Analytic model of principal Hugoniot at all pressures

We present the analytic form of the principal Hugoniot at all pressures. It is constructed by interpolating smoothly between three pressure $(P)$ regimes. Specifically, (i) the low-$P$ regime in which the Hugoniot is described by $Us=C+BUp+AUp2$⁠, where $Up$ and $Us$ are particle and shock velocities, respectively, the values of $C$ and $B$ come from the experiment, and a small non-linearity (⁠$A∼10−2$ s/km) is added to the otherwise common linear form $Us=C+BUp$ to match the next regime; (ii) the intermediate-$P$ regime where the Hugoniot is described by the quantum-statistical model of Kalitkin and Kuzmina, $Us=c+bUp+aUp2$⁠, with the values of $c$⁠, $b$⁠, and $a$ determined virtually for all $Z$s (⁠$Z$ being the atomic number); and (iii) the high-$P$ regime in which the Hugoniot is described by the Debye–Hückel model developed by Johnson. We determine the analytic form of the Hugoniot in the high-$P$ regime and match it with those in the other two regimes. We show that no additional free parameter is required for the construction of the Hugoniot at all $P$ except the six mentioned above: $C$⁠, $B$⁠, $c$⁠, $b$⁠, $a$⁠, and $Z$⁠. Comparison of the new model to experimental and/or theoretical data on aluminum, iron, silicon, and lithium fluoride, the four materials for which such data exist to very high $P$⁠, demonstrates excellent agreement. Our approach applies to both elemental substances and complex materials (compounds and alloys) and can be used to predict the analytic forms of the yet unknown Hugoniots as well as to validate experimental results and theoretical calculations. The new model can be adopted for the description of the principal Hugoniots of porous substances and can be generalized for radiation-dominated (strong) shocks.