Crystal structure coordination number

Crystal structure Coordination number Madelung s constant... 

Crystal structure Coordination number Occupied space Examples... 

Crystal Structure Coordination Number Occupied Space Elxamples... 

Both in the wurtzite and zinc blende structures (coordination number = 4) of silver iodide, stable at atmospheric pressure, the Ag—I-distances are 278 pm and 280 pm respectively. At 4 kbar the NaCl-type structure (coordination number = 6) becomes stable, in which the Ag—I-distances are remarkably greater, namely 303 pm. Increase in pressure to 100 kbar contracts all of these distances to 283 pm with a decrease in molar volume from 33.8 to 27.6 cm /mol. Thus the transformation with increase in coordination number from the low-pressure modification into the high pressure modification involves an increase in Ag—I-distances by 8.4%, but further increase in pressure does not produce another geometrical rearrangement and hence all of the equidistant bonds within the crystal lattice are shortened 34). 

The melting and boiling points of the aluminium halides, in contrast to the boron compounds, are irregular. It might reasonably be expected that aluminium, being a more metallic element than boron, would form an ionic fluoride and indeed the fact that it remains solid until 1564 K. when it sublimes, would tend to confirm this, although it should not be concluded that the fluoride is, therefore, wholly ionic. The crystal structure is such that each aluminium has a coordination number of six, being surrounded by six fluoride ions. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

Crystal Structure and Ionic Radii. Crystal stmcture data have provided the basis for the ionic radii (coordination number = CN = 6), which are summarized in Table 9 (13,14,17). For both and ions there is an actinide contraction, analogous to the lanthanide contraction, with increasing positive charge on the nucleus. 

The predominantly ionic alkali metal sulfides M2S (Li, Na, K, Rb, Cs) adopt the antifluorite structure (p. 118) in which each S atom is surrounded by a cube of 8 M and each M by a tetrahedron of S. The alkaline earth sulfides MS (Mg, Ca, Sr, Ba) adopt the NaCl-type 6 6 structure (p. 242) as do many other monosulfides of rather less basic metals (M = Pb, Mn, La, Ce, Pr, Nd, Sm, Eu, Tb, Ho, Th, U, Pu). However, many metals in the later transition element groups show substantial trends to increasing covalency leading either to lower coordination numbers or to layer-lattice structures. Thus MS (Be, Zn, Cd, Hg) adopt the 4 4 zinc blende structure (p. 1210) and ZnS, CdS and MnS also crystallize in the 4 4 wurtzite modification (p. 1210). In both of these structures both M and S are tetrahedrally coordinated, whereas PtS, which also has 4 4... 

Since the coordination number of tantalum or niobium in fluoride and oxyfluoride compounds cannot be lower than 6 due to steric limitations, further decrease of the X Me ratio (lower than 6) leads to linkage between complex ions in order to achieve coordination saturation by sharing of ligands between different central atoms of the complexes. The resulting compounds have X Me ratios between 6 and 4, and form crystals with a chain-type structure. 

Fig. 31 Crystal structure of Rb sNb30Ft8. Projection on the plane (001). Numbers in brackets are the atom coordinates on the z-axis in percents of c parameter. Structure of NbOFj chains and NbFf polyhedron. Reproduced from [209], A. I. Agulyansky, V. E. Zavodnik, V. Y. Kuznetzov et al. Neorgan. Mater. 27 (1991) 380, Copyright 1991, with permission of Nauka (Russian Academy of Sciences) publishing.

The lowest coordination number of tantalum or niobium permitted by crystal chemistry formalism is 6, which corresponds to an octahedral configuration. X Me ratios that equal 3, 2 or 1 can, therefore, be obtained by corresponding substitutions in the cationic sub-lattice. A condition for such substitution is no doubt steric similarity between the second cation and the tantalum or niobium ion so as to enable its replacement in the octahedral polyhedron. In such cases, the structure of the compound consists of oxyfluoride octahedrons that are linked by their vertexes, sides or faces, according to the compound type, MeX3, MeX2 or MeX respectively. Table 37 lists compounds that have a coordination-type structure [259-261]. 

The formulated principals correlating crystal structure features with the X Nb(Ta) ratio do not take into account the impact of the second cation. Nevertheless, substitution of a second cation in compounds of similar types can change the character of the bonds within complex ions. Specifically, the decrease in the ionic radius of the second (outer-sphere) cation leads not only to a decrease in its coordination number but also to a decrease in the ionic bond component of the complex [277]. 

S Tantalum and niobium are present in the crystal structure in the form of complex ions. The lowest coordination number, 6, corresponds to the formation of slightly distorted octahedrons. The linking and packaging of the octahedrons depends on the X Me ratio, where X is the total number of oxygen and fluorine atoms, and Me is the total number of tantalum or niobium ions as well as other metals that can replace tantalum or niobium in the octahedral polyhedron. The crystal structure type can be defined based on the X Me ratio, as follows ... 

The chemistry of silicon in very low oxidation states is one of the most fascinating research areas, which can be located between molecular compounds of silicon and elemental (perhaps amorphous) silicon [190-194]. Most interesting results have recently been obtained by structural investigations of siliddes in Zintl phases. However, compounds of silicon with negative oxidation states and very low coordination numbers of 1, 2, and 3 are so far only known in the composite of a crystal lattice. 

We have shown that 74% of the crystal s space is occupied by atoms and 26% is considered to be empty. Because the hep structure has the same coordination number of 12, we know that it is packed as densely and must have the same fraction of occupied space. 

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