Weak diffracting beams

After 30 minutes of seeding, the DRl-MMA 35/65 sample was taken off from the prism, and we tried to measure the diffracted light from a He-Ne red laser (632.8 nm, Spectra Physics) with normal illumination onto the sample. No diffraction was observed, which can be explained by the fact that there is no refractive index grating as there is no difference in the refractive index between the domains where the azo molecules are oriented in the positive or negative sense. In the case of the diffraction of the Nd YAG laser observed also after 30 minutes of seeding were performed on a sample placed on a prism, the sample was taken from the prism and irradiated with the beam at the fundamental frequency (1.06 pm), We observed two weak diffracted beams at 532 nm wavelength, placed symmetrically around the central fundamental beam. 

In the early days of protein crystallography the determination of a protein structure was laborious and time consuming. The diffracted beams were obtained from weak x-ray sources and recorded on films that had to be manually scanned and measured. The available computers were far from adequate for the problem, with a computing power roughly equal to present-day pocket calculators. Computer graphics were not available, and models of the protein had to be built manually from pieces of steel rod. To determine the... 

Equation 10 can be interpreted as the aberrations of the objective lens multiplying the intensities of the diffracted beams by a phase factor sin[2(g)], which depends on the spatial frequency. Thus, in the WPOA, the observed image is proportional to the projected potential, but is modulated by the phase factor. Without the phase shift, j, due to the lens aberrations, a weak phase object would not be visible in HRTEM (this is analogous to the interpretation of equation 6). 

The intensities of diffracted beams, or reflections as they ate commonly called, depend upon the strength of the scattering that the material inflicts upon the radiation. Electrons are scattered strongly, neutrons weakly and X-rays moderately. The basic scattering nnit of a crystal is its unit cell, and we may calculate the scattering at any angle by mnltiplying... 

The third step in the structure determination is collection of the X-ray diffraction data. This may be done with a diffractometer in which a narrow collimated pencil source of X-rays is aimed at the crystal and the intensities and positions of the diffracted beams are measured automatically. The computer-controlled diffractometer is able to measure the angles to within less than one-hundredth of a degree. If sufficient time is allowed, very weak spots can be counted. Today, diffractometers are more likely to be used for preliminary measurements, while the major data collection is done with an area detector, an... 

Second, a single molecule is a very weak scatterer of X rays. Most of the X rays will pass through a single molecule without being diffracted, so the diffracted beams are too weak to be detected. Analyzing diffraction from crystals, rather than individual molecules, solves this problem. A crystal of a protein contains many ordered molecules in identical orientations, so each molecule diffracts identically, and the diffracted beams for all molecules augment each other to produce strong, detectable X-ray beams. 

Among the main difficulties with electron crystallography are (1) sample damage from the electron beam (a 0.1-A wave carries a lot of energy), (2) low contrast between the solvent and the object under study, and (3) weak diffraction from the necessarily very thin arrays that can be studied by this method. Despite these obstacles, cryoscopic methods (Chapter 3, Section V) and image processing techniques have made electron crystallography a powerful probe of macromolecular structure, especially for membrane proteins, many of which resist crystallization. 

Table I shows the calculated diffracted beam amplitudes for the (000), (002), (004) and (006) beams for both topologies, for a crystal 60 A thick. The principal difference between the intensities for the two structures lies in the intensity of the (004) beam relative to (006). [Note that in both cases the intensity of the central (000) beam is approximately the same and hence the intensities are approximately normalised with respect to each other thus allowing direct comparison]. In the case of the Imma structure the (004) beam is weak with respect to the (006) and hence the (006) must be included to resolve the satellite channels clearly. At a limited resolution of 3.5 A the (006) beam lies outside the objective aperture and hence the satellite channels are only very faint in the image. However, for the Cmcm model the relative intensities are reversed with the (004) beam stronger than the (006) and hence even if the (006) beam is excluded from the aperture the satellite channels will be clearly resolved.

Experimental setup for the measurement of stimulated Raman spectra. The distance. sris measured from the grating to the wall or viewing screen. The diffracted beams show the pattern of the beams involving the vi ring stretching vibration of benzene not shown are additional weak features that may be seen involving the VICH or CD stretching vibrations. 

Figure 5.19. Ewald sphere diagrams and corresponding diffraction patterns illustrating the procedures for setting up the conditions for weak beam dark field imaging using the first-order diffracted beam g. Continued, p. 160)...

Microdiffraction.—Perhaps more important than SAD techniques, particularly in the context of catalyst research, microdiffraction allows the user to benefit from the small probe size generated in STEM in the structural analysis of small particles and localized areas in thin foils. If the small probe is stopped on a particle, then clearly a transmission diffraction pattern will be observable after the beam has traversed the sample, provided we have the means available for its display. In CTEM such a pattern will, of course, be formed by the imaging system in a manner identical to SAD, but in STEM the pattern must be scanned across the detector. This is accomplished by means of a set of post-specimen scan coils which once more scan the diffracted beams across the axial bright-field detector. Such a pattern is shown in Figure 13 where a beam of approximately 10 A FWHM was stopped on a small second-phase particle during the omega-phase transformation in a Zr-Nb alloy. The relatively poor definition of the reflection is a consequence of both the convergent nature in the probe (necessary in order to obtain the smallest probe sizes) and a S/N limited by the available current in the probe. Nevertheless, weak reflections with half-order indices are clearly visible between the main alloy reflections and it is therefore possible to attempt structural... 

The shape of Bragg peaks is usually represented by a bell-like function -the so-called peak shape function. The latter is weakly dependent on the crystal structure and is the convolution of various individual functions, established by the instrumental parameters and to some extent by the properties of the specimen, see Table 2.7. The shape of each peak can be modeled using instrumental and specimen characteristics, although in reality ab initio modeling is difficult and most often it is performed using various empirically selected peak shape functions and parameters. If the radiation is not strictly monochromatic, i.e. when both Kai and Kaa components are present in the diffracted beam, the resultant peak should include contributions from both components as shown in Figure 2.39. 

However, this simple explanation of Talbot images still requires plane waves corresponding to a highly collimated and therefore weak input beam. The full intensity gain of the Talbot effect is only deployed when it is applied to uncollimated and therefore much more intense molecular beams [Clauser 1994 Brezger 2002], This is realized if the single diffraction grating is re-... 

Fluorescent screens are made of a thin layer of zinc sulfide, containing a trace of nickel, mounted on a cardboard backing. Under the action of x-rays, this compound fluoresces in the visible region, i.e., emits visible light, in this case yellow light. Although most diffracted beams are too weak to be detected by this method, fluorescent screens are widely used in diffraction work to locate the position of the primary beam when adjusting apparatus. 

There is an optimum specimen thickness for the transmission method, because the diffracted beams will be very weak or entirely absent if the specimen is either too thin (insufficient volume of diffracting material) or too thick (excessive absorption). As will be shown in Sec. 9-8, the specimen thickness which produces the maximum diffracted intensity is given by l/ i, where /t is the linear absorption coefficient of the specimen. Inspection of Eq. (1-10) shows that this condition can also be stated as follows a transmission specimen is of optimum thickness when the intensity of the beam transmitted through the specimen is 1 /e, or about j, of the intensity of the incident beam. Normally this optimum thickness is of the order of a few thousandths of an inch (0.1 mm). There is one way, however, in which a partial transmission pattern can be obtained from a thick specimen and that is by diffraction from an edge (Fig. 6-13). Only the upper half of the pattern is recorded on the film, but that is all that is necessary in many applications. The same technique has also been used in some Debye-Scherrer cameras. 

This method also involves reflection of Ka radiation in transmission, but there are two additional restrictions the crystal must be nearly perfect and fairly thick, such that fit has a value of the order of 10. We would then expect the transmission factor IJIo to be = 5 x 10 , so that the transmitted and diffracted beams would be too weak to detect. Very surprisingly, Borrmann [8.24] found that both beams were fairly strong, if the crystal were set at the exact Bragg angle 6g. The Borrmann effect is also called anomalous transmission. 

Diffractometer. The incident and diffracted beams make the same angle with the sheet surface, so that the hkl reflection is abnormally strong and all others weak or absent. 

On the technical side, synchrotron X-ray radiation is necessary for most protein complexes as they have large unit cells and weak diffraction patterns. It may be necessary to protect the crystds from the beam by freezing them this was particularly valuable for obtaining data from ribosome crystals. ... 

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