Temperature dependence of elastic wave speeds by
ultrasonic interferometry
I. Jackson, L.J. Weston and S.L. Webb
For several years we have been working on the development of experimental methods for measurement of elastic wave speeds by ultrasonic interferometry within the high-temperature, moderate pressure environment (to 1600 K, 300 MPa) of an internally heated gas-charged pressure vessel. Last year we described preliminary measurements made with an assembly, comprising a compound hardened steel/polycrystalline alumina acoustic buffer rod in contact via Fe foil with a specimen of 7 mm diameter otherwise surrounded by soft-iron pressure-transmitting medium, all enclosed within a thin-walled mild steel sleeve (Figure 1). Our ultimate objective is to perform measurements on specimens of high-pressure silicate minerals typically < 3 mm in diameter. In preparation for such measurements we have this year performed measurements on a series of cylindrical specimens of progressively smaller diameter machined from the same boule of fine-grained (~3µm) synthetic polycrystalline Fo90 olivine.
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Experimental assembly for measurement of the temperature dependence of elastic wave speeds in an internally heated gas-charged pressure vessel by ultrasonic interferometry. |
With appropriate spacing between a pair of phase-coherent RF pulses applied to the transducer, interference between the echoes returning to the transducer following reflection from the near and far ends of the specimen gives rise to a series of alternate maxima and minima in the amplitude of the overlapping echoes as the carrier frequency is varied. Each of these interference extrema corresponds to a situation in which the two-way path through the specimen contains either an integral or half-integral number p of wavelengths. Consequently the traveltime t = p/f is estimated with considerable redundancy by the determination of the carrier frequencies f for a series of successive interference extrema. A representative set of traveltimes inferred in this way is shown in Figure 2. Mean traveltimes determined as averages over a fixed frequency interval are combined with the temperature-adjusted specimen length to calculate the compressional (VP) or shear (VS) wave speed.
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Compressional and shear wave speeds thus determined for cylindrical Fo90 olivine polycrystals of 5 and 3 mm diameter and 3 mm length are compared in Figure 3 with the temperature-dependent wave speeds expected from single-crystal elasticity data. The agreement is excellent indicating the considerable robustness of the technique. The temperature-dependent shear wave speed thus inferred from measurements at frequencies near 40 MHz is compared in Figure 4 with the results of torsional forced oscillation measurements at seismic frequencies (10 mHz - 1 Hz, see below). For temperatures ≤ 1200 K, there is a broad consistency within experimental error between the results obtained at these vastly different frequencies indicative of essentially elastic behaviour. At higher temperatures, the G(T) trends for the two frequency ranges diverge markedly reflecting frequency-dependent (dispersive) behaviour associated with viscoelastic relaxation. This comparison highlights the dangers inherent in the traditional direct seismological application of wave speeds measured in the laboratory with ultrasonic and opto-acoustic techniques. The temperature sensitivity of the shear modulus and hence wave speed may be seriously underestimated (Figure 4).
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Comparison of measurements performed on Fo90 specimens of two different diameters (5 and 3 mm) indicating the insensitivity of the results to the size of the specimen and also the close approach to the temperature dependent modulus calculated from single-crystal elasticity data. |
| Comparison of shear moduli measured on fine grained Fo90 olivine by ultrasonic interferometry (specimen of 5 mm diameter, average frequency ~40 MHz), and by seismic-frequency (≤ 1 Hz) forced-oscillation techniques, with expectations from single-crystal elasticity data (line). The markedly lower values of modulus and stronger temperature sensitivity observed at seismic frequencies and sufficiently high temperature ( ≥ 1300 K) are associated with substantial viscoelastic relaxation and have important implications for the interpretation of tomographic models of wave speed variability for the upper mantle. |
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The quality of the ultrasonic measurements is maximised for an echo amplitude ratio near unity. However, as the specimen diameter is reduced there is a systematic reduction in the amplitude of the echo returning from the far end of the specimen. We are seeking to improve this situation by tapering the end of the buffer rod to better match the specimen diameter. In addition we plan soon to explore the use of dual-mode transducers in making simultaneous measurements of both compressional and shear wave speeds. With these further improvements to the technique we expect to commence measurements on a suite of specimens of high-pressure silicate minerals during the coming year. This work, to be performed in collaboration with colleagues from the State University of New York at Stony Brook and Delaware State University, will address key unresolved issues concerning the elasticity of the transition zone of the Earth's mantle.