In this paper we model (111) self-interstitial defects, or crowdions, using an extended version of the analytical Frenkel-Kontorova model. We use a more general potential than the traditional sinusoidal one, and find that it can better describe the lattice potentials experienced by crowdions in the body-centred-cubic transition metals, as calculated in density functional theory. We obtain analytical formulae for the crowdion displacement field and elastic strain energy, as functions of three parameters appearing in the Lagrangian, for the generalized lattice potential. Furthermore, we investigate how the more complex structure of the generalized potential affects the effective potential experienced by the defect centre-of-mass, using a collective coordinate approach.
