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Modern technology has enabled us to explore the Earth by various methods. However, only seismology has provided us a more complete picture of the interior of the Earth. Therefore, any petrological, mineralogical, and geochemical models of the Earth's interior will be constrained by the seismological data. In the course of testing various models, it is crucial to know precisely the longitudinal and transversal sound velocities and the associated elastic properties such as bulk modulus and shear modulus of various minerals at simultaneous high pressure and high temperature conditions due to the nature of seismic waves being elastic waves.

We have thus used the diamond anvil cell (DAC) and a gigahertz ultrasonic interferometer to measure the longitudinal and transversal sound velocities of minerals at high pressures and high temperatures. A hydrothermal diamond-anvil cell equipped with heaters that are capable of achieving 10 GPa and 1200 °C was used. The typical sample dimension in the DAC was 50 µm in height and 300 µm in diameter. The pressure was measured at room temperature with the ruby fluorescence method. At high temperature samarium-doped strontium borate will be used.

Due to the small thickness of the sample, the acoustic waves need to have wavelengths of the order of 1 µm. Therefore, frequencies generally used by traditional ultrasonic measurements (10 - 100 MHz) are not sufficient. It was only after the debut of the gigahertz ultrasonic interferometer that ultrasonic interferometry on a sample loaded in DAC has become possible. Our group is the first in the world that has succeeded in combining these two technologies.

A mechanical adapter was used to couple the gigahertz ultrasonic interferometer to the DAC (Fig. 3.10-5). The sound waves, which are generated by a piezo-electrical transducer, are guided through the buffer rod into one diamond anvil and into the sample in the DAC. The thickness of the sample and the travel time in the sample yielded the sound velocity. In order to determine the travel time accurately, we used the widely used pulse superposition method, which uses the phase difference between the echo at the sample-diamond interface and the echo at the free end of the sample to determine the travel time. The precision of the travel time determined using this method can be less than 10^-4. In addition, the wide bandwidth (from 400 MHz to 1.2 GHz) is required to ensure the high precision.
 

Fig. 3.10-5: Cross section of the ultrasonic attachment and the diamond anvil cell. The transducer is attached to the end of the buffer rod.

Fig. 3.10-6 depicts the elastic constant c₁₁ in periclase (MgO) measured along the [100] direction up to 5 GPa. The result is in very good agreement with the results from Jackson and Niesler (in: High-Pressure Research in Geophysics, Akimoto and Manghnani Eds., Reidel 1982, p.93-113). Currently, we are working on the heating setup and the measurement of shear velocities.
 

Fig. 3.10-6: Plot of elastic constant c11 vs. pressure. The solid line is the least squares fit through our data points and the dashed line is calculated elastic constant using the results of Jackson and Niesler (1982).