Relationship for Condensed Materials among Heat of Sublimation, Shock-Wave Velocity, and Particle Velocity

The shock‐wave velocity $U$ and the particle velocity $u$ in many condensed materials are linearly related (in the absence of phase changes) according to the equation $\mathrm{U\hspace{0.17em}=\hspace{0.17em}a\hspace{0.17em}+\hspace{0.17em}bu}$ , where $a$ and $b$ are empirical constants. If the shock compression does not produce phase changes, $a$ is approximately equal to $a_0$ , the “adiabatic,” “bulk,” or “hydrodynamic” sound speed at the initial condition. On the basis of a theoretical analysis in which it is assumed that ${\mathrm{a\hspace{0.17em}=\hspace{0.17em}a}}_0$ , it is proposed that $a_0$ and $b$ are related to the initial cohesive energy $E_{\text{χ0}}$ by the equation $E_{\text{χ0}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}-\hspace{0.17em}a}}_0^2{\text{\hspace{0.17em}/\hspace{0.17em}2b}}^2$ , and that this relation is exact (neglecting the residual zero‐point energy) at zero pressure and temperature. This equation is consistent with experimental data for 32 metals and 11 alkali‐metal halides if $E_{\text{χ0}}$ is identified as a heat of sublimation $H_s$ . The definition of $H_s$ is a function of the material and is the energy required to transform the material from the solid state to an un‐ionized gas (diatomic in the case of the alkali‐metal halides, perhaps a diatomic–monatomic mixture for the alkali metals, and monatomic in the case of the other metals). This suggests that the molecular bonds of gases may be preserved in the condensed state, or perhaps they become effective in the shock‐compression process.