Thermal expansion, Debye temperature and Gr�neisen parameter of synthetic (Fe, Mg)SiO3 orthopyroxenes

Abstract

Thermal expansion properties of synthetic orthopyroxenes (Fe0.20Mg0.80)SiO3, (Fe0.40Mg0.60)SiO3, (Fe0.50Mg0.50)SiO3, (Fe0.75Mg0.25)SiO3 and (Fe0.83Mg0.17)SiO3 were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg) 30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO3) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO3) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Gruneisen theory of thermal expansion. The linear thermal expansion coefficients α a and α c both increase as temperature is elevated, with α c increasing faster, while α b changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order α b >α c >α a between 300 and 500 K, but at higher temperatures, the order changes to α c >α b >α a for Mg-rich orthopyroxenes and α c >α a >α b for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of α b is mainly attributed to the changes in the Fe2+ population at the M2 site and the relative stiffness of the M2(Fe2+)-O bonds compared to the M2(Mg2+)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10−6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the α V values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO3) to 561 K (FeSiO3), and are systematically higher than the corresponding acoustic Debye temperatures. The Gruneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK0/dP) are also composition-dependent and decrease from 11.2 (MgSiO3) to 8.77 (FeSiO3). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earth's upper mantle.