Lattice energies of apatites and the estimation of DeltaH f degrees (PO 4 3-, g).

Experimentally based lattice energies are calculated for the apatite family of double salts M(5)(PO(4))(3)X, where M is a divalent metal cation (Ca, Sr, Ba) and X is hydroxide or a halide. These values are also shown to be estimable, generally to within 4%, using the recently derived Glasser-Jenkins equation, U(POT) = AI(2I/V(m))(1/3), where A = 121.39 kJ mol(-)(1). The apatites exhibiting greater covalent character (e.g., M = Pb, Cd, etc.) are less well reproduced but are within 8% of the experimentally based value. The lattice energy for ionic apatites (having identical lattice ionic strengths, I) takes the particularly simple form U(POT)/kJ mol(-)(1) = 26680/(V(m)/nm(3))(1/3), reproducing cycle values of U(POT) well when V(m) is estimated by ion volume summation and employing a volume for the PO(4)(3)(-) ion (not previously quantified with an associated error) of 0.063 +/- 0.003 nm(3). A value for the enthalpy of formation of the gaseous phosphate ion, DeltaH(f)( ) degrees (PO(4)(3)(-), g), is absent from current thermochemical tabulations. Examination of solution and solid state thermochemical cycles for apatites, however, leads us to a remarkably consistent value of 321.8 +/- 1.2 kJ mol(-)(1). Experimental and estimated lattice energies were used along with other thermodynamic data to determine enthalpies, entropies, and free energies of dissolution for apatites of uncertain stabilities. These dissolution values are compared with the corresponding values for stable apatites and are used to rationalize the relative instability of certain derivatives.