DENSITY-FUNCTIONAL CALCULATIONS OF THE STRUCTURAL-PROPERTIES OF TIN UNDER PRESSURE

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 (alpha) is stable at zero pressure and low temperature, but the application of a very small pressure, a few kbar, drives Sn into t he beta-Sn structure. The transition is accompanied by a large volume reduction, almost-equal-to 20%. This is also found in the present calc ulations, and they further suggest that the beta structure is stable f or pressures up to almost-equal-to 100 kbar, above which Sn transforms into a body-centered-tetragonal phase. Experiments carried out at roo m temperature yield a transition pressure of 95 kbar, and extrapolatin g the phase diagram from 0-degrees-C to T = 0 K the experimental zero- temperature value is estimated to be 120-130 kbar. At T = 0 and P almo st-equal-to 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 p redominance 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 cl early dominating), and for pressures up to at least 2 Mbar the bcc pha se remains the phase with the lowest enthalpy when compared with alpha , beta, bct, fcc, sc, hcp, dhcp, and primitive hexagonal structures. T he bct-->bcc transition is of first order at T = 0. The pressure depen dence of the GAMMA5 and GAMMA3 phonons in beta-Sn is calculated, and a greement with recent Raman measurements is obtained.