Atomic Structure Affects the Directional Dependence of Friction

Abstract

Friction between two objects can be understood by the making, stretching, and breaking of thousands of atomic-scale asperities. We have probed single atoms in a nonisotropic surface [the H-terminated Si(100) surface] with a lateral force microscope operating in noncontact mode. We show that these forces are measurably different, depending upon the direction. Experimentally, these differences are observable in both the line profiles and the maximum stiffnesses. Density functional theory calculations show a concerted motion of the whole Si dimer during the tip-sample interaction. These results demonstrate that on an asperity-by-asperity basis, the surface atomic structure plays a strong role in the directional dependence of friction.

Subatomic-scale force vector mapping above a Ge(001) dimer using bimodal atomic force microscopy

“…As can be observed in the force component maps in Fig. 3, the F x and F y values approach zero on the surface atoms, which are in good agreement with the result of previous studies 15,26 . indicative of the force component direction reversal on both sides of the surface atom.…”

“…Although the parallel component of force has been calculated from the normal component using a potential mapping extraction technique, this method is only indirect [20][21][22][23][24] . To obtain the distribution of the parallel components in three-dimensions (3D) with a higher accuracy, the force sensor should be oscillated also in the direction parallel to the surface 25,26 . Recently, a multi-frequency AFM method was developed 4 with the quest to investigate the physical properties of materials in deeper detail 5,6 .…”

“…Therefore, both X and Y surface-parallel components of the tip-surface interaction can be obtained from both domains without the need to rotate the tip or the sample 26 . Thus, the normal (Z) and both parallel (X and Y ) components of the force interaction above the Ge(001)-c(4 × 2) surface can be obtained with this bimodal AFM method by measuring the flexural frequency shift f F simultaneously with the two torsional frequency shifts f Tx and f Ty .…”

“…In the F x and F y maps, however, the values approach zero (white colour) for the surface atoms. In addition, both F x and F y feature asymmetrically positive and negative extremal values (red and blue peaks) around the surface atoms, meaning the parallel force components reverse the direction on both sides of the surface atoms 26 . Interestingly, at the centre of a dimer in the F x mappings, the force field is weak (∼50 pN) and atoms, as intuitively expected in the strong attractive force field.…”

On the mathematical basis of solid friction

“…Other models attribute friction to a drag effect due to energy loss through phonon generation [3,9,41], or electronic drag not due to van der Waals forces but to currents in the electron cloud [39]. In seeking greater insight, attention turns to microscopic effects such as atom-scale deformations [49], macro-microscale stress interactions during relaxation [42], or third body effects of adsorbed molecules acting as pins [26], and building from these to reproduce macro-scale behaviour is where discontinuous models may help. The model (5) provides a mathematical framework by which such small-scale structure can be captured in a discontinuity, and using a toy model based on its key properties, we showed how this leads naturally to friction characteristics such as static friction and hysteresis.…”