A first-principles study of cementite (Fe3C) and its alloyed counterparts: Elastic constants, elastic anisotropies, and isotropic elastic moduli

Abstract

A comprehensive computational study of elastic properties of cementite (Fe₃C) and its alloyed counterparts (M₃C (M = Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, W, Zr, Cr₂FeC and CrFe₂C) having the crystal structure of Fe₃C is carried out employing electronic density-functional theory (DFT), all-electron PAW pseudopotentials and the generalized gradient approximation for the exchange-correlation energy (GGA). Specifically, as a part of our systematic study of cohesive properties of solids and in the spirit of materials genome, following properties are calculated: (i) single-crystal elastic constants, C_ij, of above M₃Cs; (ii) anisotropies of bulk, Young’s and shear moduli, and Poisson’s ratio based on calculated C_ijs, demonstrating their extreme anisotropies; (iii) isotropic (polycrystalline) elastic moduli (bulk, shear, Young’s moduli and Poisson’s ratio) of M₃Cs by homogenization of calculated C_ijs; and (iv) acoustic Debye temperature, θ_D, of M₃Cs based on calculated C_ijs. We provide a critical appraisal of available data of polycrystalline elastic properties of alloyed cementite. Calculated single crystal properties may be incorporated in anisotropic constitutive models to develop and test microstructure-processing-property-performance links in multi-phase materials where cementite is a constituent phase.