Elastic Properties of Metals and Minerals under Shock Compression

Citation

Duffy, Thomas Sheehan (1992) Elastic Properties of Metals and Minerals under Shock Compression. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/m63k-zj81. https://resolver.caltech.edu/CaltechETD:etd-05172007-104609

Abstract

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Comparison of laboratory elasticity data with seismic measurements of the Earth provides a means to understand the deep interior. The effect of pressure and temperature on elastic properties must be well understood for meaningful comparisons. In this work, elastic wave velocities have been measured under shock compression to 80 GPa in an Fe-Cr-Ni alloy, to 27 GPa in polycrystalline MgO, and to 81 GPa in molybdenum preheated to 1400°C. These measurements were made by recording particle velocity histories at a sample surface using the method of velocity interferometry. In addition to elastic properties, these experiments provide information on the constitutive and equation of state (EOS) properties of the sample as well as the unloading adiabats.

Compressional and bulk wave velocities in Fe-Cr-Ni alloy are consistent with third-order finite strain theory and ultrasonic data. Thermal effects on the wave velocities are less than 2% at 80 GPa. Second pressure derivatives of velocity were constrained along the Hugoniot to be: (∂²C_L/∂P²)_H = -0.16 (0.06) GPa^-1 and (∂²K_S/∂P²)_H = -0.17 (0.08) GPa^-1. The measured wave profiles can be successfully reproduced by numerical simulations utilizing elastic-plastic theory modified by a Bauschinger effect and stress relaxation. Material strength was found to increase by a factor of at least 5 up to 80 GPa and to be 2-3% of the total stress.

Compressional and bulk velocities in Fe-Cr-Ni define linear velocity-density trends and can be modeled by averaging properties of Fe, Cr, and Ni. The effect of alloying ~4 wt.% Ni with Fe would change both V_P and V_B by less than 1% under core conditions. Compressional velocities in Fe-Ni are compatible with inner core values when corrected for thermal effects. Shear velocities in Fe, determined from a combination of VP and VB data, are ~3.6 km/s at P=150-200 GPa. Low values are most likely caused by a weak pressure dependence of the rigidity and imply that partial melting is not required in the inner core.

Wave profile and EOS measurements in polycrystalline MgO define its EOS: U_S = 6.77(0.08) + 1.27(0.04)u_p. Compressional sound velocities to 27 GPa yield the longitudinal modulus and its pressure derivative: C_Lo = K_oS + 4/3G = 335 ± 1 GPa and C'_Lo = 7.4 ± 0.2, which are in good agreement with ultrasonic determinations. The unloading wave profiles can be modeled using a modified elastic-plastic constitutive response originally developed for metals. Thermal expansivities in MgO have been determined to be 12 ± 4 x 10^-6 K^-1 at P=174-200 GPa and T=3100-3600 K from shock temperature and EOS data. These results imply that the lower mantle is enriched in Si and/or Fe relative to the upper mantle.

Wave profiles in molybdenum at 1400°C are the first wave profile determinations at significantly high initial temperature. The EOS determined from these measurements agrees well with previous data. The compressive yield strength of Mo is 0.79-0.94 GPa at 1400°C, and the HEL stress is 1.5-1.7 GPa. The temperature coefficient of compressional velocity, (∂Vp/∂T)p, is found to vary from -0.35(0.13) m/s/K at 12 GPa to -0.18(0.14) m/s/K at 81 GPa and compares with an ambient pressure value of -0.26 m/s/K. It is inferred that (∂Vp/∂T)p decreases with pressure, and data for Mo are shown to be consistent with trends defined by other metals.

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