Pressure-volume-temperature behavior and heterogeneous equilibria of the non-quenchable body-centered tetragonal polymorph of metallic tin †

Abstract

Forty molar volume determinations for the high-pressure phase of metallic tin, Sn(bct), measured by energy-dispersive X-ray diffraction in a heated diamond-anvil pressure cell, form the basis for the first experimentally-determined P-V-T equation of state for any non-quenchable phase. The resulting isochores for Sn(bct) are concave towards the pressure axis; their slope varies from approx. 120 deg GPa −1 at the Sn(β)-Sn(melt) triple point at 308°C and 2.9 GPa, to approx. 290 deg GPa −1 at the room temperature Sn(β)-Sn(bct) transition at 9.4 GPa. Used in conjunction with the P-V-T data for Sn(β) from Cavaleri et al., J. Phys. Chem. Solids 49, 945 (1988) [1], these Sn(bct) volume measurements reveal that Δ V for the Sn(β)-Sn(bct) reaction remains essentially constant at approx. −0.135 J MPa −1 mol −1 whereas Δ S increases from +2.15 J deg −1 mol −1 at room temperature to +7.15J deg −1 mol −1 at the triple point. The molar volume and entropy of Sn(melt) at the triple point were determined to be 16.113 J MPa −1mol −1 and 81.91J deg −1mol −1, respectively, indicating that ΔS along the Sn(β) melt curve remains very nearly constant whereas Δ V decreases by approx. 31% from room pressure to the triple point.