Elasticity of single‐crystal orthoferrosilite

Abstract

The elastic moduli of a synthetic single crystal of pure FeSiO3, orthoferrosilite, have been measured at 1 bar and 20°C by Brillouin spectroscopy. The moduli are (in megabars) c11 = 1.98, c22 = 1.36, c33 = 1.75, c44 = 0.59, c55 = 0.58, c66 = 0.49, c12 = 0.84, c13 = 0.72, c23 = 0.55. A comparison of the pyroxene crystal structure with elasticity data shows that distortion of the tetrahedral chains parallel to c is related to c33 Straight or extended chains increase c33, and highly kinked chains weaken the structure. However, the ferrosilite data show that beyond a certain degree of distortion the tetrahedral chains are essentially passive. Previous models of pyroxene elasticity have indicated that c11 should be most sensitive to composition. This is supported by the current study and is reflected in the elasticity data via a positive linear correlation of c11 with the size of the M1 octahedron, as measured by the average M1‐0 distance. The average longitudinal modulus 11 ((c11 + c22 + c33)/3) varies linearly with composition in the system orthoenstatite‐orthoferrosilite, whereas the average shear moduli ¯44 and ¯12 are constant for Fe contents of at least 20%. By comparison, data for the solid solution forsterite‐fayalite are consistent with a linear variation of modulus versus composition between the end‐members for all three average moduli. We suggest that this difference between orthopyroxene and olivine is due to a strong preference of Fe2+ for the M2 octahedral site in pyroxene. The isotropic shear modulus μ is 30% lower for ferrosilite than enstatite. Despite a similar contrast in end‐member values of μ, the olivine data are consistent with a linear variation of μ between Fo100 and Fa100. At high temperatures, Fe and Mg in orthopyroxene will be randomly distributed, and a linear variation of μ with molar content of Fe is expected. A comparison of laboratory elasticity data with observed mantle properties shows that Vp, Vs, and ρ of the upper mantle are satisfied by pure olivine. However, the data strongly suggest that without the coexistence of a garnet phase, no more than 10% orthopyroxene may be present in a model mantle assemblage. Ca‐clinopyroxene increases the upper limit on mantle garnet content but does not greatly affect constraints on the quantity of orthopyroxene in the upper mantle.