chemical_potential

About

This repository contains a lightweight LAMMPS interface to calculate chemical potentials for solution solutions of different compositions, and fitting those chemical potentials to a regular solution model. This is particularly useful for calculating thermodynamic driving forces towards equilibrium for solid solutions out of equilibrium.

Requirements

• Bash
• Python 3 with NumPy
• LAMMPS

Calculation

The main portion of this interface is the LAMMPS input file at in.insertions. In summary, this input file tells LAMMPS to:

• Read in a lattice, interatomic interactions, and solution information from the user
• Initialize the lattice and minimize at constant pressure
• Loop through all sites (indexed by $\sigma$), place each available atom type (indexed by $\alpha$) at the site, minimize at constant voluem, and store the resulting energy $E_\sigma^{(\alpha)}$.

For details on how this data is used to calculate chemical potentials, see chemical_potential_calculation.pdf.

Example

Most customizability features are accessible through a JSON configuration file and the bash script chemical_potentials.sh. An example configuration file is provided in config.json. Run this example with:

git clone https://github.com/muexly/chemical_potential.git
chmod 755 chemical_potentials.sh
./chemical_potentials.sh config.json

This will output a file with information about free energy fitting at example/output/fit.txt, which looks like:

RMSE: 0.0007686195179619156
PCC: 0.999801
x_1 x_2 x_3 x_4 x_5 x_1x_2 x_1x_3 x_1x_4 x_1x_5 x_2x_3 x_2x_4 x_2x_5 x_3x_4 x_3x_5 x_4x_5
[-4.33727796 -4.4035419  -3.73086804 -4.10044721 -2.8015742  -0.13807349
 -0.40468946 -0.52796929 -0.44899191 -0.37090297 -0.51128121 -0.60500817
 -0.30052369 -0.69471919 -0.36634538]

which corresponds to a fit of $\mu_1 = -4.33727796 -0.13807349x_2 -0.40468946x_3 -0.52796929x_4 -0.44899191x_5$, and so on. Here, the high PCC and low RMSE denote an excellent fit.

For a tutorial on writing your own configuration file, see the documentation at docs/doc.md.

This codebase heavily builds off of the chemical potential calculation in our work on vacancy concentration. If you use any code in this repository, please cite that work as well as the repository itself:

@misc{jeffries_chemical_potential_bulk,
    author={Jacob Jeffries},
    title={Bulk Chemical Potential Calculator},
    howpublished={\url{https://github.com/muexly/chemical_potential}},
    year={2024}
}

Acknowledgements

The work was supported by the grant DE-SC0022980 funded by the U.S. Department of Energy, Office of Science.