DOI: https://doi.org/10.20535/kpi-sn.2019.1.158692

QUANTUM-MECHANICAL CALCULATIONS OF THE CARBONATE-CONTAINING CALCIUM APATITES ATOMIC AND ELECTRONIC STRUCTURE

Anastas A. Romansky, Lyubov I. Karbivska, Volodymyr L. Karbivskyy, Olena Ya. Kuznetsova, Viktor V. Stonis, Arsen P. Soroka

Abstract


Background. The inclusion of the CO32- ion into the structure of apatite leads to significant changes in the chemical and physical characteristics of the mineral. The growth rate of the hydroxyapatite crystal significantly decreases with carbonate ions, and the resistance of the tooth enamel and bones to acids is reduced. At the same time, the concentration of CO32- in bone apatite controls the shape and size of nanocrystals of this mineral, which is an important condition for the preservation of nanoscale effects of these crystals and, accordingly, plays an important role in the processes of bone metabolism.

Objective. The aim of the paper is theoretical study of the effect of the inclusion of CO32- ion into the apatite structure on the atomic and the electronic structure of the mineral.

Methods. Calculations within the density functional theory (DFT) using the Wien2k package, which based on the full-potential (linearized) augmented plane-wave ((L)APW) + local orbitals (lo) method, using the Perdew–Burke–Ernzerhof generalized gradient approximation for solids (PBEsol-GGA).

Results. Atomic coordinates, bond lengths, total and partial densities of the electronic states of apatites Са10(РO4)6(ОН)2, Са10(РO4)6СО3, Са10(РO4)6ОН(СО3)0.5, Са9Ñ(РO4)5(СО3)(ОН)2 are calculated using the density functional theory. The effect of isomorphic substitution of A and B types on the electronic structure of apatite-like compounds has been investigated. Changes in the atomic structure of apatite are analyzed when CO32- ions are included in its structure, both in the anion and the phosphate tetrahedron positions. Comparison of calculated and experimental data was carried out.

Conclusions. It was shown that the structure of the occupied part of the valence bands of both types of isomorphically substituted calcium apatites retains a pronounced band character with different lengths of individual sub-bands. Two energy-separated structural regions were revealed – the upper part of the valence band and the lower part of the valence band – subvalent states. The structure of the middle part of the valence band (the region of valence states with energies from ~14 to 19 eV) is poorly expressed. The main contribution to the formation of the main features of the upper part of the valence band of the studied apatites is made by the hybridized s-, p- and partially d-electronic states of calcium and phosphorus ions. The structure of subvalent states is determined by the s states of oxygen, phosphorus and partly metal. The sublattice of oxygen tetrahedra is decisive in the formation of the shape and main features of the total density of electronic states curve of isomorphically substituted calcium apatites. In the case of B-type substitutions, a significant spatial distortion of the carbonate ion occurs.

Keywords


Calcium apatite; Isomorphic substitution; Density functional theory; Density of electronic states; Atomic coordinates; Bond lengths

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