Structural properties of ion-beam-induced epitaxial crystallization (IBIEC) for amorphous layers of GaAs on GaAs(100), BP on BP(100) and Si1-xGex and Si1-x-yGexCy on Si(100) have been investigated. Crystallization was induced by ion bombardment with 400 keV Ne, Ar or Kr at 150 degrees C for GaAs and at 350 degrees C for Bf. Epitaxial crystallization up to the surface was observed both in GaAs and BP at temperatures much below those required for the solid phase epitaxial growth (SPEC). The growth rate per nuclear energy deposition density has shown a larger dependence on ion dose rate in cases of heavier ion bombardments both for GaAs and BP. Crystallization of a-GaAs with ions whose projected ranges are within the amorphous layer thickness was also observed at 150 degrees C. Epitaxial crystallization of Si1-xGex and Si1-x-yGexCy layers (x = 0.13 and y = 0.014 at peak concentration) on Si(100) formed by high-dose implantation of 80 keV Ge and 17 keV C ions has been observed in the IBIEC process with 400 keV Ar ion bombardments at 300-400 degrees C. Crystalline growth by IBIEC has shown a larger growth rate in Si1-x-yGexCy/Si than in Si1-xGex/Si with the same Ge concentration for all bombardments under investigation. X-ray rocking curve measurements have shown a strain-compensated growth in Si1-x-yGexCy/Si, whereas Si1-xGex/Si samples have shown a growth with strain accommodation.