Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Abstract

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO₃, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a $\varDelta P$ standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V ₀ = 875.8 ± 1.4 Å³, K ₀ = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$, assuming ${K}^{\prime}_{0} = 10$. We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO₃, and orthopyroxene solid solutions, (Mg_1−x Fe _x ) SiO₃, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.