the first derivative of the compression modulus according to the pressure at a pressure of 0 GPa:
.
This equation of state is obtained if Murnaghans integrates the following assumptions:
the compression modulus of a solid increases linearly with the pressure acting on it:
the size does not depend on the pressure.
Equation of state according to Birch (-Murnaghan)
Another way of describing the behavior of condensed matter under pressure was taken by Francis Birch. He assumed that according to the Maxwell relations there is a connection between the pressure and the free energy :
Birch represented the free energy of a solid as a series expansion :
After a series expansion, the representation of which would lead too far in this context, one obtains the Birch equation of state:
In the meantime it has become common to refer to this equation as the Birch-Murnaghan equation of state , even if Birch's approach has nothing in common with Murnaghan's approach.
literature
F. Birch: Finite elastic strains of cubic crystals , Phys. Rev. 71, 809 (1947)
B. Buras and L. Gerward: Application of X-ray energy dispersive diffraction for characterization of materials under high pressure , Prog. Cryst. Growth and Characterization 18, 93 (1989)