Temperature Derivatives Of Elastic Moduli Research Articles

Elastic wave velocity of polycrystalline Mj80Py20 garnet to 21 GPa and 2,000 K

The elastic wave velocities of polycrystalline Mj80Py20 garnet along the majorite–pyrope system have been measured at pressures up to 21 GPa and temperatures up to 2,000 K using ultrasonic interferometry in conjunction with in situ X-ray diffraction techniques in a Kawai-type multi-anvil apparatus. The elastic moduli of Mj80Py20 garnet and their pressure and temperature derivatives are determined by a two-dimensional linear fitting of the present experimental data, yielding: K S = 161.5 (7) GPa, ∂K S/∂P = 4.42 (4), ∂K S/∂T = −0.0154 (2) GPa/K, G = 86.2 (2) GPa, ∂G/∂P = 1.28 (1), ∂G/∂T = −0.0096 (5) GPa/K. The present results together with those of the studies on the majorite–pyrope solid solutions suggest the pressure and temperature derivatives of elastic moduli are insensitive to the majorite content in the majorite–pyrope system. The velocity gradients of the majoritic garnets in the majorite–pyrope system are 3 ~ 6 times lower than those required to account for the high seismic velocity gradients observed in the mantle transition zone.

Temperature derivatives of elastic moduli of MgSiO3 perovskite

Elastic properties of polycrystalline MgSiO3 perovskite were determined by means of resonance sphere technique at temperatures from 258 to 318 K under atmospheric pressure. The temperature derivatives of adiabatic bulk (∂KS/∂T)P and shear moduli (∂G/∂T)P are −0.029(2) GPa/K and −0.024(1) GPa/K, respectively. Applying the present results in interpretation of seismological observations, we suggest that the chemical composition of the earth's lower mantle is pyrolitic at the potential temperature of 1600 K.

Silicate perovskite analogue ScAlO 3: temperature dependence of elastic moduli

The elastic moduli of ScAlO 3 perovskite, a very close structural analogue for MgSiO 3 perovskite, have been measured between 300 and 600 K using high precision ultrasonic interferometry in an internally heated gas-charged pressure vessel. This new capability for high temperature measurement of elastic wave speeds has been demonstrated on polycrystalline alumina. The temperature derivatives of elastic moduli of Al 2O 3 measured in this study agree within 15% with expectations based on published single-crystal data. For ScAlO 3 perovskite, the value of (∂ K S/∂ T) P is −0.033 GPa K −1 and (∂ G/∂ T) P is −0.015 GPa K −1. The relative magnitudes of these derivatives agree with the observation in Duffy and Anderson [Duffy, T.S., Anderson, D.L., 1989. Seismic velocities in mantle minerals and the mineralogy of the upper mantle. J. Geophys. Res. 94, 1895–1912.] that |(∂ K S/∂ T) P| is typically about twice |(∂ G/∂ T) P|. The value of (∂ K S/∂ T) P for ScAlO 3 is intermediate between those inferred less directly from V( P, T) studies of Fe-free and Fe- and Al-bearing MgSiO 3 perovskites [Wang, Y., Weidner, D.J., Liebermann, R.C., Zhao, Y., 1994. P– V– T equation of state of (Mg,Fe)SiO 3 perovskite: constraints on composition of the lower mantle. Phys. Earth Planet. Inter. 83, 13–40; Mao, H.K., Hemley, R.J., Shu, J., Chen, L., Jephcoat, A.P., Wu, Y., Bassett, W.A., 1991. Effect of pressure, temperature and composition on the lattice parameters and density of (Mg,Fe) SiO 3 perovskite to 30 GPa. J. Geophys. Res. 91, 8069–8079; Zhang, Weidner, D., 1999. Thermal equation of state of aluminum-enriched silicate perovskite. Science 284, 782–784]. The value of |(∂ G/∂ T)| P for ScAlO 3 is similar to those of most other mantle silicate phases but lower than the recent determination for MgSiO 3 perovskite [Sinelnikov, Y., Chen, G., Neuville, D.R., Vaughan, M.T., Liebermann, R.C., 1998. Ultrasonic shear wave velocities of MgSiO 3 perovskite at 8 GPa and 800K and lower mantle composition. Science 281, 677–679]. Combining the results from the previous studies and current measurements on ScAlO 3 perovskite, we extracted the parameters ( q and γ 0) needed to fully specify its Mie–Grüneisen–Debye equation-of-state. In this study, we have demonstrated that acoustic measurements of K S( T), unlike V( P, T) data, tightly constrain the value of q. It is concluded that ScAlO 3 has ‘normal’ γ 0 (∼1.3) and high q (∼3.6). The high value of q indicates that ScAlO 3 has very strong intrinsic temperature dependence of the bulk modulus; similar behaviour has been observed in measurements on Fe- and Al-bearing silicate perovskites (Mao et al., 1991; Zhang and Weidner, 1999).

Seismic velocities in mantle minerals and the mineralogy of the upper mantle

Comparison of seismic velocities in mantle minerals, under mantle conditions, with seismic data is a first step toward constraining mantle chemistry. The calculation, however, is uncertain due to lack of data on certain physical properties. “Global” systematics have not proved very useful in estimating these properties, particularly for the shear parameters. A new approach to elasticity estimation is used in this study to produce estimates of unknown quantities, primarily pressure and temperature derivatives of elastic moduli, from the structural and chemical trends evident in the large amount of elasticity data now available. These trends suggest that the derivatives of unmeasured high‐pressure phases can be estimated from “analogous” low‐pressure phases. Using these predictions and the best available measurements, seismic velocities are computed along high‐temperature adiabats for a set of mantle minerals using third‐order finite strain theory. The calculation of density and moduli at high temperature, to initiate the adiabat, must be done with care since parameters such as thermal expansion are not independent of temperature. Both compressional and shear seismic profiles are well‐matched by a mineralogy dominated by clinopyroxene and garnet and with an olivine content of approximately 40% by volume. Between 670 and 1000 km, perovskite alone provides a good fit to the seismic velocities. Combining seismic velocities with recent phase equilibria data for a hypothetical pure olivine mantle suggests that a mineralogy with a maximum of 35% olivine (shear profile) or 40–53% olivine (compressional profile) by volume can satisfy the constraint imposed by the 400‐km discontinuity. Other features of the upper mantle can then be matched by appropriate combinations of pyroxenes, garnets, and their high‐pressure equivalents. While mantle models with a substantially larger fraction of olivine cannot be ruled out, they are acceptable only if the derivatives of the spinel phases are substantially different from olivine and deviate from trends in the larger data set.

Elastic Properties and the Short- and Medium-Range Structures of Lead Silicate Glasses

The elastic moduli and their pressure and temperature derivatives of lead silicate glasses were measured by the cubic resonance method and pulse superposition method. Thermal expansion coefficients and heat capacities were also measured The sound velocities, Young's modulus, shear modulus decreared monotonously with increasing PbO content, but the bulk modulus increased with increasing PbO content up to its maximum at about 50mol% PbO and then decreased remarkably. The compositional dependence of bulk modulus was interpreted based on the change in the role of Pb2+ ions in glass structure. That is, Pb2+ ions behave as a network modifier for PbO content 50mol%. The short- and medium-range structures in lead silicate glasses were discossed in terms of the three-band theory using characteristic temperatures obtained from the specific heats. It was found that the medium-range order in lead silicate glasses increased with increasing PbO content. The elastic anomaly in fused silica with negative pressure and positive temperature derivatives disappeared with increasing PbO content. Lead silicate glasses with PbO content>40mol% showed no elastic anomaly. The characteristic temperature representing the intermolecular bonding of the glass network was found to affect the pressure and temperature derivatives of elastic moduli.

Elastic properties of a single-crystal forsterite Mg2SiO4, up to 1,200 K

Elastic moduli of forsterite were measured between 300 and 1,200 K (≃ 1.6 times the Debye temperature) by the Rectangular Parallelepiped Resonance method. All the moduli decrease regularly with temperature. A summary of the results is as follows: temperature derivatives of elastic moduli, - ∂C ij /∂R in MPa/K whereC si =(C jj +C kk −2·C jk )/4; (i, j, k=1, 2, 3;i ≠j ≠k), and ρ is density in kg/m3. These data permit for the first time the calculation of elastic and thermal properties well into the classical range far above the Debye temperature. We find, for example, that the elastic constants, including the bulk moduls, closely follow standard equations throughout the measured temperature range. This information aids extrapolations up to the melting point. This data, coupled with thermal expansivity data permit the computations of thermal anharmonic parameters of minerals forT>θ.