Direct methods, diffraction

With XRD applied to bulk materials, a detailed structural analysis of atomic positions is rather straightforward and routine for structures that can be quite complex (see chapter B 1.9) direct methods in many cases give good results in a single step, while the resulting atomic positions may be refined by iterative fitting procedures based on simulation of the diffraction process. 

Noncrystalline domains in fibers are not stmctureless, but the stmctural organization of the polymer chains or chain segments is difficult to evaluate, just as it is difficult to evaluate the stmcture of Hquids. No direct methods are available, but various combinations of physicochemical methods such as x-ray diffraction, birefringence, density, mechanical response, and thermal behavior, have been used to deduce physical quantities that can be used to describe the stmcture of the noncrystalline domains. Among these quantities are the amorphous orientation function and the amorphous density, which can be related to some of the important physical properties of fibers. 

Cristobalite in respirable airborne dust Lab method using X-ray diffraction (direct method) 76... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

The relative stereochemistry of stephadiamine (16) was clarified by X-ray diffraction analysis, using the direct method, and the absolute configuration was solved by the heavy-atom method, using the N-p-bromobenzoyl derivative (6). Stephadiamine (16), a C-norhasubanan alkaloid, is not regarded as a hasubanan congener in the strict sense, but as a new member of oe-amino acid derivatives (6). 

In agreement with the Hiickel rule those annulenes and dehydroannulenes which contain (4 n + 2) 77 electrons and a reasonably planar carbon skeleton appear to be aromatic. Aromaticity in annulenes is usually equated with positive resonance energy and the absence of bond alternation. The most direct method of measuring bond alternation is by single crystal X-ray diffraction. Unfortunately this method has been applied in only a few cases. 

The three dimensional structure was obtained by means of single crystal X-ray diffraction. CuKa radiation, a graphite monochromator, and a photomultiplier tube were used to collect 1825 total reflections on an automated diffractometer. Of these, 1162 were used for the analysis. Figure 2 shows a computer generated drawing of halcinonide. The position of the chlorine atom was not clear from the Patterson map, but the direct method program "MULTAN" gave its position. 

The relatively recent development27 of the direct methods of crystal structure analysis has produced a great increase in the number of crystal structures reported in the literature, particularly with regard to the possible hydrogen bonds (also for biological molecules). Hence, the classical spectroscopic data on hydrogen bonding in solution are backed up by X-ray diffraction analysis data. 

Stmcture determination of unknown crystals by electron diffraction was performed by several research groups, on Al-Fe alloys by Gjonnes et al. (1998), on metal-cluster compounds by Weirich et al. (2000) and on zeolites by Wagner et al. (1999). Selected area electron diffraction or electron diffraction collected by a precession technique were used and the structure factor phases were deduced by direct methods, Patterson method or from convergent beam electron diffraction. 

The use of blank-disc CBED patterns for solving crystal stmctures by electron diffraction (in conjunction with direct methods for the phase problem) would seem to have many advantages ... 

Direct methods are also applicable in electron diffraction, however, the dynamic nature of the recorded structure factors needs to be taken into account. When structure factors from strong reflections were determined... 

Figure 15. Crystal structure of a-Tl2Se solved in projeetion via direct methods using quantified intensities from the selected area electron diffraction pattern shown in (a) [film data]. The potential map (E-map) in (b) was used to eonstruet an initial structural model which was later improved by kinematical least-squares (LS) refinement (c). Note that the potential of the selenium atoms in (c) appear after LS-refinement somewhat stronger than the surrounding titanium atoms (see the structural model in figure lOd). The average effective thiekness of the investigated thiekness of the crystal is about 230 A [22].

One way to solve such stmctures is to collect electron dififraction patterns from difierent zone axes of the crystal to get an essentially complete 3D electron diffraction data set. Direct methods or the Patterson method can then be applied to phase the data, similar to what is done in X-ray diffraction (Gjonnes et al., 1998 Gemmi et al., 2000 Wagner et al., 1999). 

As a stmcture becomes more complex and the number of unique atoms increases, phases derived by direct methods become less reliable, especially when the electron diffraction data deviate from the kinematical approximation because of dynamic effects. HREM combined with crystallographic image processing provides a unique method for determining such stmctures. HREM images from a number of projections along different zone axes may be combined into a 3D potential map. 

To solve a crystal structure by direct methods, difficult data are those which are incomplete in the sampling of reciprocal space, have non-atomic i.e. < 1.3A resolution) and are noisy with large (systematic) errors in the data measurements. As we have seen, this definition spans many electron diffraction data sets, but there are some of sufficient quality that they can be solved routinely using conventional direct methods packages. Often these are of inorganic materials or intermetallic compounds that are relatively resistant to radiation damage. 

Case study 2 Structural solution of zeolite from electron diffraction data, with a help of (a) Direct method, and (b) Patterson Map... 

Most of the applications of electron diffraction intensities for structure analysis rely on a kinematical approximation and thus do not account for the effects of dynamical multiple diffraction. The use of intensities which may be strongly perturbed by multiple scattering results in many cases in poor or misleading structure indications in the direct methods results. One approach which can be shown to reduce dynamical effects somewhat is to use precession electron diffraction (RED) [67] which involves conical rotation of the incident beam about a zone axis direction and thus avoids the strongly dynamical direct zone axis orientation. Although the intensities collected with this technique are still significantly perturbed by dynamical effects [68, 69] results obtained by this approach for zeoHtes are encouraging [70-72]. 

The phase problem of X-ray crystallography may be defined as the problem of determining the phases ( ) of the normalized structure factors E when only the magnitudes E are given. Since there are many more reflections in a diffraction pattern than there are independent atoms in the corresponding crystal, the phase problem is overdetermined, and the existence of relationships among the measured magnitudes is implied. Direct methods (Hauptman and Karle, 1953) are ab initio probabilistic methods that seek to exploit these relationships, and the techniques of probability theory have identified the linear combinations of three phases whose Miller indices sum to... 

No direct method exists by which monolayer film structures on water can be studied. Therefore, the LB method has been used to study molecular structures in past decades. The most useful method for investigating the detailed LB-deposited film structure is the well-known electron diffraction technique (or the scanning probe microscope [Birdi, 2002a]). The molecular arrangements of deposited mono-and multilayer films of fatty acids and their salts, using this technique, have been reported. The analyses showed that the molecules were almost perpendicular to the solid surface in the first monolayer. It was also reported that Ba-stearate molecules have a more precise normal alignment compared to stearic-acid monolayers. In some investigations, the thermal stability of these films has been found to be remarkably stable up to 90°C. 

A variety of techniques have been used to determine the extent of crystallinity in a polymer, including X-ray diffraction, density, IR, NMR, and heat of fusion [Sperling, 2001 Wunderlich, 1973], X-ray diffraction is the most direct method but requires the somewhat difficult separation of the crystalline and amorphous scattering envelops. The other methods are indirect methods but are easier to use since one need not be an expert in the field as with X-ray diffraction. Heat of fusion is probably the most often used method since reliable thermal analysis instruments are commercially available and easy to use [Bershtein and Egorov, 1994 Wendlandt, 1986], The difficulty in using thermal analysis (differential scanning calorimetry and differential thermal analysis) or any of the indirect methods is the uncertainty in the values of the quantity measured (e.g., the heat of fusion per gram of sample or density) for 0 and 100% crystalline samples since such samples seldom exist. The best technique is to calibrate the method with samples whose crystallinites have been determined by X-ray diffraction. 

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