Mechanical stability of body-centered cubic iron in Born-von Kármán parameter space via evolutionary computation

The Born-von Kármán (BvK) model of lattice dynamics, which uses effective harmonic force constants between atoms as parameters, is widely used in experimental and computational science to study phonons. We developed a genetic algorithm to explore the range of mechanical stability in reduced parameter space of body-centered cubic (BCC) iron. The genetic code of the solutions consists of the BvK force constants in the zeroth, first, and second coordination shells, while the rest of the force constants up to the fifth coordination shell are kept fixed. Phonon dispersion relations are computed from the dynamical matrix of each solution at grid points spanning the Brillouin zone, and deviation from mechanical stability conditions are used to assess its fitness. We will discuss the relationships between the force constants of the first and second nearest neighbors, the role of magnetism in stabilizing the BCC structure in iron, and how understanding mechanical stability in BvK parameter space can guide experiments and accelerate simulations.