A pressure-volume-temperature equation of state for Sn(β) by energy dispersive X-ray diffraction in a heated diamond-anvil cell

Abstract

A total of 36 molar volume determinations measured by energy-dispersive X-ray diffraction in a heated diamond-anvil pressure cell form the basis for a P-V-T equation of state for Sn(β). Isothermal Murnaghan regressions for the 25, 100, 160, and 225°C subsets of these data yield −1.38 (±0.13) × 10 −2GPa degree −1 for ( ∂K ∂T ) 00. The slopes of the Sn(β) isochores increase from approx. 235° GPa −1 at room pressure and temperature to 260° GPa −1 at the Sn triple point to 370° GPa −1 at the room temperature Sn(β)-Sn(bct) transition at 9.4 GPa, indicating that the product α P K T decreases with decreasing volume by more than 35% of its initial value. The a crystallographic direction is significantly less compressible and slightly less expandable than c; the extent of this anisotropic behavior decreases at simultaneously elevated pressure and temperature. A five-parameter temperature-corrected Murnaghan equation fits the entire data set well within the experimental error. This explicit V( T, P) equation is used to integrate literature heat capacity data to elevated pressure, yielding entropies and Gibbs energies for all pressures and temperatures within the Sn(β) stability field.