Friction of atomically stepped surfaces

The friction behavior of atomically stepped metal surfaces under contact loading is studied using molecular dynamics simulations. While real rough metal surfaces involve roughness at multiple length scales, the focus of this paper is on understanding friction of the smallest scale of roughness: atomic steps. To this end, periodic stepped Al surfaces with different step geometry are brought into contact and sheared at room temperature. Contact stress that continuously tries to build up during loading, is released with fluctuating stress drops during sliding, according to the typical stick-slip behavior. Stress release occurs not only through local slip, but also by means of step motion. The steps move along the contact, concurrently resulting in normal migration of the contact. The direction of migration depends on the sign of the step, i.e., its orientation with respect to the shearing direction. If the steps are of equal sign, there is a net migration of the entire contact accompanied by significant vacancy generation at room temperature. The stick-slip behavior of the stepped contacts is found to have all the characteristic of a self-organized critical state, with statistics dictated by step density. For the studied step geometries, frictional sliding is found to involve significant atomic rearrangement through which the contact roughness is drastically changed. This leads for certain step configurations to a marked transition from jerky sliding motion to smooth sliding, making the final friction stress approximately similar to that of a flat contact.

Figure 1

Schematic representation of the model. The step height $\delta$ varies and relates to the lattice constant $a$, i.e., the Burgers vector $b=a/\sqrt{2}$.

Figure 2

Schematic representation of the two loading directions for periodic (single) step contacts.

Figure 3

Shear stress ${\sigma }_{xz}$ in the vicinity of a single step (height $\delta =0.405$ nm).

Figure 4

Shear stress $\tau$ as a function of applied displacement $u_{\mathrm{x}}$ for different step spacing and for a flat contact, with the definition of sliding and slip depicted.

Figure 5

Average and rms variation of friction stress ${\tau }_{\mathrm{fr}}$ during sliding as a function of step spacing $w$ for both sliding directions. For clarity the data points have been shifted by $0.8\mathrm{nm}$.

Figure 6

Distribution $f\left(S\right)$ of the stress drops $S=\mathrm{\Delta }{\tau }_{\mathrm{d}}/\overline{\tau }$, where $\mathrm{\Delta }{\tau }_{\mathrm{d}}$ is the size of the stress drop and $\overline{\tau }$ is the average friction stress during sliding. The two limiting cases of Fig. 4 are shown, the stepped contact with spacing $w=15$ nm and a flat contact. The intermediate cases $w=30$ nm and $w=45$ nm are between the two limits.

Figure 7

Contact migration at $u_{\mathrm{x}}=40$ nm for (a) the step-up loading direction and (b) the step-down loading direction. Atoms that originally belong to crystal A (B) are indicated with the color red (blue). The grey atoms indicate the new position of the contact, based on CNA.

Figure 8

Normal migration distance $|u_{\mathrm{n}}|$ per unit applied displacement as a function of step spacing (i.e., box width). For clarity, the data points have been shifted $\pm 0.3$ nm for the positive and negative $x$ direction, respectively. The error bars denote the rms variation in the normal migration.

Figure 9

Ehrlich-Schwoebel barrier [10, 11] showing the asymmetry of the potential landscape near the step.

Figure 10

Average $z$ coordinate of the contact (red) and the number of atoms with HCP structure (blue) as a function of applied displacement.

Figure 11

Contact after 40 nm applied displacement in the positive $x$ direction, clearly showing vacancies generated between the initial and the current position of the contact. Only atoms that do not have a perfect local fcc structure are shown.

Figure 12

Average and rms variation of the friction stress as a function of normalized pair spacing $w_{\mathrm{sp}0}/w$ for several step heights. The line for the flat contact is the same as in Fig. 4.

Figure 13

Example of shear stress $\tau$ (red) and fractional interface roughness $(N_{\mathrm{int}}-N_{\mathrm{int},0})/N_{\mathrm{int},0}$ (blue) as function of applied displacement $u_{\mathrm{x}}$. A comparison of the two graphs shows that the large fluctuations in the friction stress coincide with the roughened contact.

Figure 14

The contact structure showing (a) jagged roughness in the jerky sliding stage at $u_{\mathrm{x}}\approx 8$ nm and (b) a smooth “wave” in the contact during the smooth sliding stage at $u_{\mathrm{x}}\approx 30$ nm. Atoms that do not belong to the interface, i.e., that have fcc structure type, are excluded.

Figure 15

Average sliding displacement and rms variation (between different realizations) at which the transition to smooth sliding occurs as a function of the relative pair width.

Figure 16

Contact with nanoscale asperities for case AB. Atoms that do not belong to the interface, i.e., that have fcc structure type, are excluded.

Figure 17

Shear stress as a function of applied displacement for different step pair widths (for large step height). One curve (light blue) shows the statistical transition to smooth sliding similar to the transition found for small height step pairs.

Figure 18

Static friction stress as a function of the normalized contact area. Error bars give the rms variation between different realizations.

Figure 19

(a) The initial contact (case AB), atoms that originally belong to crystal A(B) are indicated with the color blue(red). The grey atoms indicate the position of the contact, based on CNA. (b) Developing wear at $u_{\mathrm{x}}\approx 5$ nm.

Figure 20

Sliding displacement to closure $u_{\mathrm{c}}$ as a function of normalized contact area. This is the difference in applied displacement between the onset of sliding and full closure of the gap. The error bars indicate the rms variation between different realizations.