PSI - Issue 83

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

205

Let us estimate the average number of molecules per unit surface area. The number of molecules in a unit volume N = ρ /m, where ρ is the density of the substance, m is the mass of one molecule. In turn, the mass of a molecule can be found by dividing one gram-mole by Avogadro's number m = m = M/ N A . Thus, for N we get: N = ρ /m = ρ /(M/ N A ) = ρ N A /M, and the average number of molecules per surface unit is ଶ/ଷ . We assume that one Ti atom is bound to each molecule of tricalcium phosphate, and we calculated their binding energy E. Then, the total surface energy released from all atoms on the unit surface, or the adhesive strength for TCF/Ti (specific surface energy of adhesive destruction) γ can be obtained as: ~ ଶ/ଷ ൌ ሺ ஺ / ሻ ଶ/ଷ (4.1)

Using this formula, we will obtain critical surface energy, e.g. characteristics of strength of adhesion, for both coatings, for pure TCP coating and doped with silicon coating.

4.2. Adhesion Strength between Ti (II) and Ca 3 (PO 4 ) 2

Given that the density ρ of tricalcium phosphate depending on the amorphous or crystalline state (and in the latter case, on polymorphic modification) can vary in the range from 2.81 g / cm3 [https://ru.wikipedia.org/wiki/ Calcium Orthophosphate] to about ρ = 3.14 g / cm3 [http://ru.china-phosphate.com/Products/Tricalcium-phosphate TCP.htm], we will take for simplicity estimates ρ ≈ 3.00 g / cm3. The molar mass of tricalcium phosphate is M = 310.174 g/mol. Molar Mass Formula: ൌ σሺ ௥ ൈ ሻ (4.2) ௥ is the atomic mass of each element in the compounds, n is the number of atoms for each element in the compound. Molar mass of Ca 3 (PO 4 ) 2 = 3 (atomic mass of Ca) + 2 (atomic mass of P) + 8 (atomic mass of O) Molar mass of Ca 3 (PO 4 ) 2 = 3 (40.078 g/mol) + 2 (30.974 g/mol) + 8 (15.999 g/mol) = 310.174 g/mol Since one mole is the amount of substance containing N A particles (where N A ≈ 6 ⋅ 10²³ is Avogadro's number), the mass m of one molecule of tricalcium phosphate m = M/ N A . We assume that one Ti atom is bound to each molecule of tricalcium phosphate, and according to the above calculations, their binding energy is E = 0.492 a.u. Considering that 1 a.u. = 4.36 ꞏ 10 -18 J, that energy is 0.492 *4.36 ꞏ 10 -18 J. This way, the total surface energy released from all atoms on the unit surface, or the adhesive strength (specific surface energy of adhesive destruction) γ can be obtained accordingly to formula (4.1): ൌ ሺ0.492 x 4.36 ൉ 10ି ଵ଼ Jሻൈ ൬3.00 ௖௠ ௚ య ൈ ሺ଺ൈଵ଴ మయ ௠௢௟ షభ ଷଵ଴.ଵ଻ସ ೘ ೒ ೚೗ ൰ మ య ൎ 0.0006927 ௖௠ ௃ య ൎ6.927 ௠ ௃ మ (4.3)