Lattice dynamics of body-centered cubic Zr and FeTi from scratch

Linear fits to forces as a function of atomic displacements were performed for each time step of a quantum molecular dynamics simulation of body-centered cubic (bcc) zirconium (Zr) and the equiatomic bcc-based iron-titanium (FeTi) intermetallic alloy to determine interatomic force constants. The distributions of force constants between pairs of atoms are Gaussian with variances that depend on the atomic configuration. The symmetry operations of the bcc crystallographic point group were applied to wrap the force constants into their primitive unit cell representation. The means of the distributions were used to fit a Born-von Kármán (BvK) lattice dynamics model from which phonon dispersion curves were computed in the harmonic approximation. Phonon dispersion curves provide the energy of particular atomic vibration patterns. Several thermodynamic variables were derived from the dispersion curves and compared to experiments.