Mult-objective Genetic Algorithm for Body-Centered Cubic Crystal Stability

Knowledge of the lattice dynamics is critical for predictions of the thermodynamical stability of materials, but its acquisition is computationally expensive. We developed a multi-objective genetic algorithm integrated with the Born-von Karman (BvK) model of lattice dynamics to compute the phonon dispersions of several body-centered cubic unaries by imposing mathematical constraints that enforce mechanical stability and null translation. In particular, the fitness function optimizes the BvK parameters within the zeroth, first, and second coordination shells. Phonon dispersion relations are computed by diagonalization of the dynamical matrix over the Brillouin zone grid points, enabling the evaluation of the fitness of each solution. This approach facilitates the exploration of the relationships between the force constants of the first and second nearest neighbors, providing insights into the stabilization mechanisms of BCC crystals.