Description of crystals

Based on extensive studies of the symmetry in crystals, it is found that crystals possess one or more of the ten basic symmetry elements (five proper rotation axes 1,2,3, 4,6 and five inversion or improper axes, T = centre of inversion i, 2 = mirror plane m, I, and 5). A set of symmetry elements intersecting at a common point within a crystal is called the point group. The 10 basic symmetry elements along with their 22 possible combinations constitute the 32 crystal classes. There are two additional symmetry 

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Although evidence exists for both mechanisms of growth rate dispersion, separate mathematical models were developed for incorporating the two mechanisms into descriptions of crystal populations random growth rate fluctuations (36) and growth rate distributions (33,40). Both mechanisms can be included in a population balance to show the relative effects of the two mechanisms on crystal size distributions from batch and continuous crystallizers (41). 

Aside from the conventions mentioned for the cell choice, further rules have been developed to achieve standardized descriptions of crystal structures [36], They should be followed to assure a systematic and comparable documentation of the data and to facilitate the inclusion in databases. However, contraventions of the standards are rather frequent, not only from negligence or ignorance of the rules, but often for compelling reasons, for example when the relationships between different structures are to be pointed out. 

Pauling, L. (1960). The Nature of the Chemical Bond, 3rd ed. Cornell University Press, Ithaca, NY. A classic book that presents a good description of crystal structures and bonding in solids. 

In the description of crystal coordination formulae a coordination number was introduced, defined as the NNN of atoms X around the atom Y under consideration. 

The simplest and most useful description of crystal difiraction is still that obtained by Bragg. Strong diffraction occurs when all the wavelets add up in phase. By considering an entire crystal plane as the scattering entity, rather than each individual electron, it is easy to see from Figure 1.1 that strong diffraction results when... 

Although it has often proved useful as a mnemonic, this approach has led to a number of misconceptions about relative atomic sizes and the origin of close-packing geometry, to some of which we allude below. More relevant in the present context is the observation that one natural and simple description of crystal structures has been. overlooked, and an unnecessarily complicated and opaque one used instead. We will provide many examples throughout this article. 

An extension of this sytem of nomenclature is sometimes encountered in descriptions of crystals of hexagonal type (Fig. 12). The unit... 

For the description of crystal structures one adds to the preceding molecular parameters an appropriate combination of rotation angles and translations 6 parameters or less according the space group symmetry. 

When we consider crystal structures we usually think of the pattern and symmetry of the packing of the atoms, ions, or molecules in building the lattice based on X-ray crystallography. However, detailed descriptions of crystals and their classification are much older. The seven systems of crystals and the 32 classes of crystal symmetry were recognized by 1830. The 14 Bravais Lattices were presented by A. Bravais in 1848. 

Fig. 9a, b Schematic description of crystal thickening options, a Crystal thickening at constant crystal volume, b Crystal thickening accompanied by an increase in crystal volume... 

A recurring theme in many studies of nanocrystal doping is the propensity for dopants to be excluded from the internal volumes of the nanocrystals. We therefore begin with a description of crystal nucleation and growth, and of the... 

A Microscopic Description of Crystal Dissolution and Precipitation where H denotes the Heaviside graph,... 

For a mathematical description of crystal faces, take any three non-parallel faces (chosen to be mutually orthogonal, if possible) and take their intersections as reference axes, which are labeled OA, OB, and OC with the origin at O, as shown in Fig. 9.1.2(a). Let another face (the standard face or parametral face A B C ) meet these axes at A, B, and C, making intercepts OA = a, OB = b and OC = c, respectively. The ratios a b c are called the axial ratios. 

In general, because the value of a crystal property depends on the direction of measurement, the crystal is described as anisotropic with respect to that property. There are exceptions for example, crystals having cubic symmetry are optically isotropic although they are anisotropic with respect to elasticity. For these reasons, a description of the physical behaviour of a material has to be based on a knowledge of crystal structure. Full descriptions of crystal systems are available in many texts and here we shall note only those aspects of particular... 

The short reports solicited and edited by McCrone are models of the kind of data which should be required and included in descriptions of crystals and crystal structure reports, even if only in deposited form (Section 1.3.3). 

In the description of crystals and crystal structures the two terms/om and habit have very specific and very different meanings. Form refers to the internal crystal structure and etymologically is the descendant of the Greek morph. Hence, polymorph refers to a number of different crystal modifications or different crystal structures, and the naming of different structures as Form F or a Form follows directly from this definition and usage. As we have seen above, the difference in crystal structure is very much, although not exclusively, a function of thermodynamics. Certainly, only the structures which are thermodynamically accessible can ever exist, but there often is a question of thermodynamic vs kinetic control over which particular structure may be obtained under any particular set of crystal growth conditions. 

A description of crystallization as given by Hiazzi SA (I8 is as follows. PETN is continuously introduced from the filter into a stainless steel dissolving apparatus provided with a hot water healing jacket and a stirrer. The required amount of acetone is continuously fed from a constant-level overhead tank together with ammonia gas for neutralization. The neutralized solution of PETN in acetone fiows continuously into a series of continuous crystallizers equip(>cd with stirrers and jackets. The crystallization is earned out by adding a welt determined quantity of water. The contents of the last crystallizer flow continuously on a continuous vacuum filter where most of the waste acetone is removed. I hc dilute acetone is collected into an intermediate vacuum tank from which it is pumped to the acetone recovery unit. 

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