Relations between vacancy migration and formation energies, debye temperature and melting point

The interaction between a vacancy and the lattice vibrations is represented as a collision between a sine‐Gordon soliton and a breather. The migration to formation energy ratio of a vacancy is found to be ϵ = 2 tgh (π/8≈), where ϵ is a relaxation radius. From general considerations 0.6 < ϵ < 1.2, whence ϵ ≈ 0.91 ± 0.25 modified by crystal structure. The relationship for ϵ implies that both the energies of migration and formation are simply related to the Debye temperature. Through Lindemann's melting formula they are then proportional to the melting point.