Fig. 3: Illustration of different diffusion processes.

a Counter diffusion-induced pairing, involving the diffusion of a \({{{{{\rm{NH}}}}}_{4}}^{+}\) species in the neighboring cage. b Counter diffusion where a Cu-complex and \({{{{{\rm{NH}}}}}_{4}}^{+}\) species switch location. c Counter diffusion, where the movement of a Cu-complex enables the further diffusion of a \({{{{{\rm{NH}}}}}_{4}}^{+}\) ion.