The out diffusion rate of a volatile diffusant is determined by solving the coupled grain boundary and bulk diffusion problem for a cylindrical rod with an array of equally spaced grain boundaries lying normal to the rod axis. This grain structure may be taken as a model for the common bamboo structure of well annealed pure wires. For long diffusion periods (t > 0.1a2/D), the average concentration of the retained diffusant decay exponentially in an excellent approximation. From the decay parameter one can evaluate an apparent diffusion coefficient, Da, which gives useful bounds at the typical grain aspect ratio of the bamboo structure for the bulk diffusion coefficient: 0.93Da ≦ D ≦ Da.