The metastable free-energy diagrams of the Ti-Ni, Fe-Ni and Mo-Ni systems were calculated at room temperature using a semiempirical theory based on thermodynamic considerations. Ti-Ni and Mo-Ni form equilibrium-ordered compounds that are destabilized by particle irradiation. Effectively, Ti2Ni, TiNi, MoNi and MoNi3 amorphize after irradiation. In the present work, this experimental behaviour is understood by considering the modification of the free-energy diagrams after particle irradiation. Conversely, in the Fe-Ni system, a metastable fee solid solution evolves under irradiation towards ordered FeNi. In this system, according to our calculation, the free-energy of the amorphous phase is much higher than the free-energy of any other competing phase, so the amorphous phase cannot be produced. Each selected alloy has an intermetallic compound (TiNi3, FeNi3 and MoNi4) which does not amorphize by particle irradiation and whose composition is close to the nickel-rich end of the phase diagram. According to the calculated free-energy diagrams, the reason for this impossibility of amorphization would be the competition of the terminal solid solution with the amorphous phase.