The particle flux through a micron-sized orifice into vacuum from a source chamber filled with solid 4He exhibits a striking sequence of periodic bursts. The period increases (decreases) with pressure (temperature), vanishing at the melting point for temperatures above the upper lambda point at 1.76 K. The oscillations are attributed to a periodic collapse of the solid induced by the accumulation of excess vacancies injected at the orifice and the period provides information on vacancy diffusivity. Dramatic deviations from this behavior below 1.76 K suggest important modifications in the flow properties of solid 4He induced by the excess vacancies.