Lattice energy and mechanical stiffness of hydroxyapatite.

The lattice energy of the stoichiometric hydroxyapatite is calculated using three methods: the thermochemical method called Born-Fajans-Haber cycle (BHFC), the semi-empirical electrostatic method based on the generalized Kapustinskii equation, and the Glasser-Jenkins unit cell volume method. The three values of the lattice energy of the hydroxyapatite derived by the three methods are within 4% difference to each other (BHFC: 34,191 KJ/mole, generalized Kapustinskii equation: 32,808.9 KJ/mole, unit cell volume: 32,997.4 KJ/mole). The Voigt and Reuss effective elastic moduli of 19 simple ionic crystals, including those of the hydroxyapaptite, are calculated and are found to be linearly dependent on their volumetric lattice energy density (LED).