Fig. 1. Diffusion of water monomers on graphene.

a Illustration of the helium spin-echo method: Two wavepackets scatter from the surface with a time difference t_SE, allowing the motion of molecules on the surface to be interrogated through a loss in correlation, measured via polarisation of the beam. The diffusing water molecules are illustrated as white/red spheres for H/O and the atom colours for graphene/Ni are the same as in panel c. The inset shows a typical measurement for the diffusion of water on graphene (T_S = 125 K, ΔK = 0.2 Å⁻¹). The reduction in surface correlation with increasing spin-echo time follows a single-exponential decay (solid line), characterised by the dephasing rate, α. b The momentum transfer dependence of the dephasing rate, α(ΔK), at T_S = 125 K from which the mechanism for diffusion follows. Blue data points show single particle, or incoherent α(ΔK), deduced from the coherent scattering data (grey points, see text). The error bars correspond to the confidence bounds (1σ) upon determination of α from the measurements (see text). An analytical model (green curve) shows the expected behaviour for jumps between the centres of the graphene hexagons. c Structural model for the graphene lattice (grey spheres) on the Ni(111) substrate (green) with the principle symmetry directions ($\overline{\mathrm{\Gamma }\text{M}}$/$\overline{\mathrm{\Gamma }\text{K}}$) of the Brillouin zone.