Wear 254 (2003) 859–862

Friction and wear on the atomic scale

Enrico Gnecco∗, Roland Bennewitz, Anisoara Socoliuc, Ernst MeyerInstitute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Abstract

Friction force microscopy experiments have been performed under ultrahigh vacuum conditions. Within a small force regime (below1 nN), friction without wear is observed as a function of velocity on ionic crystals and metals. The results are discussed in the frameworkof a refined version of the Tomlinson model, which includes thermal activation. Higher normal forces lead to abrasive wear. The debrisextracted from ionic crystals can be characterized with high lateral resolution. The dependence of wear rate on velocity and normal forceis investigated.© 2003 Elsevier Science B.V. All rights reserved.

Keywords: Friction; Wear; Atomic force microscope; Ionic crystals

The well experienced phenomena of friction and wear canbe understood in detail by observing the sliding of a sin-gle contact asperity. Nowadays, this purpose is realized ina very efficient way by the atomic force microscope (AFM)[1], which first made possible the observation of frictionwith atomic features in 1987[2]. Friction between a sharpsilicon tip and a surface is measured by means of a laserbeam, which is reflected on the rear of a cantilever support-ing the tip. Essentially, the angle of reflection of the beamcorresponds to the lateral torsion of the cantilever, causedby the torque exerted by the friction force in the contact areabetween tip and sample. Different materials react in vari-ous ways to the stress exerted by the microscope tip; theenvironment plays also an important role and different be-haviors can be observed depending on the external humidity[3].

In this paper, we will focus on some recent experimentsrealized at the University of Basel. In order to investigatefriction and wear on a basic level, we have chosen simplesurfaces, i.e. ionic crystals cleaved perpendicularly to the(0 0 1) direction, and observed them in a clean environment,i.e. ultra-high vacuum (UHV). Under such conditions it waspossible to evaluate the role of mechanisms like thermalactivation. With higher normal forces, wear on the atomicscale was produced and detected for the first time in a re-producible way.

Fig. 1a shows a friction force map acquired on aNaCl(0 0 1) surface[4]. Fig. 1brepresents the friction forceacquired in a single scan forwards and backwards. Thislat-

∗ Corresponding author. Tel.:+41-61-2673730; fax:+41-61-2673784.E-mail address: enrico.gnecco@unibas.ch (E. Gnecco).

eral forceFL is opposite to the scan direction and it revealsa saw tooth behavior with the periodicity of the underly-ing lattice,a = 0.47 nm. The area enclosed by the frictionloop is 14.6 eV, which corresponds to a dissipated energyof 0.8 eV per slip. These features can be explained withinthe Tomlinson model, which we briefly summarize hereby[5].

The sliding of the tip apex is subject to both the movementof the elastic cantilever and to the interaction between tip andsurface, which can be represented in a first approximationby a sinusoidal potential. The two contributions are summedup in the total potential

Vtot(x, t) = −E0

2cos

2πx

a+ 1

2k(x − vt)2 (1)

whereE0 is the peak-to-peak amplitude of the tip-samplepotential,k the effective lateral spring constant of the contact,and v the velocity of the cantilever support. To simplifythe discussion, it is useful to introduce the quantityγ =2π2E0/ka2, which gives the ratio between the tip-sampleinteraction and the elastic energy stored in the cantilever.We will consider only the caseγ � 1. Fig. 2 shows thepotential (1) at a certain timet. The tip lies in the minimumof the potential profile on the left. The energy barrier�E+prevents the tip from jumping into the next minimum of theenergy profile. Such barrier decreases when the cantilever ismoved laterally, until it vanishes and the jump occurs. When�E+ = 0 the lateral force isF∗ = πE0/a.

Thus, the Tomlinson model predicts that the maximumof the lateral forceF∗, which corresponds to the tip slip, isfixed by the interaction between the sliding materials at agiven load. However,Fig. 1bshows that this value is different

0043-1648/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0043-1648(03)00236-9

860 E. Gnecco et al. / Wear 254 (2003) 859–862

Fig. 1. (a) Lateral force map and (b) friction loop acquired on NaCl(0 0 1) by AFM with a normal forceFN = 0.65 nN. Frame size: 5 nm.

for each slip. Another interesting fact is observed when thescan velocityv is varied. Fig. 3 shows the mean lateralforce detected on NaCl with different values ofv. A smoothlogarithmic dependence onv is revealed, which also cannotbe explained by the simple version of the Tomlinson modeldiscussed so far.

A reasonable explanation is found if we take into accountthe finite temperature at which the measurements were re-

Fig. 2. Combined potential (1) experienced by the AFM tip sliding on aperiodic surface at a given instantt. The tip lies in the minimum of thepotential profile on the left. The energy barrier�E+ prevents the tip fromjumping into the next minimum of the profile at a distancea (processk+). The reverse process (k−) is hindered by the energy barrier�E−.

Fig. 3. Friction force vs. velocity on NaCl(0 0 1) withFN = 0.44 nN (+)andFN = 0.65 nN (×).

alized. According to the reaction rate theory, the tip jumpsfrom a minimum to the next one in the potential profile be-fore �E+ = 0, due to thermal activation. The slip prob-ability increases when the tip approaches the critical point�E+ = 0, where the jump would occur in any case. Theprobability for the tipnot to jump, p, varies with time ac-cording to the master equation

dp(t)

dt= −f0 exp

(−�E+(t)

kBT

)p(t) (2)

wheref0 is a characteristic frequency of the system.Eq. (2)can be written in terms of the lateral forceFL(t), and thefirst derivative dFL/dt can be replaced bykv. At this point,further approximations can be made.Fig. 4 shows a typicaldependence�E+ = �E+(FL). In a small range around themost probable values for the tip slip, we can assume thatthis dependence is linear:

�E+ = λ(F∗ − FL) (3)

Fig. 4. Lateral force dependence of the energy barrier�E+. The valuesare typical for AFM experiments. The curve can be approximated by astraight line not too close to the critical pointFL = F∗.

E. Gnecco et al. / Wear 254 (2003) 859–862 861

Fig. 5. (a) Lateral force map and (b) friction loop acquired on Cu(1 1 1) by AFM with a normal forceFN = 0.60 nN. Frame size: 3 nm. The dissipatedenergy is 0.8 eV per slip.

Fig. 6. Lateral force images acquired at the end of a groove scratched 256 times with a normal forceFN = 20.9 nN. Frame sizes: (a) 39 nm, (b) 25 nm.

After substitutingEq. (3) in Eq. (2)and after further calcu-lations we get[4]

FL(v) = F∗ − kBT

λln

f0kBT

kλv(4)

for the most probable value of the lateral force when the tipslips. However, the approximation (3) does not hold close tothe critical pointFL = F∗, where d�E+/dFL tends to zero.For jumps occurring in that region, Sang et al. suggestedthat the following approximation should be used[6]:

�E+ = µ(F∗ − FL)3/2 (5)

which leads to[7]

FL(v) = F∗ −(

kBT

µ

)2/3(

lnπ√

2

2

f0kBT

kav

)2/3

(6)

for the force corresponding to the slip.1

1 Eq. (6) lacks validity at high velocities. A more general expressionwhich removes this unphysical limit is given in[7].

In the discussion so far, we have not considered any spe-cific properties of the tip and sample materials. Measure-ments on Cu(1 1 1) realized by Bennewitz et al. showedthat stick–slip and logarithmic dependence on velocity arealso observed on metals (Fig. 5) [8]. Interesting conclu-sions can be drawn if these measurements are comparedwith the molecular dynamics (MD) simulations performed

Fig. 7. Lateral force image of a pit scratched 256 times with a normalforce FN = 18.6 nN. Frame size: 20 nm.

862 E. Gnecco et al. / Wear 254 (2003) 859–862

Fig. 8. Lateral force images of pits produced (a) with different loadsFN = 5.7–22.8 nN (v = 25 nm/s) and (b) with different scan velocitiesv = 25–100 nm/s(FN = 14.1 nN). Frame sizes: (a) 150 nm, (b) 67 nm.

by Sørensen et al.[9]. For example, the contact area betweentip and sample predicted by continuum mechanics is belowthe unit cell size, which shows that classical mechanics can-not be applied when forces in the subnanonewton range areinvolved. On the contrary, MD simulations show that a con-tact area formed by 5–30 atoms is expected in the range ofloads applied experimentally. Another interesting predictionof MD is that a clear stick–slip effect can be observed onlyon certain faces of the crystal. The sliding of a tip on theCu(0 0 1), for example, is accompanied by wear effects. Asa matter of fact, experiments conducted on this surface leadonly to irregular and irreproducible stick–slip[10].

Metals are not the best candidates to study wear mecha-nism by AFM. Our preliminary experiments on copper andaluminium showed that the debris accumulates on the mi-croscope tip, making it blunt and not suitable for repro-ducible measurements. In the case of ionic crystals wearis observed at very low loads, i.e.FN ≈ 3 nN [11]. Fig. 6shows a small mound grown up at the end of a groove onKBr(0 0 1), which was scratched hundreds of times a fewminutes before. The debris, extracted from the groove, re-crystallizes with the same structure of the original surface,which is a clear evidence of the fact that the final part of thewear process consists in an epitaxial growth assisted by themicroscope tip[12].

More delicate is to understand how the wear process isinitiated and how the material is transported by the tip. Someindications are given by the profile of the lateral forceFLacquired while scratching. The energy loss can be estimatedfrom the mean lateral force multiplied by the length scannedby the tip. For example,Fig. 7 shows a pit drilled on theKBr(0 0 1) surface by repeated scratching on 5 nm× 5 nmlarge areas. The high resolution of this image makes possiblea direct estimation of the number of atoms removed from thesurface. A comparison with the total energy loss evaluatedfrom the friction loops suggests that a dissipation of about23 eV per atom took place, which is about three times morethan the energy required to remove the atoms from the pits.Thus, about 70% of the dissipated energy went into wearlessfriction in the case of KBr(0 0 1).

As a further step, it is interesting to observe how thesurface damage changes with different velocities and normalforces.Fig. 8 shows five pits produced by scratching withdifferent loads and velocities. It is not surprising that thenumber of atoms removed increases with higher loads. Onthe other hand, the scan velocity is not so relevant, at leastin the range of values accessible to our AFM.

In conclusion, we have shown how the AFM operated inUHV provides essential information on the physics of fric-tion and wear on the atomic scale. The instrument allowsus not only to detect mechanical properties of the materialsunder investigation, but also to modify them and realize ar-tificial structures in a controlled way. In particular, we haveshown how ionic crystals constitute a privileged class of ma-terials due to their simple structure and their low interactionwith the silicon tip of the microscope, which makes possi-ble to perform measurements in a reproducible way, withoutapparent modifications of the tip after thousands of scans.

References

[1] G. Binnig, C.F. Quate, C. Gerber, Phys. Rev. Lett. 56 (1986) 930.[2] C.M. Mate, G.M. McClelland, R. Erlandsson, S. Chiang, Phys. Rev.

Lett. 59 (1987) 1942.[3] C.A.J. Putman, M. Igarshi, R. Kaneko, Appl. Phys. Lett. 66 (1995)

3221.[4] E. Gnecco, R. Bennewitz, T. Gyalog, C. Loppacher, M. Bammerlin,

E. Meyer, H.-J. Güntherodt, Phys. Rev. Lett. 84 (2000) 1172.[5] E. Gnecco, R. Bennewitz, T. Gyalog, E. Meyer, J. Phys.: Condens.

Matter 13 (2001) R619.[6] Y. Sang, M. Dubé, M. Grant, Phys. Rev. Lett. 87 (2001) 174301.[7] E. Riedo, E. Gnecco, R. Bennewitz, H. Brune, E. Meyer, in

preparation.[8] R. Bennewitz, T. Gyalog, M. Guggisberg, M. Bammerlin, E. Meyer,

H.-J. Güntherodt, Phys. Rev. B 60 (1999) R11301.[9] M.R. Sørensen, K.W. Jacobsen, P. Stoltze, Phys. Rev. B 53 (1996)

2101.[10] R. Bennewitz, E. Gnecco, T. Gyalog, E. Meyer, Tribol. Lett. 10

(2001) 51.[11] R. Lüthi, E. Meyer, M. Bammerlin, L. Howald, H. Haefke, T.

Lehmann, C. Loppacher, H.-J. Güntherodt, T. Gyalog, H. Thomas,J. Vac. Sci. Technol. B 14 (1996) 1280.

[12] E. Gnecco, R. Bennewitz, E. Meyer, Phys. Rev. Lett. 88 (2002)215501.