Model experiments of superlubricity of graphite

Model experiments of superlubricity of graphite

Martin Dienwiebel a,*,1, Namboodiri Pradeep a, Gertjan S. Verhoeven a,Henny W. Zandbergen b, Joost W.M. Frenken a,*

a Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlandsb Laboratory of Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands

Received 6 September 2004; accepted for publication 20 December 2004

Available online 27 December 2004

Abstract

Graphite is known to be a good solid lubricant. The low-friction behavior is traditionally ascribed to the low resis-

tance to shear. We have recently observed that the ultra-low friction found in friction force microscopy experiments on

graphite is due to a effect called superlubricity [M. Dienwiebel, G. S. Verhoeven, N. Pradeep, J.W.M. Frenken, J.A.

Heimberg, H.W. Zandbergen, Phys. Rev. Lett. 92 (2004) 126101]. Here, we provide additional experimental evidence

that superlubricity has been taken place between a small graphite flake attached to the scanning tip and the graphite

surface. Finally, we speculate about the significance of this for the lubricating properties of graphite.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Tribology; Friction; Atomic force microscopy; Graphite

1. Introduction

Graphite is undoubtedly the most common so-

lid lubricant. Mainly used as flaky powder, it is

e.g. applied where liquid lubricants cannot be

used, especially in high-temperature applications,

or as friction reducing additive in oils and poly-

mers and as brushes in electrical motors. It is not

surprising that research on the tribological proper-

ties of graphite has a long history and it is well

established that the friction coefficient for many

materials against graphite in ambient conditions

is in the range of 0.08–0.18 (see e.g. [1]). Tradition-

ally, the good lubricating properties of lamellar

solids are ascribed to the weak interaction between

adjacent graphite layers [2]. However, the intuitive

idea that this would lead to ‘‘easy shear’ ’ has been

argued to be unsatisfactory. Finch [3] has pointed

0039-6028/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.susc.2004.12.011

* Corresponding authors. Tel.: +49 721 95505956; fax: +49

721 9550528 (M. Dienwiebel).

E-mail addresses: [email protected] (M. Dienwie-

bel), [email protected] (J.W.M. Frenken).

URL: http://www.physics.leidenuniv.nl1 Present address: IAVF Antriebstechnik AG, Im Schlehert

32, 76187 Karlsruhe, Germany.

Surface Science 576 (2005) 197–211

www.elsevier.com/locate/susc

out that simultaneous rupture of all bonds in a

plane, i.e. cleavage would require a very high en-

ergy. This is supported by the fact that graphite

does not shear readily, unless a high compression

is superimposed [1]. Savage and others [4–6] have

found that the friction coefficient for metals

against graphite is much higher (0.8) in vacuum

and that wear is very heavy. The high friction

was still observed after admission of hydrogen or

nitrogen. Only after admission of a few ppm of

oxygen or certain organic vapors, low friction

and low wear were restored. It has been shown

that when metal is sliding on graphite in air,

graphite is transferred to the metal surface, while

in vacuum metal is transferred to the graphite sur-

face [7]. Moreover it has been shown, that a metal

oxide layer tends to fix the transferred graphite to

the metal, leading to a smooth transfer film [8].

The combination of these observations strongly

suggests that the low friction is only obtained

when graphite slides over graphite.

The first atomic-scale friction experiment has

been performed by Mate et al. [9] using a tungsten

tip sliding over a highly ordered pyrolytic graphite

(HOPG) surface under ambient conditions. These

authors found friction coefficients between 0.005

and 0.015. Unlike in frictional force microscopy

(FFM) experiments on other materials, where usu-

ally a power law behavior is found, FF = (FN)a,

with a < 1, the dependence of the friction force

FF on the normal load FN was found to be almost

linear on graphite. Similar friction versus load

behavior and similar friction coefficients have been

observed in subsequent FFM experiments on

graphite with a variety of tip materials [10–13].

In FFM experiments on graphite and other

materials such as e.g. alkali-halides the scanning

tip performs so-called ‘‘stick-slip’’ motion, jump-

ing discontinuously over single lattice spacings.

Fujisawa et al. [14] have shown, using a two-

dimensional FFM, that lateral force images can

be explained by two-dimensional, i.e. ‘‘zig-zag’’

atomic-scale stick-slip motion. A simple classical

mechanics model [15], the so-called Tomlinson

model, in which a single-atom tip is dragged

through a sinusoidal potential, reproduced the

experimental lateral force maps of the graphite

surface quite well [16,17]. However, the normal

forces that were used in the simulations had to

be chosen one to two orders of magnitude lower

than those in the experiments [18].

We have recently shown that the ultra-low fric-

tion coefficients of graphite, found in FFM exper-

iments are caused by ‘‘superlubricity’’ between

graphite surfaces [19]. The term superlubricity

has been introduced by Shinjo and Hirano [20]

and it describes the notion that friction might van-

ish almost completely even when two crystalline

surfaces slide over each other in dry contact. This

phenomenon was first demonstrated in a quasi-

static calculation for rigid crystals with fcc, bcc

and hcp symmetry and different orientations [21].

In a consecutive study the same authors used a

Frenkel–Kontorova model (F–K model) to study

the transition from kinetic friction to superlubric-

ity in one and two dimensions. They concluded

that one way to observe this transition experimen-

tally, is to change the commensurability between

the two surfaces. The concept of superlubricity

only takes into account energy dissipation due to

excitation of phonons. Other dissipative processes,

such as ‘‘electronic friction’’ or ‘‘quantum fric-

tion’’ [22], will not depend on the degree of com-

mensurability. Therefore, even in the case of

complete, phononic superlubricity, the total fric-

tion force will not be identical to zero. The similar-

ity of the term ‘‘superlubricity’’ with similar terms

such as ‘‘superconductivity’’ and ‘‘superfluidity’’ is

therefore misleading. Nonetheless, under appro-

priate conditions, superlubricity might cause a

reduction of the friction force by orders of magni-

tude. In this article, we give a more complete ac-

count of our experimental results and we provide

firm evidence for superlubricity occurring in fric-

tion force microscopy experiments on a graphite

substrate.

2. Experimental

We have performed measurements on HOPG

samples using a homebuilt FFM [23] that allows

quantitative tracking of the forces on the scanning

tip in three directions, with a high resolution in the

lateral forces, down to 15 pN. The key feature of

our microscope is a dedicated friction force sensor,

198 M. Dienwiebel et al. / Surface Science 576 (2005) 197–211

the Tribolever [24]. It combines low and symmetric

spring constants of 5.75 ± 0.15 N/m in the two lat-

eral directions with a high stiffness of 26 ± 1 N/m

in the normal direction. The Tribolever was cali-

brated using the ‘‘added mass’’ method, developed

by Cleveland et al. [25]. A tungsten tip was glued

into the Tribolever using silver epoxy, such that

it extended 50–60 lm out of the device. The

displacements of the Tribolever tip in the X-, Y-

and Z-directions are monitored using four all-

glass-fiber interferometers. The instrument can

rotate the sample to change the relative orientation

between the tip and sample lattices. Initial mea-

surements have been performed on HOPG graph-

ite of grade ZYH, which has a nominal grain size

in the range of 30–40 nm and a mosaic spread of

3.5� ± 1.5� according to the supplier [26]. How-

ever, on our particular sample we found only

larger grains. Later measurements have been per-

formed on grade ZYA graphite, which possesses

a lateral grain size of up to 10 mm and a mosaic

spread of 0.4� ± 0.1�. The samples were cut to a

size of 2 mm · 2 mm. Therefore, the grade ZYA

sample consisted probably of a single graphite

crystal, while the grade ZYH sample was polycrys-

talline. The HOPG was freshly cleaved using

Scotch tape and then mounted in the FFM inside

a small chamber, which was continuously flushed

with dry nitrogen. The measurements were typi-

cally performed at humidities of 1–10 ± 1% RH.

The scanning speed in the experiments was

v = 30 nm/s. All force maps were recorded in the

form of two-dimensional ‘‘images’’ with 512 ·

512 pixels.

We performed two different types of measure-

ments. In the case of ‘‘lateral force imaging’’, the

external normal load FN was set to a constant value

using the feedback loop of the scan electronics.

Zero normal load was defined as the load at which

the Tribolever was not bent in the normal direc-

tion. When the tip was scanned over the surface,

we recorded the lateral forces in the two perpendic-

ular directions defined by the X- and the Y-axes of

the Tribolever, both during the forward and during

the reverse scan lines. Other than with a conven-

tional AFM cantilever, with the Tribolever it is

possible to choose any sliding direction in the mea-

surement, and always record the lateral forces par-

allel and perpendicular to the scan direction with

equal sensitivity. The lateral force was defined as

the lateral spring constant times the lateral dis-

placement of the Tribolever pyramid with respect

to the FFM base: F latX ;Y

¼ kTriboleverX ;Y

DxTriboleverX ;Y

. In gen-

eral, the X direction of the Tribolever and the fast

scanning direction (which is the ‘‘x direction’’ in a

lateral force image) will be rotated with respect to

each other. In the following, X and Y denote the

directions of the Tribolever axes, and x and y as

the fast and slow scan axes of the lateral force im-

age. By changing the fast sliding direction x, also

the angle between the x direction and the lattice

orientation changes.

One forward scan line and the subsequent re-

verse scan line together form a closed hysteresis

loop, that is often referred to as the ‘‘friction

loop’’. An example of such a friction loop is shown

in Fig. 1c. The area that is enclosed inside the fric-

tion loop corresponds to the dissipated energy dur-

ing the back and forth sliding. We calculated the

average friction force in the X and in the Y direc-

tion of the Tribolever by taking the difference be-

tween the mean value of the lateral force in the

forward direction and in the reverse direction:

F X ;Y �hF lat

fwdi � hF latrevi

2

� �

: ð1Þ

The mean value of the lateral force hFlati was only

obtained from those parts of the friction loop

where the lateral force had fully developed, e.g.

for x > 0.7 nm in the forward scan line and for

x < 2.3 nm in the reverse line in Fig. 1c.

To obtain the friction force, i.e. the component

of the average lateral force in the sliding direction,

we computed the appropriate vector addition of

the average lateral forces in the X- and the Y-

direction:

F F ¼ F X cos fþ F Y sin f; ð2Þ

where f denotes the angle between the X direction

of the Tribolever and the sliding direction of the

tip (x).

The second type of measurement that we per-

formed is referred to in the literature as ‘‘friction

force spectroscopy’’ [27]. Here, we initially set

the normal force FN to a positive value and low-

ered it at every line during the scan, until the tip

M. Dienwiebel et al. / Surface Science 576 (2005) 197–211 199

lost contact with the surface. From each single

line, i.e. each single FN value, one (FN,FF) data

point was obtained, using Eqs. (1) and (2).

Together, all the scan lines resulted in a friction

spectrum FF (FN).

3. Results

3.1. Lateral force images and friction loops

Fig. 1 shows typical lateral force images mea-

sured simultaneously in the forward X-direction

of the Tribolever (a) and in the direction perpen-

dicular to that (b) on the polycrystalline HOPG

surface. The x- and X-directions were aligned.

Not shown is the topography image (Z), obtained

at the constant normal force of FN = �3.2 nN

which does not reveal any surface features. The

rms roughness of 0.27 A, measured from the

topography image was caused by residual noise

in the detection of the Z position of the Tribolever.

The lateral force in the sliding direction exhibits a

typical saw tooth waveform (c), which can be ex-

plained by atomic-scale stick-slip motion, as has

been shown in several earlier experiments [9,14,

28,11]. Depending on the sliding direction, the lat-

eral force image in the perpendicular direction

shows different patterns. If the sliding direction is

parallel to one of the six symmetry directions of

the HOPG surface, the lateral force measured

perpendicular to the sliding direction shows a hor-

izontal stripe pattern (Fig. 1b). If the tip is scanned

under a different angle, the patterns in the X- and

the Y-images change and the tip performs a ‘‘zig-

zag’’ stick-slip movement over the graphite lattice.

This shows that the forces in the sliding direction

cannot be regarded independently from those in

the perpendicular direction. The zig-zag motion

is stronger for the Tribolever than for most ‘‘tradi-

tional’’ cantilevers, because of the equality of

kTriboleverx and kTribolever

y .

Fig. 1. Lateral force image of a tungsten tip on HOPG at FN = �3.2 nN. The tip is sliding in the x direction, which is aligned with one

symmetry direction of the surface. (a) Lateral forces in the forward x direction; grey scale: 1.7 nN. (b) Lateral forces in the

perpendicular y direction; grey scale: 93 pN. Image size 3 nm · 3 nm. (c) Experimental friction loop from (a), and (d) a force loop

calculated using a Tomlinson model for a single-atom tip. The calculation was performed using a potential energy amplitude of

V0 = 0.08 eV and lateral spring constants kx = ky = 1.8 N/m (see [39]). Throughout this paper the lateral forces during the forward scan

lines are plotted as black curves, the forces during the reverse scan lines are plotted as grey curves.


Fig. 1c and d shows a comparison between an

experimental friction force loop, obtained from

one forward scan line of Fig. 1a, plus the subse-

quent reverse line (c), and a theoretical friction

loop, obtained from a Tomlinson model calcula-

tion (d). The comparison shows good qualitative

agreement between the experimental and the

calculated friction loops, suggesting that our mea-

surements can be understood using a two-dimen-

sional Tomlinson model. However, to obtain

quantitative agreement between the force magni-

tudes in the calculated and experimental force

loops, we had to use a lateral spring constant in

the calculation which differed from the known

kTribolever. This suggests that also the elastic com-

pliance of the contact contributes to the total

spring constant. The effective spring constant can

be obtained directly from the slope of those parts

of the measured force loops where the contact

sticks [29,30]. To understand this, one can view

the measurement system as a set of springs in ser-

ies. The effective spring constant is constituted of

dF latX

dx¼ ðkTriboleverÞ�1 þ ðkcontactÞ�1

h i�1

; ð3Þ

where kTriboleverx ¼ kTribolever

y ¼ kTribolever is the known

spring constant of the Tribolever and kcontact is

called ‘‘contact stiffness’’ [29]. This contact stiffness

can be separated further in

kcontact ¼ ðkaddÞ�1

þ ðkinterfaceÞ�1

h i�1

; ð4Þ

where kinterface ¼ o2V =ox2 ¼ 2p

a

� � 2V 0 is the spring

formed by the local curvature in the wells of the

potential energy landscape of the substrate as

experienced by the tip, where the last step assumes

a sinusoidal potential with period a and amplitude

V0. The spring formed by additional elastic com-

pliances, such as the elastic compliance of the tip

and that of the sample, is symbolized by kadd.

Since we cannot distinguish between the compli-

ances introduced by the tip and those introduced

by the surface, we will take these together.

Using Eq. (3) we find a contact stiffness in Fig.

1c of 2.3 ± 0.3 N/m. Because the curvature of a cor-

rugated potential energy landscape acts also in the

Tomlinson model as a spring that contributes to

the contact stiffness, also the calculated friction

loop possesses an effective stiffness that differs from

kTribolever, but since kadd = 1 in the model, we sim-

ply have kcontact ¼ kinterface ¼ 2pa

� � 2V 0 in the model

calculation. The force at which the slip events take

place is largely determined by the amplitude of the

potential and the sum of 1/kTribolever + 1/kadd. We

obtain a simultaneous fit of the effective stiffness

and the maximum lateral force for a potential cor-

rugation of V0 = 0.08 eV and a ‘‘potential spring

constant’’ of kinterface = 15.9 N/m. Since kTribolever

is known with an accuracy of 2.3%, we can now

estimate the additional stiffness to be kadd =

2.7 N/m. The effect of the tip compliance is to lower

the effective spring constant of the Tribolever

to kTribolevereff ¼

�

ðkTriboleverÞ�1

þ ðkaddÞ�1��1

¼ 1:8 N/m.

With this value, we find indeed good agreement be-

tween the experimental force loops and the calcu-

lated one. The precise origin of the additional

elastic compliance cannot be determined from

these measurements, but it seems likely that the

elastic compliance of the tip dominates.

A clear difference between the simulated friction

loop and the experimental one, is that the posi-

tions where the slip occurs in the experimental

data display variations in the order of 25% of the

lattice spacing. In the parts of the friction loop

where the tip is sticking, the lateral force fluctua-

tions are much too small to account for these vari-

ations. This is clearly seen also in all lateral force

images, which ‘‘look’’ noisy, despite good lateral

force resolution. We believe that these fluctua-

tions, which can be seen also in other FFM exper-

iments with comparable effective spring constants

and normal loads (e.g. [31]), are thermally induced.

Using a modified Tomlinson model that included a

term representing the effect of random thermal

fluctuations, Sang et al. [32] have studied thermal

effects on atomic friction by adding a Langevin

term to the Tomlinson model. Dudko et al. [33]

used a Fokker–Planck approach, and showed that

it is equivalent with the solution of the Langevin

equation. With an effective spring constant of

keff = 0.86 N/m to fit the data from Gnecco et al.

[31], they have found that the distribution function

of the maximum lateral force in the friction trace,

which is equivalent to the slip position, had a full


width at half maximum (FWHM) of approxi-

mately 17%. In order to evaluate thermal fluctua-

tions in our experiment, we simulated them in

the Tomlinson model calculations using a simple

Monte-Carlo approach. At every time step Dt,

where Dt = Dxt/v, we calculated the transition rate

C, which is an inverse measure of the time needed

before a thermally induced jump over the energy

barrier takes place,

C ¼ f0 exp �DV ðxtÞ

kBT

� �

; ð5Þ

where f0 is the eigenfrequency of the Tribolever,

DV(xt) is the remaining energy barrier with respect

to the momentary tip position, kB is the Boltz-

mann constant and T is the temperature. The

‘‘probability’’ CDt for a thermally induced jump

over the barrier was then compared with a number

R 2 [0,1] obtained from a random number genera-

tor and, if R was lower than CDt, a jump at posi-

tion xt was induced.

Fig. 2 shows the normalized distribution for

15,000 simulated slip events using kTribolevereff ¼

1:8 N/m, V0 = 0.08 eV, v = 30 nm/s and an effective

mass of the Tribolever of 10 lg. The distribution

possesses a FWHM of 30 pm, which is 12.3% of

the graphite unit cell. In addition, the jumps oc-

curred on average 44 pm before the static case,

recovered in the Tomlinson model at T = 0.

3.2. Friction versus load

The friction versus load data strongly suggests

that the sliding has been taking place between

two graphite surfaces, one being the HOPG sub-

strate, and the other being a small piece of graph-

ite, i.e. a graphite flake, that was attached to the

tungsten tip.

Fig. 3a–f shows three lateral force maps and

friction loops measured in the forward X-direction

at different normal loads. Again, the x-direction

was aligned with the X-direction of the Tribolever.

Fig. 3g–i displays the average waveform of the lat-

eral force variations over one lattice period, ob-

tained by averaging the lateral force variations

over three lattice periods. Already at a negative

load of �3.4 nN, variations in the lateral force

with lattice periodicity are faintly visible. How-

ever, these variations do not have a ‘‘saw tooth’’

shape, typical for stick-slip motion, but a continu-

ous shape (Fig. 3g). At this normal force, the area

enclosed inside each friction loop (Fig. 3d) is very

small. In other words, the energy dissipated during

one sliding cycle is nearly negligible. Correspond-

ingly, the average friction force obtained from

the complete lateral force map, according to the

procedure described in Section 2 (Eqs. (1) and

(2)) is as low as 1:8þ16�1:8 pN. At a higher normal

load of 11.6 nN, the variations in the lateral force

increased, and the lattice can be seen more clearly

in the force map, but the average friction force did

not increase significantly, as can be seen from the

force loop in Fig. 3e.

Note, that the waveform of the lateral force

variations changed and appears ‘‘saw tooth’’-like

(Fig. 3h). At a still higher normal load of 41 nN

we observed clearly ‘‘saw tooth’’-like lateral force

variations (Fig. 3i) and an increase in the average

friction force to 62 ± 19 pN, (Fig. 3f).

Complete friction versus load curves were ob-

tained from friction force spectroscopy measure-

ments (see Section 2 for procedure). Fig. 4a

shows an example for a contact that behaved sim-

ilarly to the one shown in Fig. 3. The normal force

was reduced from 45 nN until the tip lost contact

with the surface at �24 nN, at which point the

tip was fully retracted by the feedback electronics.

The data in Fig. 4a are representative for a large

Fig. 2. Normalized distribution of the slip position at temper-

ature T = 293 K. The origin of the x-axis lies at the slip position

of xt without thermal fluctuations. The calculation was

performed using V0 = 0.08 eV and kx,y = 1.8 N/m.


number of measurements. In the normal force

range from �24 to approximately +30 nN the fric-

tion force stayed almost constant at a very low

value of 28 ± 16 pN. The frictional behavior as a

function of normal load obtained from the friction

force spectroscopy experiment shown in Fig. 4a is

in agreement with the friction forces obtained

from individual lateral force images at different,

constant normal loads. As in Fig. 3, we see very

low energy dissipation up to about FN = 40 nN.

For normal loads above 40 nN we observe a slight

increase. A smaller number of measurements pro-

duced entirely different friction versus load curves.

An example is shown in Fig. 4b. The curve was

measured under similar conditions as the one in

Fig. 4a. Now, the friction force between �11 and

+24 nN normal load is on average 453 ± 16 pN,

which is a factor 16 higher than in the measure-

ment shown in 4a. The friction force remained at

a high and almost constant level until the tip lost

contact at FN = �16 nN. In these ‘‘high-friction’’

measurements, the typical increase in friction be-

tween loads of 0 and 25 nN was as low as 0.05–

0.4%. For other substrates, FFM measurements

Fig. 3. Lateral force images in the forward x-direction (a–c) and force loops (d–f) for different normal loads. Graphs (g–i) show the

typical waveform obtained from the forward scan lines shown in (d–f) by averaging over three lattice spacings. (a,d,g) FN = �3.4 nN,

(b,e,h) FN = 11.6 nN, (c,f,i) FN = 42.6 nN; Image size 3 nm · 3 nm.

(a) (b)

Fig. 4. Friction force FF versus normal load curves for two different contacts. Notice that in both curves the friction force varies little,

but the average friction force in (b) is about a factor of 16 higher than in (a).


usually show a substantial load dependence,

which, for modest loads, can be attributed to the

elastic variation in the contact area with the load

(e.g. [34]). Load-independent friction has also been

observed in FFM experiments on thermally oxi-

dized MoS2, and it was proposed that MoO3 nano-

crystals, that grew during the oxidation process on

the MoS2 surface [35], acted as a spacer between

the tip and the sample, such that the contact area

remained unchanged upon loading. In the present

case, the contact area would be completely deter-

mined by the flake size, which would be indepen-

dent of the loading force. Hence, the friction

would only increase slightly with normal load as

the result of the increase in contact pressure.

Each friction versus load measurement on the

polycrystalline HOPG surface resulted in a curve

of one of the two types shown in Fig. 4, but with

different precise values of the average friction

force. The measured friction force curves switched

back and forth between the two types (Fig. 4a and

b) randomly in intervals ranging from days to sev-

eral weeks. Subsequent measurements that were

performed within a short period of several hours

were highly reproducible. The switching in the

average friction force could not be attributed to

changes in the ambient conditions such as the

humidity inside the FFM chamber, e.g. we did

not observe systematic changes in friction when

we varied the humidity from 9% to 42% RH dur-

ing one experiment. Also, no systematic differences

were found between the friction force on freshly

cleaved HOPG and on surfaces that had been ex-

posed to ambient conditions for several days.

The possibility of dissipationless motion was

probably first mentioned by Prandtl already in

1928 [36] who developed what is now referred to

as the Tomlinson model in order to explain

stress–strain curves of metals. However, he also

pointed out the application of the model towards

dry friction. Much later, it has been pointed out

by Tomanek et al. [37] that it is possible to obtain

frictionless sliding in with a FFM when a single-

atom tip is moving over the surface without insta-

bilities, i.e. without the familiar stick-slip motion

and this has very recently been demonstrated

experimentally by Socoliuc et al. [38]. This can oc-

cur when the tip is moving through a potential en-

ergy landscape with a corrugation amplitude that

is small with respect to the stiffness of the measure-

ment system. However, in our case, this would re-

quire a spectacularly low potential corrugation

and an unrealistically high yield strength of the

tip to maintain a single-atom contact at a normal

load of 30 nN. Here, the difference between the

high- and low-friction force loops is attributed to

the difference in commensurability between the

flake and the substrate, the high friction corre-

sponding to a fully commensurate contact and

the low friction to an incommensurate contact.

Within the context of superlubricity it is possible

for a sliding contact to remain in the frictionless

regime also at much higher loads.

The seemingly random selection of either low or

high friction states can be explained easily by the

slow drift of the FFM or the irreproducibility of

the mounting procedure of the HOPG sample

holder after cleaving. This results in a change of

the measurement location from one grain of the

ZYH-quality polycrystalline HOPG substrate to

the next, differently oriented grain. We will return

to this point in Section 3.5.

3.3. Friction versus sample rotation

In order to obtain further evidence for our

interpretation, we rotated the graphite sample in

small steps with respect to the tip, using the U-

motor of our FFM. Because the U-motor does

not rotate perfectly concentrically around the tip,

the tip did not stay at the same location on the

sample during rotation. Therefore, we used the

single crystalline HOPG sample (ZYA-grade) to

make sure that the lattice orientation of the sample

would not change because the tip would land on a

different grain after a few rotational steps. For

each orientation, we performed a complete friction

force spectroscopy measurement for loading forces

between +25 nN and pull-off (�22 nN). We re-

corded the lateral forces in the X- and the Y-direc-

tion of the sensor and calculated the average

friction force in the sliding direction of the tip

according to Eqs. (1) and (2).

Fig. 5 shows lateral force maps and force loops

measured in the X-direction for different rotational

orientations. Note that the X- and x-direction are


not aligned here, because the scan piezo rotates to-

gether with the sample. A typical force loop is

shown in Fig. 5d, which was measured at a normal

force of 18 nN. The lateral force in Fig. 5d displays

clearly resolved atomic-scale stick-slip sliding and

the average friction force parallel to the sliding

direction is 203.3 ± 20 pN. Fig. 5b,e and c,f show

FFM measurement measured with the graphite

substrate rotated +12� and �22� with respect to

5a,d around an axis normal to the surface, and

parallel to the tip. The rotation by 12� has caused

the average friction force to reduce by more than

one order of magnitude, to 15 ± 15 pN. Rotating

22� away from the first measurement in the oppo-

site direction also has caused a reduction to

8þ16�8 pN, which is equal to zero friction within

the detection limit of our instrument. This varia-

tion of the friction force with angle U was com-

pletely reversible. Notice that the ultra-low

lateral forces in Fig. 5e and f still exhibit regular

variations with the periodicity of the graphite

substrate.

Fig. 6 displays the average friction forces mea-

sured over a 100� range of substrate rotation an-

gles. We recognize two narrow angular regions

with high friction, separated by a wide angular

interval with nearly zero friction. The distance be-

tween the two friction peaks is 61 ± 2�, which cor-

responds well with the 60� symmetry of individual

atomic layers in the graphite lattice. This result

corresponds precisely with the expectation within

the scenario of superlubricity. After every 60�

Fig. 5. Lateral force images (forward direction) and friction loops measured in the X-direction at 60� (a,d), 72� (b,e) and 38� (c,f)

rotation angle U. Normal force (a,d,c,f) FN = 18 nN; (b,e) FN = 30.1 nN. Grey scale (a) 590 pN, (b) 270 pN, (c) 265 pN. Image size

3 nm · 3 nm.

Fig. 6. Average friction force versus rotation angle U of the

graphite sample around an axis normal to the sample surface.

Two narrow peaks of high friction are observed at 0� and 61�,

respectively. Between these peaks a wide angular range with

ultra-low friction, close the detection limit of the instrument, is

found. The first peak has a maximum friction force of 306 ±

40 pN, and the second peak has a maximum of 203 ± 20 pN.

The curve through the data points shows results from a

Tomlinson model for a symmetric 96-atom graphite flake

sliding over the graphite surface (for details about the calcu-

lation see [39]).


rotation, the lattices of the substrate and the

graphite flake align and the friction is high. For

intermediate angles, the lattices are incommensu-

rate and the friction force is close to zero.

The maximum friction forces of the two peaks

were found to differ by 103 pN. This possibly re-

flects the fact that due the AB stacking, graphite

does not really possess a 60� symmetry but rather

a 120� symmetry, which should have an influence

in case the flake is more than one layer thick.

Unfortunately, we could not measure a third peak

in the present experiment, so that we have not been

able to test this hypothesis experimentally.

We can use the peak width in Fig. 6 to estimate

the flake diameter. As an illustration, a single-

atom tip should show high friction for all orienta-

tions, while an infinitely large contact would be

completely superlubric, except for infinitely nar-

row angular ranges around perfect registry, if we

assume that no energy can be dissipated via elastic

deformations within the contact. For finite-size

contacts, the cancellation of lateral forces, which

causes superlubricity, can be considered complete

when the mismatch between the two lattices adds

up to one lattice spacing over the diameter of the

contact. The mismatch condition provides us with

the estimate that tan(DU) = 1/D, where DU is the

full width at half maximum of the friction peak,

and D is the flake diameter, expressed in lattice

spacings. From the widths of the two peaks in

Fig. 6, of 5.4 ± 1.0� for the first peak and 6.5 ±

0.8� for the second, we estimate that the flake

diameter is between 7 and 12 lattice spacings.

The solid curve in Fig. 6 is the result obtained from

a modified Tomlinson model calculation in which

we moved various rigid graphite flakes, connected

to the Tribolever springs, in a rigid hexagonal po-

tential, reflecting the periodicity of the graphite

surface. More details on this calculation are pre-

sented in a recent publication by Verhoeven et al.

[39]. Shown here is the calculation for a symmetric

96-atom flake (diameter of 11 atomic spacings).

It provides an excellent fit to the experimental

friction data.

We have to mention here that reproducible

measurements, such as those in Fig. 6, in which

the same relative orientations always led to the

same friction loops, were rare, the fixed-flake situ-

ation occurring as the exception, rather than the

rule. More often, results were obtained of the type

described in the next section.

3.4. A ‘‘loose’ ’ flake

Fig. 7 shows two lateral force maps, measured

in the X-direction, before (a) and after (b) a delib-

erate, modest misalignment by less than 2� of an

initially aligned contact. While the friction force

in Fig. 7a is as high as 550 ± 21 pN (see also Fig.

7c), the friction force in the upper part of Fig. 7b

is reduced to 27 ± 16 pN (see also Fig. 7d). In

the course of a few scan lines, the friction force

gradually restored back to about 431 ± 17 pN

(Fig. 7e) and at the last scanline of Fig. 7b the fric-

tion was as high as in Fig. 7a. We interpret these

events as the effect of the torque exerted by the sur-

face on a nearly aligned flake, which was attached

to the tungsten tip sufficiently loosely to rotate

back into registry. During the restoration of the

high friction force the lateral force exhibited irreg-

ular sharp peaks, which might have been caused by

the dynamic process of reorientation of the flake.

3.5. Large-scale images on polycrystalline graphite

The effect of a change in commensurability be-

tween a flake and the surface was also observed

on the polycrystalline graphite sample. In Section

3.2 we already ascribed the switching from low fric-

tion to high friction and vice versa to the different

orientations of neighboring grains on the polycrys-

talline substrate. Fig. 8a is a large-scale topo-

graphic image of the polycrystalline grade ZYH

sample. The image shows a grain boundary that

runs across the surface. The height and lateral

dimensions of the boundary are similar to those

for grain boundaries on HOPG that have been ob-

served in STM experiments [40]. Fig. 8c shows the

lateral force image in the forward direction of the

same area. The grain in the upper right corner of

the image exhibits a significantly lower friction

force than the grain in the lower left corner. This

can be also seen from the friction loop shown in

8d, measured in the x-direction, where the friction

force on the left grain was found to be 319 ±

30 pN and on the right grain 222 ± 29 pN. Also


Fig. 8. Topography image (a) and lateral force map in the forward x-direction (c), showing a grain boundary running across the

polycrystalline HOPG surface. Graph (b) shows a cross section along the line indicated by the markers in (a). Graph (d) shows a force

loop along the line indicated by the markers in (c); Normal force FN = 5.1 nN. Image size 500 nm · 500 nm.

Fig. 7. Lateral force images (a,b) and friction force loops (c–e) before and after a modest rotation DU of less than 2� of an initially

aligned contact. The three pairs of markers at the sides of the images indicate the positions where the three force loops were taken.

Normal force (a) FN = 23 nN; (b) FN = �0.9 nN; Image size 3 nm · 3 nm.


from atomic-scale measurements (3 nm · 3 nm) we

found a change in the friction force in the sliding

direction from 326 ± 33 pN on the left grain to

221 ± 18 pN on the right grain. The height line

(8b) taken from the topographic image shows also

a change in the slope by 0.7� between the two

grains. Ruan et al. [41] have proposed a ‘‘ratchet

mechanism’’, in which the local friction coefficient

in microscale measurements should scale with the

slope h of the sample. Therefore, it might be possi-

ble that the change in friction between the two

grains was slope induced. However, the change in

the friction coefficient, expected due to the change

in slope, is only Dl = 0.05% and cannot explain

the observed large change in the friction. Again

we conclude that the change in the friction from

one grain to another is the effect of a change in com-

mensurability between a flake and the substrate.

3.6. TEM analysis of the tip

We have used high-resolution transmission elec-

tron microscopy (TEM) to image the tungsten tip

after our friction experiments. For this purpose,

we glued the central part of the force sensor with

the tip onto a holder that fitted inside the TEM

holder. The TEM analysis showed that the tung-

sten tip had a radius of about 80 nm and was cov-

ered with a smooth amorphous layer of 7 nm thick

tungsten oxide. Unfortunately, thorough TEM

inspection of the tip was not possible due to rapid

removal of the amorphous layer by the electron

beam. Before the tip was modified by the electron

beam, which occurred within minutes, it was not

possible to properly correct for astigmatism. This

is seen in Fig. 9, which displays the tip after

approximately 5 min of exposure to the electron

beam. The amorphous layer has been almost com-

pletely removed by the electron irradiation. In the

image, we find several locations that look like lay-

ered structures similar to graphite sheets (indicated

by circles). At a first glance, one might be tempted

to identify these as graphite flakes. However, at

that point of the TEM observation the tip was al-

ready strongly modified by the electron beam and,

in addition, it is possible that these features merely

appeared like layered structures due to astigma-

tism. Therefore, the present TEM analysis cannot

provide definite evidence for the presence or the

absence of either a multilayer flake or a single layer

of graphite.

3.7. Friction anisotropy

The measurements of the friction force versus

sample rotation, presented in Section 3.3, were

taken for a single sliding direction with respect to

the substrate. Miura et al. found for the sliding of

a 1 mm · 1 mm large MoS2 flake on a MoS2 sur-

face [42], as well as for a 1 mm · 1 mm large graph-

ite flake on HOPG [43], a variation in the friction

force between 0 and 2 nN as a function of sliding

Fig. 9. High-resolution TEM micrographs of the tungsten tip about 5 min after the tip was first exposed to the electron beam. The

circles show areas in which layered structures were observed that are consistent with multilayer graphite flakes. A zoom-in into one of

these regions is shown in the inset.


direction. Before we discuss friction anisotropy in

our experiment, we first clarify the terminology.

Often friction anisotropy refers to the variation in

friction as a function of the sliding direction [44],

whereas other authors use this term also for

changes in friction as a function of relative orienta-

tion, i.e. commensurability [45] (superlubricity), or

for both phenomena [42]. To avoid misunderstand-

ings, we will use the term friction anisotropy

strictly for the variation of friction with respect to

the sliding direction. In the measurements of Figs.

5–7, where we recorded the friction force as a func-

tion of the rotation angle U of the sample, the slid-

ing direction did not change with respect to the

substrate lattice because the scan piezo rotated to-

gether with the sample. This is why we can directly

rule out anisotropy as a cause for the observed

peaks. However, if a graphite/graphite contact does

exhibit high friction anisotropy, the dependence of

the friction force on the degree of incommensura-

bility might change dramatically with sliding direc-

tion. In order to investigate this, we measured the

friction force for a number of sample rotation an-

gles U as a function of the sliding direction f. We

invariably observed that the friction force FF var-

ied between high and low simultaneously, for all

sliding directions f. The friction anisotropy was

very modest (at most 25%) and did not interfere

with the commensurability effect. As an example,

Fig. 10 shows the friction force as a function of

sliding angle for a commensurate contact, with

high friction. Whereas the friction forces in the X-

and Y-directions of the sensor strongly varied as

a function of the sliding angle, the total friction

force in the sliding direction remained nearly con-

stant. In our modified Tomlinson model [39], for

a graphite flake sliding over a graphite surface, a

modest anisotropy was found for all sample rota-

tion angles U, as illustrated for the aligned contact

in Fig. 10.

4. Discussion

All measurements presented in this article were

consistent with friction between a graphite flake

and the graphite substrate. In fact, the notion that

graphite flakes adhere frequently to the tip of scan-

ning probe microscopes has originated already

many years ago in order to explain ‘‘unusual’’ con-

trast in scanning tunneling microscopy images (see

e.g. [46,47]). Although we have not been able to

convincingly observe the presence of a graphite

flake with TEM, our friction measurements pro-

vide firm evidence that a flake caused the observed

superlubricity.

A few earlier experiments provided indications

of superlubricity. Hirano et al. [45] found a modest

reduction in friction between two mica sheets from

8 · 10�4 N to 2 · 10�4 N, caused by rotating the

two sheets with respect to each other. In a

modified scanning tunnelling microscope (STM)

experiment [48] the same authors claimed the

observation of superlubricity between a tungsten

tip and a Si(001) sample. However, the evidence

provided in their paper has been rather incomplete.

No normal force was measured or controlled, and

the tip was actually only in tunnelling range from

the substrate. The friction force was measured only

for two relative orientations. No typical friction

loops were shown. Ko et al. [49] have shown that

variations in the friction coefficient caused by the

rotation of two (100) metal surfaces with respect

to each other do not necessarily have to be the re-

sult of a change in lattice mismatch.

Fig. 10. Friction as function of the sliding angle f for a

commensurate contact (U = 0).The data points show the friction

FF measured in the sliding direction. The dotted line shows

calculated friction forces, obtained using a Tomlinson model for

a symmetric, 96-atom graphite flake (for details about the

calculation see [39]).


Beyond showing the existence of superlubricity

between graphite surfaces on the nanometer scale,

which might explain the ultra-low friction coeffi-

cients as well as the large variations found in

previous FFM experiments on graphite, our obser-

vation might also have important implications for

understanding the macroscopic lubrication prop-

erties of solid lamellar lubricants.

Indications that also in a macroscopic sliding

contact of lamellar solids rotated flakes are cre-

ated, come from transmission electron microscopy

(TEM) observations by Martin et al. [50] on MoS2.

In contrast to our single-contact FFM experiment,

macroscopic-scale friction involves multiple micro-

contacts with different sizes and orientations.

Based on our observations, one may speculate that

in the case of macroscopic lubrication by graphite

a large fraction of the graphite–graphite contacts

will be in the ‘‘superlubric state’’, while only a

small fraction will be in registry. This should lead

to a tremendous reduction in the average friction

force, experienced in the ensemble of micro-con-

tacts, and thus might explain the excellent lubrica-

tion by graphite and similar, layered materials,

such as MoS2 and Ti3SiC2. It was shown by Liu

et al. [51] that under sliding conditions, a graphi-

tized tribolayer is formed on top of diamond-like

carbon (DLC) coatings, which goes hand in hand

with a decrease of the friction coefficient after

run-in. Therefore, also the excellent lubrication

properties of DLC films might be caused by super-

lubric graphitic contacts.

We suppose that for sufficiently large contacts

superlubricity might break down, as the two lat-

tices are not perfectly rigid, and a network of misfit

dislocations should form between the two. There-

fore, to give an estimate to what percentage super-

lubricity contributes to the good lubrication

properties of solid lubricants, more experiments

are needed to find out at which contact size and

normal load superlubricity breaks down and to

find out, how many of the ‘‘loose’’ flakes, which

might form the majority species in a real tribolog-

ical contact, twist back into registry. A first indica-

tion that superlubricity breaks down at higher

contact pressures might be found already in Fig.

4a, where we observed a reversible slight increase

in the friction above 40 nN normal load.

Other graphitic systems have been found that

show remarkable tribological properties, which

might also be attributed to the phenomenon of

superlubricity. TEM observations [52] suggest that

nested carbon nanotubes (CNT) possess very low

inter-wall friction. In most cases, the inner and

outer tubes in a multiwall CNT form an incom-

mensurate graphitic system, similar to a rotated

flake that slides over a graphite surface. Similarly,

Falvo et al. have found that carbon nanotubes that

are pushed sideways over HOPG when they are out

of registry, whereas they can only roll when they

are in registry with the underlying surface [53,54].

5. Conclusions

By measuring atomic-scale friction as a function

of the rotational angle between a tungsten tip and

a graphite surface we have shown that the origin of

the ultra-low friction of graphite in friction force

experiments lies in the incommensurability be-

tween a flake that is attached to the tip and the

graphite surface. The observation of two narrow

peaks in the friction force that are separated by

60� provided clear experimental evidence of super-

lubricity. The width of the two peaks allowed us to

estimate the contact diameter to be 7–12 lattice

spacings. Our conclusions are further substanti-

ated by the calculations presented in [39].

The occurrence of superlubricity in layered

materials might explain why these materials are

good solid lubricants.

Acknowledgments

This work is part of the research program of the

‘‘Stichting voor Fundamenteel Onderzoek der

Materie (FOM)’’ and was made possible by finan-

cial support from the ‘‘Nederlandse Organisatie

voor Wetenschappelijk Onderzoek (NWO)’’.

Ref erences

[1] J. Spreadborough, Wear 5 (1962) 18.

[2] W. Bragg, An Introduction to Crystal Analysis, G. Bell

and Sons Ltd., London, 1928, p. 64.


[3] G.I. Finch, Proc. Phys. Soc. A 63 (1950) 785.

[4] R.H. Savage, J. Appl. Phys. 19 (1948) 1.

[5] F.P. Bowden, F.R.S. Young, J.E. Young, Proc. Royal.

Soc. A. 208 (1951) 444.

[6] R.H. Savage, D.L. Schaefer, J. Appl. Phys. 27 (1956)

136.

[7] M. El Mansori, M. Schmitt, D. Paulmier, Surf. Coat.

Technol. 108–109 (1998) 479.

[8] F.P. Bowden, D. Tabor, The Friction and Lubrication of

Solids, vol. 2, Clarendon Press, Oxford, 1964.

[9] C.M. Mate, G.M. McClelland, R. Erlandsson, S. Chiang,

Phys. Rev. Lett. 59 (1987) 1942.

[10] J.-A. Ruan, B. Bhushan, J. Mater. Res. 8 (1993) 3019.

[11] U.D. Schwarz, O. Zworner, P. Koster, R. Wiesendanger,

Phys. Rev. B. 56 (1997) 6987.

[12] E. Liu, B. Blanpain, J.-P. Celis, J.R. Roos, J. Appl. Phys.

84 (1998) 4859.

[13] R. Buzio, E. Gnecco, C. Boragno, U. Valbusa, Carbon 40

(2002) 883.

[14] S. Fujisawa, Y. Sugawara, S. Ito, S. Mishima, T. Okada,

S. Morita, Nanotechnology 4 (1993) 138.

[15] G.A. Tomlinson, Phil. Mag. 7 (1929) 905.

[16] H. Holscher, U.D. Schwarz, O. Zworner, R. Wiesendan-

ger, Phys. Rev. B. 57 (1998) 2477.

[17] N. Sasaki, K. Kobayashi, M. Tsukada, Phys. Rev. B. 54

(1996) 2138.

[18] N. Sasaki, M. Tsukada, S. Fujisawa, Y. Sugawara, S.

Morita, K. Kobayashi, Phys. Rev. B. 57 (1998) 3785.

[19] M. Dienwiebel, G.S. Verhoeven, N. Pradeep, J.W.M.

Frenken, J.A. Heimberg, H.W. Zandbergen, Phys. Rev.

Lett. 92 (2004) 126101.

[20] K. Shinjo, M. Hirano, Surf. Sci. 283 (1993) 473.

[21] M. Hirano, K. Shinjo, Phys. Rev. B. 41 (1990) 11837.

[22] J.B. Pendry, J. Phys. Cond. Mat. 9 (1997) 10301.

[23] M. Dienwiebel, J.A. Heimberg, T. Zijlstra, E. van der

Drift, E. de Kuyper, L. Crama, D.-J. Spaanderman, D.G.

van Loon, J.W. M. Frenken, Rev. Sci. Instrum., in press.

[24] T. Zijlstra, J.A. Heimberg, E. van der Drift, D. Glastra

van Loon, M. Dienwiebel, L.E.M. de Groot, J.W.M.

Frenken, Sens. Actuators A 84 (2000) 18.

[25] J.P. Cleveland, S. Manne, D. Bocek, P.K. Hansma, Rev.

Sci. Instrum. 64 (1993) 403.

[26] Surface Preparation Laboratory, Penningweg 69 F, 1507

DE Zaandam, The Netherlands.

[27] E. Meyer, R. Luthi, L. Howald, M. Bammerlin, M.

Guggisberg, H.-J. Guntherodt, J. Vac. Sci. Technol. B.

14 (1996) 1285.

[28] S. Fujisawa, S. Kishi, Y. Sugawara, S. Morita, Phys. Rev.

B. 51 (1995) 7849.

[29] M.A. Lantz, S.J. O�Shea, M.E. Welland, K.L. Johnson,

Phys. Rev. B. 55 (1997) 10776.

[30] R.W. Carpick, D.F. Ogletree, M. Salmeron, Appl. Phys.

Lett. 70 (1997) 1548.

[31] E. Gnecco, R. Bennewitz, T. Gyalog, C. Loppacher, M.

Bammerlin, E. Meyer, H.-J. Guntherodt, Phys. Rev. Lett.

84 (2000) 1172.

[32] Y. Sang, M. Dube, M. Grant, Phys. Rev. Lett. 87 (2001)

174301.

[33] O.K. Dudko, A.E. Filippov, J. Klafter, M. Urbakh, Chem.

Phys. Lett. 352 (2002) 499.

[34] R.W. Carpick, N. Agraıt, D.F. Ogletree, M. Salmeron, J.

Vac. Sci. Technol. B. 14 (1996) 1289.

[35] J. Wang, K.C. Rose, C.M. Lieber, J. Phys. Chem. B 103

(1999) 8405.

[36] L. Prandtl, ZS. Angew. Math. Mech. 8 (1928) 85.

[37] D. Tomanek, W. Zhong, H. Thomas, Europhys. Lett. 15

(1991) 887.

[38] A. Socoliuc, R. Bennewitz, E. Gnecco, E. Meyer, Phys.

Rev. Lett. 92 (2004) 134301.

[39] G.S. Verhoeven, M. Dienwiebel, J.W.M. Frenken, Phys.

Rev. B 70 (2004) 165418.

[40] P. Simonis, C. Goffaux, P.A. Thiry, L.P. Biro, Ph. Lambin,

V. Meunier, Surf. Sci. 511 (2002) 319.

[41] J.-A. Ruan, B. Bhushan, J. Appl. Phys. 76 (1994) 5022.

[42] K. Miura, S. Kamiya, Europhys. Lett. 58 (2002) 610.

[43] K. Miura, N. Sasaki, S. Kamiya, Phys. Rev. B. 69 (2004)

075420.

[44] H. Bluhm, U.D. Schwarz, K.-P. Meyer, R. Wiesendanger,

Appl. Phys. A. 61 (1995) 525.

[45] M. Hirano, K. Shinjo, R. Kaneko, Y. Murata, Phys. Rev.

Lett. 67 (1991) 2642.

[46] J.B. Pethica, Phys. Rev. Lett. 59 (1986) 1942.

[47] M. Salmeron, in: K. Miyoshi, Y.W. Chung (Eds.), Surface

Diagnostics in Tribology, World Scientific, Singapore,

1993, p. 75.

[48] M. Hirano, K. Shinjo, R. Kaneko, Y. Murata, Phys. Rev.

Lett. 78 (1997) 1448.

[49] J.S. Ko, A.J. Gellman, Langmuir 16 (2000) 8343.

[50] J.M. Martin, C. Donnet, T. LeMogne, T. Epicier, Phys.

Rev. B. 48 (1993) 10583.

[51] Y. Liu, A. Erdemir, E.I. Meletis, Surf. Coat. Technol. 86–

87 (1996) 564.

[52] J. Cumings, A. Zettl, Science 289 (2000) 602.

[53] M.R. Falvo, R.M. Taylor II, A. Helser, V. Chi, F.P.

Brooks Jr., S. Washburn, R. Superfine, Nature 397 (1999)

236.

[54] M.R. Falvo, J. Steele, R.M. Taylor II, R. Superfine, Phys.

Rev. B 62 (2000) R10665.


Model experiments of superlubricity of graphite

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