DFT investigation of carbon-expanded α phase with different alloying element

The structures of carbon-expanded α phase (α_C) phase were modeled with nominal molecular formula of Fe_13-xCr₃Ni_xC_y (x = 0, 1, y = 0,1,2,3,4) based on body-centered cubic α-Fe and calculated by first-principles calculation using density functional theory (DFT). The results show that Fe₁₃Cr₃C_y (y = 0,1,2,3,4) structures with less than 11.11 at% carbon (y = 2) can be easily formed and exist stable. The Young's moduli of stable Fe₁₃Cr₃, Fe₁₃Cr₃C, and Fe₁₃Cr₃C₂ are 227.08 GPa, 209.71 GPa and 189.19 GPa, respectively. The theoretical hardness of stable Fe₁₃Cr₃C_y (y = 1, 2) are obviously improved and can be up to 8.26 GPa. As for Fe₁₂Cr₃NiC_y (y = 0,1,2), Young’ s moduli of Fe₁₂Cr₃Ni, Fe₁₂Cr₃NiC, and Fe₁₂Cr₃NiC₂ are 155.82 GPa, 258.24 GPa and 207.44 GPa, respectively. The hardness of Fe₁₂Cr₃NiC_y (y = 1,2) can be as high as 17.88 GPa. Ni element can stabilize the structures of Fe₁₃Cr₃C_y (y = 1,2) and improve their theoretical hardnesses. The toughness of Fe₁₃Cr₃C_y (y = 1,2) structures are shown in ductility based on Pugh's ratio criterion, while the Fe₁₂Cr₃NiC_y (y = 1,2) structures are shown in brittleness. Electronic structure calculation shown that there are mixture bonding of metal bonding, covalent bonding, and ionic bonding in Fe_13-xCr₃Ni_xC_y (x = 0,1, y = 1,2) structures, which should account for the high hardness of the structure for α_C phase.