Equations of state of matter from shock wave experiments

Abstract

An interpretation of the shock wave Hugoniot relation is made by using the Mie-Grüneisen equation of state. Isothermal pressure-volume curves for various metals are calculated from the data of McQueen and Marsh and Al'tshuler et al. A linear relation between shock wave velocity us and particle velocity up is assumed, and the numerical integration is extended beyond the range of the experiments. Independent calculations are made by using either the Slater or the Dugdale-MacDonald formula. Results thus obtained do not differ appreciably. The result for iron is in good agreement with that obtained by Al'tshuler et al., who used an experimentally determined value of the Grüneisen ratio. The equations of state thus calculated are well approximated by the Murnaghan-Birch equation of state with the second-order coefficient ξ varying from −½ to ½. The use of the TFD model is not valid below 100 Mb. However, inspection of the results gives the impression that for some metal the P-p curve will approach the TFD curve at pressures higher than 100 Mb. The density and incompressibility of the earth's core are compared with those of iron. The general conclusion is that the density of the earth's core is about 1 to 1.5 g/cm^3 less than the density of iron at corresponding pressure and temperature. The difference in incompressibility is very small. Bullen's incompressibility-pressure hypothesis is tested on the basis of the result obtained here. The variation of the values of incompressibility among the metals studied here is too large even at the pressure of 4 Mb to support the hypothesis. A detailed inspection of the result for the in-compressibility obtained here, however, implies that it is still difficult to avoid the conclusion arrived at from the incompressibility-pressure hypothesis that the inner core is solid.