Diffraction geometry resolution

Fig. la. Laue diffraction geometry showing the accessible region of reciprocal space between the Ewald spheres associated with and and the sample resolution limited d . O is the origin of of reciprocal space, b. A ray with n orders inside the d in sphere can have a recorded multiplicity m < n where (n — m) RLPs are outside the accessible region. The diagram shows the case of n = 5 and m = 2. Only the upper section of the volume of resolution of the accessible region is shown. (From [9])... 

Figure 7.2 (a) Laue diffraction geometry showing the accessible region of reciprocal space between the Ewald spheres associated with Amin and Amax and the sample resolution limit d ax O is the origin of reciprocal space. 

Good semi-quantitative agreements are found in diffraction patterns and proposed models obtained by molecular-dynamics[14], because the results of the ex-periments[31-34] are consistent with the atomic models proposed by us[14]. However, in the present state of high-resolution electron microscopy, taking into account, moreover, the number of sheets and the complicated geometry of the helix, it seems unlikely to directly visualize the pentagon-hexagon pairs. 

When low-temperature studies are performed, the maximum resolution is imposed by data collection geometry and fall-off of the scattered intensities below the noise level, rather than by negligible high-resolution structure factor amplitudes. Use of Ag Ka radiation would for example allow measurement of diffracted intensities up to 0.35 A for amino-acid crystals below 30 K [40]. Similarly, model calculations show that noise-free structure factors computed from atomic core electrons would be still non-zero up to O.lA. 

Scolecite gave the opportunity to relate the electron density features of Si-O-Si and Si-O-AI bonds to the atomic environment and to the bonding geometry. After the multipolar density refinement against Ag Ka high resolution X-ray diffraction data, a kappa refinement was carried out to derive the atomic net charges in this compound. Several least-squares fit have been tested. The hat matrix method which is presented in this paper, has been particularly efficient in the estimation of reliable atomic net charges in scolecite. 

The concept of resolution in AFM is different from radiation-based microscopies because AFM imaging is a three-dimensional imaging technique. There is an important distinction between images resolved by wave optics and those resolved by scanning probe techniques. The former is limited by diffraction, whereas the latter is limited primarily by apical probe geometry and sample geometry. Usually the width of a DNA molecule is loosely used as a measure of resolution, because it has a known diameter of 2.0 nm in its B form. 

Figure 7.5 shows images of a Pd/AI2CF catalyst in bright and dark field mode. In the latter, the geometry was chosen such to selectively detect the (111) and (200) diffraction rings of Pd. Features indicated by arrows clearly demonstrate the better contrast and resolution of the dark field image [14],... 

Comparisons of the measured coupling constants to the geometry of the H-bond are hampered by the limited availability of very high-resolution diffraction data. Especially, no crystallographic data are available for most of the nucleic acids for which H-bond cou-... 

In this chapter we discuss double-crystal topography, in which we obtain a map of the diffracting power of a crystal compared to that of a reference. We first treat the principles and geometries, the mechanisms of image contrast and resolution and the ttse of laboratory and synchrotron radiation. We then discuss applicatiorrs wafer inspection, strain contour mapping, topography of curved crystals. 

---