Crystal structure determination of Hagg carbide, χ-Fe5C2 by first-principles calculations and Rietveld refinement

X-ray powder-diffraction data recorded using different wave lengths as well as neutron powder diffraction data on Flagg carbide, chi-Fe5C2, were evaluated by Rietveld or Fawley refinements, respectively. Likewise, employing different starting models, first-principles calculations using density functional theory (DFT) involving structure optimisation with respect to energy were performed for chi-Fe5C2. The results from diffraction and DFT imply a crystal structure having a monoclinic C2/c symmetry with a quite regular (monocapped) trigonal-prismatic coordination of C by Fe atoms. The anisotropy of the microstrain broadening observed in the powder-diffraction patterns agrees with the anisotropy of the reciprocal Young's module obtained from elastic constants calculated by DFT. The anisotropic microstrain broadening can to some degree, be modelled allowing for a triclinic distortion of the metric of chi-Fe5C2 (deviation of the lattice angle gamma from 90 degrees) involving reflection spitting, which mimics the hkl-dependently broadened reflections. This distortion corresponds to the most compliant shear direction of the monoclinic chi-Fe5C2. The anisotropic microstrain broadening results from microstress induced e.g. by anisotropic thermal expansion inducing misfit between the grains, in association with the intrinsic anisotropic elastic compliance of chi-Fe5C2. This anisotropic microstrain broadening was likely the origin of previous proposals of triclinic P (1) over bar space-group symmetry for the crystal structure of chi-Fe5C2, which is rejected in the present work.