In phase-field modelling, the temperature effect should be explicitly included in energy potential functions like f (T ). However, force field potentials, which we employed in this study, does not include temperature explicitly because the temperature is a result from the velocity of atoms in MD. Therefore, our phase-field modelling does not include the effect of temperature at now. The same discussion is applicable to the effects of pressure. Moreover, phenomena related to momentum cannot be treated as discussed the above. Thus, we must further modify energy potentials to include such effects.