Lattice repulsion energy

The free electron resides in a quantized energy well, defined by k (in wave-numbers). This result Ccm be derived from the Schroedinger wave-equation. However, in the presence of a periodic array of electromagnetic potentials arising from the atoms confined in a crystalline lattice, the energies of the electrons from all of the atoms are severely limited in orbit and are restricted to specific allowed energy bands. This potential originates from attraction and repulsion of the electron clouds from the periodic array of atoms in the structure. Solutions to this problem were... 

Table 5.37 Lattice energy terms for C2/c pyroxenes. Values in kJ/mole. bhf = energy of Born-Haber-Fayans thermochemical cycle U- = lattice energy Ec = coulombic energy = repulsive energy Edd = dipole-dipole interactions E q = dipole quadrupole interactions =...

A second major contributor or the lattice energy of an ionic crystal is the repulsive energy. Following Born and Huang (1954), the repulsive energy per mole may be written as... 

The lattice energy is the sum of the electrostatic and repulsive energies, and per mole is given by... 

Rule 11.4 (Principle of close packing). Like ions tend to lie on close packed lattices, since this arrangement minimizes their repulsive energy when they are confined to a fixed volume. 

The structural energy difference theorem requires that we prepare the lattices so that they all display the same repulsive energy. It follows from eqs (8.45)-(8.47) that the repulsive energy per AB unit may be written... 

Returning to Eq. 4.5 we see that unless there is a repulsion energy to balance the attractive coulombic energy, no stable lattice can result The attractive energy becomes infinite at infinitesimally small distances. Ions are, of course, not point charges but consist of electron clouds which repel each other at very close distances. This repulsion is shown by the dashed line in Fig. 4.6. It is negligible at large distances but increases very rapidly as the ions approach each other closely... 

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