High-pressure Hugoniots of porous silicates

Abstract

Porous Hugoniots as formuated by Hermann’s constitutive approach are expected to be accurate at shock pressures only below 1 Mbar because his equation of state does not include elastic and electronic contributions to the total pressure and because he assumes a density variation of the Grüneisen parameter which is suitable only at low pressures. In contrast, the method presented here is valid only above about 1 Mbar. We first interpret porous aluminum data in a new way, finding shock pressure U analytically related to particle velocity u through the distention parameter m, where m=V00/V0 and V0 is standard unshocked specific volume. That is, we develop an equation U=U (u,m) which fits available shock data with excellent statistical correlation coefficients. In the U (u) plane each distinct value of m defines a straight line which is one of a family of aluminum lines. Turning to quartz data, we hypothesize that, as far as high-pressure shocks are concerned either macroscopically porous sandstone or structural polymorphs of quartz may be considered as porous forms of stishovite; stishovite is assigned a distension of unity. In accord with that hypothesis, we find the family of quartz curves derivable from the family of aluminum curves by a rotational variation in the U (u) plane. On the basis of that successful rotational correlation between the aluminum and quartz families, we predict high-pressure (above 1 Mbar) porous Hugoniots of diabase, an astrogeologically interesting material which is compositionally about one-half quartz and is in density comparable to aluminum.