Direct geometry

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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. 

The low final energy has another consequence. In comparison with direct geometry instruments ( 3.4.3), the data from low final energy... 

Direct geometry instruments use choppers or crystal monochromators to fix the incident energy and they are found on both continuous and pulsed sources. To compensate for the low incident flux resulting from the monochromation process, direct geometry instruments have a large detector area. This makes the instruments expensive, they are generally twice the price of a crystal analyser instrument. At present, they are used infrequently for the study of hydrogenous materials, so we will limit our discussion to a chopper spectrometer at a pulsed source and a crystal monochromator at a continuous source. 

Fig. 3.25 Scattering triangles for a direct geometry instrument, (a) Detectors at different angles give different Q at constant energy transfer and (b) an individual detector measures energy transfer at constant Q.

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". ...

Fig. 3.30 Schematic of the direct geometry spectrometer IN4 at the ILL. Reproduced from [32] with permission from the Institut Laue Langevin.

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 simple analysis suggests that the double inelastic event is detrimental to the spectra collected on all instruments, whereas the (elastic + inelastic) case is detrimental only for direct geometry instruments. This is true even for powder samples, since the magnitude of the momentum transfer is also lost. This contamination is most problematic for data obtained from the low scattering angle detectors. The data in these detectors are nominally obtained at low Q but multiple scattering injects high Q information into their data. 

MERUN ISIS (UK) Direct geometry 0-4000 2-4 Successor to HET. Operational 2005 [37]... 

J-PARC (Japan) Direct geometry Proposed for 2007 start of J-PARC ... 

The ratio of the intensity of an overtone to its fundamental is given by the effective mass, men, which increases as extra vibrational contributions increase the total displacements of the scattering atoms. Ultimately, the effective mass, Weff, may be quite different from the oscillator mass, /Xy. This is related to, but subtly different from, effects observed on direct geometry spectrometers ( 5.3.2). 

Molecular systems using a direct geometry spectrometer... 

The special case of liquid helium allows us to present one aspect of direct geometry spectroscopy in particular. Since helium atoms interact so weakly, there are almost no restoring forces in the liquid and only the conservation of momentum plays a significant role in its INS spectrum. The spectrum of a mixture of liquids He and He is shown in Fig. 5.9 [21], as can be seen from the figure it consists of two continuous traces. The first response, with a slope of 5.6, is from the light isotope of helium, He. The second response, of slope 4.2, is from the common isotope of helium, mass four. (The ratio of the slopes is 4.2/5.6 = 3/4.) There are no excitations in the spectrum and the observed response is the result of atomic recoil. 

The INS spectrum of rubidium hexahydridoplatinate(IV), Rb2[PtH6], obtained on the direct geometry spectrometer MARI, is given in Fig. 5.10. As anticipated from the considerations presented above the spectrum consists of a series of ridges, all relatively well-defined in energy but broad as a function of Q. The point where the scattering reaches a maximum (as a function of Q) defines the mass-line that joins that point to the origin, for an effective mass, /Weff. 

Fig. 5.10 The INS spectrum of Rb2[PtH]j, taken on a direct geometry spectrometer (MARI, ISIS) [20]. Showing the ridges that are due to the variation of band intensities with momentum and energy transfer.

It is stressed that spectral contamination of transition intensities is a common feature of INS data at all energy transfers and on all types of instrument. It arises from the spectral congestion typical of molecules (even those as simple as benzene) and the effects of phonon wings. The effects of congestion can be exacerbated on direct geometry spectrometers if their energy resolution is not good. 

The impact of phonon wings on the spectra observed on direct geometry spectrometers can be as taxing as their effects on indirect geometry spectrometers at the same Q values. The spectrum of Rb2[PtH6]... 

Direct geometry spectrometers have better access to low Q regimes at higher energy transfers than low-bandpass spectrometers and this is a considerable advantage. At low Q the phonon wing has not yet developed and its contaminating effects are much reduced. 

The observed transitions can be used to parameterise the potential, either according to simple models or, in terms of the symmetry adapted spherical harmonics for the most general potential [51]. The advantage of this approach is that the wavefimctions of the hydrogen in its excited states can be extracted. Further the full form of the Scattering Law (see Fig. 2.4) for any transition can be calculated. These can be compared with those observed on direct geometry spectrometers ( 5.3.2.1) [64]. 

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