Crystal Structure by X-Ray Diffraction

The object of this experiment is to determine the crystal structure of a solid substance from x-ray powder diffraction patterns. This involves determination of the symmetry classification (cubic, hexagonal, etc.), the type of crystal lattice (simple, body-centered, or face-centered), the dimensions of the unit cell, the number of atoms or ions of each kind in the unit cell, and the position of every atom or ion in the unit cell. Owing to inherent limitations of the powder method, only substances in the cubic system can be easily characterized in this way, and a cubic material will be studied in the present experiment. However, the recent introduction of more accurate experimental techniques and sophisticated computer programs make it possible to refine and determine the structnres of crystals of low syimnetiy from powder diffraction data alone. 

Knowledge of the crystal structure permits determination of the coordination munber (the munber of nearest neighbors) for each kind of atom or ion, calculation of interatomic distances, and elucidation of other structural featmes related to the nature of chemical bonding and the imderstanding of physical properties in the solid state. 

A perfect crystal constitutes the repetition of a single very small imit of structme, called the unit cell, in a regular way so as to fill the volume occupied by the crystal (see Fig. 1). 

A ciystal may for some purposes be described in terms of a set of three crystal axes a, b, and c, which may or may not be of equal length and/or at right angles, depending on the syimnetiy of the crystal. These axes form the basis for a coordinate system with which the crystal may be described. An important property of crystals, known at least a centrrry before the discovery of X rays, is that the crystal axes for any crystal can be so chosen that all crystal faces can be described by eqrratiorrs of the form 

The crystal axes for a given crystal may be chosen in many different ways however, they are conventionally chosen to yield a coordinate system of the highest possible symmetry. It has been found that crystals can be divided into six possible systems on the basis of the highest possible symmetry that the coordinate system may possess as a result of the symmetry of the crystal. This symmetry is best described in terms of symmetry restrictions governing the values of the axial lengths a, b, and c and the interaxial angles a, (3, and y. 

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H. Yang and A. Natansohn, Macromolecules, 25, 5331 (1992). Polyamines from Ter-ephthalaldehyde and Aliphatic Diamines. 2. Studies of the Crystal Structure by X-Ray Diffraction. 

With sufficiently large crystals of the bacterial reaction centers available, the determination of crystal structure by X-ray diffraction became possible and in 1983, Deisenhofer, Epp, Miki, Huber and Michel determined tbe crystal structure of the Rp. viridis reaction centers at 3 A resolution [later refined to 2.3 A ]. From the electron-density map, the spatial arrangement of the polypeptide subunits, the pigment molecules and the electron carriers in the reaction center was determined. For this work, Deisenhofer, Michel and Huber were awarded the Nobel Prize in 1988. 

Glycogenin and the mutant proteins, Phel94 and Thrl94, could also transfer glucose from UDP-Glc to maltose to form maltotriose." However, no further conversion to a higher oligosaccharide occurred. Analysis of the crystal structure by X-ray diffraction indicated that glycogenin existed similar to dimers." ... 

Illustration of the closepacking of two types of motifs, such as the Na" " and cr ions in NaCI as proposed in 1898 just before it became possible to analyse crystal structures by X-ray diffraction. 

Structure of B12 Derivatives. Analysis of crystal structures by X-ray diffraction not only provided the chemical nature of 1, but also revealed the structure and organometallic nature of coenzyme B12 (2). In such complete ... 

Ferrocene We have recently found that DCA forms inclusion compounds with ferrocene and its derivatives. Particularly DCA-ferrocene inclusion compound is very easy to get a large crystal enough to analyze the crystal structure by X-ray diffraction method. It was found from the analysis of a single crystal that ferrocene molecules are tightly accommodated into a DCA canal in an array different from those of crystals of ferrocene itself [18]. It was also ascertained that DCA-ferrocene inclusion compounds are doped with iodine. On the other hand, apoCA does not form an inclusion compound with ferrocene itself, but with its derivatives. 

The study of crystal structure by x-ray diffraction is discussed in Chapter 11. 

The determination of crystal structure by x-ray diffraction is one of the most important ways of determining the structures of molecules. Because of its ordered structure, a crystal consists of repeating planes of the same kind of atom. These planes can act as reflecting surfaces for x rays. When x rays are reflected from these planes, they show a diffraction pattern, which can be recorded on a photographic plate as a series of spots (see Figure 11.47). By analyzing the diffraction pattern, you can determine the positions of the atoms in the unit cell of the crystal. Once you have determined the positions of each atom in the unit cell of a molecular solid, you have also found the positions of the atoms in the molecule. ... 

A novel crystalline form of the boron-containing antibacterial drug (5 )-3-(aminomethyl)-7-(3-hydroxypropoxy)benzo[c][l,2]oxaborol-l(3H)-ol hydrochloride has been studied by solid-state NMR and single-crystal X-ray diffraction techniques. After determination of the crystal structure by X-ray diffraction, solid-state NMR spectroscopy of this form is performed to obtain structural information using experimental approaches based on dipolar correlation, chemical shift analysis, and quadrupolar interaction analysis. solid-state NMR experiments at 16.4 T using MAS and homonuclear dipolar decoupling, 2D solid-state NMR experiments based on and dipolar heteronuclear correlation, and DFT... 

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