A Complete E, P, V, T, S Thermodynamic Description of Metals Based on the P, u Mirror-Image Approximation

Abstract

The well‐known practice of using the mirror‐image, in the P, u plane, of the shock Hugoniot curve about a vertical line through the shocked state P_H, u_H is shown to give a complete thermodynamic description of metals when the U (shock velocity) vs u_H relationship and α≡V^‐1(δV /δT)_P≈0 are known. Use of the experimental relationship U = c₀+au_H (a and c₀ constants) and α = constant, leads to a thermodynamic description which results in the metal appearing less compressible than if described by the Mie—Grüneisen equation of state. Furthermore, the existance of an anomalous behavior of c_p in the low pressure neighborhood (simultaneous existence of a Hugoniot satisfying the linear U vs u_H relationship, of isentropes satisfying the mirror‐image assumption, and of a constant value of α in this neighborhood. Thermodynamic functions for 16 metals are calculated up to 2 Mbars and compared with the results obtained from the Mie—Grüneisen equation of state.