Crystallography crystal systems

The list of alternate symbols arises because at an earlier stage in the history of X-ray crystallography, it was the accepted convention to call the unique axis b. The reader can easily see that if this is done, the alternate symbols become correct. Since in the other crystal systems with a unique direction (i.e., tetragonal and hexagonal) the unique direction is called c, the formally correct practice is now to do the same for the monoclinic system. However, the literature is still replete with the old choice of axes and it is necessary to be cognizant of both systems and of their relationship. 

Creutzfeldt-Jakob disease 248 Crick, Francis H. C. 84, 200 Cristae of mitochondria 14 Crossing-over 18 Crosslinking 79 Crotonase. See Enoyl hydratase Crowfoot Hodgkin, Dorothy M. 84 Cruciform structure in nucleic acids 229 Crustacea 24 Cruzain 619 Cryoenzymology 469 elastase 616 Cryoprotectants 191 Crystallins 169 Crystallography 131-137 electron 131 X-ray 132-137 Crystals, liquid 392-394 Crystal systems 133 Cubic symmetry... 

Figure 7.18 shows the information provided by the International Tables for X-Ray Crystallography, Volume I (and also the newer Volume A) for that most frequent and popular of space groups for organic crystals, P2i /c. The top line in Fig. 7.18 identifies the crystal system (monoclinic), the full international symbol (P 1 2 /c 1), which says that the lattice is primitive (P), that along the... 

The description of the shape of crystals (their morphology) is the subject of the science of crystallography. Crystals are divided into six systems, on the basis of their symmetry ... 

Table 1.17. The 230 crystallographic space groups arranged according to seven crystal systems and 32 crystallographic point groups as they are listed in the International Tables for Crystallography, vol. A. The centrosymmetric groups are in bold, while the non-centrosymmetric groups that do not invert an object are in italic. The remaining are non-...

Deviations from the standard are most often observed in the monoclinic crystal system, because there are many different ways that result in a nonstandard setting in this crystal system. This uncertainty is even reflected in the International Tables for Crystallography, where there are two different settings in the monoclinic crystal system. When the unique two-fold axis is parallel to b (i.e. to T-axis), this setting is considered a standard choice, but when it is parallel to c (or to Z-axis), this is an allowed alternative setting. In addition, the unique two-fold axis can be chosen to be parallel to a (i.e. to X-axis), which is considered a non-standard setting. 

Crystal Systems. To understand several aspects of crystallization, it is useful to know about a few of the rudiments of crystallography. 

Note that this emphasis on the symmetry of the lattices has a profound effect on thinking about structures. Up to now, the lattice type has been characterised by the lattice parameters, the lengths of the lattice vectors and the inter-vector angles. Now, however, it is possible to define a lattice in terms of the symmetry rather than the dimensions. In fact this is the norm in crystallography. As we will see, the crystal system of a phase is allocated in terms of symmetry and not lattice parameters. To pre-empt future chapters somewhat, consider the definition of a monoclinic unit cell in terms of the lattice parameters a b c a = 90°, ft 90°, y = 90° (see Chapter 1). The unit cell may still be regarded as monoclinic (not orthorhombic) even if the angle /I is 90°, provide that the symmetry of the structure complies with that expected of a monoclinic unit cell. 

Experimentally, a perfect crystal gives a diffraction pattern consisting of sharp reflections or spots. This is the direct result of the translational order that characterises the crystalline state. The translational order allowed in a crystal (in classical crystallography) has been set out earlier in this book. To recapitulate, a crystal can only be built from a unit cell consistent with the seven crystal systems and the 14 Bravais... 

For SR protein crystallography two main designs for the monochromator system have been utilised to date based on either the bent oblique-cut single crystal or ( +, —) parallel double crystal system. In the next sections (sections 5.2.3 and 5.2.4) we describe their properties in detail. 

In earlier centuries, crystallography developed via two independent routes. The first of these was observational. It was long supposed that the regular and beautiful shapes of mineral crystals were an expression of internal order, and this order was described by the classification of external shapes, the habit of crystals. All crystals could be classified into one of 32 crystal classes, belonging to one of seven crystal systems. The regularity of crystals, together with the observation that many crystals could be cleaved into smaller and smaller units, gave rise to the idea that all crystals were built up from elementary volumes, that came to be called unit cells, with a shape defined by the crystal system. A second route, the mathematical descrip-... 

Monoclinic ma-n9- kli-nik [ISV] (ca. 1864) adj. Of a crystal (or crystal system) having two axes that are mutually perpendicular to the third one, but not to each other. An example is the /i-form of elemental sulfur, which is stable between 112 and 119°C, but slowly converts to the rhombic form below 112°C. Rhodes G (1999) Crystallography made crystal clear a guide for users of macromolecular models. Elsevier Science and Technology Books, New York. Hibbard MJ (2001) Mineralogy. McGraw-Hill Co. Inc., New York. 

Disregarding any detailed morphological models proposed for the lamellar crystals in semicrystalline polymers in the past half centiny, crystal imit cells in semicrys-talUne poisoners exactly obey the rules of classical crystallography, which consist of 7 crystal systems and 14 Bravais lattices (more precisely, there are only 6 crystal systems in polymer crystals, and the cubic system does not exist). Most of the unit cell determinations of the semicrystalline polymers rely on the wide-angle x-ray diffraction (waxd) experiments on oriented poisoner fibers and films. This is be-canse of small crystal sizes in polymers, which lead to a difficult experimental task to obtain single-crystal waxd results on semicrystalfine polymers. It is also possible to nse electron diffraction (ed) method in transmission electron microscopy (tern) to determine polymer lamellar crystal unit cell structures, dimensions, and symmetries. 

Shibata, A. Kaji, N. Nakahara, M. Yano, K. Tayama, T. Nakamura, K Washiya, T. Myochin, M. Chikazawa, T. Kikuchi, T. (2009). Current Status on Research and Development of Uranium Crystallization System in Advanced Aqueous Reprocessing of FaCT Project, Proceedings of International Conference on The Nuclear Fuel Cycle Sustainable Options Industrial Perspectives (GLOBAL 2009), pp. 151-157, Paper 9154, Paris, France, September 6-11, 2009 Staritzky, E. Truitt, A. L. (1949). Optical and Norphological Crystallography of Plutonium Compounds, LA-745, Los Almos National Laboratory, Los Alamos, New Mexico, USA... 

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