Ordinal number

An unstable lower oxidation stale is found in Cd - CdCl and Cd - CdCl - AICI3 melts and may contain Cd — Cd bonds. The common co-ordination number for Cd is 6 (octahedral) although 4 and 5 co-ordination are known. 

The co-ordination number in ionic compounds is determined by the radius ratio - a measure of the necessity to minimize cationic contacts. More subtle effects are the Jahn-Teller effect (distortions due to incomplete occupancy of degenerate orbitals) and metal-metal bonding. 

This then is the limiting radius ratio for six nearest neighbours— when the anion is said to have a co-ordination number of 6. Similar calculations give the following limiting values ... 

For eight nearest neighbours (a co-ordination number of 8) the radius ratio r /r must not be less than 0.73. 

Examples of two crystal structures for each co-ordination number are included in the table. 

Fluorite. CaF,. and rutile. TiO,. are minerals in CaFj, each Ca is surrounded by eight F ions, each F by tour C r ions, while in TiO, ihe corresponding co-ordination numbers are 6 and 3. Co-ordination number is generally referred to the cation. 

Central unit Ligand Co-ordination number Ligand type Complex ion Shape... 

Note that the Be ion has a co-ordination number of 4 whereas most cations have a co-ordination number of six. This is again the result of the very small size. 

Here ao is the lattice parameter of die ctystal. An approximate value for the bond energy, , for this structure where the co-ordination number, Z, equals twelve is given by... 

Turning to non-metallic catalysts, photoluminescence studies of alkaline-earth oxides in dre near-ultra-violet region show excitation of electrons corresponding to duee types of surface sites for the oxide ions which dominate the surface sUmcture. These sites can be described as having different cation co-ordination, which is normally six in the bulk, depending on the surface location. Ions on a flat surface have a co-ordination number of 5 (denoted 5c), those on the edges 4 (4c), and dre kiirk sites have co-ordination number 3 (3c). The latter can be expected to have higher chemical reactivity than 4c and 5c sites, as was postulated for dre evaporation mechanism. 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

In liquid metal solutions Z is normally of the order of 10, and so this equation gives values of Ks(a+B) which are close to that predicted by the random solution equation. But if it is assumed that the solute atom, for example oxygen, has a significantly lower co-ordination number of metallic atoms than is found in the bulk of die alloy, dieii Z in the ratio of the activity coefficients of die solutes in the quasi-chemical equation above must be correspondingly decreased to the appropriate value. For example, Jacobs and Alcock (1972) showed that much of the experimental data for oxygen solutions in biiiaty liquid metal alloys could be accounted for by the assumption that die oxygen atom is four co-ordinated in diese solutions. 

Generalized methods for ealeulating random paeking fraetions and eo-ordination number of size distributions have been proposed, but are very eomplex and usually apply to spheres having partieular size distributions. Unfortunately, the produets of industrial erystallizers frequently eontain a wide variety of both shape and size distribution not amenable to eonventional theories, leading to error in voidage estimation. Often therefore, voidage is simply a measured quantity for a partieular industrial material. 

Ordnungszahl, /. number in a series, serial number, specif, atomic number ordinal number, org., ab ev. (organiseh) organie. 

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