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The Mössbauer spectroscopy of iron carbides (α-Fe, γ'-FeC, η-Fe₂C, ζ-Fe₂C, χ-Fe₅C₂, h-Fe₇C₃, θ-Fe₃C, o-Fe₇C₃, γ'-Fe₄C, γ''-Fe₄C, and α'-Fe₁₆C₂) is predicted utilizing the all electron full-potential linearized augmented plane wave (FLAPW) approach across various functionals from LDA to GGA (PBE, PBEsol, and GGA + U) to meta-GGA to hybrid functionals. To validate the predicted MES from different functionals, the single-phase χ-Fe₅C₂ and θ-Fe₃C are synthesized in experiment and their experimental MES under different temperature (from 13 K to 298 K) are determined. The result indicates that the GGA functional (especially, the PBEsol) shows remarkable success on the prediction of Mössbauer spectroscopy of α-Fe, χ-Fe₅C₂ and θ-Fe₃C with delocalized d electrons. From the reliable simulations, we propose a linear relationship between B_hf and μ_B with a slope of 12.81 T/μ_B for iron carbide …