Birch–Murnaghan equation of state

The state equation for Birch Murnaghan describes the relationship between the volume V of a solid body and acting on it, the outer hydrostatic pressure p. This state equation is a function of two parameters, the compression module at a pressure of 0 GPa, and the first derivative of the bulk modulus of elasticity according to the pressure at a pressure of 0 GPa. These are defined as follows:

Murnaghan was assumed that the bulk modulus of a solid increases linearly with the pressure acting on it. Another important assumption is that the size is independent of pressure.

After integration we obtain the equation of state Murnaghan

Or

Wherein the volume of the solid body at a pressure of 0 GPa.

Another way to describe the behavior of condensed matter under pressure, was taken by Francis Birch. He believed that after the Maxwell relations, there is a relationship between the pressure p and the free energy F:

Birch presented the free energy of a solid as a series expansion is:

Here are pressure-dependent coefficients, is the so-called Eulerian strain.

After a series expansion whose representation is beyond the scope of this framework, the equation of state is then obtained by Birch:

It has become naturalized to call this equation as the equation of state to Birch - Murnaghan, even if the approach of Birch with the approach of Murnaghan has nothing in common.