Ultrasonic Interferometry in Multianvil Apparatus

The acoustic signals are generated and received using disk-shaped (3.2 mm diameter), 40 MHz LiNbO3 transducers (36° Y-cut for compressional wave and 41° X-cut for shear waves). The transducer is mounted onto the exposed corner of the buffer rod cube using Aremco Crystalbond. Truncations on the edges of the three bottom first-stage cylinder anvils, originally designed for thermocouple feedthroughs, provide a channel for the coaxial cables to connect the interferometer and the transducer. A spring-loaded sliding pin is placed in the vertical gap between the bottom three anvils to make contact with one electrode of the transducer while the buffer rod cube serves as the electrical ground. A 50 ohm resistor connected in parallel with the transducer provides appropriate electrical termination. At elevated pressure, the transducer remains stress-free since it is located in the gap between the first-stage anvils and the second-stage cubes, allowing precise travel-time measurements over a wide frequency range (20 to 70 MHz).

The ultrasonic phase-comparison method implemented on the Australian Scientific Instruments Ultrasonic Interferometer employed in our laboratories has been described in detail in previous studies [Rigden et al., 1988; Niesler and Jackson, 1989, Rigden et al., 1992]. Briefly, the output from a continuous wave source is gated to produce a pair of phase-coherent, high frequency pulses. These pulses are applied to the transducer which is bonded to the buffer rod. The elastic waves generated by each pulse are reflected and transmitted at the buffer rod/sample interface, and the transmitted portion reverberates inside the sample, resulting in a series of 'sample' echoes following the buffer rod echo. If the applied pulses are separated by the apparent two-way travel time through the sample, the first buffer echo from the second applied source pulse will superimpose with the first sample echo from the first source pulse. As the carrier frequency is varied, alternate constructive and destructive interferences between the superimposed signals will occur, resulting in a series of maxima and minima on the amplitude spectrum modulated by the transducer response envelope. Frequencies for pth and (p+n)th interference extrema, fp and f p+n can be used to estimate the apparent travel time by t¢est = n / (f p+n * fp ); then the p value is calculated from p = fpt¢est and the closest half or integral value is therefore assigned to frequency fp and all remaining extrema can be assigned sequentially. In practice, the interference minima are normally used to reduce the travel-time data because they are sharper than the maxima. For the situation in which the amplitude ratio of the first buffer rod echo and the first sample echo (B1/S1) is very different from unity, the perturbation to travel time from the transducer response envelope has to be taken into consideration, especially for interference maxima [see Jackson et al., 1981; Niesler and Jackson, 1989].

The acoustic signals at different stages are compared in Figure 3 from an S wave measurement experiment on polycrystalline alumina (see details in following section). Initially, after the cell assembly is loaded into the press and before oil pressure is applied, one sees only a series of echoes from the bottom triangular face of the WC buffer rod (top photo), due to inadequate mechanical coupling between the buffer rod, the gold foil, and the specimen (Figure 1). When the ram load is increased to some 7 ~10 tons (estimated cell pressure 0.2 GPa), contact is made and multiple sample echoes appear following the buffer rod echoes (middle photo), and the amplitude ratio B1/S1 decreases rapidly with further pressurization. The B1/S1 reaches a stable level at pressures of about 1~2 GPa and varies only slightly with further increase of pressure. The bottom photo in Figure 3 shows the acoustic signals at ~10 GPa; it is evident that the quality of the acoustic signals is maintained as pressure is increased. The interference spectrum between B1 and S1 at ~10 GPa is shown in Figure 3b from 15 to 55 MHz, and the apparent travel times obtained from these interference extrema are shown in Figure 3c. The dispersion from 20 to 40 MHz (~ 1%) is much more pronounced than that at frequencies higher than 40 MHz in which range the travel times are insensitive to the frequency. This characteristic of the dispersion persists at all pressures in our experiments.

However, the observed dispersion in the frequency range lower than 40 MHz is not considered to be intrinsic to the sample (i.e. change of velocity with frequency). Instead, the dispersion is largely caused by departures from the assumption of wave propagation in an infinite medium, due to the small size of the sample as has been suggested by Rigden et al. [1992]. Small samples are likely to be effected by the sidewall reflections from the sample at certain low frequencies. Comparison of the results of this study with measurements for samples of the same material but larger diameters [I. Jackson, personal communication, 1996] show that the dispersion in the frequency range 20-50 MHz decreases from 1% to 0.3% as the sample diameter increases from 2.9 to 7 mm. Further measurements in the frequency range of 120-150 MHz on both polycrystalline alumina and forsterite samples (diameter 2.7-2.9 mm) used in this study show a very good agreement (better than 10-3) with measurements at frequency range 40-70 MHz, confirming that the travel times at low-frequency range are influenced by the experimental configuration, and reliable travel times can be obtained at the high-frequency range [Li et al., 1996b, Figure 5]. The uncertainties in the measured travel times in this study are thus estimated to be about 0.3%.

As shown in Figure 1, a thin gold foil (2-mm thickness) is inserted between the buffer rod and the sample (both polished with 1-mm diamond paste finish) to enhance mechanical bonding by smoothing the interface at high pressures. However, the reverberation of the acoustic energy inside the bonding layer causes an unwanted phase shift in the buffer rod and sample echoes. The perturbation by these phase shifts have to be removed from the measured travel times. Quantitative studies on this subject have been performed both experimentally and theoretically [Davies and O'Connell, 1977, Jackson et al., 1981]. Theoretically, the phase shift can be calculated by summing to infinity the reverberations within the bonding layer from the known thickness of the bond and the reflection/transmission coefficients at the interface determined by the acoustic impedances of buffer rod, bond material and sample. In this study, we have applied the same bond thickness (2 mm) corrections to the measured travel times at all pressures due to the negligible thickness change [estimated to be l / l0 ~ P / 3K ( ~ 2% at 10 GPa), where P is the pressure and K is the bulk modulus of gold (~ 166 GPa)].