Where is the Simple Hexagonal Structure in Tin?
The heavier elements of periodic table column IV exhibit number of structural phase transitions under pressure. Si and Ge transform from the ground-state diamond structure to, successively, the $\beta$-Sn structure, a body-centered orthorhombic structure, the simple hexagonal structure, etc., ending at a close-packed phase (fcc or hcp) near 200 GPa. Tin also transforms from diamond to $\beta$-Sn, but then to a body-centered tetragonal phase, ending with the body-centered cubic phase. The simple hexagonal phase is not seen, despite the fact that numerous tin-rich alloys exhibit a simple hexagonal structure. To understand this we performed DFT calculations on tin in various crystal structures, using both full-potential LAPW and VASP with a PAW potential. Surprisingly, we find that the simple hexagonal phase is degenerate with $\beta$-Sn over pressures at which the $\beta$-Sn phase is seen experimentally. This holds both for LAPW and VASP calculations, in both the LDA and the GGA. We expl
