Measurements of Elastic moduli and Equation of State on High Density Minerals by means of Resonant Sphere Technique

温度控制系统和缓冲棒材料的改进提高了共振法光谱测量的精度。同时，对三层振荡体系进行了理论分析，并将分析结果应用于高压测量，得到了各向同性材料弹性模量的压力导数。在高压下，圣卡洛斯橄榄石转变为β和γ相。将小样品制成球形并用于光谱测量。高达700 K的弹性数据被用来估计在高压和高温下的弹性速度。过渡层周围橄榄石含量的体积比约为30~50倍。剪切模量C_S（=（C_-C_）/2）具有特殊的温度依赖性。<11><12>用尖晶石中阳离子的有序/无序转变解释了这一现象。反应的活化能E_a = 300 kJ/mol。在900 K以上，内耗Q_（？）也出现了特殊的变化，这可能是由于反应引起的能量耗散.在环境压力下，体积模量K_S与温度的关系可用公式K_S = K_-gE表示，或更一般地，对于弹性刚度M，可用公式M = M_0-gE表示.利用这些公式，即修正的Wachtman方程，我们可以得到对每种模量K_S，C_，C_，C_或μ几乎相同大小的德拜温度θ.<44><-1><S0><11><12><44>这些方程也适用于橄榄石的弹性数据。

Improvements in the temperature control system and buffer rod materials have brought increase of accuracy in spectral measurement with the resonance method. Also, theoretical analyses of three-layered oscillatory system were made and those results were applied to high pressure measurements to find pressure derivatives of elastic moduli of an isotropic material.Beta and gamma phases were converted from San Carlos olivine at high pressures. The small specimens were shaped into spheres and used for spectrum measurements. Elasticity data up to 700 K were used to estimate elastic velocities at high pressures and temperatures. The volume ratio of olivine content around the transition layer is estimated to be 30 to 50 percents.Accurate spectral measurements were made for a spinel MgAl_2O_4 sphere. One of the shear moduli, C_S (=(C_<11>-C_<12>)/2), shows peculiar temperature dependence. This phenomenon is explained with the order/disorder transitions of cations in spinel. Activation energy of the reaction is estimated to be E_a=300 kJ/mol. Peculiar variation is also found in internal friction Q_<44>^<-1> above 900 K.This phenomenon may arises from energy dissipation associated with the reaction.Temperature dependence of bulk modulus K_S at ambient pressure may represented by an eqtuation K_S=K_<S0>-g E, or more generally, M=M_0-g E for elastic stiffness M.Using these equations, modified Wachtman equations, we could obtain the Debye termperature θ with almost same magnitudes for each modulus K_S, C_<11>, C_<12>, C_<44> or μ. These equations are also applicable to the elasticity data of olivine.