Yoshio Sumino

Elastic properties of garnet solid-solution series

The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xjs are the properties of the end-members j (j = pyrope, almandine, spessartine, grossular and andradite). The Xjs are determined for density ρ, bulk modulus K, and shear moduli Cs = (C11 − C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are: Almandine Pyrope Spessartine Grossular Andradite K 1.779 ± 0.008 1.730 ± 0.009 1.742 ± 0.009 1.691 ± 0.008 1.379 ± 0.017 Cs 0.981 ± 0.004 0.925 ± 0.004 0.964 ± 0.004 1.106 ± 0.004 0.979 ± 0.007 C44 0.958 ± 0.005 0.919 ± 0.005 0.937 ± 0.005 1.017 ± 0.006 0.827 ± 0.010 The elasticity systematics such as Birchs, Anderson-Andersons, and their modifications hold only approximately in a garnet solid solution. For example, Anderson-Andersons relation on the constancy of the bulk modulus and molar volume product holds as a general trend, but it does not satisfy the data in the almandine-pyrope series. It is pointed out that the elastic properties of pyralspite (pyrope-almandine-spessartine) and of ugrandite (uvarovite-grossular-andradite) are markedly different. Based on the present data and the approximate elasticity systematics, an estimation of the elastic parameters of garnet in the upper mantle is given; νP ≅ 8.9 km/s and νS ≅ 5.0 km/s almandine-pyrope garnet in the uppermost mantle, and νP = ∼8.9–9.0 km/s and νS ≅ 5.1 km/s for complex garnet in the deep upper mantle.

Temperature coefficients of elastic constants of single crystal MgO between 80 and 1,300 K

AbstractElastic constants of single crystal MgO have been measured by the rectangular parallelepiped resonance (RPR) method at temperatures between 80 and 1,300 K. Elastic constants Cij (Mbar=103 kbar) and their temperature coefficients (kbar/K) are:

Thermal expansion of fayalite, Fe2SiO4

\begin{gathered} {\text{ }}C_{{\text{11}}} {\text{ }}C_{{\text{12}}} {\text{ }}C_{{\text{44}}} {\text{ }}K_s {\text{ }}C_s \hfill \\ C_{ij} {\text{ 300 K 2}}{\text{.966 0}}{\text{.959 1}}{\text{.562 1}}{\text{.628 1}}{\text{.004}} \hfill \\ \partial C_{ij} {\text{/}}\partial T{\text{100 K }} - {\text{0}}{\text{.259 0}}{\text{.013 }} - {\text{0}}{\text{.072 }} - {\text{0}}{\text{.078 }} - {\text{0}}{\text{.136}} \hfill \\ {\text{ 300K }} - {\text{0}}{\text{.596 0}}{\text{.068 }} - {\text{0}}{\text{.122 }} - {\text{0}}{\text{.153 }} - {\text{0}}{\text{.332}} \hfill \\ {\text{ 800 K }} - {\text{0}}{\text{.619 0}}{\text{.009 }} - {\text{0}}{\text{.152 }} - {\text{0}}{\text{.200 }} - {\text{0}}{\text{.314}} \hfill \\ {\text{ 1,300 K }} - {\text{0}}{\text{.598 0}}{\text{.036 }} - {\text{0}}{\text{.130 }} - {\text{0}}{\text{.223 }} - {\text{0}}{\text{.218}} \hfill \\ \end{gathered}

Elastic Constants of ReO3

By combining the present results with the previous data on the thermal expansivity and specific heat, the thermodynamic properties of magnesium oxide are presented and discussed. The elastic parameters of MgO at very high temperatures in the earths lower mantle are also clarified.

Change of Acoustic Attenuation in Sodium during Melting and Solidification Processes

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:Elastic moduli Cij in GPaT/KC11C22C33C44C55C660337.0205.6241.169.4953.5283.43300328.7199.8235.566.7880.9580.571,200292.9174.7207.155.3769.1467.22Temperature derivatives of elastic moduli, −∂Cij/∂T in MPa/K30038.426.929.412.312.514.11,20040.128.232.112.813.315.0temperature derivatives of elastic moduli, - ∂Cij/∂R in MPa/K whereCsi=(Cjj+Ckk−2·Cjk)/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.

Attenuation of sound in indium at melting point

Thermal expansion of single-crystal fayalite has been measured by a dilatometric method at temperatures between 25 °C and 850 °C. The results show the presence of anomalous expansion in the b axis, which is correlated to the anomalous variation of elastic moduli with temperature. Grüneisens parameter is 1.10 and the thermal Debye temperature is 565 K, which is close to the acoustic Debye temperature of 511 K.

Ultrasonic Behavior of Liquid Tin-Bismuth Alloys above Melting Point

The thermal expansion of tephroite (Mn2SiO4) at temperatures between 25 and 850°C has been determined by a dilatometric technique. The analysis of data in terms of Grüneisens theory yields the Grüneisens parameter γ=1.04, and the pressure derivative of rigidity (∂G/∂P)=0.7.

Repeatable Measurements of Baseline Length by Global Positioning System in Central Japan

Elastic constants of ReO 3 were determined between –195°C and 30°C by a rectangular parallelepiped resonance technique. It was found that the elasticity of ReO 3 is highly anisotropic. Discussions were made on the Debye temperature, intermolecular force constants, and the effective charges of the ions.