Machine Learning the Ground-State and Free Energies of Iron-Vanadium alloys from Molecular Dynamics Simulations via Cluster Expansions

The ground state energy and the entropy (collectively called the free energy) determine the structure of crystals, so they are from main concern in solid-state physics and materials science. Solids with crystal lattices in nature are always found in the atomic structure that has the lowest free energy, and determining the theoretical atomic arrangement of a system is an important step towards predicting its macroscopic properties. This project intends to predict the ground state energy for different compositions of alloys of iron (Fe) and vanadium (V) by using a machine learning algorithm called Cluster Expansion, which is based on the idea that the properties of a system can be predicted based on the chemical configuration of specific sets of atoms called clusters. After the ground-state value is predicted, entropy is added to the simulation and the value of the Free Energy is simulated to calculate the Phase Transition Diagram for the different compositions of the alloy. A total of 9 Fe-V compositions are simulated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). A total of 2000 atoms at 10 Kelvin were simulated in each case for the ground-state value calculation. Results include that the Meam potential used was able to predict the ground-state energy for all compositions with less than 0.4% error from the experimental results obtained by Seki et al., and the Cluster Expansions model was able to predict the ground-state value calculated using LAMMPS with less than 1% error in all cases.