The equation of state of solids

An equation of state for solids, in reduced variables, is obtained within the context of a system-independent formulation of the thermodynamics of high pressures. This formulation is valid for materials obeying a linear relationship between shock and particle velocities. An adequate set of scaling factors for pressure, compression, specific energy, and temperature, is first introduced. A modified Mie-Grüneisen equation, as well as many other thermodynamic relationships and coefficients, are then expressed in terms of reduced variables. Explicit expressions for the temperature along the Hugoniot, and for the equation of state, are obtained. It is also shown that when given in their reduced form, each of the two thermodynamic coefficients appearing in the equation of state can be considered as having the same constant value for many different materials. The possibility and convenience of using a “standard material” is discussed. Numerical results obtained using this reduced variables formalism are in good agreement with those computed or measured, by different authors, for various materials over a wide range of pressures. This is a good indication of the “universality” of the reduced equations obtained, and of the usefulness of the formalism.