Peierls potential for crowdions in the bcc transition metals.

We present the first derivation of the analytic expression for the Peierls-Nabarro potential for crowdion migration using the double sine-Gordon model. The analysis is guided by the group-specific trend in the shapes of the periodic lattice potentials calculated for the body-centered-cubic transition metals in groups 5B and 6B of the periodic table. We combine density-functional calculations of the crowdion's profile and environment with an extended version of the analytical Frenkel-Kontorova model, and determine the effective potential experienced by the defect's center of mass. This reveals important underlying differences between the metals in these groups, which are inaccessible to either the numerical or analytical approaches alone, and accounts for the previously unexplained significantly higher crowdion migration temperatures observed in the metals of group 6B relative to those of group 5B.