To study the evolution of silicate dust in different astrophysical environments we simulate, in the laboratory, interstellar and circumstellar ion irradiation and thermal annealing processes. An experimental protocol that follows different steps in the dust life-cycle was developed. Using the silicate 10 $\mu$m band as an indicator, the evolution of the structural properties of an ion-irradiated olivine-type silicate sample, as a function of temperature, is investigated and an activation energy for crystallization is determined. The obtained value of ${E_{\rm a}}/k$ = 41 700 $\pm$ 2400 K is in good agreement with previous determinations of the activation energies of crystallization reported for non-ion-irradiated, amorphous silicates. This implies that the crystallization process is independent of the history of the dust. In particular, the defect concentration due to irradiation appears not to play a major role in stimulating, or hindering, crystallization at a given temperature. This activation energy is an important thermodynamical parameter that must be used in theoretical models which aim to explain the dust evolution from its place of birth in late type stars to its incorporation into young stellar environments, proto-stellar discs and proto-planetary systems after long passage through the interstellar medium.