Tribological properties of quasicrystals: Effect of aperiodic versus periodic surface order

We investigated the nanoscale tribological properties of a decagonal quasicrystal using a combination of atomic force microscopy and scanning tunneling microscopy in ultrahigh vacuum. This combination permitted a variety of in situ measurements, including atomic-scale structure, friction and adhesion force, tip-sample current, and topography. We found that thiol-passivated tips can be used for reproducible studies of the tip-quasicrystal contact while nonpassivated probes adhere irreversibly to the clean quasicrystalline surface causing permanent modifications. The most remarkable results were obtained on the twofold surface of the $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ decagonal quasicrystal where atoms are arranged periodically along the tenfold axis and aperiodically in the perpendicular direction. Strong friction anisotropy was observed on this surface, with high friction along the periodic direction and low friction in the aperiodic direction.

Figure 1

Current vs voltage curves between a $\mathrm{TiN}$ tip and atomically clean $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ twofold surface at an applied load of $50\mathrm{nN}$. They illustrate the metallic vs semiconducting nature of the interface for an unpassivated and an alkylthiol-passivated tip.

Figure 2

Atomically resolved STM image $(50\times 75\mathrm{nm})$ of the $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ twofold surface. Tunneling bias and current are $+1.5\mathrm{V}$ and $0.2\mathrm{nA}$. Atomic rows separated by long and short distances $(L,S)$ are marked by lines.

Figure 3

(a) Force-distance curves at $0\mathrm{V}$ bias, for passivated and unpassivated tips. The tip was coated with $\mathrm{TiN}$ (spring constant $2.5\mathrm{N}∕\mathrm{m}$) and the surface was the clean twofold $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ surface. (b) Adhesion force as a function of peak applied load, at a sample bias of $0\mathrm{V}$ measured on the twofold $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ decagonal surface. Open circles represent data for the passivated tip, and closed squares the unpassivated tip.

Figure 4

AFM contact mode images, $500\mathrm{nm}\times 500\mathrm{nm}$. (a) Topography, (b) friction, and (c) current acquired simultaneously in the plastic regime with an unpassivated probe (bare metal coated tip) revealing unstable and irreversible features. Applied load=$0\mathrm{nN}$, and sample bias=$0.1\mathrm{V}$. (d) Topography, (e) friction, and (f) current in the elastic regime measured with a passivated probe. Applied load=$0\mathrm{nN}$, and sample bias=$1.5\mathrm{V}$. Fast scanning was in the vertical direction. Features characteristic of the tip sticking to the surface at the start of the scan lines are visible at the bottom of the images.

Figure 5

(Color online) (a) Schematic of the rotational scanning of the AFM head used to investigate the friction anisotropy on the twofold decagonal quasicrystal. (b) A force $F_x$ (red arrow) in the sample plane acting along the lever axis can be resolved into a “buckling” component along the line connecting the tip apex to the lever base (blue arrow), and a component normal to the sample surface marked by the green (light gray) arrow. Friction forces along the lever axis modulate the normal load. (c,d) Effect of buckling forces on the measured normal force (deflection response). In (c), the tip experiences a frictional force while scanning in the direction indicated by the gray arrow. The response of the lever resolves a component of the friction force normal to the surface, increasing the effective load, and a component along the lever, buckling the cantilever and decreasing the deflection signal. In (d), the scanning direction is reversed, and the friction force reduces the effective load and increases the deflection signal. These changes in effective load in turn modify the friction and the lever torsional response.

Figure 6

(Color online) Calculated torsional response for an isotropic surface $(\beta =1)$ and for an anisotropic surface with $\beta =8$ and $\varphi =-45°$ for a friction coefficient ${\mu }_1=0.19$ as a function of scanning angle. The red lines show the “trace” and the blue lines the “retrace” response calculated with Eq. (7). The dashed black lines show the uncorrected response from Eqs. (2, 3). Although lever effects modulate the friction by about 15%, these effects cancel out to first order when trace and retrace are averaged.

Figure 7

(a) AFM image $(500\mathrm{nm}\times 500\mathrm{nm})$ of a silicon oxide surface with a roughness of $2–3\mathrm{\AA }$. (b) Plot of torsional response measured as a function of scanning angle in open loop, along with the predictions (continuous curve) of our friction model (see text) describing the coupling between cantilever twist and buckling deformations.

Figure 8

Torsional response as a function of applied load for periodic and aperiodic directions, showing a friction anisotropy ratio of $\sim 8$. The adhesion force is $130\mathrm{nN}$. The lines are fits to the DMT model for contact shear stresses of 690 and $85\mathrm{MPa}$.

Figure 9

(a) Torsional response of the cantilever measured as a function of scanning angle on the twofold surface of the $\mathrm{Al}\text{−}\mathrm{Ni}\text{−}\mathrm{Co}$ decagonal quasicrystal at zero external load. The torsional response was higher along the periodic direction than along the aperiodic direction. The solid line shows the calculated torsional response with scanning angle for an elliptical anisotropy factor (ratio of torsional response) of 8. Current at the sample bias of $1.0\mathrm{V}$ was measured at the same time as torsional response. Its constancy reflects the elastic tip-sample contact, and the fact that uniformity of the applied load is within 5%. (b) Effective friction forces (torsional response after compensation for rotational scanning) as a function of the scanning angle. The solid line shows the calculated friction force after inclusion of a friction anisotropy value of 8. The exact shape of the calculated friction force is associated with the elliptical anisotropic model described in the text.

Figure 10

(Color online) (a) Torsional response vs applied load measured with the molecule-passivated AFM probe after exposing the surface to $100\mathrm{L}$ ethylene. (b) Torsional response vs applied load on the air-oxidized quasicrystal surface after “long air oxidation” as described in text.

Figure 11

Torsional response as a function of the scanning speed measured in periodic and aperiodic directions.