Frictional force microscopic detection of frictional asymmetry and anisotropy at (101̄4) surface of calcite

Abstract

Frictional asymmetry due to the tilt of carbonate ions at (101̄4) surface of calcite (CaCO₃) was detected with frictional force microscopy. The asymmetry signal was recorded by scanning the probe across the boundary between two surfaces of oppositely placed crystals in [421̄] direction. Observed asymmetry was in striking contrast with previous results for tilted S=O bonds of CaSO₄(100), lower friction being observed when the probe was scanned against the tilt. The difference was explained by the tilt angles of C=O and S=O bonds, which are described as mass-spring systems, from surface normal. More tilted C=O bonds of calcite support the normal load mainly by the reaction against bending of the springs, while less tilted S=O bonds support the load by the reaction against compression of the springs. As was expected, the asymmetry signal was strongest along the [421̄] direction, while no asymmetry was observed along the [010] direction. Compared to the case of CaSO₄, the asymmetry signal at the calcite surface took a large proportion of the total friction. The anisotropy in the total friction was also studied at the same surface, weakest total friction being observed along the [010] direction. Travelling straight in that direction, the tip atom at the probe surface frequently meets bridge sites where they can interact with two oxygen atoms of the carbonate ions. The result was in accordance with a similar experiment with a corrugated CaSO₄(001) surface.

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1. Introduction

Frictional force microscopy (FFM) has been found to be sensitive to the tilt of molecules in two-dimensional molecular arrangement at surfaces. Overney et al. first reported on frictional anisotropy with organic bilayer assembly.¹ Bluhm et al. proposed distinction between frictional anisotropy and asymmetry (difference between forward and backward scan), with ferroelectric organic crystals containing sulfate groups.^2,3 Liley et al. compared FFM images with Brewster angle microscope images of a lipid monolayer, and pointed out that asymmetry signal cannot be intuitively related to the molecular tilt of the 2D assembly.⁴

On the other hand, Shindo et al. detected frictional asymmetry at well-defined crystal faces of CaSO₄(100), SrSO₄(001) and BaSO₄(001), and proved that intuitive interpretation is correct in the cases of tilted chemical bonds like S=O bonds of sulfate groups.^5,6 In those cases, the absolute orientations of the crystal faces were determined by comparing asymmetric shapes of monatomic etch pits with the crystal structures. It is desirable that we get more direct evidences of absolute orientations of the crystal faces.

Calcite has the crystal structure shown in Fig. 1. An atomically-flat (101̄4) face is easily obtained by cleavage. In contrast to the cases of the sulfate minerals, planar carbonate ions here are tilted to the same direction at all the ionic layers. In the cases of sulfate surfaces previously studied, the frictional asymmetry was detected at monatomic steps where the tilt directions of the sulfate ions were reversed. In order to detect the frictional asymmetry at the calcite surface, we need to scan the FFM probe in one stroke at the surfaces of two crystals placed in opposite orientations.

Fig. 1 Structure of calcite crystal viewed in [010] direction. Carbonate ions are tilted in the same direction at (101̄4) surface, where frictional asymmetry is expected upon scanning with an FFM probe.

Frictional anisotropy is another important aspect of friction in the atomic level. In the cases of alkali halide crystals, the arrangements of cations and anions along the scan directions were the major causes of anisotropy.⁷ At the calcite surface, however, the O atoms of carbonate ions are located at higher levels than Ca ions. The probe surface interacts solely with the O atoms bearing negative charges. The frictional anisotropy at this surface should be determined mostly by the geometric arrangement of the outermost O atoms, just as in the case of corrugated CaSO₄(001) surface previously studied.⁸

2. Experimental

The calcite crystal (rhombohedral, R3̄c) used was of natural origin. The crystallographic orientations are known from its rhombic outer shape.⁹ The hexagonal unit cell was chosen according to custom. Solely {101̄4} surfaces are obtained by cleavage. Great care must be taken to assign the crystallographic orientations at this surface, since incorrect notations are often seen in recent AFM works.

A thin slice of the crystal was cut into two. One piece was turned around 180°. The two crystals were set as shown in the optical microscopic image in Fig. 2. The sidewalls of both crystals should lean toward the boundary. The other way around, the upper edges of the crystals do not touch each other. Several trials were needed to minimize the height gap between the two parts. Across the boundary, the tilt direction of carbonate ions is reversed as shown in the figure.

Fig. 2 Optical microscope image of an oppositely placed calcite crystal pair (about 3 mm long and 1 mm thick). Upon scanning the probe across the boundary in [421̄] direction, frictional asymmetry is detected due to change in the tilt direction of carbonate ions.

NanoScope III AFM of Digital Instruments was used in LFM mode. The FFM probe with a square pyramidal tip of silicon nitride was scanned across the boundary. A topographic image and friction images in two scan directions were recorded at the same time. The friction loop showing the torsion of the cantilever was also recorded. Use of a wide scanner (155 μm maximum) was necessary. The normal load was set at 125 nN. Co-planarity of the two crystal faces was checked by taking profiles of the topographic images.

Angular dependence of the friction was studied by rotating the sample on the sample holder. The scan angle was measured clockwise from [010] direction. Largest frictional asymmetry is expected in [421̄] direction.

3. Results and discussion

3.1 Frictional asymmetry

In Fig. 3 are shown the AFM and FFM images with forward and backward scans along the [421̄] direction across the crystal boundary. The height difference between the two crystal faces as measured with Fig. 3a was 2.1 μm.

The dark and bright frictional contrast was reversed across the boundary in Figs. 3b and 3c. Similar appearance of the contrast change in the two figures is typical of frictional asymmetry due to the change in the tilt directions of chemical bonds.^5,6

Fig. 3 AFM(a) and FFM images in two scan directions (b,c) across the boundary of oppositely placed (101̄4) surfaces of calcite (100 μm square). There is a height gap of 2.1 μm between the two surfaces. Geometry of carbonate ions are shown in (b), topmost O atoms being drawn as large spheres. The letters H and L indicate higher and lower friction, respectively. The reversal of friction levels (similar dark and bright contrast) with the scan direction (b and c) is typical with the change in tilt directions of chemical bonds at surfaces. Friction loop was recorded along the broken line in (b).

The friction loop obtained along the broken line in Fig. 3b is shown in Fig. 4. Except for the crystal boundary region in the middle, steady torsion signal was recorded at either crystal surface. At this surface the proportion of the asymmetry component of the total friction was quite large (30–40%). In the previous cases of the sulfate minerals, the proportion was only 10% or less.^5,6

Fig. 4 Friction loop showing actual torsion signal of cantilever due to friction at (101̄4) surfaces of calcite. Except for the crystal boundary region in the middle, stable signals are obtained. The relation between the asymmetry signal and the scan directions is typical with tilted chemical bonds. The asymmetry component takes a large percentage of the total friction.

The geometry of carbonate ions is also shown in Fig. 3b. Relative to the (101̄4) surface, the molecular plane of the carbonate ion is rotated 44.6° around the [010] axis. The O atoms at the highest level are drawn as large circles. The top C=O bonds are tilted by 52.5° from surface normal.

It is surprising that higher friction was observed upon scanning the probe following the tilt. Similar result was reported in the case of a thiolipid monolayer on mica, which was described as ‘counterintuitive’ by the authors themselves.^4,10

In our previous studies of sulfates, higher friction was observed when the probe was scanned against the tilt. It was easy to explain the mechanism of the frictional asymmetry by analogy with touching the head of foxtail grass or a scrubbing brush with our fingers.⁶ How can we explain the present result in the same framework?

The main difference between the cases of carbonate and the sulfate is the tilt angle of the C=O and S=O bonds from surface normal. The C=O bonds at the (101̄4) surface of calcite is tilted by 52.5°, while the S=O bonds at CaSO₄(100) is tilted by 35.3°.

In the case of the sulfate surface, we explained the frictional asymmetry as a mechanical interaction between a flat surface and an array of mass-spring systems as is demonstrated in Fig. 5a.⁶ Just for simplicity, we assume here the probe surface as a flat one. This will not be a bad approximation since the probe sharpness is limited in the atomic level. Generality is not lost in the following discussion of frictional asymmetry.

Fig. 5 Mechanical models of interaction between the FFM probe and tilted chemical bonds as mass-spring systems (a,b), and a 2D molecular layer (c) at sample surfaces. F_ax and F_tan indicate the axial and tangential components of the reactive force against applied normal load, respectively. Relative importance of the two components varies with the tilt angle of the chemical bonds. The direction of the horizontal component included in the total reaction may change depending on the tilt angle of the chemical bonds. Being pressed by the probe, close-packed long chain molecules will act as in a solid due to intermolecular repulsion, giving a result similar to the case of a chemical bond tilted further.

At any given lateral position, the probe surface would experience frequent collisions with multiple mass-spring systems at the sample surface due to molecular and lattice vibrations. Total collisions of the masses are represented as the bent spring shown in Fig. 5a.

When pressed by the probe surface, the spring is compressed axially in the bond direction, while relatively small deformation occurs tangentially. Of the total reaction force by the spring, the normal component balances with the preset normal load, while the remaining horizontal component pushes the probe surface as indicated by the bold arrow in the figure.

The simple model explained well the observed experimental results with the sulfate surface. The mechanism is readily acceptable for our intuition. However, the present experiment with the calcite surface gave an opposite result, which must be explained using a similar mechanical model.

Let us, now, consider the case when the mass-spring systems are more tilted as shown in Fig. 5b. In this case, the recovery force of the spring nearly in tangential direction must bear most of the normal load applied, since the axial component is geometrically less effective. The total reaction will, then, include a horizontal component which pushes the probe as indicated by the bold arrow in the figure. This qualitatively explains the asymmetry observed with calcite.

In the similarly counterintuitive result with the lipid monolayer,⁴ lower friction was detected against the nap of the molecules than along the nap. The authors estimated the tilt angle of the alkyl chains to be only 10 ± 5° using Brewster angle microscopy observation and electron diffraction. However, long alkyl chains should be much weaker as springs than S=O or C=O bonds. They will be tilted much more when pressed by the probe.

In addition, the molecules as long as 4.5 nm in an LB film should not be considered to be independent. In that case, too, we can expect relative importance of tangential component of reaction. The molecular layer will resist against compression in that direction due to intermolecular repulsion as shown in Fig. 5c. That will give response similar to the case of Fig. 5b.

The arrangement of atoms at the (101̄4) surface is shown in Fig. 6. The top-most O atoms of carbonate groups are drawn as large circles, since only they can touch the probe surface. The surface unit cell as shown in the figure was recognized in atom-resolved AFM image observed in air.

Fig. 6 Plan view of the (101̄4) surface of calcite. Carbon atoms are shown as filled circles. Largest circles indicate O atoms lying above the surface. They form a surface unit cell as shown. Only they can interact strongly with the probe surface. Ca ions are indicated by the thick circles of medium size. Along the trajectory in the [01̄0] direction, the tip atom frequently meets bridge sites, as indicated by open and filled squares, where it can interact with two O atoms. The interaction potential (PE) between the tip and the sample will oscillate as shown. In the [421̄] direction, however, the tip must go through unstable sites as indicated by hatched triangles. The potential energy will oscillate in a large amplitude.

The carbonate ions take two orientations at the surface. Each ion pushes back the probe surface in O → C direction projected on the surface. Since the probe surface touches several carbonate ions at the same time, combined reaction force in horizontal direction will be close to the [421̄] direction. Angular dependence is, then, expected for the frictional asymmetry.

In the next series of experiments, the sample was set at different angles on the scanner and the asymmetry signals were recorded as friction loops. The relative humidity was 12%. The scan angle was measured clockwise from the [010] direction in Fig. 6.

The results are shown in Fig. 7a. As was expected, the asymmetry signal peaked at 90° along the [421̄] direction. On the other hand, no asymmetry was detected in the [01̄0] direction. The experimental results support the above discussions on the frictional asymmetry.

The fact that opposite results can arise from tilted bonds or molecules discouraged our expectation that the detection of frictional asymmetry can be used in determining absolute surface orientations. More elaboration is required for that purpose. It should be pointed out again that the asymmetry component takes a large proportion of the total friction in the counterintuitive case of calcite. This may be related to the number of springs supporting the probe. Fewer springs will support the same normal load if the tilt angle is smaller.

Fig. 7 Angular dependence of (a) the asymmetry component and (b) the total friction at (101̄4) surface of calcite. The angle was measured clockwise from the [010] direction shown in Fig. 6. The asymmetry signal peaks along [421̄] direction and is lost along [01̄0]. The total friction hits minimum along the [01̄0] direction and increases toward [421̄].

3.2 Frictional anisotropy

Angular dependence of the total friction was also studied using the (101̄4) surface. The results are shown in Fig. 7b. The total friction is lowest along the [010] direction, and highest along the [421̄] direction.

According to literature, friction is explained as partial dissipation, with the stick–slip action, of the mechanical energy stored in the mass-spring systems at the contact of two surfaces in relative motion horizontally.^11–14 Higher friction is, then, expected when the interaction potential between the two surfaces oscillates in larger amplitude during the motion.

In our previous FFM study of frictional anisotropy at (001) surfaces of alkali halides and magnesium oxide, the lower friction observed along the [110] direction compared to [100] was explained by calculating potential gradient of the electrostatic interactions between an electric dipole at the probe tip and the ions at the sample surfaces.⁷ When the probe travels in [100] direction alternately above cations and anions, the electrostatic interaction alternates between attractive and repulsive. The potential, then, oscillates in larger amplitude. In [110] direction, on the other hand, the probe travels above one kind of ions, cations ‘or’ anions. The interaction may be either attractive ‘or’ repulsive all the way, and the interaction potential should be fairly stable during the scan.

The frictional anisotropy observed is closely related to translation-gliding in crystals of NaCl type structure. For example, [110] gliding is observed at (001) surfaces of PbS and PbTe, and [11̄0] gliding is observed at (110) surfaces of NaCl, MgO, NaF, etc.¹⁵

Frictional anisotropy can arise from geometrical arrangement of surface atoms. At a corrugated CaSO₄(001) surface, the probe surface can interact strongly only with O atoms located at higher positions than Ca ions. The lower friction observed along the corrugation rather than across it was explained simply by counting the numbers of O atoms touching the probe at given positions.⁸ We estimated that the potential oscillation would be smaller if positions having the same level of interaction with the probe atoms are aligned with short intervals at the surface. The same approach is chosen here since the situation is similar in the case of the calcite surface. We consider here the probe surface as a curved one.

Two trajectories are shown in Fig. 6. The filled and open squares indicate positions where a tip atom of the probe surface can interact most strongly with two O atoms nearby. Let us call them bridge sites. Although the total normal load is supported not only by the two atoms, they would bear the largest proportion.

Along the [01̄0] direction, the bridge sites are aligned with a relatively short interval of 250 pm. In between the filled and open squares, the tip atom gets a little closer to one of the O atom. Due to a stronger repulsion by the atom, the interaction potential will oscillate as demonstrated in the bottom of the figure.

Along the [421̄] direction, on the other hand, the bridge sites are aligned with a much longer interval of 405 pm. In between the bridge sites, at positions indicated by hatched triangles, the tip atom must get very close to one O atom experiencing a much stronger repulsion. The interaction potential will oscillate in much larger amplitude as shown in the left part of Fig. 6. Higher total friction is expected in this direction.

We considered only straight trajectories assuming rigid probe and sample surfaces, since we applied a strong normal load of 120 nN. If a much smaller normal load was applied, curved trajectories might be possible.^16–18 In that case, we would expect lower friction in the diagonal directions of the surface unit cell shown in Fig. 6, since we can smoothly connect the bridge sites in those directions. However, in our case of multi-atomic contact, the anisotropy was as shown in Fig. 7, friction taking a clear minimum along the [01̄0] direction. The straight and dense alignment of the O atoms, and the bridge sites, along the [010] direction is the cause of the lower friction. If we try to connect the bridge sites with a straight line in other directions, we cannot avoid unstable sites.

We could give only qualitative explanations for the present experimental results. However, it will be worthwhile to present experimental results with various cases of friction at well-defined crystal surfaces in order to understand the mechanism of friction in atomic levels.

Finally, we want to discuss our friction measurement in relation to macroscopic measurement. In our previous study of frictional anisotropy at (001) surfaces of alkali halides and MgO,⁷ we calculated the frictional coefficients (μ) from the observed torsion signals, by analyzing the sensitivity of optical detection system of the FFM apparatus and by calculating stiffness of the cantilevers used.¹⁹ We can compare the μ with those measured by classical methods.

Bowden and Brookes measured μ at (001) surfaces of MgO and LiF using diamond styluses with different cone angles.²⁰ The data depended heavily on the cone angle in the macroscopic measurement. With a cone angle of 170°, they observed no apparent damage on the surface, although the angle was too large to observe anisotropy. The μ measured for MgO and LiF were 0.06 and 0.2, respectively, independent of the scan direction.

Our FFM observation with oxide sharpened silicon nitride tip gave μ(100) = 0.16 and μ(110) = 0.075 for MgO, and μ(100) = 0.16 and μ(110) = 0.065 for LiF. The frictional coefficients obtained in macroscopic and microscopic experiments are fairly close to each other. We can compare the total friction data obtained with FFM, with those obtained in macroscopic experiments using atomically-flat samples, a hard stylus and in nearly wearless conditions. If we can rely upon μ measured in FFM, we can compare the frictional properties of different samples.

FFM has additional advantage over classical experiments in its sensitiveness to the frictional anisotropy and asymmetry due to molecular arrangement and geometry. Unfortunately, however, macroscopic friction data were not available with the calcite surface. It will be worthwhile to check whether the anisotropy and asymmetry are detectable in macroscopic friction measurements.

Acknowledgements

The work was supported by The Salt Science Research Foundation (grant Nos. 0018, 0108, 0306), The Ministry of Education, Science, Sports and Culture (Grant-in-Aid for Scientific Research No. 12440188), and The Promotion and Mutual Aid Corporation for Private Schools of Japan.

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