Electrostatic bond strength

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

Let a be the coordination number of an anion. Of the set of its a adjacent cations, let nt be the charge on the i-th cation and kl its coordination number. The electrostatic bond strength of this cation is ... 

Let the cation M2+ in a compound MX2 have coordination number 6. Its electrostatic bond strength is s = 2/6 = The correct charge for the anion, z = -1, can only be obtained when the anion has the coordination number a = 3. 

Let the cation M4+ in a compound MX4 also have coordination number 6 its electrostatic bond strength is s = 4/6 = . For an anion X- having coordination number a = 2 we obtain = + = for an anion with a = 1 the sum is = . For other values of a the resulting p deviate even more from the expected value z = -1. The most favorable structure will have anions with a = 2 and with a = 1, and these in a ratio of 1 1, so that the correct value for z results in the mean. 

The electrostatic valence rule usually is met rather well by polar compounds, even when considerable covalent bonding is present. For instance, in calcite (CaC03) the Ca2+ ion has coordination number 6 and thus an electrostatic bond strength of s(Ca2+) =. For the C atom, taken as C4+ ion, it is s(C4+) =. We obtain the correct value of z for the oxygen atoms, considering them as O2- ions, if every one of them is surrounded by one C and two Ca particles, z = -[2s(Ca2+) + s(C4+)] = -[2 j + ] = -2. This corresponds to the actual structure. NaN03 and YBOs have the same structure in these cases the rule also is fulfilled when the ions are taken to be Na+, N5+, Y3+, B3+ and 02. For the numerous silicates no or only marginal deviations result when the calculation is performed with metal ions, Si4+ and 02 ions. 

The electrostatic valence rule has turned out to be a valuable tool for the distinction of the particles O2-, OH- and OH2. Because H atoms often cannot be localized reliably by X-ray diffraction, which is the most common method for structure determination, O2-, OH- and OH2 cannot be distinguished unequivocally at first. However, their charges must harmonize with the sums pj of the electrostatic bond strengths of the adjacent cations. 

Kaolinite, Al2Si205(0H)4 or Al203-2Si02-2H20 , is a sheet silicate with A1 atoms in octahedral and Si atoms in tetrahedral coordination the corresponding electrostatic bond strengths are ... 

Calculate the electrostatic bond strengths of the cations and determine how well the electrostatic valence rule is fulfilled. Calculate the expected individual V-O bond lengths using data from Table 7.2 and the values d(V4+0) = 189 pm and b(V4+0) = 36 pm. 

The coordination of an O2- ion is three Al3+ ions within an A1404 cube and one Mg2+ ion outside of this cube. This way it fulfills the electrostatic valence rule (Pauling s second rule, cf p. 58), i.e. the sum of the electrostatic bond strengths of the cations corresponds exactly to the charge on an O2- ion ... 

These principles are phrased in the language of the ionic model, but they provide a simpler and more explicit description of stable structures than that given by the ionic model s energy minimization principle. Among the important ideas captured by Pauling s rules are those of local charge neutrality, the definition of electrostatic bond strength, and the rule of parsimony which is closely... 

OH and OH2 cannot be distinguished unequivocally at first. However, their charges must harmonize with the sums pj of the electrostatic bond strengths of the adjacent cations. Example 7.3... 

The atoms in a sheet are situated in planes with the sequence O(l)-Al-O(2)-Si-O(3) (cf. Fig. 16.21e, p. 183). The particles 0(2), which are shared by octahedra and tetrahedra, have c.n. 3 (2xAl, IxSi), the other O particles have c.n. 2. We calculate the following sums of electrostatic bond strengths ... 

Pauling s second mle is the electrostatic valence mle. It states that the charge on an ion must be balanced by an equal and opposite charge on the surrounding ions. A cation, coordinated by n anions, has an electrostatic bond strength (BBS) for each bond defined as ... 

The number, q, of valence electrons on sites with different electrostatic bond strength sums in MgAl<0,N)2. Four different structures with this composition are considered. In these calculations ail anions were given identical parameters intermediate between those of O and N, so that variations in q reflect differences associated with the sites, not the nature of the anions. 

A priori probabilities and electrostatic bond strengths of the different types of oxygens present in an Al modified spinel. 

This rule implies that as far as possible the environment of all chemically similar atoms in a structure will be similar. Thus, even if the second rule admits several types of co-ordination about the anions, only one of these types of co-ordination may be expected to obtain and to be common to all anions. To illustrate this rule we may consider the structure of garnet. This mineral, the structure of which will be considered later ( 11.12), in one form has the composition Ca3Al2Si3012, and for our present purposes may be treated as an ionic crystal. The Ca2+, Al3+ and Si4+ ions are 8-, 6- and 4-co-ordinated, respectively, by O2-ions, so that the electrostatic bond strengths of the several bonds are as follows ... 

The electrostatic bond strength depends strongly on the value assumed for the dielectric constant, and therefore on the separation of the charges and the proximity of any water molecules. One reason why the theoretical prediction of protein three-dimensional structure from the amino acid sequence is so difficult is because of the prevalence of water in vivo and the large value of the dielectric constant for water (80) as a result the force between charges varies dramatically depending on the number of water molecules interposed between the charges. 

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