Star-tetrahedron transformation and calculation of bond energies at the crystal-mother phase boundary

It is shown how a crystal structure, consisting of coupled tetrahedra with π ions in the centre, can be transformed in a π free structure with a new set of bonds. This transformation is called the star-tetrahedron transformation. A spin formalism is used in which ions of a crystallographic structure are supposed to be either in a solid or a fluid state. In the formalism only first nearest neighbour bonds are taken into account. Expressions are derived from which the bond energies of the new system of bonds can be calculated from the old system. The formalism leads to a broken bond approach, so giving a basis for a PBC analysis according to the morphological theory of Hartman and Perdok. It is shown that the degree of association of growth units in the mother phase is taken into account.