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X-ray powder-diffraction data recorded using different wave lengths as well as neutron powder diffraction data on Hägg carbide,  χ -Fe 5 C 2 , were evaluated by Rietveld or Pawley 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  χ -Fe 5 C 2 . The results from diffraction and DFT imply a crystal structure having a monoclinic  C 2/ 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  χ -Fe 5 C 2  (deviation of the lattice angle  γ  from 90°) involving reflection spitting, which mimics the  hkl -dependently broadened reflections. This distortion corresponds to the most compliant shear direction of the monoclinic  χ -Fe 5 C 2 . 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  χ -Fe 5 C 2 . This anisotropic microstrain broadening was likely the origin of previous proposals of triclinic  P -1 space-group symmetry for the crystal structure of  χ -Fe 5 C 2 , which is rejected in the present work.

Crystal structure determination of Hägg carbide, χ -Fe 5 C 2 by first-principles calculations and Rietveld refinement