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At ambient pressure tin transforms from its ground-state semi-metal$\alpha$-Sn (diamond structure) phase to the compact metallic $\beta$-Sn phaseat 13$^\circ$C (286K). There may be a further transition to the simplehexagonal $\gamma$-Sn above 450K. These relatively low transition temperaturesare due to the small energy differences between the structures, $\approx20$\,meV/atom between $\alpha$- and $\beta$-Sn. This makes tin an exceptionallysensitive test of the accuracy of density functionals and computationalmethods. Here we use the high-throughput Automatic-FLOW (AFLOW) method to studythe energetics of tin in multiple structures using a variety of densityfunctionals. We look at the successes and deficiencies of each functional. Asno functional is completely satisfactory, we look Hubbard U corrections andshow that the Coulomb interaction can be chosen to predict the correct phasetransition temperature. We also discuss the necessity of testinghigh-throughput calculations for convergence for systems with small energydifferences.

The Tin Pest Problem as a Test of Density Functionals Using High-Throughput Calculations