Activation energy of hydrogen and muon in transition metals

The quantum theory of diffusion due to Flynn and Stoneham is used to calculate the activation energies of H, D, ${\mu }^{+}$, O, and N in bcc transition metals Nb, V, Ta, Mo, $\alpha$-W, and $\alpha$-Cr, and in fcc metals Pd, Ni, Cu, Ag, Au, and Al. It is found that the symmetric-mode contribution to the activation energy dominates in fcc metals while the reverse is the situation for bcc metals. The strain field produced by ${\mu }^{+}$ is found to be almost isotropic. The larger anisotropy and the volume of solution leads to large activation energy for heavy impurities. The calculated activation energies are found in good agreement with the experimental values. The variation of activation energy with the anisotropy parameter is also studied.