X-ray diffraction from crystals

When Max Planck wrote his remarkable paper of 1901, and introduced what Stehle (1994) calls his time bomb of an equation, e = / v , it took a number of years before anyone seriously paid attention to the revolutionary concept of the quantisation of energy the response was as sluggish as that, a few years later, whieh greeted X-ray diffraction from crystals. It was not until Einstein, in 1905, used Planck s concepts to interpret the photoelectric effect (the work for which Einstein was actually awarded his Nobel Prize) that physicists began to sit up and take notice. Niels Bohr s thesis of 1911 which introduced the concept of the quantisation of electronic energy levels in the free atom, though in a purely empirical manner, did not consider the behaviour of atoms assembled in solids. 

Bragg s Law (Equation 1-11) is obeyed so well that it is possible to use x-ray diffraction from crystals for highly precise determinations either of d or of A. The former type of determination is basic in establishing crystal structure. 

Watanabe, N., Semi-automatic protein crystallisation system that allows in situ observation of X-ray diffraction from crystals in the drop. Acta CrystaUogr. 2002, D58, 1527-1530. 

Striking confirmation of the cubic structures of BP I and BP II was obtained by Onusseit and Stegemeyer and others, who succeeded in growing beautiful single crystals of up to a few hundred microns in size (fig. 4.8.2(a)). Optical Kossel diagrams, analogous to the Kossel lines observed in X-ray diffraction from crystals, have confirmed their symmetry (fig. 4.8.2(f))). 

Figure 2.7. X-ray diffraction from crystal planes or smectic layers.

X-ray diffraction from crystals provides one of the most accurate ways of determining Avogadro s number. Silver crystallizes in a face-centered cubic lattice with all atoms at the lattice points. The length of an edge of the unit cell was determined by x-ray diffraction to be 408.6 pm (4.086 A). The density of silver is 10.50 g/cm. Calculate the mass of a silver atom. Then, using the known value of the atomic weight, calculate Avogadro s number. 

The structure of the metallocene cation energy minimised with the Car-Parrinello method agrees well with the experimentally obtained crystal structures of related complexes. Typical features of the structure as obtained from X-ray diffraction on crystals of very similar neutral complexes (e.g., the dichlorides), such as small differences in distances between C atoms within a cyclopentadienyl (Cp) ring, as well as differences in distances between the C atoms of the Cp ring and the Zr atom, were revealed from the simulations. 

J.S. Wark, R.R. Whitlock, A. Hauer, J.E. Swain, and P.J. Solone, Short-Pulse X-Ray Diffraction from Laser-Shocked Crystals, in Shock Waves in Condensed Matter 1987 (edited by S.C. Schmidt and N.C. Holmes), Amsterdam, 1988, pp. 781-786, Elsevier Science. 

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. 

In the three-dimensional stmcture of actin, the environment of the phosphate moiety of the nucleotide appears roughly the same when CaADP or CaATP is bound. This observation argues against two different conformations. The reason why this is so is unclear. However, it must be stressed that the three-dimensional stmcture is derived from X-ray diffraction of crystals of the DNasel-actin complex, which, like G-actin, is unable to hydrolyze ATP. The conformation obtained may therefore correspond to G-actin frozen in the G-ATP state independently of the bound nucleotide. Stmctural studies in conjunction with site-directed mutagenesis experiments should eventually solve this problem. 

The crystal structures of four chlorinated derivatives of di-benzo-p-dioxin have been determined by x-ray diffraction from diffractometer data (MoKa radiation). The compounds, their formulae, cell dimensions, space groups, the number of molecules per unit cell, the crystallographic B.-factors, and the number of observed reflections are given. The dioxin crystal structures were performed to provide absolute standards for assignment of isomeric structures and have been of considerable practical use in combination with x-ray powder diffraction analysis. 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

The use of X-ray diffraction from crystalline samples can result in a complete three-dimensional crystal structure of a molecule, but requires a single crystal suitable for proper diffraction (see Section 3.3). X-ray absorption spectroscopy (XAS) can yield limited molecular structural information on noncrystalline (amorphous) solid... 

Unlike simple inorganic compounds (e.g., NaCl or KC1), polymers do not have a perfectly ordered crystal lattice formation and are not completely crystalline. In fact, they contain both crystalline and amorphous regions. Hence, the X-ray diffractions from them are found to be a mixture of sharp as well as diffused patterns. 

X-ray diffraction from crystalline samples can result in a complete three-dimensional crystal structure of a molecule, but requires a single crystal suit-... 

Table I. Comparison of the X-Ray Diffraction from PBT Fiber and Crystal-Solvate...

For high-throughput data collection, sample centring via loop detection is currently the method of choice for placing crystals in the X-ray beam. Alternative methods rely on the direct detection of the crystal itself by monitoring the intensity of either X-ray diffraction from the crystal or X-ray fluorescence from an element in the crystal that is not present in the cryoprotectant (Pohl et al., 2004). Both of these approaches have drawbacks. First, some of the limited X-ray lifetime of the crystal (Section 12.6) must be committed to detection instead of data collection. Second, the loop itself has to be placed close to the X-ray beam prior to crystal detection, followed by step-wise translation of the crystal through the beam, thereby increasing the time required to centre the sample. 

The structures of iron oxides have been determined principally by single crystal X-ray diffraction or neutron diffraction with supplementary information coming from infrared spectroscopy, electron diffraction and high resolution electron microscopy. A few years after the first successful application of X-ray diffraction to crystal structure determination, this technique was used to establish the major features of the structures of magnetite (Bragg, 1915 Nishikawa, 1915) and hematite (Bragg Bragg, 1918). 

In X-ray diffraction one is interested in exploring the intensity of X-rays diffracted from the crystal planes. Note that the Bragg equation does not contain information about the scattered intensity from a given plane. It only provides the... 

Reaction Time. The rate of formation of to at reflux temperature is illustrated in Figure 2. The rate was estimated by taking samples from the reaction mixture at various times and examining them by x-ray diffraction. The crystallization is characterized by an unusually long induction period of about 13 hr, which is followed by a relatively slow crystal growth. No alteration of the zeolite was observed during an extra 50 hr reaction time after crystallization had been completed. 

While X-ray diffraction single-crystal data must always be the most accurate method for structure determination of copper(I) complexes in the solid state,18 useful information can be obtained from other techniques. In general the stoichiometry m of a complex will provide... 

The structures of several proteins have been solved by both NMR in solution and x-ray diffraction from the crystal, and the correspondence is excellent. Sometimes there are discrepancies at the contacts between neighboring molecules in the crystal lattice. Crystal packing can lead to such problems. 

In this study, in order to better understand the fundamentals of the laser-cluster interaction, we have carried out systematic investigations of the properties of X-ray radiation from high-density and high-temperature cluster plasma created by the action of superintense laser irradiation. The interrelationship between the X-ray radiation properties and ion kinetic energies has been examined for the first time via simultaneous measurements of X-ray radiation spectra and ion energy spectra. The time scale and mechanism of the X-ray emission process are discussed here based on a time-dependent plasma kinetics model. Moreover, in order to demonstrate the practical capabilities of the X-rays thus produced, pulse X-ray diffraction from an Si crystal using this source has been examined. 

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