Minimum model for the main feature of shock Hugoniot near its maximum compression ratio

Abstract

When being compressed by a single shock, most materials show a maximum compression ratio beyond the ideal-gas limit of four. In most cases, this phenomenon has long been conjectured to originate from the ionization of core electrons, but a clear physical picture is still lacking. Here we present a simple illustration from the energy-band picture of dense plasmas, where the total energy includes only the contributions from ionization of the bound electrons in addition to those from ideal-gas-like free particles. This additional energy term (ionization energy) directly leads to an additional term in the compression ratio $\ensuremath{\eta}$, which gives a peak on the Hugoniot adiabat. Furthermore, peaks given by different bound states are shown to add linearly ($\ensuremath{\eta}\ensuremath{\approx}4+{\ensuremath{\sum}}_{i}\mathrm{\ensuremath{\Delta}}{\ensuremath{\eta}}_{i}$), yielding multipeaked Hugoniots. Quantitative predictions regarding those Hugoniot peaks can be provided systematically by using this minimum model, showing a good agreement with first-principles calculations and experimental data.