First Principles Investigation of Mineral Component of Bone: CO₃ Substitutions in Hydroxyapatite

First principles calculations are used to investigate carbonated hydroxyapatite, a naturally occurring mineral and also the inorganic component of animal bone. Two types of carbonate substitution are studied: A-type in which the carbonate ion substitutes for an OH and B-type where the substitution is for a phosphate. Both types have unbalanced charges and various forms of charge compensation are treated. The methods, which are based on density functional theory and first principles pseudopotentials, yield equilibrium atomic arrangements, changes in lattice parameters, and total energies for different types of substitution. When calculated energies of selected stable compounds are used, the formation energies of different carbonate substitutions with accompanying charge compensation defects can be compared. The results indicate that compact complexes are energetically favored, and a B-type material with charge compensation by a calcium vacancy together with a hydrogen atom which bonds to a neighboring phosphate is the most stable of all those considered.