Ionic radii coordination numbers

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. 

Fig. 25. The quantity Af//°(inCl3, cr) — Afff°(In3+,aq) as a function of the ionic radius (coordination number 6) , monoclinic and o hexagonal structure.

Ion Ionic radius Coordination number Typical geometry of inner-sphere complex First of [M(H20) ]"+T 2 " 22... 

Symbol Ho atomic number 67 atomic weight 164.93 a lanthanide series rare earth element electron configuration [Xe]4/ii6s2 valence state +3 metallic radius (coordination number 12) 1.767A atomic volume 18.78 cc/mol ionic radius Ho3+ 0.894A one naturally occurring isotope. Ho-165. 

Symbol Lu atomic number 71 atomic weight 174.97 a lanthanide series element an /-block inner-transition metal electron configuration [Xe]4/i45di6s2 valence -1-3 atomic radius (coordination number 12) 1.7349A ionic radius (Lu3+) 0.85A two naturally-occurring isotopes Lu-176 (97.1%) and Lu-175(2.59%) Lu-172 is radioactive with a half-life of 4xl0i° years (beta-emission) several artificial isotopes known, that have mass numbers 155, 156, 167—174, 177—180. 

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. 

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]. 

X Me Second cation present, with coordination number greater than 6 (second cation s ionic radius > tantalum/niobium ionic radius) Only cations that can fit into/occupy octahedral voids are present (second cation s ionic radius tantalum/niobium ionic radius)... 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

The Fe—O distances in hematite are 1.99 and 2.06 A. The (Mn,Fe)—O distances in bixbyite are expected to be the same in case that (Mn, Fe) has the coordination number 6, and slightly smaller, perhaps 1.90 A, for coordination number 4. The radius of 0= is 1.40 A, and the average O—O distance in oxide crystals has about twice this value. When coordinated polyhedra share edges the O—O distance is decreased to a minimum value of 2.50 A, shown by shared edges in rutile, anatase, brookite, corundum, hydrargillite, mica, chlorite, and other crystals. Our experience with complex ionic crystals leads us to believe that we may... 

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

The ions that tend to be involved in AB cements include such species as Al , Mg, Ca and Zn. These are all capable of developing a coordination number of six, and hexaquo cations are known to be formed by each of these metal ions (Huckel, 1950). The typical requirements for an ion to develop such coordination characteristics are that the ion should exist in the -I- 2 or -1-3 oxidation state, and in this state should be of small ionic radius (Greenwood Earnshaw, 1984). 

The ionic radii listed in Tables 6.3 and 6.4 in most cases apply to ions which have coordination number 6. For other coordination numbers slightly different values have to be taken. For every unit by which the coordination number increases or decreases, the ionic radius increases or decreases by 1.5 to 2 %. For coordination number 4 the values are approximately 4 % smaller, and for coordination number 8 about 3 % greater than for coordination number 6. The reason for this is the mutual repulsion of the coordinated ions,... 

Several additional, more complicated structure types are known for ionic compounds. For example, according to the radius ratio, one could expect the rutile type for strontium iodide (rSr2+ /i = 0.54). In fact, the structure consists of Sr2+ ions with a coordination number of 7 and anions having two different coordination numbers, 3 and 4. 

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