Tin-pest problem as a test of density functionals using high-throughput calculations

Abstract

At ambient pressure tin transforms from its ground-state semi-metal α-Sn (diamond structure) phase to the compact metallic β-Sn phase at 13 • C (286K). There may be a further transition to the simple hexagonal γ-Sn above 450K. These relatively low transition temperatures are due to the small energy differences between the structures, ≈ 20 meV/atom between α-and β-Sn. This makes tin an exceptionally sensitive test of the accuracy of density functionals and computational methods. Here we use the high-throughput Automatic-FLOW (AFLOW) method to study the energetics of tin in multiple structures using a variety of density functionals. We look at the successes and deficiencies of each functional. As no functional is completely satisfactory, we look Hubbard U corrections and show that the Coulomb interaction can be chosen to predict the correct phase transition temperature. We also discuss the necessity of testing high-throughput calculations for convergence for systems with small energy differences.

Machine learning search for stable binary Sn alloys with Na, Ca, Cu, Pd, and Ag

“…84 First, it is worth reviewing how the DFT predictions agree with experimental observations. The likely overestimation of the Δ E β–α energy difference in common DFT approximations along with the limitations of the standard harmonic approximation for evaluating free energies leads to notably higher estimates of the T α→β transition temperature, 24,33,84,85 540 K in our case versus measured 286 K. 86 This discrepancy makes it difficult to make definitive predictions about possible high- T ground states at the Sn-rich end of the phase diagram. The PBE results at T = 0 K also indicate stability of hcp-Sn in the 5.5–15 GPa window not detected experimentally and favorability of bco over bct up to about 20 GPa in disagreement with reported data.…”

“…Since it was not parameterized to model compressed Sn configurations, it is not unexpected to see its less accurate performance resolving competing phases under high pressures. At the same time, the MEAM significantly disfavors the viable but elusive γ-Sn with the simple hexagonal structure [21] and our MEAM-based evolutionary searches uncovered an artificial ground state (oI4-Immm, a = 3.2485 Å, b = 4.5366 Å, c = 8.3219 Å, and a single 4j (1/2,0, 0.3276) Wyckoff position) 11 meV/atom below α-Sn at 0 K and 0 GPa. Finally, an interesting hybrid model, a combination of EAM and rapid artificial NN potential, has been recently developed and demonstrated to have a much-improved description of Sn phases in a wide range of temperatures and pressures [82].…”

“…Tin is a post-transition metal observed in various elemental and multicomponent crystal structure phases. [24][25][26][27][28][29] At ambient temperature and pressure, 'white tin' crystallizes in the b-Sn structure and is known as a soft, malleable, and ductile metal. Below 13 1C, 'grey tin' adopts the a-Sn diamond structure and exhibits a semimetallic behavior.…”

Prediction of stable Li-Sn compounds: boosting ab initio searches with neural network potentials

“…5(l)) that breaks the tP14-Li 2 Sn 5 ↔ α-Sn tie-line at 510 K. This temperature estimate is particularly sensitive to the description of pure Sn. The difficulty of reproducing α → β transition temperatures and pressures for group-XIV Si and Sn has been pointed out in several studies [70][71][72][97][98][99][100]. The overestimated temperature value for the α-Sn to β-Sn transformation obtained in our standard PBE calculations is 540 K. A lower free energy of the reference β-Sn could shift the mS40-LiSn 4 stabilization to significantly higher temperatures.…”

“…Analysis of phase stability at high T Identification of high-T ground states is commonly done by including the vibrational entropy contribution to the Gibbs free energy for a pool of low-enthalpy phases found in global structure searches at T = 0 K [2,9]. The relative change in Gibbs free energy can reach a few dozen meV/atom for structures with substantially different phonon density of states (DOS) observed, e.g., in α-Sn and β-Sn [70][71][72]. Given the demanding nature of phonon calculations at the DFT level, we used the following protocol to examine high-T phase stability.…”