PSI - Issue 83

Alla V. Balueva et al. / Procedia Structural Integrity 83 (2026) 196–207

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It is crucial to emphasize again as the change in the charge of the titanium was very significant with the charge of the titanium bonded to the Ca 3 (SiO 3 ) 2 , implying the formation of an ionic bond. Comparing the ground state energies of the structure, TiCa 3 (SiO 3 ) 2 possesses the higher ground states energy which could indict to it having a higher stability than TiCa 3 (PO 4 ) 2 . The binding energy of TiCa 3 (PO 4 ) 2 was calculated to be 0.492 a.u. and the binding energy TiCa 3 (SiO 3 ) 2 was calculated to be 0.94 a.u, which would support that the structure TiCa 3 (SiO 3 ) 2 is more stable than the TiCa 3 (PO 4 ) 2 structure. 4. Calculation of Critical Surface Energy, which is the adhesive strength characteristics of the materials 4.1 Molecule-Molecule Bound Surface StatesMethod In the previous section, from atomistic calculations, we found the binding energy of tricalcium phosphate Ca 3 (PO 4 ) 2 with titanium Ti 2+ to be 0.492 a.u. and the binding energy of tricalcium silicon dioxide Ca 3 (SiO 3 ) 2 to be 0.94 a.u. These are microscopic characteristics. How now to move from microscopic to macroscopic characteristics of the adhesion strength of the materials, which can be already compared with the experiment? We will repeat here briefly the Dashevskiy’s method of Approximation of Molecule-Molecule Bound Surface States, that was developed in our previous paper [Dashevskiy et al., 2019]. 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 (or Ca 3 (SiO 3 ) 2 ) with titanium Ti 2+ and obtaining their binding energy, we can now estimate the adhesive strength (specific adhesion energy, adhesion work, adhesion strength) of this compound. Critical surface energy is the energy of the unit of surface to bind two materials. After Gaussian calculations, we were able to find the binding energy between unit cells of two materials. Then, to calculate the critical surface energy, we need to multiply the binding energy of unit cell by the number of unit cells per unit surface area (see Fig. 6).

Fig. 7. Calculation of critical surface energy