Elastic anisotropy of γ′-Fe4N and elastic grain interaction in γ′-Fe4N1-y layers on α-Fe: First-principles calculations and diffraction stress measurements

T. Gressmann, M. Wohlschlögel, S. Shang, U. Welzel, A. Leineweber, E. J. Mittemeijer, Z. K. Liu

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The three independent single-crystal elastic-stiffness constants Cij of cubic γ′-Fe4N (face-centred cubic (fcc)-type iron substructure) have been calculated by first-principles methods using the density functional theory: C11 = 307.2 GPa, C12 = 134.1 GPa and C44 = 46.0 GPa. The Zener elastic-anisotropy ratio, A = 2C44/(C11 - C12) = 0.53, is strikingly less than 1, implying 〈1 0 0〉 as stiffest directions, whereas all fcc metals show A > 1. This elastic anisotropy is ascribed to the ordered distribution of N on the octahedral interstitial sites. X-ray diffraction lattice-strain measurements for a set of different h k l reflections recorded from γ′-Fe4N1-y layers on top of α-Fe confirmed the "abnormal" elastic anisotropy of γ′-Fe4N1-y. Stress evaluation, yielding a compressive stress of about -670 MPa parallel to the surface, was performed on the basis of effective X-ray elastic constants determined from the calculated single-crystal elastic constants Cij and allowing a grain interaction intermediate between the Reuss and the Voigt models.

Original languageEnglish (US)
Pages (from-to)5833-5843
Number of pages11
JournalActa Materialia
Issue number17
StatePublished - Oct 1 2007

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys

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