The effect of chemical potential on the thermodynamic stability of carbonate ions in hydroxyapatite

First-principles calculations were performed for CO32− ions in hydroxyapatite in order to investigate the atomic structures and thermodynamic stability of CO32− and its related defects. Two different chemical equilibrium conditions in high-temperature and aqueous-solution environments were considered, and atomic and ionic chemical potentials for the individual chemical equilibrium conditions were evaluated to calculate defect formation energies. It was found that A-type CO32− (substituting OH−) is energetically more favorable than B-type CO32− (substituting PO43−) in the high-temperature environment, whereas B-type is preferred to A-type in the aqueous solution environment. This result successfully reproduces experimentally observed trends. In the formation of A-type and B-type CO32−, OH− vacancies or protons (interstitial or substitutional) act as charge-compensating defects.