A first-principles investigation on the effects of magnetism on the Bain transformation of $α$-phase FeNi systems

The effects of magnetism on the Bain transformation of $\alpha$-phase FeNi systems are investigated by using the full potential linearized augmented plane wave (FLAPW) method based on the generalized gradient approximation (GGA). We found that Ni impurity in bcc Fe increases the lattice constant in ferromagnetic (FM) states, but not in the nonmagnetic (NM) states. The shear modulus $G$ and Young's modulus $E$ of bcc Fe are also increased by raising the concentration of nickel. All the compositions considered show high shear anisotropy and the ratio of the bulk to shear modulus is greater than 1.75 implying ductility. The mean sound velocities in the $[100]$ directions are greater than in the $[110]$ directions. The Bain transformation, which is a component of martensitic transformation, has also been studied to reveal that Ni$_{x}$Fe$_{1-x}$ alloys are elastically unstable in the NM states, but not so in the FM states. The electronic structures explain these results in terms of the density of states at the Fermi level. It is evident that magnetism cannot be neglected when dealing with the Bain transformation in iron and its alloys.