I think you mean the surface layers (liquid phase) due to the substrate temperature and ion energy bombardment effects. one should take into account re- crystallization in the case of alkali halides or amorphization and recrystallization in semiconductors, so if you can able to find the energy acquired from thermal and ion energy in comparison with binding energy on can estimate the time required for phase change
Yes, I am interesting in ion - solid interaction and a possible phase transition during the process. The energy released in a cascade initiated by a primary ion is equal to the ion energy. It is know value (few keV, depends on ion source used used). The time of life of the cascade is limited by approximately 1 ps. The binding energy is known value as well: we can use the sublimation energy for surface atoms (2-5eV), or the displacement energy for volume atom (15-35eV). But I don't see how these parameters can me help calculate the phase transition time.