Atomic displacements in bcc dilute alloys

We present here a systematic investigation of the atomic displacements in bcc transition metal (TM) dilute alloys. We have calculated the atomic displacements in bcc (V, Cr, Fe, Nb, Mo, Ta and W) transition metals (TMs) due to 3d, 4d and 5d TMs at the substitutional site using the Kanzaki lattice static method. Wills and Harrison interatomic potential is used to calculate the atomic force constants, the dynamical matrix and the impurity-induced forces. We have thoroughly investigated the atomic displacements using impurities from 3d, 4d and 5d series in the same host metal and the same impurity in different hosts. We have observed a systematic pattern in the atomic displacements for Cr-, Fe-, Nb-, Mo-, Ta-and W-based dilute alloys. The atomic displacements are found to increase with increase in the number of d electrons for all alloys considered except for V dilute alloys. The 3d impurities are found to be more easily dissolved in the 3d host metals than 4d or 5d TMs whereas 4d and 5d impurities show more solubility in 4d and 5d TMs. In general, the relaxation energy calculation suggests that impurities may be easily solvable in 5d TM hosts when compared to 3d or 4d TMs.