Crystalline solids coordination number

Coordination number is the number of positions around a central atom where ligands can be attached in the formation of a complex. Applied to a crystalline solid, coordination number signifies the number of nearest neighboring atoms (or ions of opposite charge) to any given atom (or ion) in a ciystal. 

In structures of inorganic crystalline compounds, coordination numbers (Nc) vary from 2 up to 12. Here and further by Nc we mean the number of atoms coordinated around the central metal atom the Nc of non-metals in MnXm structures is equal to Nc(M)n/m. In solid compounds with a framework lattice, the Nc multiplied by the ligand valence (vx) always exceeds the valence of the metal ... 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

Table 8.53 shows the main features of XAS. The advantages of EXAFS over diffraction methods are that the technique does not depend on long-range order, hence it can always be used to study local environments in amorphous (and crystalline) solids and liquids it is atom specific and can be sensitive to low concentrations of the target atom (about 100 ppm). XAS provides information on interatomic distances, coordination numbers, atom types and structural disorder and oxidation state by inference. Accuracy is 1-2% for interatomic distances, and 10-25 % for coordination numbers. 

Polymerization in electrostatic systems like the ones mentioned above is stericaUy inhibited by alkyl substitution at the a-carbon which must assume a coordination number greater than 4. Coates and Glockhng have treated this inhibition of polymerization in terms of decreased electronegative character of the branched alkyl groups. Therefore, stimulated by the idea that f-afkylhthium compounds may exist as low polymers or even as monomeric molecules, Weiner and coworkers and Kottke and Stalke have isolated f-butyllithium as a pure substance for the first time and characterised it by spectroscopic methods and X-ray diffraction. The colourless crystalline solid was found to be tetrameric over a range of concentrations in both benzene and hexane ... 

Traditionally, X-ray absorption edge measurements have been used to determine oxidation states of metals in complex materials. The extended X-ray absorption fine structure (EXAFS), on the other hand, provides structural information such as bond distances and coordination numbers even with powdered samples, crystalline or amorphous, the fine structure essentially resulting from short-range order around the absorbing atom. The technique is also useful for studying solid surfaces (SEXAFS). The observation of fine structure beyond the K-absorption edges of materials dates back to... 

This calculation is still hypothetical, in that the actual substance formed when sodium metal reacts with difluorine is solid sodium fluoride, and the standard enthalpy of its formation is -569 kJ mol-1. The actual substance is 311 kJ mol-1 more stable than the hypothetical substance consisting of ion pairs, Na+F (g), described above. The added stability of the observed solid compound arises from the long-range interactions of all the positive Na+ ions and negative F ions in the solid lattice which forms the structure of crystalline sodium fluoride. The ionic arrangement is shown in Figure 7.5. Each Na+ ion is octahedrally surrounded (i.e. coordinated) by six fluoride ions, and the fluoride ions are similarly coordinated by six sodium ions. The coordination numbers of both kinds of ion are six. 

The general intransigence of the crystalline iminolithium hexamers toward further interaction with Lewis bases is not shown by the amorphous diaryliminolithiums. This may reflect their extensively stacked nature (Section II,A Fig. 10), which, while raising the lithium coordination number to four in all but the outer rings of the polymer, will presumably weaken individual N—Li bonds. These materials dissolve quite readily in several polar solvents, e.g., THF (66), pyridine (66, 78, 85), and HMPA (86). Crystalline complexes can be recovered from these solutions. Two of these, both derivatives of (Ph2C=NLi) , have been characterized structurally in the solid state. The tetrameric cubane (Ph2C=NLipyridine)4 (7) is depicted in Fig. 14 (78, 85). 

Experimental trends in Si shielding observed experimentally arise from variations in the coordination number (i.e. the number of atoms in the 1st coordination sphere), the extent of polymerization of the silicate tetrahedra, the degree of replacement of one net-work forming cation by another (e.g. coupled Na+, Al+3 for Si+4 substitution), the size of the rings of tetrahedra present and the Si-O-Si angles (1,2). Similar trends are seen in gas-phase molecules, species in aqueous solution and in both crystalline and amorphous solids. Polarized double-zeta basis set Hartree-Fock level calculations using small molecular cluster models reproduce these trends semiquantitatively, as we will show. 

If the immediate neighbor atoms (coordination number) m is known such as in a crystalline solid, the question can be answered readily by invoking the binomial theorem. Since in the liquid state the coordination number m varies dynamically throughout the system, the answer to this question requires more thought. We know that for a given P (the atomic composition of B), there exists an average number of B s surrounding A and that the number n (P) can be written as ... 

There seems to be even less structural similarity for many other metal halides as the crystalline systems are compared with the molecules in the vapor phase. Aluminum trichloride, e.g., crystallizes in a hexagonal layer structure. Upon melting, and then, upon evaporation at relatively low temperatures, dimeric molecules are formed. At higher temperatures they dissociate into monomers (Figure 9-58) [107], The coordination number decreases from 6 to 4 and then to 3 in this process. However, at closer scrutiny, even the dimeric aluminum trichloride molecules can be derived from the crystal structure. Figure 9-59 shows another representation of crystalline aluminum trichloride which facilitates the identification of the dimeric units. A further example is chromium dichloride illustrated in Figure 9-60. The small oligomers in its vapor have structures [108] that are closely related to the solid structure [109], Correlation between the molecular composition of the vapor and their source crystal has been established for some metal halides [110],... 

Table 53 gives a list of a number of cobalt(III)-superoxo complexes which have been isolated as crystalline solids. There is a marked preponderance of complexes of the type [Co(SB)(B)(02)] (SB = SchifF base). The base adducts of simple Co11 porphyrins have low affinities for dioxygen at room temperature and consequently their 1 1 adducts with 02 are not isolable. In contrast, exposure of a solid sample of Collman s picket fence porphyrin system [Co(TpivPP)(iV-Meim)] to 1 atm of dioxygen for 24 h produces [Co(TpivPP)(A(-Meim)(02)] (200).654 The pivalamido pickets in this compound exercise control of solvation about the coordinated dioxygen moiety and the stability is comparable with that of CoMb02,655 where the globin protein environment performs the same function. 

It has been proposed [4(c)] that this melt contains the very weakly solvated cation Ti2+. The solid state spectrum in Fig. 5(c) is of crystalline NaCl, in which the coordination number of the cations is six, and which had been doped at... 

Polyhedra in these high coordination numbers are often necessarily irregular, but when all the ligands are identical, near-icosahedral geometries occur for the 12-coordinate [Pr(l,8-naphthyridine)6] + and [La(N03)6] ions in crystalline salts. It should also be remembered that the geometries discussed here are found in the solid state, but on dissolution in a solvent, where the influence of counter-ions is lessened, matters may be different (see the aqua ions. Sections 4.3.1 and 4.3.2). In principle, isomers are often possible, but because of the lability of lanthanide complexes they are very rarely observed. 

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