The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4

Abstract

Abstract. The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, FezSiO4, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40 ~ C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: Vp-6.67km/s; V~ = 3.39 km/s; K = 127.9 GPa; # = 50.3 GPa; (~K/SP)r = 5.2; (8 #/SP)r = 1.5;(~ K/~ T)e = --0.030 GPa/K; and, (~#/8 T)p = -0.013 GPa/K (the pressure and temperature data are referred to 25~ and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks.Compared to the single-crystal elastic properties of forsterite, MgzSiO4, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (Cij for which i=j) values, and generally higher for the off-diagonal (Cij for which i*j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (#) and d#/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.

Thermodynamic mixing properties of olivine derived from lattice vibrations

“…Figure 4 shows that sound wave velocities of Graham et al (1988) and Isaak et al (1993) are well represented by models G and I, respectively. Figure 4 also indicates that the transverse sound wave velocities given by Graham et al (1988) are not significantly different from that reported by Isaak et al (1993). The difference is significant for the longitudinal sound wave velocity.…”

“…We used our method described by de Jong (2005a, 2007) as an inversion technique to conduct analyses of thermodynamic, vibrational and sound velocity data aiming at a consistent description of these properties. Because the adiabatic bulk modulus of fayalite measured by Graham et al (1988) and those by Isaak et al (1993) deviate from each other by about 10 GPa, we performed two analyses directing the optimization to either of these two datasets. Table 1 shows the result of two analyses obtained by a least-squares optimization process.…”

“…Fayalite Figure 2 indicates a difference of about 10 GPa between the adiabatic bulk modulus for fayalite measured by Sumino (1979) vis a vis Graham et al (1988), static compression measurements resulting in the lowest values for this property. Isaak et al (1993) performed a detailed analysis of the source for this discrepancy in the acoustic measurements.…”

“…Isaak et al (1993) performed a detailed analysis of the source for this discrepancy in the acoustic measurements. Their recommended values are based on their own new measurements and those of Sumino (1979), Graham et al (1988) and Wang et al (1989). Their conclusion is that the discrepancy arises from the different ways in which the various experimental techniques sample compositional and microstructural heterogeneities in the probed specimen.…”

“…Because of the much larger uncertainty in the bulk modulus of fayalite vis a vis forsterite, about 1 GPa, we performed two analyses. In analysis G we directed the optimization towards the data of Graham et al (1988) and in analysis I we directed it towards the recommended data of Isaak et al (1993). Here we investigate the effect of these analyses on the thermophysical properties of fayalite.…”