Structural lubricity under ambient conditions

Despite its fundamental importance, physical mechanisms that govern friction are poorly understood. While a state of ultra-low friction, termed structural lubricity, is expected for any clean, atomically flat interface consisting of two different materials with incommensurate structures, some associated predictions could only be quantitatively confirmed under ultra-high vacuum (UHV) conditions so far. Here, we report structurally lubric sliding under ambient conditions at mesoscopic (∼4,000–130,000 nm2) interfaces formed by gold islands on graphite. Ab initio calculations reveal that the gold–graphite interface is expected to remain largely free from contaminant molecules, leading to structurally lubric sliding. The experiments reported here demonstrate the potential for practical lubrication schemes for micro- and nano-electromechanical systems, which would mainly rely on an atomic-scale structural mismatch between the slider and substrate components, via the utilization of material systems featuring clean, atomically flat interfaces under ambient conditions.

experiences a friction force of ~100 nN. Adapted from Ref. [1]. Copyright 2013 by the American Physical Society. 4

Supplementary Figure 4 | High-resolution, cross-sectional TEM image of an individual
antimony island. The high-resolution image reveals that the crystalline bulk of the antimony island is surrounded by an amorphous antimony oxide layer, leading to the breakdown of structural lubricity during sliding. Adapted from Ref. [1]. Copyright 2013 by the American Physical Society. 5

Supplementary Note 1: Structural lubricity vs. superlubricity
In nanotribology literature, the expressions structural lubricity and superlubricity are often used interchangeably, which typically leads to certain confusion regarding the associated physical mechanisms as well as misleading comparisons to the phenomenon of superconductivity 2 . While the term superlubricity may refer to any state of ultra-low friction sliding regardless of the underlying physical principles, structural lubricity deals with a state of ultra-low friction sliding arising specifically due to structural incommensurability associated with atomically flat surfaces in contact 3 . On the other hand, ultra-low friction (i.e., superlubric) sliding may be obtained by alternative methods including (i) the reduction of the interfacial load below a threshold value during AFM-based friction experiments to enter a quasi-static sliding regime 4 , (ii) the deliberate mechanical excitation of the tip-sample contact during AFM experiments 5,6 , and (iii) increased temperatures leading to the onset of the thermolubric regime 7 , characterized by the disappearance of stick-slip behavior and substantial reduction in friction. 6

Supplementary Note 2: Graphite and humidity
It has been known for multiple decades that the macroscopically observed lubricative properties of graphite improve significantly with increasing humidity 8 Fig. 1). While such a low diffusion energy barrier for the material system in question is unlikely, the corresponding results nevertheless confirm that the experimental data are still in the regime defined for structurally lubric sliding. 8

Supplementary Note 4: Breakdown of structural lubricity due to oxidation
The basic theory behind structural lubricity predicts that sliding at any clean interface consisting Antimony was chosen as a test material due to the availability of experimental data regarding its frictional behavior 1,11 . To test a limiting case for antimony, the slab was rotated only slightly away from the commensurate configuration with the underlying graphite substrate such that a "nearly commensurate" alignment is achieved. The gold and antimony slabs were slid along the dashed arrows displayed in Supplementary Fig. 2 (at zero temperature) and the resulting differences in energy were calculated as a function of sliding distance d (Supplementary Figure 2c,d). Subsequently, the friction forces that would be experienced by the sliding slabs were approximated by considering the steepest slope of the energy landscape in the direction of sliding that needs to be surmounted. Results reveal that the gold slab exposing 28 atoms to the graphite surface is predicted to be subjected to a friction force of ~11 pN. With the experimentally obtained scaling factor of 0.16, this result translates to a friction force of ~41 pN for a gold slider with 10 5 sliding atoms, within the range of our experimental findings, thus confirming the validity of the computational approach employed here. On the other hand, the antimony slab exposing 26 atoms to the graphite surface is expected to be subject to a friction force of ~23 pN. The same order of magnitude friction forces calculated for gold and antimony