Crystals coordination number

The accumulation of lattice constants gave rise to a growing Hbrary of interatomic (and interionic) distances, providing atomic and ionic radii. In 1929 Pauling published five principles (rules) that formed the first rational basis for understanding aystal structures. For example, the ratio of the ionic radii of cations to anions determines coordination number in crystals coordination number 6 for each chlorine and sodium ion in NaCl coordination number 8 for each ion in CsCl. 

A metal that crystallizes in the body-centered cubic (bcc) structure has a crystal coordination number of... 

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. 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

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 fluoride ion is the least polarizable anion. It is small, having a diameter of 0.136 nm, 0.045 nm smaller than the chloride ion. The isoelectronic E and ions are the only anions of comparable size to many cations. These anions are about the same size as K" and Ba " and smaller than Rb" and Cs". The small size of E allows for high coordination numbers and leads to different crystal forms and solubiUties, and higher bond energies than are evidenced by the other haUdes. Bonds between fluorine and other elements are strong whereas the fluorine—fluorine bond is much weaker, 158.8 kj/mol (37.95 kcal/mol), than the chlorine—chlorine bond which is 242.58 kJ/mol (57.98 kcal/mol). This bond weakness relative to the second-row elements is also seen ia 0-0 and N—N single bonds and results from electronic repulsion. 

Chromium (II) also forms sulfides and oxides. Chromium (II) oxide [12018-00-7], CrO, has two forms a black pyrophoric powder produced from the action of nitric acid on chromium amalgam, and a hexagonal brown-red crystal made from reduction of Cr202 by hydrogen ia molten sodium fluoride (32). Chromium (II) sulfide [12018-06-3], CrS, can be prepared upon heating equimolar quantities of pure Cr metal and pure S ia a small, evacuated, sealed quartz tube at 1000°C for at least 24 hours. The reaction is not quantitative (33). The sulfide has a coordination number of six and displays a distorted octahedral geometry (34). 

K2Cr(02)4, is obtained as stable red-brown crystals when H2O2 is added to a basic solution of K CrO maintained at 0°C (64). The geometry of Cr(V) in these crystals is dodecahedral, and its coordination number is 8 (63). 

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... 

The distinction between the first member of the group and the two heavier members, which was seen to be so sharp in the early groups of transition metals, is much less obvious here. The only unsubstituted, discrete oxoanions of the heavier pair of metals are the tetrahedral [Ru 04] and [Ru 04]. This behaviour is akin to that of iron or, even more, to that of manganese, whereas in the osmium analogues the metal always increases its coordination number by the attachment of extra OH ions. If RUO4 is dissolved in cold dilute KOH, or aqueous K2RUO4 is oxidized by chlorine, virtually black crystals of K[Ru 04] ( permthenate ) are deposited. These are unstable unless dried and are reduced by water, especially if alkaline, to the orange... 

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 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 ... 

Figure 6-3. Top Structure of the T6 single crystal unit cell. The a, b, and c crystallographic axes are indicated. Molecule 1 is arbitrarily chosen, whilst the numbering of the other molecules follows the application of the factor group symmetry operations as discussed in the text. Bottom direction cosines between the molecular axes L, M, N and the orthogonal crystal coordinate system a, b, c. The a axis is orthogonal to the b monoclinic axis.

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. 

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