Indirect geometry instruments

Instruments that work with any fixed final energy are conventionally known as indirect geometry instruments. However, we shall limit our consideration to those spectrometers with low final energies. They are remarkably simple to design, relatively cheap to build, easy to operate and have an output, which is both similar to optical spectra and easily compared to calculation. They are ideally suited to exploitation by the chemical and biological scientific communities. 

Indirect geometry spectrometers have no requirement (within the limitations implied by the use of S (Q,a ), 2.5.1) to calibrate detector efficiencies, on either continuous or pulsed sources (compare 3.4.3). Since the final energy of the neutrons never varies the detection efficiency is constant. Variations arising from differing discrimination levels ( 3.3.2) could play a significant role, except that (on low final energy instruments) all detectors follow almost the same path in Q,o ) space ( 3.4.2.3). Occasionally there is a need to calibrate the detected intensity in respect of the sample mass and standard analytical chemical techniques can be readily adapted to this circumstance. 

Graphite filters work on exactly the same principles but their cut-off is at even lower energy, ca 12 cm , but is less discriminating and should be operated in conjunction with beryllium. The filter materials are compared in Fig. 3.13. 

The incident energy is selected stepwise across the spectrum and, since the final energy is fixed below 40 cm, the energy transfer is obtained. This is the working principle of the spectrometer INlBeF [16] at the ILL, which was, for many years, the best spectrometer for neutron vibrational speetroscopy. 

An increase in sensitivity (x 4) is planned by the use of a double focussing monochromator, where many small crystals will be arranged on a curved surface, analogous to a parabolic mirror. This will provide an incident flux of almost 10 neutrons cm s . 

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For INS spectroscopy there are three main types of spectrometer in use triple axis ( 3.4.1), which is rarely used to study hydrogenous materials more relevant are instruments that fix the final energy which are known as indirect geometry instruments and those that fix the incident energy which are known as direct geometry instruments. Examples of indirect geometry ( 3.4.2, filter and analyser) spectrometers and direct geometry ( 3.4.3, chopper) instruments are discussed in turn. 

As shown in Fig. 3.24, and implied by Eq. (3.18), the trajectory through (Q,a>) space is almost independent of the scattering angle. This is the trajectory taken by all indirect geometry instruments that have fixed low final energies, say less than 40 cm", and applies regardless of the techniques used to define the final energy... 

Fig. 3.26 Trajectories in (Q,a>) space for a direct geometry spectrometer with detectors at angles 3, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 and 135° and with an incident energy of 4000 cm. The dashed lines are the trajectories of an indirect geometry instrument (low-bandpass) using scattering angles of 45 (long dashes, forward scattering)) and 135° (short dashes, backscattering) and a final energy of 28 cm". ...

Clearly both types of instruments are highly complementary and both have strengths and weaknesses. Ideally, the same sample would be run first on an indirect geometry instrument which would provide a rapid, but still fairly detailed overview of the subject. In many instances this would be sufficient. Subsequent measurements on a direct geometry instrument would allow detailed aspects of the spectroscopy to be probed. Table 3.2 gives a list of INS (excluding triple axis) spectrometers that have recently been in operation, are in operation, or are planned. 

This is a much less serious problem for indirect geometry instruments with low final energies. These spectrometers work close to the maximum... 

The Debye-Waller factor, that suppresses all neutron intensities ( 2.5.1.2), is strongly temperature dependent and INS measurements are generally carried out at 30K, or less, this is almost mandatory on indirect-geometry low final energy instruments. As an example, Fig. 3.32 shows the spectrum of perdeuteropolyethylene at room temperature and... 

AE/E 3.14 relative energy transfer uncertainty (instrumental resolution of indirect geometry spectrometers) ... 

D SPNs, and stochastic fractal geometry, would enable us to dispense with indirect laboratory measurements which require expensive instruments. 

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