PSI - Issue 23

Alla V. Balueva et al. / Procedia Structural Integrity 23 (2019) 173–178 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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general summary of methods and procedures carried out in order to obtain more data for use in further investigation and/or application. Thus, research in this frontier is successful but more progress is pending. Tooth implants composed of titanium steel coated with hydroxyapatite are possible. The biggest challenge faced right now is acquiring more information on the efforts to improve adhesion strength of hydroxyapatite coatings on the implants. 2.1. Binding energy of HAp and TCP components ions and Titanium We used Density Functional Theory [e.g. Kohn and Holthausen, 2001] to describe the chemical reaction of different configurations of Hydroxyapatite Ca 10 (PO 4 ) 6 (OH) 2 and Tricalcium Phosphate Ca 3 (PO 4 ) 2 component ions and Titanium and determined their geometric and chemical properties. By using the B3LYP hybrid-exchange correlation functional (Becke three-parameter Lee-Yang-Parr functional), which is well examined for ab initio calculations [Gross et. al., 1998], we determined the ground state energy of polyatomic complexes in the Ti (II) - hydroxyapatite system. The goal is a theoretical calculation of the energy of bonds of the HAp and titanium coatings. 2. Density Functional Theory and Molecular Dynamics Simulation Method

Fig. 3. Reaction path; calculations of binding energy Optimized structures for the complexes were obtained and frequency calculations were performed to ensure no imaginary frequencies were found [Kwon and Kubicki, 2004], and that therefore the obtained structures represent a global minimum [Jonsson and et.al, 1998]. For example, the vibrational frequency in polyatomic complex Ti(OH), which indicates as interaction between Ti (II) and the oxygen atom, the calculation gives a reasonable value of about 970 cm- 1 (e.g. Kwon and Kubicki, 2004). The stable complexes were used in the calculations of the binding energies. Binding energies were approximated as the difference between the individual energies of the reactants (Ca 3 (PO 4 ) 2 and Ti) and the product (Ca 3 (PO 4 ) 2 -Ti). The binding energies were obtained for Ca 3 (PO 4 ) 2 and its ion constituents. All calculations were carried out with the Gaussian 16 revision D.03 electronic structure package [Frisch et. al., 2016]. Pictures were generated with GaussView 16. In part I of the calculations, for Ti 2+ and different polyatomic complexes of different combinations of anions of hydroxyapatite, namely OH - , PO 4 3- , we found the ground state energy first, and then calcualted potential energy surfaces (PES) and the reaction pathways, to observe new stable configurations of the products of the reaction of Ti 2+ and the constituents of the hydroxyapatite coating, that deliver a minimum on the PES [e.g., Carr et. al., 2005]. In part 2, we added cations of Ca 2+ and repeated the calculations. In our single atom calculations, we modeled a Ti cation with a 2+ charge, because that is the most stable oxidation state for Ti. The phosphate, PO 4 3- , and hydroxide, OH - , are anions, and so negative anions cancel with positive cations of Ti to make neutral complexes.

3. Results of Ab-initio Calculations

3.1. Binding energy of Hydroxyapatite (Ca 10 (PO 4 ) 6 (OH) 2 ) components ions and Titanium Calculations for the polyatomic complexes in the Ti (II) -hydroxyapatite system were performed. These images