Ab initio analysis of phonon contributions to the negative
thermal expansion of α-tin

a 2024

Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ

Základní údaje

Originální název

Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin

Autoři

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ

Vydání

NANOCON, 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

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova česky

Tin alloys; quantum-mechanical calculations; phonon spectra; alpha tin; beta tin; gamma tin

Změněno: 17. 3. 2025 21:57, doc. Mgr. Jana Pavlů, Ph.D.

Anotace

V originále

Tin alloys have historically been used in a wide range of products, from organ pipes and everyday items to jewellery. In more recent times, industrial applications have included food cans and a significant proportion of electrical-engineering products, especially those using Pb-Sn solders. While Pb-containing ones were recently banned in favor of lead-free solders, the need of basic research of tin is more important than ever. In this theoretical study, we applied quantummechanical calculations to investigate the thermodynamic and dynamic stability of tin in its various allotropic forms. Specifically, phonon spectra and vibrational contributions to free energy were computed for the cubic diamond-structured alpha tin, as well as the body-centered tetragonal beta tin and metastable hexagonal gamma tin, using the harmonic approximation and quasi-harmonic approximation. Focusing specifically on the alpha-Sn, our results showed a negative thermal expansion in it within the temperature range from T = 0 K to T = 45 K. No similar phenomenon appears in spectra of other allotropic modifications of tin. That means that origin of this behaviour is connected to the diamond structure of alpha tin. I investigated behaviour of Grüneisen constant of alpha tin in reciprocal space to explain causes of this phenomenon. There are interesting temperature-dependent contributions of individual phonon modes from different kpoints in the reciprocal space. In particular, these contributions are negative at all studied temperatures for the k-points around k-point X (0, 0, 0.5) and positive around k-point Γ (0, 0, 0). Negative thermal expansion of alpha tin at low temperatures is related to behaviour of phonons around k-points X, M and N.

Návaznosti

90254, velká výzkumná infrastruktura

Název: e-INFRA CZ II

Citovat

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ. Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin. In NANOCON. 2024.

@proceedings{2484897,
   author = {Čípek, Petr and Friák, Martin and Pavlů, Jana},
   booktitle = {NANOCON},
   language = {eng},
   title = {Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin},
   year = {2024}
}

TY  - CONF
ID  - 2484897
AU  - Čípek, Petr - Friák, Martin - Pavlů, Jana
PY  - 2024
TI  - Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin
N2  - Tin alloys have historically been used in a wide range of products, from organ pipes and everyday items to jewellery. In more recent times, industrial applications have included food cans and a significant proportion of electrical-engineering products, especially those using Pb-Sn solders. While Pb-containing ones were recently banned in favor of lead-free solders, the need of basic research of tin is more important than ever. In this theoretical study, we applied quantummechanical calculations to investigate the thermodynamic and dynamic stability of tin in its various allotropic forms. Specifically, phonon spectra and vibrational contributions to free energy were computed for the cubic diamond-structured alpha tin, as well as the body-centered tetragonal beta tin and metastable hexagonal gamma tin, using the harmonic approximation and quasi-harmonic approximation. Focusing specifically on the alpha-Sn, our results showed a negative thermal expansion in it within the temperature range from T = 0 K to T = 45 K. No similar phenomenon appears in spectra of other allotropic modifications of tin. That means that origin of this behaviour is connected to the diamond structure of alpha tin. I investigated behaviour of Grüneisen constant of alpha tin in reciprocal space to explain causes of this phenomenon. There are interesting temperature-dependent contributions of individual phonon modes from different kpoints in the reciprocal space. In particular, these contributions are negative at all studied temperatures for the k-points around k-point X (0, 0, 0.5) and positive around k-point Γ (0, 0, 0). Negative thermal expansion of alpha tin at low temperatures is related to behaviour of phonons around k-points X, M and N.
ER  -

ČÍPEK, Petr; Martin FRIÁK a Jana PAVLŮ. Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin. In \textit{NANOCON}. 2024.

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