Formation Energies of Substitutional Sodium and Potassium in Hydroxyapatite

Abstract

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⁺.