Kanzaki lattice static method is used to calculate the atomic displacements due to substitutional impurities in 3d (Cr) and 4d (Nb, Mo) metals. Wills and Harrison interatomic potential is used to calculate dynamical matrix and the impurity-induced forces up to second nearest neighbors. The calculated atomic displacements for 3d, 4d and 5d impurities in Cr (V, Mn, Fe, Ni, Nb, Mo, Ta and W), Nb (V, Cr, Mn, Fe, Zr, Mo, Ta and W) and Mo (V, Cr, Mn, Fe, Zr, Nb, Ta and W) are tabulated up to 10 NN’s. The strain field due to 3d impurities is least in Cr metal while it is larger in Nb and Mo metals. For 4d and 5d impurities the strain is larger in Cr metal than in Nb and Mo hosts. Similar trend is found for relaxation energies also.

The strain field due to body centered substitutional transition metal impurities in Ni and Pd metals are investigated. The calculations are carried out in the discrete lattice model of the metal using Kanzaki lattice static method. The effective ion-ion interaction potential due to Wills and Harrison is used to evaluate dynamical matrix and the impurity-induced forces. The results for atomic displacements due to 3d, 4d and 5d impurities (Fe, Co, Cu, Nb, Mo, Pd, Pt and Au) in Ni and (Fe, Co, Cu, Ni, Nb, Mo, Pt and Au) impurities in Pd are given up to 25 NN’s of impurity and these are compared with the available experimental data. The maximum displacements of 4.6% and 3.8% of 1NN distance are found for NiNb and PdNb alloys respectively, while the minimum displacements of 0.63% and 0.23% of 1NN distance are found for NiFe and PdFe alloys respectively. Except for Cu, the atomic displacements are found to be proportional to the core radii and d state radius. The relaxation energies for 3d impurities are found less than those for 4d and 5d impurities in Ni and Pd metals. Therefore, 3d impurities may easily be solvable in these metals.

The embedded-atom method have been applied to study the strain field produced by the self-interstitial impurity at the octahedral site in Ni. The calculation have been carried out consistently on the basis of discrete lattice theory, using Kanzaki method. The atomic force constants are evaluated using Wills and Harrison interatomic potential. The dynamical matrix and external force are evaluated considering the interaction up to first nearest neighbors. The atomic displacements are tabulated up to 20NN’s. These displacements are of oscillatory nature and of decreasing magnitude with NN’s distance. The physical properties such as self-interstitial formation energy and volume change calculated using atomic displacements are in accordance with the earlier studies.

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.

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of $7.36$% and $4.3$% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion $\Delta V /V = 0.177$ for Cu and 0.145 for Pd.