PSI - Issue 42

Alla V. Balueva et al. / Procedia Structural Integrity 42 (2022) 9–17 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3. Titanium dioxide [ TiO 2 ] post- geometric optimization. The white/grey atom is titanium while the red atoms are oxygens.

Fig. 2. Phosphate [ PO 4 ] post- geometric optimization. The orange atom Is phosphorus while the red ones are the oxygens.

Figure 3 shows the optimized structure of titanium dioxide TiO 2 after Gaussian09 calculations and it has a ground state energy of -999.8 a.u. The charge of the titanium is 1.073, and the bond length between Ti and each O is 1.71 Å. The bond angle between the titanium and oxygens is 180 degrees. We can see that the titanium, originally with a charge of 2+, changed to 1.073+. Each oxygen, initially with a charge of 1-, changed to 0.537-, which means a part of electrons from oxygen atoms were accepted by Ti , to have this structure TiO2 in more favorable configuration with the minimum of energy. Notice that 1.073+(-0.537-0.537) ≈ 0. All the charges cancel each other out, meaning the molecule has a total charge of 0. 3.2. Reaction of Titanium dioxide with Tricalcium phosphate (TiO 2 Ca 3 (PO 4 ) 2 ) After running the previous steps and adding three calcium atoms on this step, the product of the reaction of the coating, titanium dioxide, TiO 2 , and the substrate tricalcium phosphate, Ca 3 (PO 4 ) 2 , the structure we have been trying to construct, was successfully built from the bottom up (Figures 4a and 4b). The final product TiO 2 Ca 3 (PO 4 ) 2 has a ground-state energy of ‒ 4317.3 a.u. The bond angle increased in TiO 2 structure increased from 126.43 degrees to 134.68 degrees. The charge of the titanium decreased even more, from 1.191+ to 0.963+, while the charge of other big atoms in this structure, two phosphorus (1.485+ and 1.544+), almost did not change, which indicates to the redistribution of electrons from P toward Ti , which makes the final structure stronger. And really, the binding energy significantly increased |( ‒ 2283.9 + 3[ ‒ 677.5]) ‒ ( ‒ 4317.3)]a.u.= 0.90 a.u. The bond length between the Ti and O increased to 1.76 Å, while the other also decreased to 1.79 Å. Pre-calculation, we see the migration of an oxygen of one phosphate group towards the titanium dioxide. This rearrangement could account for the increased binding energy and better bonding of the titanium to the bone. Post-calculation, we see the emergence of a possible lattice structure forming, meaning it will be more stable. The calculation converged on the first attempt as all the frequencies were real.

Fig. 4a. Tricalcium phosphate [ TiO 2 Ca 3 (PO 4 ) 2 ] pre-geometric optimization. The white/grey atom is titanium, the yellow one is

Fig. 4b. [ TiO 2 Ca 3 (PO 4 ) 2 ] post-geometric optimization. A lattice