Exploring the intrinsic ductile metastable Fe-C compounds: Complex chemical bonds, anisotropic elasticity and variable thermal expansion

Abstract

As the vitally important phases in iron and steel, the Fe-C binary compounds are investigated by first-principles calculations combined with quasi-harmonic approximation (QHA). The formation enthalpy and Gibbs free energy are positive, but the phonon dispersion are stable, indicating θ-Fe3C, o-Fe7C3, h-Fe7C3, γ-Fe23C6, χ-Fe5C2, η-Fe6C, η-Fe2C and ε-Fe3C are metastable phases in this binary system for the first time. The electronic structure indicates that the complex bonding behavior of these carbides are the combinations of covalent, ionic and metallic bonds, which determines the anisotropic elastic properties and novel intrinsic ductility of these carbides. The mechanical modulus is nearly proportional to the carbon content. o-Fe7C3 has the largest B value as 379 GPa and The anisotropic bulk modulus, shear modulus and Young's modulus are discussed by the anisotropic index and three-dimensional surface contours. The shear modulus range from 40 GPa to 204.2 GPa and the Young's modulus vary from 113.7 GPa to 512.6 GPa. Intrinsic hardness is predicted by semiempirical models. The thermal electronic contributions to thermodynamic properties are studied using the Mermin statistics for the dynamic stable phases. The volumetric thermal expansion coefficients of these Fe-C compounds vary between 1.0 × 10−5 K−1 to 5.0 × 10−5 K−1 at 1200 K. θ-Fe3C, h-Fe7C3 and η-Fe2C have the closest thermal expansion coefficient to α-Fe. Considering the thermal electronic contribution, the calculated heat capacity of θ-Fe3C is in good agreement with experimental results. η-Fe2C has the largest CP value as 0.72 J g−1 K−1 and η-Fe6C has the smallest CP value as 0.56 J g−1 K−1 at 1200 K.