The Murnaghan and the Birch–Murnaghan equations
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[1] 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.
Francis Dominic Murnaghan ( mathematician )
Advantages and limitations
Despite its simplicity, the Murnaghan equation is able to reproduce the experimental data for a range of pressures that can be quite large, on the order of K0/2.[8] It also remains satisfactory as the ratio V/V0 remains above about 90% .[9] In this range, the Murnaghan equation has an advantage compared to other equations of state if one wants to express the volume as a function of pressure.
If the reduction in volume under compression is low, i.e., for V/V0 greater than about 90%, the Murnaghan equation can model experimental data with satisfactory accuracy. Moreover, unlike many proposed equations of state, it gives an explicit expression of the volume as a function of pressure V(P). But its range of validity is limited and physical interpretation inadequate. However, this equation of state continues to be widely used in models of solid explosives. Of more elaborate equations of state, the most used in earth physics is the Birch–Murnaghan equation of state. In shock physics of metals and alloys, another widely used equation of state is the Mie–Gruneisen equation of state.
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