Murnaghan equation of state

The Murnaghan equation of state is a relationship between the volume of a body and the pressure to which it is subjected. This is one of many state equations that have been used in earth sciences and shock physics to model the behavior of matter under conditions of high pressure. It owes its name to Francis D. Murnaghan who proposed it in 1944 to reflect material behavior under a pressure range as wide as possible to reflect an experimentally established fact: the more a solid is compressed, the more difficult it is to compress further.The next simplest reasonable model would be with a constant bulk modulus The Murnaghan equation of state is a relationship between the volume of a body and the pressure to which it is subjected. This is one of many state equations that have been used in earth sciences and shock physics to model the behavior of matter under conditions of high pressure. It owes its name to Francis D. Murnaghan who proposed it in 1944 to reflect material behavior under a pressure range as wide as possible to reflect an experimentally established fact: the more a solid is compressed, the more difficult it is to compress further. The Murnaghan equation is derived, under certain assumptions, from the equations of continuum mechanics. It involves two adjustable parameters: the modulus of incompressibility K0 and its first derivative with respect to the pressure, K'0, both measured at ambient pressure. In general, these coefficients are determined by a regression on experimentally obtained values of volume V as a function of the pressure P. These experimental data can be obtained by X-ray diffraction or by shock tests. Regression can also be performed on the values of the energy as a function of the volume obtained from ab-initio and molecular dynamics calculations.