Abstract
The transition temperature between the low-temperature alpha phase of tin to beta tin is close to the room temperature (Tαβ = 130C), and the difference in cohesive energy of the two phases at 0 K of about ΔEcoh =0.02 eV/atom is at the limit of the accuracy of DFT (density functional theory) with available exchange-correlation functionals. It is however critically important to model the relative phase energies correctly for any reasonable description of phenomena and technologies involving these phases, for example, the performance of tin electrodes in electrochemical batteries. Here, we show that several commonly used and converged DFT setups using the most practical and widely used PBE functional result in ΔEcoh ≈0.04 eV/atom, with different types of basis sets and with different models of core electrons (all-electron or pseudopotentials of different types), which leads to a significant overestimation of Tαβ. We show that this is due to the errors in relative positions of s and p –like bands, which, combined with different populations of these bands in α and β Sn, leads to overstabilization of alpha tin. We show that this error can be effectively corrected by applying a Hubbard +U correction to s –like states, whereby correct cohesive energies of both α and β Sn can be obtained with the same computational scheme. We quantify for the first time the effects of anharmonicity on ΔEcoh and find that it is negligible.
Highlights
Tin (Z=50) is part of the group IV materials
The transition temperature between the low-temperature alpha phase of tin to beta tin is close to the room temperature (Tαβ = 130C), and the difference in cohesive energy of the two phases at 0 K of about ∆Ecoh =0.02 eV/atom is at the limit of the accuracy of DFT with available exchange-correlation functionals
A difference in cohesive energies of about 0.04 eV/atom is persistent among different computational setups and is different by about 0.02 eV/atom from experimental estimates of about 0.02 eV/atom.[47]. This results in a significant overestimation of the transition temperature, e.g. value Tαβ = 475 K is obtained in VASP using the harmonic approximation, Eq (2)
Summary
Tin (Z=50) is part of the group IV materials. to its lighter counterparts (C, Si, and Ge), Sn exists in the diamond-type crystal structure, commonly called alpha Sn (α-Sn, space group 227; Fd-3m) or grey tin; this is the most stable low-temperature phase, and it is a zero-gap semiconductor.[1]. The proximity of Tαβ to room temperature means that the α − β transition can be of practical importance, as the relative phase stability can be changed by perturbations to the lattice by e.g. doping or strain. Tin has been shown to be a high capacity anode material for Li, Na, and Mg ion batteries.[2,3,4,5] in Li ion batteries, for which Sn-based electrodes have been most studied,[6,7] the formation of α Sn upon lithiation of (initially β phase) Sn electrodes has been reported in experimental studies.[8,9] This beta-to-alpha phase transformation in battery electrodes is still not fully understood. To produce reliable ab initio models of this process or other processes which can affect the phase stability at room temperature, the transition temperature and ∆Ecoh need to be reproduced accurately
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
