The two-dimensional growth of Au on Ru(0001) in the submonolayer range has been investigated with scanning tunneling microscopy. Upon deposition at room temperature, highly dendritic islands of one layer thickness grow on large Ru terraces. These irregular island shapes are removed upon annealing to 650 K. The dendritic islands exhibit a fractal character, and a dimensional analysis yields a fractal dimension of 1.72 ±0.07. The results are in quantitative agreement with a two-dimensional diffusion-limited-aggregation growth mechanism.

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the contact width, and L is the nanotube length. These quantities are dif®cult to measure independently and calculations are modeldependent. As a guide, we apply a JKR model for the contact of cylinders 25 and ®nd a contact width of 3 nm for a tube radius of 13.5 nm. Our measurements of 0.006 N m -1 for the friction force per unit length is then consistent with a shear stress of 2 3 10 6 Pa. This can be compared with a value of 5 3 10 6 Pa, as inferred from AFM tip/graphite measurements 16 . To compare rolling and sliding in a single tube, we can calculate the force (4 nN for L 590 nm) and that would be needed to slide tube B, which in fact rolls. Finally, we note that the area under the lateral force trace is a direct measure of energy loss in rolling. For tube B, we measure an energy loss of 8 6 3 3 10 2 16 J per revolution. The sliding energy loss expected for this distance (85 nm) can be calculated using the frictional force of 4 nN, yielding 3 3 10 2 16 J.When we compare our lateral force measurements for sliding and rolling cases, we ®nd that the stick peaks in rolling are higher than the lateral force needed to sustain sliding, and that the energy cost for rolling is larger than that of the sliding cases. Why should the nanotubes roll? We speculate that, owing to the size and surface features of the rolling nanotubes, a stick peak for sliding in side-on pushing might exist that is larger than the threshold for rolling. Atomic-scale substrate interactions may also play a roll as we have observed this characteristic rolling only on graphite. Rolling behaviour has been accompanied by a preferential, threefold, inplane orientation that indicates intimate nanotube/graphite contact, and perhaps lattice registry. Rolling may occur only when both the nanotube and the underlying graphite have long-range order. In these cases that there may be a barrier for sliding which is larger than that for rolling and may preclude the direct measurement of sliding friction 7 . M

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