Structural, elastic, and electronic properties of Fe3 C from first principles

Using first-principles calculations within the generalized gradient approximation, we predicted the lattice parameters, elastic constants, vibrational properties, and electronic structure of cementite (Fe3 C). Its nine single-crystal elastic constants were obtained by computing total energies or stresses as a function of applied strain. Furthermore, six of them were determined from the initial slopes of the calculated longitudinal and transverse acoustic phonon branches along the [100], [010], and [001] directions. The three methods agree well with each other; the calculated polycrystalline elastic moduli are also in good overall agreement with experiments. Our calculations indicate that Fe3 C is mechanically stable. The experimentally observed high elastic anisotropy of Fe3 C is also confirmed by our study. Based on electronic density of states and charge density distribution, the chemical bonding in Fe3 C was analyzed and was found to exhibit a complex mixture of metallic, covalent, and ionic characters.