Valence rule, electrostatic

Silica, the silicates and, in general, crystals containing oxygen or fluorine and metal atoms which can form noble-gas type cations are found to satisfy the electrostatic valence rule and the other rules for ionic crystals, which indicates that the ionic character of these substances is of greatest importance. The sulfides of metals other than the alkalies and alkaline earths, on the other hand, do not satisfy these rules magnetic evidence further shows these substances not to be ionic. 

The structure leads to a general formula for the micas namely, KXMY.1Oio(OH,r )2, with 2 < < 3, in which X represents cations of coordination number 6 (Al+3, Mg+, Fe++, Fe+3, Mn++, Mn+3, Ti+ Li+, etc.) and Y cations of coordination number 4 (Si+4, A1+3, etc.). The subscript n can have any value between 2 (hydrargillite layer) and 3 (complete octahedral layer). K+ can be partially replaced by Na+ and possibly to some extent by Ca++. This formula represents satisfactorily the.numerous recently published mica analyses almost without exception.6 The distribution of the various ions X and Y must be such as to give general agreement with the electrostatic valence rule. 

The electrostatic valence rule is satisfied. The bond strength from S7+4, A +3, and Na+ are 1, -, and respectively, since the cations all have the coordination number 4. Each oxygen ion is in contact with 1 Si + i, 1 Al+i, and 1 Na+, giving JbV = 2, and each chlorine ion in contact with 4 Na+, giving Xs = 1, in agreement with their valences. 

Helvite was found to have a unit of structure with a0 = 8.25 A, containing %(Mn, Fe)iBe3Si3012S. The structure is similar to that of sodalite, the parameters having the values u = 0.175, x — 0.113, y = 0.416, z = 0.137. Both structures satisfy the electrostatic valence rule. 

Each oxygen ion is common to four octahedra, and has U = 2. in accordance with the electrostatic valence rule. ... 

The only remaining positions for 20 or 24 silicon atoms are 16 a plus one or two of the positions 4b, 4c, 4d, and 4e. Agreement with the electrostatic valence rule with silicon tetrahedra in 4 b (or c, d, e) is reached only when the corners are shared with other tetrahedra. The crystals must consequently contain groups of five tetrahedra such as shown in Fig. 2. 

Agreement with the electrostatic valence rule is satisfactory except for the oxygen atoms G (Fig. 4), common to only three oc-tahedra. It is seen, however, that these atoms occur in groups of four, which can be combined to tetra-hedra by placing aluminum ions in positions 4e, the total bond strengths then becoming 2 . The four chlorine ions occupy positions 4 c, 4 b being ruled out by the small Cl -0= distance it leads to (2.72 A, sum of radii 3.21 A). 

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. 

YIG (yttrium iron garnet), Y3Fe5012, has the same structure as garnet. Which are the appropriate sites for the Y3+ and Fe3+ ions If the electrostatic valence rule is insufficient for you to come to a decision, take ionic radii as an additional criterion. 

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 ... 

Since all cations have the same charge (+3), the electrostatic valence rule is of no help. The larger Y3+ ions will take the sites with c.n. 8. 

The electrostatic valence rule has turned out to be a valuable tool for the distinction of... 

The Number of Polyhedra with a Common Corner The Electrostatic Valence Rule.—In silica crystals, Si02, each silicon ion is surrounded by four oxygen ions64 at tetrahedron corners. In order for the stoichio-... 

Two adjacent aluminum tetrahedra, sharing a corner, contribute two bonds of strength f to the shared oxygen atom. The total of (which might be increased by a small amount by bonds from alkali or alkaline-earth ions) represents a deviation from the electrostatic valence rule such that in general in aluminosilicates of the tetrahedral framework type the Al/Si ratio does not exceed 1, and when it equals 1 there is good ordering, with alternation of the aluminum and silicon tetrahedra. 

There are many ways in which the electrostatic valence rule can be used oilier than those relating directly to the structure of crystals. Some of the e are discussed in the following paragraphs. 

The electrostatic valence rule can be satisfied for sulfuric acid by the formation of OHO hydrogen bonds between molecules, the strength of the electrostatic bond of a shared proton being taken as . This situa-... 

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