Triangular monochromator

Fig. 15. A Weissenberg photograph of (o-amino acid pyruvate aminotransferase (mercury derivative). A single bent triangular Si(lll) monochromator and a Weissenberg camera for macromolecular crystallography were used. The oscillation angle 30° the radius of the camera 287 mm, exposure time 4.7 min...

Fig. 23. Schematic design of a double focussing mirror-monochromator camera at DORIS The middle of the mirror is at 20 m from the source point. A bent, triangular monochromator crystal is used for horizontal focussing and a segmented mirror (quartz) for vertical focussing. The ionization chamber is designated by-I-...

A triangular bent Ge(l 11) monochromator and a segmented quartz mirror are used as optical elements. The fixed wavelength of 1.5 A which is obtained for a monochromator angle of 26.5° is a compromise between the transmission of Beryllium used as a window material, the efficiency of gasfilled detectors and -especially for biological samples — the transmission of water. 

Greenhough, T. J., Helliwell, J. R., and Rule, S. A. Oscillation camera data processing. 3. General diffraction spot size, shape and energy profile formalism for polychromatic diffraction experiments with monochromatized synchrotron X-radiation from a singly bent triangular monochromator. J. Appl. Cryst. 16, 242-250 (1983). 

The source size varies for the different synchrotrons. At SRS it is 9.9 mm (horizontal) and 0.3 mm (vertical). Since the sample is about 20 m away, careful attention to monochromatisation and focussing optics is required so that the source size matches the crystal size. A curved crystal monochromator which is based on a triangular shaped crystal plate and uses germanium (111) reflection was first described by Lemonier et al. [225] at LURE. Similar focussing monochromators are now in use... 

The second optical element is a triangular Ge (111) monochromator with an oblique cut of 10.5° placed approximately 10 m from the mirror. The monochromator can be bent to provide a vertical demagnification of the source of approximately 10 1 in the horizontal direction at the camera. The wavelength used in the experiments described below was usually 1.488 A or 1.608 A. The wavelength spread, AX/X, was typically 10-3. The arrangement on the wiggler station is similar. 

An oscillation camera film data collection facility has been established at Stanford. This station (beam line VI1-1) uses 1 mrad of beam from an eight-pole multipole wiggler (Winick and Spencer 1980). The optics consists of a bent Ge(lll) triangular monochromator followed by a bent metal coated mirror. The small number of available mrad of beam is easily compensated by the number of poles in the wiggler. The station has been used extensively. Examples of structures reported using data collected on this station are given in chapter 10. 

Table 6.1. Instrument smearing effects Example instrument settings based on a bent triangular monochromator (section 5.2.3) focussing in the horizontal plane and a horizontal rotation axis of the crystal sample. 

When a spectrum is measured on a dispersive instrument, the true spectrum is convolved with the instrumental line shape (ILS) of the monochromator, which is the triangular slit function. The situation with the FT technique is equivalent, except that the true spectrum is convolved with the (sinx)/x function (no apodization) or with the FT of an appropriate apodization function. Hence, FT instruments offer a free choice of ILS according to the apodization selected and thus make it possible to optimise the sampling condition for a particular application. 

Fig. 9. Spectral power distribution for 77,200 1/4 m Monochromator with various slits. This is for a spectrally flat source uniformly filling the input. Note the shape is triangular and not the rectangular profile one might intuitively expect (29).

To compute the convolution of these two functions, Eq. 2.19 requires that/(v) be reversed left to right [which is trivial in this case, since/(v) is an even function], after which the two functions are multiplied point by point along the wavenumber axis. The resulting points are then integrated, and the process is repeated for all possible displacements, v, of/( relative to B v). One particular example of convolution may be familiar to spectroscopists who use grating instruments (see Chapter 8). When a low-resolution spectrum is measured on a monochromator, the true spectrum is convolved with the triangular slit function of the monochromator. The situation with Fourier transform spectrometry is equivalent, except that the true spectrum is convolved with the sine function/(v). Since the Fourier transform spectrometer does not have any slits,/(v) has been variously called the instrument line shape (ILS) Junction, the instrument function, or the apparatus function, of which we prefer the term ILS function. 

The FWHH criterion is more usefiil for monochromators with a triangular sht function than for I f-IR spectrometers. Two triangularly shaped lines of equal intensity and half-width are not resolved until the spacing between the fines is greater than the FWHH of either line [5,6]. The FWHH of a fine whose shape is a sine function given by Eq. 2.18 is 0.605/A, but two lines with sine x lineshapes are not resolved when they are separated by this amount. In practice, a dip of approximately 20% is found when the two fines with a sine x ILS are separated by 0.73/A, as shown in Figure 2.6c. 

No matter what type of spectrometer is used, a measured spectrum is always slightly different from the true spectrum because of the measurement process, and it is important to recognize that instrumental effects often determine how well Beer s law is obeyed for any chemical system. For example, when a monochromator is used to measure a spectrum, the true spectrum is convolved with the spectrometer s slit function. The effect of this convolution is to decrease the intensity and increase the width of all bands in the spectrum. The convolution of Lorentzian absorption bands with a triangular slit function was reported over 50 years ago in a classic paper by Ramsay [1]. Ramsay defined a resolution parameter, p, as the ratio of the full width at half-height (FWHH) of the slit function to the true FWHH of the band. He showed how the measured, or apparent, absorbance, A, at the peak of a Lorentzian band varied as a function of the true peak absorbance, peak> resolution parameter. Not surprisingly, Ramsay showed that as... 

The series of curves shown in Figure 8.3 is quite similar to the corresponding series of curves calculated by Ramsay for a monochromator with a triangular slit function. However, with the triangular apodization function, the slope of the plot of log A pg versus log Ap j can be as small as indicating that Ap can vary as (Ap j ) when Apg is very large. 

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