Fitting of Brich-Murnaghan equation of state

Question

After performing high-pressure calculations for my ABO4 compounds using the VASP software, I am now interested in fitting the Birch-Murnaghan equation of state to either pressure versus volume or energy versus volume data.

I would appreciate guidance on the best fitting procedure and, if possible, the provision of a Python or MATLAB script for this purpose. Your assistance would be greatly appreciated.

Answer 1

If you know Julia, I have a package called EquationsOfStateOfSolids.jl that is designed to do this.

It currently can fit and evaluate $E(V)$, $P(V)$, and $B(V)$ on several equations of state:

1. Murnaghan 1st EOS
2. Birch–Murnaghan EOS family:
   1. Birch–Murnaghan 2nd
   2. Birch–Murnaghan 3rd
   3. Birch–Murnaghan 4th
3. Vinet EOS
4. Poirier–Tarantola EOS family:
   1. Poirier–Tarantola 2nd
   2. Poirier–Tarantola 3rd

It can even reversibly solve the $V$ from a given $P$ or $E$ for certain equations of state.

The documentation is here.

The fitting method used is from this paper.

Answer 2

Here are some references from my own work:

• a script that reads energy-volume data from a csv file and fits a Vinet equation of state: https://github.com/flokno/tools.mlff/blob/main/mlfftools/scripts/eos_fit_data.py which I used to do the analysis around Fig. 2 and 3 in https://pubs.aip.org/aip/jcp/article/159/17/174105/2919546/Stress-and-heat-flux-via-automatic-differentiation
• the script is based on the EquationOfState class in ASE: https://wiki.fysik.dtu.dk/ase/tutorials/eos/eos.html
• if you prefer Birch-Murnaghan over Vinet, it is included in ASE: https://gitlab.com/ase/ase/-/blob/master/ase/eos.py?ref_type=heads#L40-50

Things to look out for:

• I would consistently work with energy per atom, which is a normalized quantity
• use a consistent energy baseline (typically the smallest total energy of interest) which you subtract from your energies to stabilize the fit