Publication details
Ab initio analysis of phonon contributions to the negative thermal expansion of α-tin
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Conference abstract |
| MU Faculty or unit | |
| Citation | |
| Description | 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 ? (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. |