Crystallographic classification

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. 

The degree of supersaturation of the mother liquor or difference in concentration of solute on opposite sides of a growing crystal influences crysfal habif. The effecl of supersaturation on the change in habit was described by an equation, yjx = kAG", where y/x is the ratio of crystal length to breadth, k is a coefficient of proportionality depending on diffusion, AG is the degree of supersaturation (moles/1000 mol of solvent at the moment of nuclei formation), and n is a number that depends on the crystallographic classification and the chemical composition of the substance. 

However, the crystallographic classification of the system of reticular points involves some definitions the present discussion follows (Chiriac-Putz-Chiriac, 2005). 

Thus, beyond any crystallographic classification of S mimetiy, one can phenomenological and principally resumed that ... 

With the aid of the Pearson indexing the inverse path of the crystallographic classification is crossed, i.e., by reducing the classification of the chemical compounds to the set of 230 space groups to the number of 14 Bravais lattice, yet leaving open (like a variable) the total number of atoms present in the elementary cell, a number that varies from case to case. 

Classification and analysis of crystallographic and structural data for Sn-com-plexes with heterocyclic ligands 98MI65. 

Niobium coordination compounds classification and analysis of crystallographic and structural data. C. E. Holloway and M. Melnik, Rev. Inorg. Chem., 1985,7,162 (198). 

In the previous paragraphs a brief account has been given of the fundamental aspects of the crystallographic description of the structures and structure types of solid phases. A number of symbols and names have been defined and their application to intermetallic compounds exemplified. It must, however, be underlined that both for historical reasons and for the need to improve classification and interpretation of the structural characteristics of intermetallic phases, other symbols and nomenclature criteria have been invented. Some of them have a mathematical basis, others are more colloquial. A selection of these criteria will be given in the following. 

Concluding this section, we may mention a paper by Daams and Villars (1993) concerning an atomic environment classification of the chemical elements. Critically evaluated crystallographic data for all element modifications (and recommended atomic volumes) have been reported. Special structural stability diagrams were used to separate AET stability domains and to predict the structure (in terms of environment types) of hitherto unknown high-pressure and high-temperature modifications. Reference to the use of AET in thermodynamic (CALPHAD) modelling and calculation has been made by Ferro and Cacciamani (2002). 

Fig. 5.12 Classification of calcium hydroxide morphology based on a c to a crystallographic axis ratio (Berger).

The remaining exceptions concern the lanthanide series, where samarium at room temperature has a particular hexagonal structure and especially the lower actinides uranium, neptunium, and plutonium. Here the departure from simple symmetry is particularly pronounced. Comparing these three elements with other metals having partly filled inner shells (transition elements and lanthanides), U, Pu, Np have the lowest symmetry at room temperature, normal pressure. This particular crystallographic character is the reason why Pearson did not succeed to fit the alpha forms of U, Pu, and Np, as well as gamma-Pu into his comprehensive classification of metallic structures and treated them as idiosyncratic structures . Recent theoretical considerations reveal that the appearance of low symmetries in the actinide series is intimately linked to the behaviour of the 5f electrons. 

Melnik. M. Heterrurtetallic Coordination Copper Hi Compounds Classification and Analysis of Crystallographic and Structural Guta. Nova Science Publishers. Inc., Huntington. NY. 1999. 

Figure 1.2 Classification of the crystallographic groups by their electrical properties...

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