Thermal Conductivity and Thermal Diffusivity of Ferrosilite under High Temperature and High Pressure

Abstract

Orthopyroxene is an important constitutive mineral in the crust and the upper mantle. Its thermal properties play a key role in constructing the thermal structure of the crust and the upper mantle. In this study, we developed a new method to synthesize polycrystalline ferrosilite, one end-member of orthopyroxene, via the reaction of FeO + SiO₂ → FeSiO₃. We found that the P-T condition of 3 GPa and 1 273 K is suitable to synthesize dense ferrosilite samples with low porosity. We employed the transient plane-source method to investigate the thermal conductivity κ and thermal diffusivity D of synthetic ferrosilite at 1 GPa and 293–873 K, of which, κ = 1.786 + 1.048 × 10³ T ⁻¹ − 9.269 × 10⁴ T ⁻² and D = 0.424 + 0.223 × 10³ T ⁻¹ + 1.64 × 10⁴ T ⁻². Our results suggest phonon conduction should be the dominant mechanism at P-T conditions of interest since the thermal conductivity and the thermal diffusivity of ferrosilite both decrease with increasing temperature. The calculated heat capacity of ferrosilite at 1 GPa increases with temperature, which increases with increasing temperature with about 10% per 100 K (<500 K) and 4% per 100 K (>500 K). Iron content of an asteroid significantly influences its thermal evolution history and temperature distribution inside. It is expected that the mantle temperature of the Fe-rich asteroid will be higher and the Fe-rich asteroid’s cooling history will be longer.

Keywords

ferrosilite / high pressure / thermal conductivity / thermal diffusivity / synthesis

References

[1] Akimoto S I, Fujisawa H, Katsura T. Synthesis of FeSiO₃ Pyroxene (Ferrosilite) at High Pressures. Proceedings of the Japan Academy, 1964, 40(4): 272-275.

[2] Bowen N L, Schairer J F. The System MgO−FeO−SiO₂. American Journal of Science, 1935, 29(170): 151-217.

[3] Chang Y Y, Hsieh W P, Tan E, . Hydration-Reduced Lattice Thermal Conductivity of Olivine in Earth’s Upper Mantle. PNAS, 2017, 114(16): 4078-4081.

[4] Clauser C. Thermal Storage and Transport Properties of Rocks, I: Heat Capacity and Latent Heat, 2011, Dordrecht: Springer, 1423-1431

[5] Dzhavadov L N. Measurement of Thermophysical Properties of Dielectrics under Pressure. High Temperatures-High Pressures, 1975, 7(1): 49-54

[6] Fu H F, Zhang B H, Ge J H, . Thermal Diffusivity and Thermal Conductivity of Granitoids at 283–988 K and 0.3–1.5 GPa. American Mineralogist, 2019, 104(11): 1533-1545.

[7] Gaul O F, Griffin W L, O’Reilly S Y, . Mapping Olivine Composition in the Lithospheric Mantle. Earth and Planetary Science Letters, 2000, 182(3/4): 223-235.

[8] Gibert B, Seipold U, Tommasi A, . Thermal Diffusivity of Upper Mantle Rocks: Influence of Temperature, Pressure, and the Deformation Fabric. Journal of Geophysical Research: Solid Earth, 2003, 108(B8): 2359

[9] Giuli G, Paris E, Wu Z Y, . Fe and Mg Local Environment in the Synthetic Enstatite-Ferrosilite Join: An Experimental and Theoretical XANES and XRD Study. European Journal of Mineralogy, 2002, 14 2 429-436.

[10] Hofmeister A M. Pressure Dependence of Thermal Transport Properties. PNAS, 2007, 104(22): 9192-9197.

[11] Hofmeister A M. Thermal Diffusivity of Orthopyroxenes and Protoenstatite as a Function of Temperature and Chemical Composition. European Journal of Mineralogy, 2012, 24(4): 669-681.

[12] Hofmeister A M, Pertermann M. Thermal Diffusivity of Clinopyroxenes at Elevated Temperature. European Journal of Mineralogy, 2008, 20(4): 537-549.

[13] Hugh-Jones D A, Angel R J. Effect of Ca²⁺ and Fe²⁺ on the Equation of State of MgSiO₃ Orthopyroxene. Journal of Geophysical Research: Solid Earth, 1997, 102(B6): 12333-12340.

[14] Hunt S A, Walker A M, McCormack R J, . The Effect of Pressure on Thermal Diffusivity in Pyroxenes. Mineralogical Magazine, 2011, 75(5): 2597-2610.

[15] Khan A, Liebske C, Rozel A, . A Geophysical Perspective on the Bulk Composition of Mars. Journal of Geophysical Research: Planets, 2018, 123(2): 575-611.

[16] Kung J, Li B S. Lattice Dynamic Behavior of Orthoferrosilite (FeSiO₃) Toward Phase Transition under Compression. The Journal of Physical Chemistry C, 2014, 118(23): 12410-12419.

[17] Lindsley D H, Davis B T, MacGregor I D. Ferrosilite (FeSiO₃): Synthesis at High Pressures and Temperatures. Science, 1964, 144(3614): 73-74.

[18] Newnham R E. Structure-Property Relations, 1975, Berlin: Springer-Verlag, 60-64.

[19] Ono S, Oganov A R. In situ Observations of Phase Transition between Perovskite and CaIrO₃-Type Phase in MgSiO₃ and Pyrolitic Mantle Composition. Earth and Planetary Science Letters, 2005, 236(3/4): 914-932.

[20] Osako M, Ito E, Yoneda A. Simultaneous Measurements of Thermal Conductivity and Thermal Diffusivity for Garnet and Olivine under High Pressure. Physics of the Earth and Planetary Interiors, 2004, 143/144: 311-320.

[21] Ringwood A E. Composition and Petrology of the Earth’s Mantle, 1975, New York: McGraw-Hill

[22] Ringwood A E. Phase Transformations and Their Bearing on the Constitution and Dynamics of the Mantle. Geochimica et Cosmochimica Acta, 1991, 55(8): 2083-2110.

[23] Sanchez J A, Reddy V, Kelley M S, . Olivine-Dominated Asteroids: Mineralogy and Origin. Icarus, 2014, 228(2): 288-300.

[24] Saxena S K, Shen G Y. Assessed Data on Heat Capacity, Thermal Expansion, and Compressibility for some Oxides and Silicates. Journal of Geophysical Research: Solid Earth, 1992, 97(B13): 19813-19825.

[25] Schatz J F, Simmons G. Thermal Conductivity of Earth Materials at High Temperatures. Journal of Geophysical Research, 1972, 77(35): 6966-6983.

[26] Stalder R. Influence of Fe, Cr and Al on Hydrogen Incorporation in Orthopyroxene. European Journal of Mineralogy, 2004, 16(5): 703-711.

[27] Stalder R, Kronz A, Schmidt B C. Raman Spectroscopy of Synthetic (Mg, Fe)SiO₃ Single Crystals: An Analytical Tool for Natural Orthopyroxenes. European Journal of Mineralogy, 2009, 21(1): 27-32.

[28] Sunshine J M, Bus S J, Corrigan C M, . Olivine-Dominated Asteroids and Meteorites: Distinguishing Nebular and Igneous Histories. Meteoritics & Planetary Science, 2007, 42(2): 155-170.

[29] Wang C, Yoneda A, Osako M, . Measurement of Thermal Conductivity of Omphacite, Jadeite, and Diopside up to 14 GPa and 1 000 K: Implication for the Role of Eclogite in Subduction Slab. Journal of Geophysical Research: Solid Earth, 2014, 119(8): 6277-6287.

[30] Xiong J, Lin H Y, Ding H S, . Investigation on Thermal Property Parameters Characteristics of Rocks and Its Influence Factors. Natural Gas Industry B, 2020, 7(3): 298-308.

[31] Xu J G, Fan D W, Zhang D Z, . Phase Transition of Enstatite-Ferrosilite Solid Solutions at High Pressure and High Temperature: Constraints on Metastable Orthopyroxene in Cold Subduction. Geophysical Research Letters, 2020, 47(12): 1-10.

[32] Yoneda A, Osako M, Ito E. Heat Capacity Measurement under High Pressure: A Finite Element Method Assessment. Physics of the Earth and Planetary Interiors, 2009, 174(1/2/3/4): 309-314.

[33] Zhang B H, Ge J H, Xiong Z L, . Effect of Water on the Thermal Properties of Olivine with Implications for Lunar Internal Temperature. Journal of Geophysical Research: Planets, 2019, 124(12): 3469-3481.

[34] Zhang B H, Yoshino T. Effect of Temperature, Pressure and Iron Content on the Electrical Conductivity of Orthopyroxene. Contributions to Mineralogy and Petrology, 2016, 171(12): 1-12.

[35] Zhang Y Y, Yoshino T, Yoneda A, . Effect of Iron Content on Thermal Conductivity of Olivine with Implications for Cooling History of Rocky Planets. Earth and Planetary Science Letters, 2019, 519: 109-119.