  Using first-principles calculations within the generalized gradient
approximation, we predicted the lattice parameters, elastic constants,
vibrational properties, and electronic structure of cementite (Fe3C). 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 Fe3C is mechanically stable. The
experimentally observed high elastic anisotropy of Fe3C is also confirmed by
our study. Based on electronic density of states and charge density
distribution, the chemical bonding in Fe3C was analyzed and was found to
exhibit a complex mixture of metallic, covalent, and ionic characters.
