Pressure-volume-temperature behavior of γ-Fe₂SiO₄ (spinel) based on static compression measurements at 400° C

Abstract

Thirteen energy-dispersive x-ray diffraction spectra for γ-Fe₂SiO₄ (spinel) collected in situ at 400° C and pressures to 24 GPa constitute the basis for an elevated-temperature static compression isotherm for this important high-pressure phase. A Murnaghan regression of these molar volume measurements yields 177.3 (±17.4) GPa and 5.4(±2.5) for the 400° C, room pressure values of the isothermal bulk modulus (K _{P 0}) and its first pressure derivative (K′ _{P 0}), respectively. When compared to the room-Tdeterminations of K _{P 0} available in the literature, our 400° C K _{P 0} yields -4.1 (±6.2)×10^-2 GPa/degree for the average value of (∂K/∂T) _{P 0} over the temperature interval 25° C<T<400° C.

A five-parameter V(P, T) equation for γ-Fe₂SiO₄ based on simultaneous regression of our data combined with the elevated P-Tdata of Yagi et al. (1987) and the extrapolated thermal expansion values from Suzuki et al. (1979) yields isochores which have very little curvature [(∂² T/∂P ²) _v ≅0], in marked contrast to the isochores for fayalite (Plymate and Stout 1990) which exhibit pronounced negative curvature [(∂T/∂P ²) _v <0]. Along the fayalite/γ-Fe₂SiO₄ reaction boundary ΔV_Rvaries from a minimum of approximately 8.3% at approximately 450° C to approximately 8.9% at 1200° C. Extrapolation of the fayalite and γ-Fe₂SiO₄ V(P, T) relationships to the temperature and pressure of the 400 km discontinuity suggests a ΔV _R of approximately 8.4% at that depth, approximately 10% less than the 9.3% ΔV _R at ambient conditions.