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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calcium, the orange one is phosphorus, and the red ones are oxygen. structure is forming due to the oxygens having to interact with so many electropositive atoms. We can see the charge of the titanium decreased even more from 1.191+ to 0.963+ with the addition of the three calcium s, while the phosphorous almost didn’t change, as they moved from 1.558+ to 1.544+ and 1.485+, respectively. The charges of the two oxygens attached to the titanium decreased from 0.334 ‒ to 0.782 ‒ and from 0.376 ‒ to 0.850 ‒ , respectively. It is interesting to see the contribution of atoms of calcium to the structure, so their charge also doesn’t change so dramatically compared to titanium, as calcium changes from 2+ to 1.472+, 1.518+, and 1.508+, respectively, which means that most of the electrons still go to titanium in this structure. This creates stability in the structure and we see the binding energy of the structure reach its peak. 4. Theoretical method of calculating the adhesion strength of Tricalcium Phosphate coating on titanium substrate The surface energy of adhesion is a characteristic of the adhesion strength of the material. After ab initio calculations of the reaction of tricalcium phosphate Ca 3 (PO 4 ) 2 with titanium dioxide TiO 2 and obtaining their binding energy, now we can calculate the surface energy of this compound. We propose the following method [Balueva et al., 2020]. The surface energy, or energy per unit of the newly created surface, is used to measure the bonding strength in the interface. The surface energy, γ, was calculated using these formulas [Balueva and Dashevskiy, 2017]:   / / HA Ti HA Ti E E E A     (4.1) are the bonding energies of tricalcium phosphate with titanium obtained by atomistic calculations in the previous section (see (2.1)). A , the area of the unit cell, is obtained in the following way [Balueva et. al., 2019]: first we find a unit cell from Cambridge Data base, next optimize it in GAUSSIAN to ensure a ground state geometry, which gives us the geometry as the exit data in a log file (area + volume). We can also calculate the area of the interface another way. For model calculations, we will take a hexagonal closed packed structure (Figure 8a of hexagonal crystal structure), which is typical to calcium phosphates. The height of the hexagonal prism is c = 468.55 pm . For a x-y dimensional cross section, the perimeter of the prism is 6 a = 1.7705 nm, which means that each of the six sides of the prism is 295.08 pm wide (on Fig 5a the prism is clearly labelled with a and c). The equation for the surface area of a hexagon (Figure 8b) is A = 3√ 2 3 2 . Since each lateral side of the prism is simply a rectangle (see Figure 5a) the total surface area of the prism is 1.282x10 6 pm 2 . But since the TiO 2 molecule will only approach either the top of the unit cell or one of the sides of the unit cell, we will only consider where A represents the area of the interface, and W bon = / TP Ti TP Ti E E E  

3 3





2

5

2

2.66 10

a

pm

5 2 (1.38)10 ac pm  or

for surface energy calculations.



2