A classification of crystals

Crystals consisting of infinite 2-dimensional complexes The simplest structures of this group are those of 

In crystals of groups (a), (b) and (c) all the atoms together form the 3D complex. Closely related to these are two other types of structure in which there is a 3D framework extending throughout the crystal but in addition discrete ions or molecules occupy interstices in the structure  

Inclusion of foreign molecules in crystals of (a) Pd2Br4[As(CH3)3]2, (b) Ni(CN)2NH3. nCeH j, (c) a urea-hydrocarbon complex, (d) d-quinol. 

Related structures containing layers of the same general type 

Graphite Intcrlamellar compounds of graphite, e.g. CgK, CigK CaSi2 

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A classification of crystals based on bonding is useful in understanding structure-property relations in solids. Five types of solids are readily defined on bonding considerations ionic, covalent, metallic and molecular (van der Waals) and hydrogen-bonded. In Table 1.2, the important characteristics of the five types of solids are presented. In real situations, however, solids may exhibit features of more than one type of bonding. 

Crystallization cannot occur without supersaturation. A main function of any crystallizer is to cause a supersaturated solution to form. A classification of crystallizing equipment can be made based on the methods used to bring about supersaturation as follows (1) supersaturation produced by cooling the solution with negligible evaporation—tank and batch-type crystallizers (2) supersaturation produced by evaporation of the solvent with little or no cooling—evaporator-crystallizers and crystallizing... 

This brief review has indicated many of the different kinds of defects which exist in otherwise perfect crystalline solids. Table 1 gives a classification of crystal defects. The purpose of this chapter is to briefly introduce each category of defect to give a broad picture of the complete field so that the individual chapters in this treatise may be placed in proper perspective. The classification is convenient for... 

Adsorption of acetic acid on Pt(lll) surface was studied the surface concentration data were correlated with voltammetric profiles of the Pt(lll) electrode in perchloric acid electrolyte containing 0.5 mM of CHoCOOH. It is concluded that acetic acid adsorption is associative and occurs without a significant charge transfer across the interface. Instead, the recorded currents are due to adsorption/desorption processes of hydrogen, processes which are much better resolved on Pt(lll) than on polycrystalline platinum. A classification of adsorption processes on catalytic electrodes and atmospheric methods of preparation of single crystal electrodes are discussed. 

The given discussion shows that rather universal and simple classification of porous materials equivalent to classification of crystals is absent. However, one can consider a system of interrelating classifications that take into account order, morphology and sizes at different hierarchical levels, degrees of integrity, structure, heterogeneity of a various type, etc. Such a systematic approach can be used as well for adequate modeling of various hierarchical levels of a porous material structure. 

Special devices for classification of crystals may be used in some applications. Figure 14 shows a draft-tube-baffle (DTB) crystallizer that is designed to provide preferential removal of both fines and classified product. As shown, feed is introduced to the fines circulation line so that any nuclei formed upon introduction of the feed can be dissolved as the stream flows through the fines-dissolution heat exchanger. The contents of the crystallizer are mixed by the impeller, which forces the slurry to flow in the indicated direction. A quiescent zone is formed between the... 

Of course, more complicated situations may exist, such as n m stoichiometries or ternary salts. See, for example, Graja [142] for a classification of molecular conductors on the basis of conductivity, crystal packing, and charge transfer. See also Pouget [114] for a discussion of charge transfer and instabilities in a number of materials. 

In 1970, Heller suggested a classification of borates based on the number of boron atoms in the fundamental building block . In 1971, J. R. Clark added, in an article on crystal chemistry of borates , a further principle as the fifth rule, namely that "the boric acid group, B(OH)3, may exist in isolated form in the presence of more complex polyanions, or such insular groups may themselves polymerize and attach to side-chains of more complex polyanions , as first observed in the crystal structures of veatchite and paraveatchite. In 1977, Christ and Clark reviewed the various principles and classifications in their article on a crystal-chemical classification of borate structures with emphasis on hydrated borates . In addition to a sixth rule. 

Crystalline compounds exist in a great many crystal forms. The accepted method for the crystallographic classification of crystals is based on the angles between the crystal faces. In this classification system, the types of crystal forms are not related to the relative sizes of the crystal faces, since the relative development of the faces is characteristic of the specific material. The cubic system, for example, is characterized by the fact that the faces of a cubic crystal can be referred to three equal and mutually perpendicular axes. The actual macrocrystal may be a cube, a needle, a plate, or an aggregate of imperfect crystals. 

Crystal systems A classification of point groups as triclinic, monoclinic, orthorhombic, trigonal, tetragonal, hexagonal, or cubic as determined by symmetries. 

One of the many unique features of crystals is crystal habits. Crystals can have different shapes and faces that make them unique and distinct from hquid or gaseous materials. In view of the focus of this book, crystal morphology means the approximate shape of crystals. Our purpose is to describe quahtatively the aspect ratios of crystals in three-dimensional space with relevance to the crystallization process. Therefore, we refer the reader to (Mullin 2001, Chapter 1) for a more thorough and comprehensive classifications of crystal morphology. 

A Spectroscopic Constants, Coefficients, and Matrix Elements B Irreducible Tensors and Tensor Operators C Classification of Crystal-Eield Terms and Multiplets D Calculated Energy Levels and Magnetic Parameters References... 

Here we use bond-valence theory (Brown 1981) and its developments (Hawthorne 1985a, 1994, 1997) to consider structure topology and hierarchical classification of crystal structures, and we point out that bond-valence theory can be considered as a simple form of molecular-orbital theory (Burdett and Hawthorne 1993 Hawthorne 1994, 1997). 

The systematic description of crystal structures is presented primarily in the well-known Structurbericht. The classification of crystals by the Structurbericht does not reflect their crystal class, the Bravais lattice, but is based on the crystaUochemical type. This makes it inconvenient to use the Structurbericht categories for comparison of some individual crystals. Thus, there have been several attempts to provide a more convenient classification of crystals. Table 5 presents a compilation of different classifications which allows the reader to correlate the Structurbericht type with the international and Schoenflies point and space groups and with Pearsons symbols, based on the Bravais lattice and chemical composition of the class prototype. The information included in Table 5 has been chosen as an introduction to a more detailed crystal-lophysical and crystaUochemical description of solids. 

A chirality classification of crystal structures that distinguishes between homochiral (type A), heterochiral (type B), and achiral (type C) lattice types has been provided by Zorkii, Razumaeva, and Belsky [11] and expounded by Mason [12], In the type A structure, the molecules occupy a homochiral system, or a system of equivalent lattice positions. Secondary symmetry elements (e.g., inversion centers, mirror or glide planes, or higher-order inversion axes) are precluded in type A lattices. In the racemic type B lattice, the molecules occupy heterochiral systems of equivalent positions, and opposite enantiomers are related by secondary lattice symmetry operations. In type C structures, the molecules occupy achiral systems of equivalent positions, and each molecule is located on an inversion center, on a mirror plane, or on a special position of a higher-order inversion axis. If there are two or more independent sets of equivalent positions in a crystal lattice, the type D lattice becomes feasible. This structure consists of one set of type B and another of type C, but it is rare. Of the 5,000 crystal structures studied, 28.4% belong to type A, 55.6% are of type B, 15.7% belong to type C, and only 0.3% are considered as type D. 

The Laue classes represent a classification of the crystal classes. The other significations of the word class were discussed in Section 2.5.1. 

The crystal systems are a classification of the symmetry groups. They are not a classification of the different types of metric. The metric is determined by the symmetry but the metric does not determine the symmetry. 

On the other hand, a classification of a sorption process on the basis of kinetics data must be conditioned by other chemical properties of the phosphate-soil mixture. For example, if the soil solution is supersaturated initially with respect to some phosphate solid, precipitation is likely to influence the sorption reaction from the beginning. If the soil minerals have a low degree of crystallinity and/or a high degree of hydration, precipitation may be the dominant sorption mechanism even in the rapid stage.In general, low phosphate concentrations and well-crystallized, relatively unhydrated soil minerals tend to favor adsorption as the phosphate reaction mechanism. Other chemical properties, such as the pH value of the soil solution and the kinds of metals in soil clay minerals, exert a quantitative influence on the rapid stage of phosphate sorption, as do such physical properties as temperature. ... 

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