or Laue methods with a single incident energy or a white neutron spectrum, respectively, may be applied [25, 81, 82]. Inspection of the Brookhaven protein database [6] shows that only some 200 protein structures out of 175,000 have been determined by neutrons, while the dominant method is X-ray scattering. A major application of neutrons consists in the determination of proton positions, which is not possible with X-rays. The treatment of neutron data follows similar lines as of X-ray diffraction and is not discussed here.

In spite increasing the performance of sources and instruments, the large minimum crystal sizes remain an issue for neutrons. A very recent neutron diffraction paper [83] on a sugar-binding protein (8DHD) is based on crystals with sizes of 3–10 mm3. This seems to be tiny, but even in a somewhat older review on X-ray diffraction [84], it is claimed that crystals 0.1–0.3 mm in size are sufficient for this technique. This corresponds to a crystal volume of 0.001–0.01 mm3, which is still about a factor of 1000 lower than for neutrons. Taking into account the efforts made by biochemists to grow single crystals for structural studies on thousands of proteins, this difference in sensitivity may be decisive for the choice of X-rays rather than neutrons.

Inelastic scattering (INS)Triple-axis spectrometer

The genuine type of instrument for INS at a continuous reactor source is the triple-axis spectrometer (Fig. 20), which was mentioned in the textbook of solid-state physics by Kittel [1]. As the name says, angles at three axis are variable (cf. Fig. 20). The energy and momentum transfers are calculated according to Eqs. (4) and (6) and Fig. 2, respectively. A wide range of energy and momentum transfers can be scanned. By collimation of the incident and scattered beams, the resolution of \(Q\) and \(E\) can be adjusted. As the instrument detects low count rates, heavy shielding is afforded to prevent spurious background radiation from reaching the detector. In combination with the large beam size, big masses have to be moved, and a special technique was developed to mount the sample and detector on pressurized air cushions, which glide on a polished marble table with an area of several m2 (“Tanzboden” instruments). As the sensitivity of this setup with only one detector covering a small steric angle of scattered neutrons is small, one usually measures coherent intensity, which is concentrated in a small angular range with well-defined \(Q\) transfer.

Fig. 20

Modern triple-axis spectrometer: schematic layout of IN8 at a thermal beam (ILL, Grenoble) [47], reprinted by kind permission, ©ILL wwww.ill.eu. The “white” neutron beam (from the right) passes through a diaphragm (orange) to a monochromator drum with three crystals (blue is active, red and gray). The wavevector \(}_\) and the corresponding energy Ei of the incident neutrons are determined by this monochromator. The Bragg angle at the monochromator may be varied by rotating the drum (first axis) and the shielding (blue dots and dark gray) appropriately. After passing through the monitor, which measures the number of neutrons passing to the sample and a second diaphragm, the beam passes the sample (red circle) and finally the beam stop. The background level is reduced by further shielding (gray). The scattering angle at the sample is varied by rotating the analyzer/detector unit (green) and adapting the shielding around the sample accordingly (second axis). The final wavevector \(}_\) and the energy Ef of the scattered neutrons is measured by Bragg reflection at the second crystal, the so-called analyzer (light blue). This energy is scanned by rotating this crystal and the detector unit (green polygon) with a counter tube inside around the third axis. The monochromator and analyzer consist of large single crystals for selecting wavelengths by Bragg reflections

Dispersed modes phonons

In extended crystals with high translational symmetry, vibrations of the particles are usually not independent, but the relative phase between adjacent equivalent oscillators is well defined. Such lattice vibrations or so-called phonons have wavelengths in the order of a few lattice constants. That means that oscillators, which are only a few nanometers apart from each other, vibrate with opposite phases. With a typical sound velocity of \(v=6000\frac}}\) [85], a wave spreading through the MgO crystal, a so-called phonon, with a frequency of \(\nu =5\mathrm= 5\cdot ^}^\) has a wavelength of \(\lambda =12\,}\), which corresponds to three lattice constants, i.e., is on an atomic length scale. Equivalent oscillations, which differ only by the phase difference between adjacent oscillators, have different frequencies, and such modes are called “disperse.”

The wavelength of optical radiation in an appropriate frequency range below, e.g., 25 THz (Fig. 21) is higher than 12 µm, which is at least four orders of magnitude higher than a typical lattice constant. Thus, only phonons, where adjacent unit cells vibrate nearly in phase, can be observed by radiation with such long wavelength or small wavevector k. Due to this “k = 0” selection rule, acoustic phonons normally do not appear in the IR and Raman spectra. For optical phonons, the full dispersion curves are not seen, but only the limit, where the whole lattice oscillates in phase (cf. * in Fig. 21). In variance to optical radiation, wavelengths and energies of thermal neutrons both match the range of lattice vibrations, and numerous complete phonon spectra of systems with extended periodicity such as crystalline MgO were measured by coherent INS [87, 88].

Fig. 21

Phonon dispersion curves of solid MgO [86]. Optical techniques only yield few results (*) for optical phonons at the Γ-point, where all elementary cells oscillate in phase. Only the systematic neutron measurements in a wide range of wavevectors and energies (frequencies in THz) yield sufficient data (open symbols) for calibrating electron structure calculations on the crystal (full lines). Reprinted from J. Phys. Chem. Solids., 61, Parlinski K, Łaz˙ewskib J, Y. Kawazoe, “Ab initio studies of phonons in MgO by the direct method including LO mode”, 87–90, Copyright 1999, with permission from Elsevier

Textbooks for solid-state physics [1] typically propose very simple approaches for the crystal vibrations such as the Debye model, not respecting internal interactions and being insufficient for any specific description of the solid. By neutron scattering, one obtains phonon dispersion curves as a function of the crystal orientation. From the phonons, a series of physical properties are derived such as a precise density of vibrational states, specific heat, sound velocity, and elastic constants. Interaction potentials in the crystal may be calibrated by comparing measured and calculated dispersion curves.

Backscattering spectrometer

Very high-energy resolutions are attained with backscattering spectrometers such as IN13 and IN10 in Grenoble. This is a special spectrometer type with energy definition by Bragg scattering at crystals, being designed for resolving very small energy transfers from the elastic line [47]. These spectrometers make use of the fact that the wavelength resolution on an ideal crystal in the limit of backscattering (\(\Theta =90^\circ\)) may, in principle, go to infinity. We obtain from the Bragg condition for the first refraction order:

$$\begin \lambda&=2 \cdot d_ \cdot }\left( \Theta \right) \Rightarrow \Delta \lambda=2 \cdot d_ \cdot }\left( \Theta \right) \cdot \Delta \Theta \hfill \\ &\Rightarrow \frac=\frac \cdot }\left( \Theta \right)}} \cdot }\left( \Theta \right)}} \cdot \Delta \Theta=}\left( \Theta \right) \cdot \Delta \Theta \to 0 \cdot \Delta \Theta }\Theta \to 90^\circ \hfill \\ \end$$

(61)

and if the neutrons scattered from the sample are collected in a finite angular range \(\Delta \Theta\), the corresponding wavelength spread still is very small.

In these spectrometers, in general, monochromator and analyzer are crystals of the same material (e.g., CaF2) with essentially the same lattice constant. By heating or by periodic motion, the effective lattice constant of the analyzer is slightly shifted with respect to that of the monochromator due to thermal expansion or Doppler shift, respectively, and the detected scattered neutrons have a slightly different wavelength than the incident beam, corresponding to a small energy transfer. In practice, typical resolutions are 1–10 µeV at energy transfers of 50–500 µeV. An important application of spectrometers for small transition energies is tunneling spectroscopy, since tunneling splitting usually has energies well below the vibrational spectra [40].

Spectroscopy of methyl groups in condensed phases

Many organic molecules contain methyl groups, and their dynamics are intensively studied by inelastic neutron scattering. In organic chemistry, one usually considers CH3 groups which are connected by a single C–C bond to the body of the molecule, as freely rotating around this bond. In fact, it is very unlikely that the energy of this bond is completely independent of the rotation angle. In practice, “freely rotating” means that the barrier height against rotation is only in the order of a few \(R\cdot T\) with \(T\approx 300 K\), and that rapid thermally activated reorientation and redistribution over all angles is observed. In condensed phases, the methyl group usually is trapped in a cage of arbitrarily arranged atoms. Perturbation of the rotation around the figure axis is due to intramolecular and, in condensed phases, also to intermolecular interactions. Even though usually much weaker than in hydrogen bonding systems, they still hinder the rotation.

In an angular dependent potential as in Fig. 22 bottom, the rotation of the methyl group around its figure axis is hindered. Now, three transitions are possible: (1) the molecule undergoes torsional vibrations around the figure axis without changing the arrangement of the protons with respect to the cage. These so-called librations often have transition energies of a few meV and are discussed in “Librations of methyl groups in solid”; (2) at low temperatures, the protons can tunnel simultaneously from the respective minima (at 60°, 180°, 300°) through the potential barriers (at 120°, 240°, 0°) to the respective next minimum; and (3) at higher temperatures, thermally activated reorientation occurs as jumps over the barriers, in some analogy to the translational jump diffusion described above.

Fig. 22

Tunneling and torsional vibration of a methyl group around its figure axis, cf. [36]. Top: schematic view of a methyl group in a cage seen from top. In the condensed phases the methyl group in the center may be surrounded by other atoms yielding an angular dependent potential. An arbitrarily chosen arrangement of vanderWaals spheres of carbon (full black), oxygen (full red), and hydrogen (open circles) is plotted. As the methyl group will not undergo significant polarization and has a symmetric charge distribution around its figure axis, steric vanderWaals interactions will yield a major contribution to the interaction of CH3 with its cage. Bottom: interaction with the cage yields a rotational hindrance potential, which depends on the angle Φ of the methyl group around its figure axis (blue line). Independently of the cage structure, this potential is strictly three-fold symmetric since a rotation by 120° corresponds to a permutation of the indistinguishable hydrogen atoms [36]. In most cases, the potential is deep enough for providing three deep potential wells and corresponding equilibrium orientations of the group. Inside the potential well, a ground state and at least one excited librational state are found. Both the ground and the first excited librational states are split into two energy levels each (thin black lines), see text

In a classic picture, we could number the protons n = 1,2,3, and distinguish three identical ground states, e.g., by watching which of the protons points to the left in Fig. 22, top. We see librations maintaining the rotational orientation and thermally activated reorientation. For a quantum mechanical description, the three protons can no longer be distinguished, and any stationary wave function must be adapted to the three-fold symmetry of the system. If we now prepare the methyl group in a state where indeed one proton is fixed, e.g., pointing to the left in Fig. 22 top, we obtain a state that is not adapted to the symmetry of the system and thus is nonstationary. It will evolve, and the protons will exchange their positions by “tunneling” through the potential wells with a frequency \(_}\). Looking for stationary states leads to a different result than in the classical description. We again get three states in the librational ground state, but they all have nonzero energy due to the zero-point energy of the libration (cf. Fig. 22, bottom). Further on, the three states result from a superposition of the three orientations and are symmetry adapted. In the frame of group theory for a three-fold symmetric system (symmetry group C3) we obtain a totally symmetric single A and a doubly degenerate E level. The tunnel splitting \(\Delta _}\) between both has a similar origin as the well-known umbrella splitting of the ground state of the nonplanar NH3 molecule. Tunnel splitting of stationary states and tunnel frequency of the nonstationary states are connected by \(\Delta _}=h\cdot _}\). This \(\Delta _}\) sensibly depends on the barrier and rapidly decreases with increasing height. As is known from the basics of quantum mechanical tunneling, the splitting also depends on the barrier width. Thus, e.g., a six-fold potential in a symmetric cage induces a higher splitting than the shown threefold at equal height. The rotational modes of the methyl group are related to the nuclear spin of the system, and the transition between the A and E states afford a flip of the total nuclear spin of the three protons. Such transitions are optically forbidden, but can be excited by neutrons having a magnetic moment.

Energy and momentum transfer definition by time-of-flight (TOF) techniques

Whereas monochromators on the basis of Bragg reflections are well known from X-ray sources, especially synchrotrons, neutrons offer a second possibility for defining the energy by determining their flight time over a given distance. The so-called time-of-flight methods use pulsed beams: in a pulse all neutrons start at the same position, usually the sample, and at the same time, and a time dependent detector measures the number of neutrons as a function of their time of arrival. Thereby, the neutron velocity is determined with adequate precision. This method has no analogy in X-ray scattering, but neutron instruments scan a large incident energy range this way.

Choppers and velocity selectors in the primary spectrometer

The incident pulse is shaped by choppers and usually has a width of only a few µs. Usually, all incident neutrons have a well-defined energy and hit the sample at the same time.

Pulsed beams

Pulsed neutron sources are only spallation sources, with the exception of the pulsed reactor in Dubna [48]. At pulsed sources, virtually all spectrometers apply TOF techniques, which make ideal use of the available neutron flux. The neutron sources usually are designed for yielding sufficiently short pulses with reasonable time frames, and the source pulse can be used directly for determining the neutron start time instead of a first chopper. Choppers are only required for velocity determination, as each pulse consists of a wide spectrum of neutrons with different velocities. Two choppers with well-defined phase shifts with respect to the source pulse or a velocity selector are sufficient to filter the desired energy range. Often, the pulse width at spallation sources is proportional to the inverse velocity and filtering results in constant relative resolution for TOF experiments at different wavelengths.

At continuous reactor sources, pulsed beams for inelastic scattering can only be obtained with a great loss of average flux. The incident beam is chopped into pulses with a width of, e.g., 40 µs, which puts a lower limit to the instrument resolution. The distance between two pulses, the so-called frame time, determines the energy range and is typically 2–10 ms. Already with 2 ms, the duty cycle is only 2%.

There are two different approaches for velocity determination in the primary spectrometer:

For elastic scattering without energy analysis in the secondary spectrometer, velocity selectors are used that consist of one piece looking somewhat like an Archimedean screw and filtering incident neutrons with a rather high-duty cycle at a continuous source. These selectors admit frame overlap, i.e., fast scattered neutrons from the next pulse reach the detector at the same time as slow ones from the earlier pulse. These devices work for scattering without energy resolution and are preferably used for small-angle neutron scattering (SANS) (see below). A fairly low-velocity resolution is sufficient, about 10%, and the resulting neutron beam has a high flux. Consequently, SANS instruments with velocity selectors may also be used at smaller neutron sources.

If energy analysis in the secondary spectrometer is afforded for inelastic scattering, one uses distinct choppers generating an incident beam of short pulses with defined energy. During the scattering process, the neutrons change their velocity and reach the detectors at different times. For measuring this time spread, short pulses with significant distance are necessary, which is attained by choppers with small duty cycles. By a second chopper with the same rotational speed, but with a fixed phase shift \(\Delta \varphi\), only those neutrons are taken out of the pulse from the first chopper and reach the sample, which have a selected velocity. In analogy to light, this beam is called “monochromatic.”

There are several possibilities for constructing neutron choppers. One option is to use slit choppers with pairs of discs rotating in opposite sense. Another possibility is to put a tight neutron collimator into the rotator, which set up is called a Fermi chopper (Fig. 23). The collimator may consist of a package of thin aluminum foils that are covered by Gadolinium layers. As long as the collimator is perfectly aligned to the beam, the neutrons pass through the aluminum without major attenuation. As soon as the chopped rotates a few degrees out of this position, the neutrons hit the Gadolinium and are adsorbed. Short pulse widths are obtained by high rotation speeds of 5000–30,000 rpm.

Fig. 23

Scheme of a Fermi chopper with a rotating collimator consisting of a pile of aluminum foils (white) and thin Gd layers (black). Left: open position, neutrons (orange) are only slightly attenuated by the aluminum. In the open position, the Gd layers are parallel to the beam and shade off only a small part of it (thin white lines on the right). Right: if the rotating collimator is only slightly inclined with respect to the open position, the neutrons hit the Gd foil and the beam is closed. Thereby a small duty cycle is obtained

Velocity selection principle

Generating monochromatic neutron beams by choppers or velocity selectors works somewhat like the green wave at a traffic light for cars. Two traffic lights are switched with the same frequency, but the second one is shifted by just the time a car needs to reach it starting with the prescribed speed at the first one. Only cars with the desired velocity pass without problems, the others have to stop at this second traffic light (the difference to neutrons is that cars with a wrong velocity should not just be absorbed and disappear and that the duty cycle of a traffic light should be higher than just a few percent as for a neutron chopper).

Figure 24 demonstrates the generation of pulsed monochromatic neutron beams for inelastic neutron scattering, since this technique has no analogy in optical or X-ray methods. The crystal monochromator transmitted higher refraction orders than 1, and thus shorter wavelengths. Velocity selectors and choppers suppress these higher orders, but choppers have some transmission for longer not shorter wavelengths than the selected one, and thus three instead of two pulse shaping devices are needed. In our example of the green wave, you can also pass through at somewhat less than half the speed, e.g., 20 instead of 50 km/h just skipping one green phase. This will not make the drivers behind you happy, but is not prevented by just two traffic lights. One needs a third light somewhere in between, which switches at the same frequency and in appropriate phasing with respect to the outer traffic lights to stop the car with half the speed. Similarly to the green wave for cars, two choppers also let neutrons pass with a lower than the desired velocity, which is a lower-order contamination. In variance to the high-order contamination at monochromator crystals, this problem can be sorted out by a third chopper in between. This is a major advantage with respect to wavelength determination at monochromator crystals.

Fig. 24