Radiation damage effects on the structures of GaAs and 4H-SiC single crystals are investigated after irradiation with 300 keV Ar ions at room temperature. It is found that despite having contrasting physical and chemical properties, 0.3 displacement per atom (dpa) is the threshold of fractional disorder above which there is a rapid damage build-up behavior exhibited by both GaAs and 4H-SiC. 1 dpa means that all atoms are displaced at least once from their respective lattice sites. This study reveals that disordering in irradiated binary semiconductor materials is a discontinuous two-step process wherein various stages of irradiation are marked by different damage growth mechanisms.