Alloying effects on the elastic parameters of ferromagnetic and paramagnetic Fe from first-principles theory

The elastic properties of paramagnetic face-centered-cubic (fcc) Fe _1-xM_x (M Al, Si, V, Cr, Mn, Co, Ni, and Rh; 0 ≤x ≤0.1) random alloys are investigated using the exact muffin-tin orbitals density functional method in combination with the coherent-potential approximation. We find that the theoretical lattice parameter of fcc Fe is strongly enlarged by Al, V, and Rh and slightly reduced by Si, Cr, and Co, while it remains nearly constant with Mn and Ni. Both positive and negative alloying effects appear for the elastic constants C_ij(x) of fcc Fe. These findings are in contrast to those obtained for ferromagnetic body-centered-cubic (bcc) Fe alloys, where all alloying elements considered here are predicted to enlarge the lattice parameter and decrease the C₁₁(x) and C ₁₂(x) elastic constants of bcc Fe. With some exceptions, alloying has much larger effects on ferromagnetic bcc alloys than on paramagnetic fcc ones. Based on the theoretical elastic parameters of the paramagnetic fcc and ferromagnetic bcc phases, simple parameterizations in terms of chemical composition of the equilibrium lattice constants, single-crystal elastic constants, and polycrystalline elastic moduli of Fe-based alloys are presented.