Shock compression of a free-electron gas

The shock compression curve (Hugoniot) of a free-electron gas was calculated and evaluated numerically for a metal with a Fermi energy of 5 eV. Shock pressure, internal energy, and temperature were calculated as functions of compression. The Hugoniot curve has a limiting compression of fourfold of initial density and agrees with expected limiting values at small and large compressions. Above a compression of ∼3.3-fold of initial density, a shock pressure of ∼250 GPa (2.5 Mbar), and a temperature of ∼10 eV, free electrons are a nondegenerate ideal gas. Shock pressures of the free electron gas are a factor of 104 larger at all compressions than those of an ideal gas of nuclei with the same number density, indicative of the strong effect of Fermi–Dirac and Maxwell–Boltzmann statistics. This simple free-electron model calculates shock compression curves of Li and Na, which differ by ∼50% from experimental data, illustrating that interactions between electrons and nuclei must be taken into account, as expected.