A systematic mu SR study on nano-Cu has demonstrated that the diffusio
n of mu(+) in nanocrystalline metals is influenced by both features of
the nanostructure, i.e., by the very small grain size and by the comp
aratively large fraction of grain boundaries. The former feature yield
s a size effect of the phonon-assisted muon tunneling, but only at par
ticle diameters below 20 nm. The latter feature, in samples with cryst
allite sizes above 20 nm diameter, i.e., with bulk diffusional behavio
ur, establishes a connection between mu(+) diffusion coefficient and p
article size: if one of these quantities is known, the other could be
evaluated.