Coordination-number-bond-strength relationship

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... 

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. 

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... 

Knowing the coordination numbers, one can solve a number of crystal chemical problems. Thus, 80 years ago Goldschmidt discovered the dependence of the chemical bond length on the coordination number of a cation [245], At the same time Pauling introduced the concept of bond strength [246], according to which the valence of an atom i, which is linked to atoms j, obeys the relationship... 

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