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

Andreas Leineweber, Shunli Shang, Zi Kui Liu, Marc Widenmeyer, Rainer Niewa

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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 5C 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 5C 2. 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 χ-Fe 5C 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 5C 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 5C 2. This anisotropic microstrain broadening was likely the origin of previous proposals of triclinic P1 space-group symmetry for the crystal structure of χ-Fe 5C 2, which is rejected in the present work.

Original languageEnglish (US)
Pages (from-to)207-220
Number of pages14
JournalZeitschrift fur Kristallographie
Issue number4
StatePublished - Apr 1 2012

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Condensed Matter Physics
  • Inorganic Chemistry


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