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First-Principles Study on Temperature-Dependent Phase Transitions of Sn Polymorphs
New Phys.: Sae Mulli 2019; 69: 227~233
Published online March 29, 2019;
© 2019 New Physics: Sae Mulli.

Seong Min JANG, Chul Hong PARK*

Department of Physics Education, Pusan National University, Busan 46241, Korea
Correspondence to:
Received January 3, 2019; Revised January 22, 2019; Accepted January 22, 2019.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Based on first-principles electronic structure calculations, we estimated the variations in the thermodynamic free energies of lattice vibrations with temperature for various polymorph structures of Sn: we examined the $\alpha$ and $\beta$ polymorphs, two kinds of hexagonal structures, through which we are able to investigate their thermal-induced phase- transition characteristics. Similar to the experimental results, a phase transition from alpha-Sn to beta-Sn was observed with increasing temperature, because the entropy of beta-Sn is larger than that of alpha-Sn. Thus, the entropy effect of phonons appears to have played an important role in the phase transition. The hexagonal structure can be more stable than the beta structure at a high temperature, but the transition temperature was higher than the melting temperature of Sn; thus, hexagonal Sn is thought to be a metastable phase.
PACS numbers: 63.20.D-,, 63.70.+h
Keywords: Sn, Phase transition, Entropy, First-principles calculation, Phonon

March 2019, 69 (3)
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