The solid-phase epitaxial regrowth of 175 keV Rb ϩ -implanted ␣-quartz during thermal annealing in air or 18 O 2 was studied as a function of the temperature ͑р1170 K͒ and the implanted Rb fluence ͓(0.1-6)ϫ10 16 ions/cm 2 ͔. Rutherford backscattering channeling spectrometry was used to characterize the damage profiles. The role of the oxygen exchange between the annealing gas and the SiO 2 matrix was highlighted by measuring the 16 O and 18 O profiles by means of time-of-flight elastic recoil detection analysis. Complete epitaxial recrystallization of the amorphized layers was observed after a 1 h annealing in air ͑at 1170 K͒ or in 18 O 2 ͑at 1130 K͒. The recrystallization rate in air follows a two-step Arrhenius process, with activation energies of 2.7Ϯ0.4 and 0.6Ϯ0.2 eV above and below an annealing temperature of 1070 K. The three processes, namely, planar recrystallization of the amorphized a-SiO 2 layer, alkali ion out-diffusion, and 16 O⇔ 18 O exchange, are highly correlated. This correlation is discussed with the help of the concept of the SiO 2 network topology. Finally, the surface topography was measured using an atomic force microscope, which gave evidence of swelling of the SiO 2 matrix during implantation and recompaction during epitaxy.