Informace o publikaci
Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys
| Autoři | |
|---|---|
| Rok publikování | 2024 |
| Druh | Konferenční abstrakty |
| Fakulta / Pracoviště MU | |
| Citace | |
| Popis | The Sn-rich Pb-Sn alloys were historically used for numerous products, from organ pipes to jewelries. Later industrial applications include food cans or a vast majority of electrical-engineering products containing Pb-Sn solders. While recently banned in favor of lead-free solders, the Pb-Sn alloys are still important not only when studying historical artifacts or handling millions of tons of electrical-engineering waste, but also when developing new Sn-containing materials. In our theoretical study, we employed quantum-mechanical calculations to determine the thermodynamic and dynamical stability of both elemental tin and selected Pb-Sn alloys. In particular, phonons and vibrational contributions to the free energy were determined for the cubic diamond-structure phase as well as body-centered tetragonal and hexagonal phases within the harmonic approximation. Our results clearly indicate an important role played by phonons in the stability of studied phases. In particular, the contribution of the free lattice vibration energy causes a shift in the stability, i.e. in the energy order between the alpha, beta and gamma tin at higher temperatures. At T = 0 K, the alpha phase is the most stable structure of pure tin, the second most stable structure is the gamma phase and the least stable is the beta tin. This order changes at temperature T = 115 K when the beta tin becomes more stable than the gamma tin and, at higher temperatures, it becomes the most stable form of tin. Very similar trends were observed in the temperature dependence of the free energy contribution for Pb-Sn structures with 9.375 atomic percent of lead. The T = 0 K order of stability was the same as for pure tin, but the hexagonal gamma structure remains more stable than the beta structure and it crosses the energy line of the alpha Pb-Sn structure at temperature of T = 260 K. The beta Pb-Sn structure becomes more stable than the alpha Pb-Sn structure at temperature T = 298 K. |