Coordination-number-bond-strength

The coordination-number-bond-strength relationship is qualitatively captured in simple tight-binding schemes in which the energy per bond can be assumed to scale with sfC leading to... 

Properties of the generated gel structure at the point of gelation Structure, primary, coordination number, porosity, strength of solid bonds or type of particle-particle interactions... 

It can be readily confirmed thaf by decreases as the number of bonds N increases and/or llieir length (r ) decreases. This relationship between the bond strength and the number of neighbours provides a useful way to rationalise the structure of solids. Thus the high coordination of metals suggests that it is more effective for them to form more bonds, even though each individual bond is weakened as a consequence. Materials such as silicon achieve the balance for an infermediate number of neighbours and molecular solids have the smallest atomic coordination numbers. 

Table 1. Coordination Number and Bond Strengths of Oxides ...

The IR stretching frequencies o(SN) and o(SF) occur at higher wave numbers and the S-N and S-F distances are significantly shorter in the octahedral cations [M(NSF)6] than those in the free ligand, indicating an increase in S-N and S-F bond strength upon coordination. 

Ion Radius ratio Predicted coordination number Observed coordination number Strength of electrostatic bonds... 

The Number of Polyhedra with a Common Corner. The Electrostatic Valence Principle.—The number of polyhedra with a common corner can be determined by the use of an extended conception of electrostatic valence. Let ze be the electric charge of a cation and v its coordination number. Then the strength of the electrostatic valence bond going to each comer of the polyhedron of anions about it is defined as... 

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. 

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. 

Rumpf (R4) has derived an explicit relationship for the tensile strength as a function of porosity, coordination number, particle size, and bonding forces between the individual particles. The model is based on the following assumptions (1) particles are monosize spheres (2) fracture occurs through the particle-particle bonds only and their number in the cross section under stress is high (3) bonds are statistically distributed across the cross section and over all directions in space (4) particles are statistically distributed in the ensemble and hence in the cross section and (5) bond strength between the individual particles is normally distributed and a mean value can be used to represent each one. Rumpf s basic equation for the tensile strength is... 

We saw in Chapter 5 that the length of a bond also depends on the coordination number of the atom to which it is bonded, increasing with increasing coordination number. So we can summarize the factors determining bond strengths and lengths as follows ... 

Oxide ratio, 18 815 Oxides, 16 598 acidic, 22 190-191 bond strengths and coordination numbers of, 22 570t diorganotin, 24 819 glass electrodes and, 14 28 gold, 22 707 iron, 14 541-542 lead, 14 786-788 manganese, 15 581-592 nickel, 27 106-108 niobium, 27 151 plutonium, 29 688-689 in perovskite-type electronic ceramics, 14 102... 

---