The additive relation between composition and the unit-cell dimension (a) is explored for the few examples of francolites and dahllites for which adequate chemical data are available. This work yields estimates of coefficients for several atoms: Cl (+0.115), F (−0.015), C (−0.070) Å. A mean value for H (+0.0075) cannot at present be resolved to account for the several mechanisms by which protons may enter the apatite structure to produce hydrated carbonate apatites. The constant for the compositional model, Ca10(PO4)6X2, is evaluated as 9.404 Å.
Large coefficients for Cl, positive for a, negative for c, are significant with respect to several interpretations.
In carbonate apatites (CO3F) or (CO3OH) substitution for (PO4) completely fails to account for observed cationic ratios. The substitution of (CO3) for 2 F has not been demonstrated in any natural (well-crystallized) carbonate apatite; it has been surmised as an explanation for some poorly-characterized preparations, some of which certainly are not a single apatitic phase. Many reports in the literature are unreliable because only isolated aspects of the problem were considered.