Total-energy calculations within the local-density approximation (LDA) to the density-functional theory are used to study the properties of tin under pressure. It is known experimentally that the cubic diamond structure (α) is stable at zero pressure and low temperature, but the application of a very small pressure, a few kbar, drives Sn into the β-Sn structure. The transition is accompanied by a large volume reduction, ≊20%. This is also found in the present calculations, and they further suggest that the β structure is stable for pressures up to ≊100 kbar, above which Sn transforms into a body-centered-tetragonal phase. Experiments carried out at room temperature yield a transition pressure of 95 kbar, and extrapolating the phase diagram from 0 °C to T=0 K the experimental zero-temperature value is estimated to be 120–130 kbar. At T=0 and P≊105 kbar the calculation predicts the structure to be bct with c/a=0.91. At finite temperatures the c/a ratio in this phase is expected to range from 0.85 to 1.06, but with increasing pressure a predominance of structures with c/a=1.00 is predicted. Above 300–400 kbar the structure may be characterized as bcc (i.e., c/a=1.00 is clearly dominating), and for pressures up to at least 2 Mbar the bcc phase remains the phase with the lowest enthalpy when compared with α, β, bct, fcc, sc, hcp, dhcp, and primitive hexagonal structures. The bct→bcc transition is of first order at T=0. The pressure dependence of the ${\mathrm{\Gamma }}_5$ and ${\mathrm{\Gamma }}_3$ phonons in β-Sn is calculated, and agreement with recent Raman measurements is obtained.

• Received 22 March 1993

DOI:https://doi.org/10.1103/PhysRevB.48.5797