Theoretical investigation of the defect formation mechanism relevant to nonstoichiometry in hydroxyapatite

Abstract

Electronic and atomic structures of vacancies and protons in hydroxyapatite ͑HAp͒ are analyzed by using first-principles band structure calculations. From total energies of supercells for monoclinic HAp, defect formation energies and equilibrium concentrations are evaluated, assuming chemical equilibrium between HAp and aqueous solution saturated with respect to HAp. It is found that interstitial and Ca-substitutional protons form H 2 O groups or acid phosphates of HPO 4 2− and are stabilized by making hydrogen bonding with adjacent PO 4 3− groups. Moreover, defect association considerably decreases the defect formation energies, and, in particular, interstitial protons bonded to OH − groups become most stable when associated with Ca-substitutional protons. Due to abundant formation of the associated defect comprising interstitial and Ca-substitutional protons, Ca contents in HAp decrease with lowering pH, which explains pH dependence of Ca/ P molar ratios of HAp observed experimentally.

Theoretical Defect Energetics in Calcium Phosphate Bioceramics

“…For calcium phosphate bioceramics, chemical equilibrium between calcium phosphate and the surrounding aqueous solution is often encountered. Because the atomic species i generally dissolves in aqueous solution as the ionized state of charge z i , it is convenient to express not by the atomic chemical potentials μ i but by the ionic chemical potentials 78 . Note that the chemical potentials of the ionic species is obtained by , can be rewritten as E T and Δ V av can be obtained from first‐principles calculations.…”

First-principles investigation of polarization and ion conduction mechanisms in hydroxyapatite

“…In Ref. 13, it was reported that interstitial protons can be stabilized in low pH conditions in Ca-deficient HAp, and that the most stable position for the interstitial proton is on the OH − ion, forming an H 2 O-molecule like structure. Bonding with PO 3− 4 with an O-H· · · O linkage with an adjacent PO 3− 4 group was also found to be locally stable.…”

Calcium orthophosphates

“…It is considered that a portion of PO 4 3- ions is either protonated (as HPO 4 2- ) or substituted by other ions (e.g., CO 3 2- ) 320 . Theoretical investigations of the defect formation mechanism relevant to non-stoichiometry in CDHA are available in reference 321.…”