Spontaneous acoustic emission from strong shocks in solids

The role of free electrons in the stability of strong shock waves in metals under spontaneous acoustic emission is investigated. For that purpose, a t hree-term form of the equation of state is employed in order to describe th e cold pressure, the thermal atomic pressure and the thermal pressure of fr ee electrons. The equation of state enables the calculation of the sound ve locity behind the shock, which in turn is utilized in the Dyakov-Kontorovic h criteria for the shock stability. The integral over the Fermi-Dirac distr ibution function that describes the specific internal energy of free electr ons is replaced by a model algebraic function that possesses correct asympt otic limits at low and high temperatures. It is shown that strong shock wav es in all metals are prone to instability under spontaneous emission. Howev er, the threshold for that instability is shifted to higher Mach numbers if free electrons are taken into account. It is further shown that the stabil izing effect of free electrons is vastly overestimated if the expressions f or degenerate electron gas are employed for temperatures that are larger th an the Fermi temperature.