Formation Energies of Substitutional Sodium and Potassium in Hydroxyapatite

First-principles calculations are performed to investigate atomic and electronic structures of Na+ and K+ ions substituting for Ca2+ in hydroxyapatite (HAp). Formation energies of the substitutional defects are obtained from total energies of defective HAp supercells and chemical potentials determined by assuming chemical equilibrium between HAp and HAp-saturated aqueous solution containing Na+ or K+. It is found that substitutional Na+ with a charge-compensating interstitial proton is more stably formed, as compared to substitutional K+. This may be related to the fact that Na+ is generally more abundantly involved in bones and tooth enamels than K+.