State equation of condensed matter at high pressure: D-U diagram approach

Abstract

For solids and liquids, an equation of state is suggested at high pressures up to a few megabars, for densities greater than that at normal conditions and for temperatures up to the melting point. Shock wave loading test data are analyzed for 40 basic chemical elements, and they prove the state equation suggested, within the limits of test error. The method is based on the analysis of D-U diagrams where D is the shock wave velocity and U is the material velocity behind the shock wave (both with respect to the material in front of the shock wave). Based on the state equation suggested the velocity of shock wave is shown to be a linear function of the material velocity behind the shock wave, the function being a specific characteristic of the material and its structure. Most significant anomaly belonging to carbon, iron, ice, and water is explained by the formation of new phases at high pressure, with two new phases of iron, and one phase in the case of water. For water, a simple nearly exact equation of state is suggested for pressures from 0.1 MPa to 150 GPa. For pressures from 0.1 to 300 MPa, it fits very well the extremely complicated state equation of the American standard obtained by static tests, and for pressures from 2 to 50 GPa it fits well the data of shock wave tests. In the pressure range from 45 to 1500 GPa liquid water becomes solid, which equation of state coincides with that of alkaline metal sodium. The model of ideal solid as contrary to ideal gas is introduced, with internal energy of ideal solid depending only on stresses or strains (and only on pressure or density, at high pressures). The equations of state for iron, diamond, pyrolithic graphite, and for several phases of ice are as well derived based on test data.