Quantum-mechanical study of phonon contributions to stability
of Pb-Sn alloys

a 2024

Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ

Základní údaje

Originální název

Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys

Autoři

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ

Vydání

33rd International Conference on Metallurgy and Materials (METAL 2024), 2024

Další údaje

Jazyk

angličtina

Typ výsledku

Konferenční abstrakt

Obor

10403 Physical chemistry

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/24:00139096

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

quantum-mechanical calculations; Pb-Sn alloys; phonons; alpha tin; beta tin; gamma tin

Změněno: 17. 3. 2025 18:15, doc. Mgr. Jana Pavlů, Ph.D.

Anotace

V originále

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.

Návaznosti

90254, velká výzkumná infrastruktura

Název: e-INFRA CZ II

Citovat

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ. Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys. In 33rd International Conference on Metallurgy and Materials (METAL 2024). 2024.

@proceedings{2484880,
   author = {Čípek, Petr and Friák, Martin and Pavlů, Jana},
   booktitle = {33rd International Conference on Metallurgy and Materials (METAL 2024)},
   keywords = {quantum-mechanical calculations; Pb-Sn alloys; phonons; alpha tin; beta tin; gamma tin},
   language = {eng},
   title = {Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys},
   year = {2024}
}

TY  - CONF
ID  - 2484880
AU  - Čípek, Petr - Friák, Martin - Pavlů, Jana
PY  - 2024
TI  - Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys
KW  - quantum-mechanical calculations
KW  - Pb-Sn alloys
KW  - phonons
KW  - alpha tin
KW  - beta tin
KW  - gamma tin
N2  - 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.
ER  -

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ. Quantum-mechanical study of phonon contributions to stability of Pb-Sn alloys. In \textit{33rd International Conference on Metallurgy and Materials (METAL 2024)}. 2024.

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