Ionic bond 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]. 

Ionic bond, 287, 288 dipole of, 288 in alkali metal halides, 95 vs. covalent, 287 Ionic character, 287 Ionic crystal, 81, 311 Ionic radius, 355 Ionic solids, 79, 81, 311 electrical conductivity, 80 properties of, 312 solubility in water, 79 stability of, 311... 

Ions stack together in the regular crystalline structure corresponding to lowest energy. The structure adopted depends on the radius ratio of cation and anion. Covalent character in an ionic bond itnposes a directional character on the bonding. 

Ionic radii are quoted in Tables 2.3 and 2.5 for a large number of cations including those of the elements in groups 13, 14, 15, and 16, which do not form predominately ionic bonds. These values were obtained by subtracting the fluoride or oxide ion radius obtained from predominantly ionic solids from the length of a bond that is not predominantly ionic. The very small values for the radii of cations obtained in this way do not bear much relation to the real size of the atom in the crystal or molecule. 

Chromium has a similar electron configuration to Cu, because both have an outer electronic orbit of 4s. Since Cr3+, the most stable form, has a similar ionic radius (0.64 A0) to Mg (0.65 A0), it is possible that Cr3+ could readily substitute for Mg in silicates. Chromium has a lower electronegativity (1.6) than Cu2+ (2.0) and Ni (1.8). It is assumed that when substitution in an ionic crystal is possible, the element having a lower electronegativity will be preferred because of its ability to form a more ionic bond (McBride, 1981). Since chromium has an ionic radius similar to trivalent Fe (0.65°A), it can also substitute for Fe3+ in iron oxides. This may explain the observations (Han and Banin, 1997, 1999 Han et al., 2001a, c) that the native Cr in arid soils is mostly and strongly bound in the clay mineral structure and iron oxides compared to other heavy metals studied. On the other hand, humic acids have a high affinity with Cr (III) similar to Cu (Adriano, 1986). The chromium in most soils probably occurs as Cr (III) (Adriano, 1986). The chromium (III) in soils, especially when bound to... 

The overall distribution of lanthanides in bone may be influenced by the reactions between trivalent cations and bone surfaces. Bone surfaces accumulate many poorly utilized or excreted cations present in the circulation. The mechanisms of accumulation in bone may include reactions with bone mineral such as adsorption, ion exchange, and ionic bond formation (Neuman and Neuman, 1958) as well as the formation of complexes with proteins or other organic bone constituents (Taylor, 1972). The uptake of lanthanides and actinides by bone mineral appears to be independent of the ionic radius. Taylor et al. (1971) have shown that the in vitro uptakes on powdered bone ash of 241Am(III) (ionic radius 0.98 A) and of 239Pu(IV) (ionic radius 0.90 A) were 0.97 0.016 and 0.98 0.007, respectively. In vitro experiments by Foreman (1962) suggested that Pu(IV) accumulated on powdered bone or bone ash by adsorption, a relatively nonspecific reaction. On the other hand, reactions with organic bone constituents appear to depend on ionic radius. The complexes of the smaller Pu(IV) ion and any of the organic bone constituents tested thus far were more stable (as determined by gel filtration) than the complexes with Am(III) or Cm(III) (Taylor, 1972). 

Equation (2) contains the value of actual dimensional bond characteristic of the given atom in the structure. In crystals with basic ionic bond, the ion radius can be applied as such dimensional bond characteristic (with a certain approximation), i.e. the stabilization condition for such structures is as follows ... 

IONIC BOND IONIC RADIUS IONIC STRENGTH ISOTONIC BUFFERS DAVIES EQUATION DEBYE-HOCKEL THEORY Ion-ion interactions,... 

Element Non-bonded radius MIV covalent radiusb M" ionic radiusb Mn ionic radiusb... 

Covalent Radii. Just as with ionic bonds (Eq. 3.16), attempts have been made to express observed distances between covalently bonded atoms as the sum of two contributions, each term corresponding to the radius of one atom. The result of these efforts, a listing of covalent radii, is given in Table 4.4. 

For the trivalent lanthanides99-100 and actinides,99 as well as for yttrium and scandium,75 the equilibrium constant for the extraction reaction has been shown to vary inversely with the ionic radius of the metal ion. It has therefore been concluded that the extracted complexes are all of the M(HA2)3 type, involving predominantly ionic metal—ligand bonds.75 The similarity of the IR spectra of the scandium(III) and thorium(IV) complexes of D2EHPA to those of the alkali metals is also indicative of the importance of ionic bonding.102... 

The electron cloud around an atomic nucleus makes the concept of atomic size somewhat imprecise, but it is useful to refer to an atomic radius. One can arbitrarily divide the distance between centers of two bonded atoms to arrive at two radii, based on the crude picture that two bonded atoms are spheres in contact. If the bonding is covalent, the radius is called a covalent radius (see Table 8-2) if it is ionic, the radius is an ionic radius (see Table 9-2). The radius for non-bonded atoms may be defined in terms of the distance of closest non-bonding approach such a measure is called the van der Waals radius. These three concepts of size are illustrated in Figure 7-2. 

Since an a priori definition of the effective region is hardly possible, each atomic region is usually approximated by a spherical region around the atom, where the radius is taken as its ionic, atomic, or covalent bond radius. The radial distribution of electron density around an atom is also useful to estimate the effective radius of an atom, particularly in ionic crystals. In an ionic crystal, the distance from the metal nucleus to the minimum in the radial distribution curve generally corresponds to the ionic radius. As an example, the radial distribution curves around K in o-KvCrO., (85) are shown in Fig. 19a. The radial distributions of valence electrons (2p electrons) exhibit a minimum at 1.60 A for K(l) and 1.52 A for K(2), respectively. These distances correspond to the ionic radii in crystals (1.52-1.65 A)... 

In reality H+, a bare proton, cannot exist alone except in isolation inside a high vacuum. The radius of H+ is about 1.5 x 10-15 m, which is 105 times smaller than other atoms. When H+ approaches another atom or molecule, it can distort the electron cloud of the latter. Therefore, other than in a gaseous ionic beam, H+ must be attached to another atom or molecule that possesses a lone pair of electrons. The proton as an acceptor can be stabilized as in pyramidal hydronium (or hydroxonium) ion H30+, tetrahedral NH4, and linear H2F+. These cations generally combine with various anions through ionic bonding to form salts. 

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