Machine learning the ground state energy of iron-Vavnadium 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. A total of 9 Fe-V compositions are simulated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), a molecular dynamics simulator software: Fe, Fe0.875V0.125, Fe0.75V0.25, Fe0.625V0.375, Fe0.5V0.5, Fe0.375V0.625, Fe0.25V0.75, Fe0.125V0.875, V. The energy of each composition as a function of volume was computed and the ground state energy extracted by minimization. A total of 2000 atoms at 10 Kelvin were simulated in each case. The correlation functions were manually calculated for the 9 compositions and then numerically calculated for arbitrary compositions using a code developed for that purpose. Preliminary results show the model can predict the ground state energy of arbitrary compositions with less than 1% margin of error.

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