The atomic size effect in binary alloy systems during solid-state amorphization by particle irradiation is studied using molecular dynamics simulations. The critical dosage of irradiation for amorphization is decreased by increasing the atomic size mismatch or the solute concentration. The analysis of the atomic level strain shows that that the atomic-level strain distribution depends on the atomic species in the crystalline lattice, while it is almost the same in all glass systems. Amorphization occurs when the atomic-level strain reaches the universal critical value, which is independent of packing fraction, density, concentration and atomic size ratio. The nature of the universal strain is discussed in relation to the glass transition phenomenon.