Coordination numbers, lead structures

Although in most of the above reports structural information is based on X-ray data, Au Mossbauer spectroscopy has also been successfully employed for the investigation of two-, three-, and four-coordination in gold(I) complexes.2551 An increase in coordination numbers leads to a decrease in the isomer shift (IS) by 1-2mm s 1 (three-coordination) or 2-4mm s 1 (four-coordination) relative to two-coordination. For the same ligands, the quadrupole splitting (QS) for three-coordinated complexes is expected to be very similar to that for the two-coordinate derivatives, while that for complexes with Td symmetry should be zero. 

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... 

Chlorates and bromates feature the expected pyramidal ions X03 with angles close to the tetrahedral (106-107°). With iodates the interatomic angles at iodine are rather less (97-105°) and there are three short I-O distances (177-190 pm) and three somewhat longer distances (251-300 pm) leading to distorted perovskite structures (p. 963) with pseudo-sixfold coordination of iodine and piezoelectric properties (p. 58). In Sr(I03)2.H20 the coordination number of iodine rises to 7 and this increases still further to 8 (square antiprism) in Ce(I03)4 and Zr(I03)4. 

The ratio between the anionic and cationic radii leads to coordination numbers, the lowest of which is 6, which correspond to a octahedral polyhedron of anions around a central cation [135]. In this case, the compound structure type depends on the ratio of total number of anions and cations. The total number of anions (X) is calculated by summing up the number of oxygen (O) ions and of fluorine (F) ions X=0+F, while the total number of cations (Me) is the number of tantalum ions, niobium ions and other similar cations. 

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. 

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]. 

The structure leads to a general formula for the micas namely, KXMY.1Oio(OH,r )2, with 2 < < 3, in which X represents cations of coordination number 6 (Al+3, Mg+, Fe++, Fe+3, Mn++, Mn+3, Ti+ Li+, etc.) and Y cations of coordination number 4 (Si+4, A1+3, etc.). The subscript n can have any value between 2 (hydrargillite layer) and 3 (complete octahedral layer). K+ can be partially replaced by Na+ and possibly to some extent by Ca++. This formula represents satisfactorily the.numerous recently published mica analyses almost without exception.6 The distribution of the various ions X and Y must be such as to give general agreement with the electrostatic valence rule. 

Fig. 6. A schematic view of the [3Fe-4S] Emd [4Fe-4S] cores, as versatile structures. The absence of one site leads to the formation of a [3Fe-4S] core. The cubane structure can incorporate different metals (in proteins, M = Fe, Co, Zn, Cd, Ni, Tl, Cs), and S, N, O may be coordinating atoms from hgands (Li). The versatihty csm be extended to higher coordination number at the iron site and a water molecule can even be a ligand, exchangeable with substrate (as in the case of aconitase (,87)). The most characteristic binding motifs are schematically indicated, for different situations proteins accommodating [3Fe-4S], [4Fe-4S], [3Fe-4S] + [4Fe-4S], and [4Fe-4S] -I- [4Fe-4S] clusters. A disulfide bridge may replace a cluster site (see text).

Instead, we believe the electronic structure changes are a collective effect of several distinct processes. For example, at surfaces the loss of the bulk symmetry will induce electronic states with different DOS compared to bulk. As the particle sizes are decreased, the contribution of these surface related states becomes more prominent. On the other hand, the decrease of the coordination number is expected to diminish the d-d and s-d hybridization and the crystal field splitting, therefore leading to narrowing of the valence d-band. At the same time, bond length contraction (i.e. a kind of reconstruction ), which was observed in small particles [89-92], should increase the overlap of the d-orbitals of the neighboring atoms, partially restoring the width of the d-band. 

That may seem a silly question to ask at a silicon conference But silicon is of exceptional structural interest. A primary reason is silicon s position in the Periodic Table. In its normal compounds it is 4-coordinate, and so has no vacant s or p orbitals, which would lead to very fast reactions. Compounds of lower coordination number can be made, but they must be stabilized by bulky groups. Silicon also has... 

The rather low coordination in the (100) and (110) surfaces will clearly lead to some instability and it is perhaps not surprising that the ideal surface structures shown in Figure 1.2 are frequently found in a rather modified form in which the structure changes to increase the coordination number. Thus, the (100) surfaces of Ir, Pt and Au all show a topmost layer that is close-packed and buckled, as shown in Figure 1.3, and the (110) surfaces of these metals show a remarkable reconstruction in which one or more alternate rows in the <001 > direction are removed and the atoms used to build up small facets of the more stable (111) surface, as shown in Figure 1.4, These reconstructions have primarily been characterised on bare surfaces under high-vacuum conditions and it is of considerable interest and importance to note that chemisorption on such reconstructed surfaces can cause them to snap back to the unreconstructed form even at room temperature. Recently, it has also been shown that reconstructions at the liquid-solid interface also... 

When spherical objects are stacked to produce a three-dimensional array (crystal lattice), the relative sizes of the spheres determine what types of arrangements are possible. It is the interaction of the cations and anions by electrostatic forces that leads to stability of any ionic structure. Therefore, it is essential that each cation be surrounded by several anions and each anion be surrounded by several cations. This local arrangement is largely determined by the relative sizes of the ions. The number of ions of opposite charge surrounding a given ion in a crystal is called the coordination number. This is actually not a very good term because the bonds are not coordinate bonds (see Chapter 16). For a specific cation, there will be a limit to the number of anions that can surround the cation because... 

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