This repository hosts two examples on how to compute the free energy of solids using LAMMPS. The simulations are small enough to be run in a laptop in about 2min. The methods for free-energy calculation are the Frenkel-Ladd and the Reversible Scaling. Details about algorithm implementation, syntax, and theoretical aspects can be found in

"Nonequilibrium free-energy calculation of solids using LAMMPS"
Rodrigo Freitas, Mark Asta, and Maurice de Koning.
Computational Materials Science
DOI:10.1016/j.commatsci.2015.10.050

LAMMPS needs to be compiled with some nonstandard packages in order to be able to perform free energy calculations. Follow the commands below in order to install LAMMPS. Starting from an empty directory use the following commands:

git clone https://github.com/lammps/lammps.git lammps
cd lammps/src
cp USER-MISC/fix_ti_spring.* .
make yes-MANYBODY
make -j 8 serial

This will create an executable named lmp_serial inside lammps/src. Go back to the original directory and clone this repository:

cd ../..
git clone https://github.com/freitas-rodrigo/FreeEnergyLAMMPS.git
cd FreeEnergyLAMMPS

Now you should be ready to run free-energy calculations of solids.

The documentation for the commands used during free-energy calculations is available here. Alternatively, a detailed explanation of the method can be found here.

Notice that in the LAMMPS input scripts, the fix ti/spring should be declared before any other fix that modifies the forces on the particles (such as thermostats). This is necessary because one of the actions of fix ti/spring is to scale all forces on the particles, hence any forces added by fix commands declared before fix ti/spring will be wrongly modified.

The two examples below demonstrate how to compute the free energy of the body-centered cubic (bcc) phase of iron at zero pressure for temperatures ranging from 100K to 1600K. The interatomic potential employed is the EAM potential described here, available in this repository: Fe.eam. By following the examples below you should be able to reproduce Figure 3 of this article.

The Frenkel-Ladd simulation can be run with the following commands:

cd frenkel_ladd
bash job.sh

In my personal laptop it took about 40 seconds to run the calculation for 6 different temperatures. After the calculations are done, it is necessary to perform the lambda integration and plot the results:

cd post_processing
python integrate.py
python plot.py

You will need python's modules numpy and matplotlib installed to run the post-processing scripts. If the code ran correctly you should obtain the following figure:

Once the Frenkel-Ladd calculation is done, the Reversible Scaling simulation can be run using the following commands:

cd ../../reversible_scaling
bash job.sh

In my personal laptop it took about 15 seconds to run the simulation. After the calculation is done, it is necessary to perform the lambda integration and plot the results:

cd post_processing
python integrate.py
python plot.py

If the code ran correctly you should obtain the following figure:

This figure reproduces the results of Figure 3 of this article.

Rodrigo Freitas | [email protected]