(Color online) (a) Schematic of an AFM experiment, and a 100 × 100 nm2 topographic AFM image of the Au(111) surface showing large terraces separated by monatomic steps. Inset above: TEM image of the Pt-coated probe. (b) Snapshot of an atomistic tip/substrate model. (c) Lateral force image on Au(111). Inset: Fourier low-pass filtered image. (d) Top view of the model Au(111) substrate. White arrows in (c) and (d) denote the fast scanning direction. Scale bars are 1 nm. (e), (f) Variation of the experimental (e) and simulated (f) lateral force along the horizontal lines shown in (c) and (d), respectively. The simulation and experimental results are obtained under optimally matched conditions: materials Pt/Au(111), incommensurate orientation, effective stiffness 6 N/s, contact area 7.3 nm2, normal load 0.6 nN, and temperature 293 K. Only sliding speeds differ significantly: 149 nm/s in experiment and 1 m/s in simulation (Ref. 2 ). Reprinted with permission from Li et al., Phys. Rev. Lett. 106, 026101 (2011). © 2011 by American Physical Society.
AFM measurement of mean friction as a function of rotation angle between graphite surfaces. The highest friction occurs in aligned contact (0° and 60°) (Ref. 48 ). Reprinted with permission from Dienwiebel et al., Phys. Rev. Lett. 92, 126101 (2004). © 2004 by American Physical Society.
(Color online) Friction from a Pt tip sliding on the (a) Au(100) and (b) Au(111) surfaces from MD simulation. In (a) the Pt tip is worn off almost immediately due to junction formation and no stable friction pattern observed while in (b) a stable bimetallic interface forms and regular stick-slip friction arises. Note that the scales of the y-axes differ in the two plots. Simulation parameters: EAM potential, load 0 nN, temperature 10 K, speed 1 m/s, and contact area 1.2 nm2 (aligned).
(Color online) MD simulation of mean friction as a function of rotation angle between Pt(111) tip and Au(111) substrate. Due to the similar lattice constants ( and ) and FCC structure of both materials, high friction arises at aligned contact and low friction at misaligned contact. Inset: representative friction traces at aligned and misaligned contact, where S is the position of the support. Simulation parameters: EAM potential, load 0 nN, temperature 10 K, speed 1 m/s, and contact area 7.3 nm2.
(Color online) Upper images: Atomic distribution in the buried interface (top) where the light-colored dots are substrate atoms and the dark-color dots are tip atoms. The relative rotation of the surfaces forms superstructures called Moiré patterns. Lower images: Shear stress (color scale in units of bar × Å3) distribution of the atoms in the lowermost layer of the tip. Atom and stress distributions shown at relative rotation angles of (a) 0°, (b) 15°, and (c) 30°. Simulation parameters: EAM potential, load 0 nN, temperature 10 K, speed 1 m/s, and contact area 7.3 nm2 (Ref. 57 ). Reprinted with permission from Dong et al., Modeling Simul. Mater. Sci. Eng. 19, 065003. © 2011 IOP Publishing.
(Color online) Schematic illustration of the elastic contact between spherical bodies used to derive an expression for contact stiffness in the framework of contact mechanics. Variables are defined in the text.
(Color online) Illustration of an MD simulation with compliance introduced through three harmonic springs (kx , ky , and kz ) connected to the top layers of the tip apex. Along the x-direction, the support moves at contact speed to drag the tip apex to slide against the substrate.
(Color online) Experimental measurements the area-dependence of friction of sliding nanoparticles. Friction can increase with area as exhibited by the non-vanishing friction cases in (a), (b) and (c); friction can also be independent of contact area as exhibied by the vanishing friction cases in (a) and (c). Data in (a) and (b) from UHV measurements and data in (c) taken under ambient conditions. Lines are linear fits to the data (Ref. 115 ). Reprinted with permission from Dietzel et al., Phys. Rev. Lett. 101, 125505 (2008). © 2008 by the American Physical Society.
(Color online) Schematic illustration of the continuum and atomic perspectives of the interface between an AFM tip and substrate.
(Color online) Friction as a function of contact area at different orientation angles between Pt(111)/Au(111) measured by MD simulation; 0° corresponds to perfectly aligned contact. Simulation parameters: EAM potential, load 0.6 nN, temperature 293 K, and speed 1 m/s.
(Color online) MD simulation of mean friction as a function of normal load for a Pt/Au(111) system. Inset are illustrations of atomic configurations during sliding at N = 10 nN (left) and N = 17.5 nN (right). Simulation parameters: EAM potential, temperature 10 K, speed 1 m/s, and contact area 1.2 nm2 (30° misalignment angle).
(Color online) (a) AFM measurement of the slip-inducing forces (maximum friction) as a function of sliding velocity at different temperatures. (b) All experimental data at different temperatures and velocities fall onto the same curve predicted by the thermal activation theory given in Eq. (10) . The inset shows a plot of the attempt frequency as a function of temperature (Ref. 134 ). Reprinted with permission from Jansen et al., Phys. Rev. Lett. 104, 256101 (2010). © 2010 by American Physical Society.
(Color online) Illustrations of (a) an AFM cantilever pulling the tip to slide over a substrate and (b) the corresponding PT model in which the AFM system is reduced to a mass-spring system. In the PT model, the model tip is confined within the potential well and hops over the energy barrier with the assistance of thermal activation.
(Color online) (a) Temperature of the contact interface varying with sliding distance from an MD simulation with Pt(tip)/Au(substrate) system. The initial temperature of the simulation is 300 K. Once sliding begins, the average temperature increases with distance if there is no thermostat to remove thermal energy from the system (solid line) but fluctuates about the prescribed temperature if the Nosé–Hoover thermostat is applied (dashed line). (b) Mean friction as a function of temperature from an MD simulation of atomic friction between a Pt(tip) and Au(substrate). Inset is a schematic illustrating a thermostat being applied to atoms away from the contact in a simulation of atomic friction. Simulation parameters: EAM potential, load 0 nN, speed 2 m/s, and contact area 1.3 nm2 (aligned).
(Color online) Schematic of a reduced-order system. (a) In hyperdynamics the potential is modified by adding a positive bias to increase the transition rate. (b) Schematic of parallel replica dynamics. The original system is replicated to help find the transition path.
(Color online) (a) Relative friction variation (variation divided by mean friction) predicted using parallel replica dynamics when run on 128 replicas vs 64 replicas (circles and insets) and the expected relative variation due to MD simulation noise (solid line). (b) Mean friction as a function of sliding velocity measured between Cu(111)/Cu(111) interface: squares represent ParRep simulation and the solid line is a logarithmic fit to that data. Simulation parameters: EAM potential, load 0 nN, temperature 300 K, and contact area 1.3 nm2 (aligned) (Ref. 167 ). Reprinted with permission from Martini et al., Tribol. Lett. 36, 63 (2009), Fig. 5 . © 2009 by Springer + Business Media.
(Color online) Mean friction measured by AFM (squares) for speeds between 1 and 1000 nm/s, and predicted via ParRep MD simulation (triangles) for speeds between 0.005 m/s and 2 m/s between Pt/Au(111). The dashed curve and dotted curve are fitted using the thermal activation model [(Eq. (10) ] for experimental and simulation data, respectively. All other parameters from materials, orientation, effective stiffness, contact area, normal load and temperature between AFM and MD are optimally matched based on the methods introduced in previous sections (Ref. 170 ). Reprinted with permission from Dong et al., Tribol. Lub. Tech. Feb. 17 (2012). © 2012 by Society of Tribologists and Lubrication Engineers.
Article metrics loading...
Full text loading...