Coordination number ionic crystals

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. 

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 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 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 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... 

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... 

Probably, the first series of lanthanide complexes with neutral oxygen donor ligands is that of AP with the lanthanide nitrates. In 1913, Kolb (79) reported tris-AP complexes with lighter lanthanide nitrates and tetrakis-AP complexes with heavier lanthanide nitrates. Subsequently, complexes of lanthanide nitrates with AP which have a L M of 6 1 and 3 1 have also been prepared (80-82). Bhandary et al. (83) have recently shown through an X-ray crystal and molecular structure study of Nd(AP)3(N03)3 that all the nitrates are bidentate and hence the coordination number for Nd(III) is nine in this complex. Complexes of AP with lanthanide perchlorates (81, 84), iodides (81, 85), and isothiocyanates (66, 86, 87) are known. While the perchlorates and iodides in the respective complexes remain ionic, two of the isothiocyanates are coordinated in the corresponding complexes of AP with lanthanide isothiocyanates. 

Table 1.11 Effective crystal radii (CR) and ionic radii (IR) of Shannon (1976). CN = coordination number SP = spin sp = square planar py = pyramidal EIS = high spin LS = low spin data in A. 

Symbol Ba atomic number 56 atomic weight 137.327 a Group llA (Group 2) alkaline earth element electronic configuration [Xejs valence state +2 ionic radius of Ba2+ in crystal (corresponding to coordination number 8) 1.42 A first ionization potential lO.OOeV stable isotopes and their percent abundances Ba-138 (71.70), Ba-137 (11.23), Ba-136 (7.85), Ba-135 (6.59), Ba-134 (2.42) minor isotopes Ba-130 (0.106) and Ba-132 (0.101) also twenty-two radioisotopes are known. 

Symbol Na atomic number 11 atomic weight 22.9898 a Group lA (Group 1) alkali metal element electron configuration [NejSs valence +1 atomic radius 1.85A ionic radius, Na" in crystals 1.02A (for a coordination number 6) ionization potential 5.139 eV standard electrode potential, E°(Na+ + e Na) -2.71 V one naturally-occurring stable isotope, Na-23 (100%) sixteen artificial radioactive isotopes in the mass range 19-22, 24—35 longest-lived radioisotope, Na-22, ti/2 2.605 year shortest-lived isotope Na-35, ti/2 1.5 ms. 

However, since only values of rexpti are obtained, it is necessary to assume a value for the ionic radius of either r+ or r- in order to derive the ionic radius of the other. It is usual to assume a value of 1.40 A for the radius of the and 1.94 A for the radius of CP (Pauling, 1948) because these are half the minimum anion-anion distances found in crystal structures. Values for ionic radii (Shannon and Prewitt, 1969 Shannon, 1976 Brown, 1988) are listed in Table V for a coordination number of 6 around the metal atoms. Thus, values of radii are hypothetical, based on the idea of an additivity rule and a few initial assumptions on anion size. 

---