Quartz-crystal microbalance studies of the slippage of solid and liquid krypton monolayers
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PHYSICAL REVIEW B 72, 235414 共2005兲
Quartz-crystal microbalance studies of the slippage of solid and liquid krypton monolayers
on metal(111) and C60 surfaces
T. Coffey* and J. Krim
Physics Department, Box 8202, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
共Received 11 August 2005; revised manuscript received 25 October 2005; published 12 December 2005兲
We report a quartz-crystal microbalance 共QCM兲 study of the nanotribology of solid and liquid krypton
monolayers adsorbed on Cu共111兲, Ag共111兲, Ni共111兲, and C60 substrates at 77.4 K. We document the liquid-
solid phase transition and compare the slip times of the krypton for the various substrates. The slip times for
the solid krypton monolayers are longer than the slip times for liquid krypton monolayers on metal substrates
and monolayer C60 films, as observed previously for krypton/Au共111兲. However, for bilayer C60 films, the jump
in slip time at the liquid-solid phase transition is absent. We discuss the data within the context of recent
molecular dynamics simulations and suggest several potential explanations for the experimental observations.
DOI: 10.1103/PhysRevB.72.235414 PACS number共s兲: 68.35.Af, 68.43.Pq, 68.60.⫺p
I. INTRODUCTION reproduced the 1991 experimental results of Krim et al.
Their simulations included only one source of friction:
As technology tends towards the nanometer scale, the phononic friction. Given the close match between the simu-
importance of understanding the fundamental origins of lations and the QCM experiments, the combined 1991 and
friction has increased. The quest to understand friction has 1994 publications constituted the first ever demonstration of
led to experiments conducted in extremely simple and the existence of phononic friction, which had been predicted
well-characterized systems at the nanoscale, such as decades earlier in 1929. In a later publication, Robbins and
studies of monolayer films sliding on substrates. These Krim8 hypothesized that any electronic contribution to fric-
systems are characterized by the viscous friction law tion for this system should be relatively constant with cov-
F = 共m / 兲v ; F / A = S = v, where m, , and v are the mass, slip erage, and would only serve to decrease the height of the
time, and velocity of the adsorbates, and A, S, and are the jump in slippage due to the phase transition. The central
area, shear stress, and friction coefficient for the systems. results of their study are presented in Fig. 1.
Viscous friction is believed to arise from two sources, Is it possible, however, that the electronic friction does
phononic p and electronic e, where = p + e. At the change slightly for liquid vs solid phases of krypton. Elec-
atomic scale, phononic friction, or the energy dissipation tronic friction has been related to the surface resistivity,9 and
caused by the excitation of atomic lattice vibrations it is well known that the resistivity of a system is dependent
共phonons兲, is believed to dominate. Electronic friction, or on lattice defects. Resistivity, and hence electronic friction,
energy dissipation caused by the excitation of electron-hole
pairs, has also been suggested as a possible source of friction
if one of the materials is a conductor. To date, most of the
modeling efforts have focused on phononic friction.
The quartz-crystal microbalance 共QCM兲 technique is an
extremely sensitive probe of viscous friction, capable of de-
tecting submonolayer films and measuring subnanosecond
slip times of adsorbate films on surfaces.1–3 In 1991, Krim,
Solina, and Chiarello utilized QCM measurements of the
friction of krypton monolayers sliding on Au共111兲 at
77.4 K.4 Krypton is a liquid at 77.4 K at low film coverage.
As the monolayer coverage increases, krypton undergoes a
two dimensional liquid-solid phase transition.5,6 This phase
change can be seen in the QCM frequency, dissipation, and
slip time data. Krim and colleagues saw the phase change in
the QCM slip time data, observing a distinct increase in the FIG. 1. The filled triangles represent slip time data acquired by
slip time for solid vs liquid monolayers of Kr/ Au共111兲. In Krim et al. for Kr/ Au共111兲 共Ref. 4兲. The solid line shows the nu-
other words, the surface was “slippery when dry.” merical model of Cieplak et al., which fit the experimental data
In 1994, Cieplak, Smith, and Robbins7 employed standard using only phononic friction 共Ref. 7兲. The dashed lines represent
molecular dynamics algorithms to model mobile krypton at- their numerical model with electronic friction included, and equal to
oms on a perfectly rigid gold substrate. In their simulations, 1 / 3, 1 / 2, and 9 / 10 of the friction at high coverage due to electronic
the frictional force comes from the vibrations 共phonons兲 of friction, from bottom to top. Note that electronic friction serves to
the krypton adsorbates as they slide atop the rigid gold sub- decrease the jump in slip time attributable to the phase transition
strate. Scaling the surface corrugation to fit the data, they 共Ref. 8兲.
1098-0121/2005/72共23兲/235414共5兲/$23.00 235414-1 ©2005 The American Physical SocietyT. COFFEY AND J. KRIM PHYSICAL REVIEW B 72, 235414 共2005兲
occurs when conduction electrons scatter off of the lattice.
The more imperfections and defects present, the higher the
resistivity. A liquid phase has more imperfections in a lattice
than a solid phase; it therefore follows that a two-
dimensional liquid phase might have a higher resistivity, and
hence higher electronic friction and lower slip times, than a
two-dimensional solid phase.
Inspired by the fact that the jump in slip time may be an
indication of the phononic and electronic friction levels, we
report here a series of QCM experiments for Kr sliding on
Ag共111兲, Cu共111兲, Ni共111兲, and C60 substrates at 77.4 K.
Specifically, we examine the change in slippage before and
after the liquid-solid phase transition. It is our hope that these
experiments will be modeled and will further elucidate the
origins of friction for these model systems.
FIG. 2. Frequency and inverse quality factor shifts for krypton
adsorbed on Cu共111兲 共squares兲, Ni共111兲 共circles兲, and Ag共111兲
II. EXPERIMENTAL PROCEDURE 共triangles兲. Note the frequency shift for Kr/ Cu共111兲 is reduced due
to the large slip⬘page of the krypton film.
The microbalance crystals for these studies were
overtone-polished 8 MHz AT-cut quartz that had quality fac- 共␦ f兲 are proportional to the mass per unit area of the film that
tors near 105. For the Cu共111兲 sample, the copper was depos-
tracks the QCM motion.15 Film slippage results in some frac-
ited atop a QCM with a 20 nm titanium precoat, to prevent
tion of the mass of the film decoupling from the oscillation
roughening of the copper electrode.10 The base pressure of
of the substrate, and a concomitant reduction in the fre-
the vacuum system ranged from 8 ⫻ 10−11 to 5 ⫻ 10−10 Torr.
quency shift.16 The relation between the frequency shift of a
Thermal evaporation was then used to deposit 60 nm of
film if it were not slipping 共␦ f film兲 and the experimentally
99.999% pure Cu or 80 nm of 99.999% pure Ag atop the
observed frequency shift 共␦ f兲 are as follows:
titanium precoat or blank QCM, respectively, producing a
mosaic structure with a 共111兲 fiber texture.11 C60 substrates ␦ f film 2m f c f ␦ f film
were prepared by thermally evaporating C60 monolayers atop =− , ␦f = . 共1兲
f qt q 1 + 共兲2
an 80 nm thick Ag共111兲 electrode on a blank QCM. The
QCM frequency shift was monitored during the C60 deposi- Here, m f and c f are the atomic mass in grams and coverage
tion; one monolayer of C60 corresponds to a frequency shift in atoms per cm2 of the adsorbed film, and q 共2.65 g / cm3兲
of 21+ / −1 Hz, or a mass uptake of 73+ / −4 ng/ cm2. The and tq 共0.021 cm for f = 8 MHz兲 are the density and thickness
C60 was deposited immediately after the Ag共111兲 deposition. of the QCM. The change in amplitude 共A兲 is proportional to
The 80 nm Ni共111兲 films were deposited using an electron the change in quality factor 共Q兲 : ␦共Q−1兲 = c␦共A−1兲. To deter-
beam evaporator in UHV onto a blank QCM. The deposition mine the proportionality constant c, the samples are cali-
rate was several angstroms per second. All samples were brated with helium gas adsorption after completion of the
immediately transferred in situ with a magnetic transfer rod krypton uptake measurements.1 Frequency and quality factor
to the adsorption cell, and then chilled to 77.4 K by submer- shifts can also be caused by gas pressure, tensile stress, and
sion in a liquid nitrogen bath. The cell is a metal and ceramic temperature. The latter effects were negligible in this experi-
socket, and the socket is electrically connected to an external ment, and the gas pressure corrections were performed ac-
Pierce oscillator circuit via an electrical feed through. The cording to the procedure described by Bruschi and Mistura.3
Pierce circuit is powered with a dc voltage supply of The expression derived by Krim and Widom in 1986 共Ref. 2兲
10– 15 V, which results in QCM oscillation amplitudes of was used to calculate characteristic slip times 共兲:
冉冊
approximately 60– 80 mV. We estimate our oscillation am-
plitudes to therefore be approximately 10 nm.12 Bruschi and 1
␦ = 4共␦ f兲. 共2兲
colleagues13 saw a threshold oscillation amplitude for slip- Q
page. Below this threshold of approximately 0.3 nm, the
films would not slip. Above this threshold, there was little
dependence of slippage on oscillation amplitude, consistent III. RESULTS
with a prior study of the amplitude dependence of the slip
time of Kr/ Au monolayers reported by Mak and Krim.4 We Representative frequency shift and quality factor data for
have exceeded this threshold for all measurements reported the krypton uptake on Cu共111兲, Ag共111兲, Ni共111兲, and C60
here and our observations are entirely consistent with those are shown in Figs. 2–4. At 77.4 K, krypton first forms a
reported by Bruschi et al. liquid monolayer with a coverage of 0.066 atoms/ Å2
After the samples had come to thermal equilibrium, they 共⬇26.6 Hz for f o = 8 MHz crystals兲. As the coverage in-
were exposed to research grade krypton gas,14 and frequency creases, the krypton monolayer becomes more tightly packed
and amplitude shifts were monitored as a function of increas- and changes phase to a solid, with a monolayer coverage of
ing pressure. The experimentally observed frequency shifts 0.078 atoms/ Å2 共⬇31.4 Hz兲.4–7 There are slight variations
235414-2QUARTZ-CRYSTAL MICROBALANCE STUDIES OF THE… PHYSICAL REVIEW B 72, 235414 共2005兲
FIG. 3. Frequency and inverse quality factor shifts for krypton
adsorbed on monolayer C60 for sample A 共inverted triangles兲 and
sample B 共diamonds兲. FIG. 5. QCM slip time data for krypton sliding on Cu共111兲
共squares兲, Ag共111兲 共triangles兲, and Ni共111兲 共circles兲. The coverage
in the frequency shift for a monolayer of krypton owing to 共corrected for slip effects兲 is obtained by solving the right expres-
slightly different surface textures for the different surfaces sion in Eq. 共1兲 for 共␦ f film兲 and then substituting the value into the
that result in small variations in surface area.17 A second left expression in Eq. 共1兲.
layer is observed to condense, as indicated by a second
step in those isotherms where data were recorded at suffi- Cu共111兲, Ag共111兲, Ni共111兲, and the C60 monolayer surfaces,
ciently high pressure. The stepwise nature of the isotherms attributable to the liquid-solid phase transition. For the C60
indicates that the substrates are highly uniform, with atomi- bilayer surface, there is no jump in slip time at monolayer
cally flat regions 共30 nm兲2 or more in size.5,18 In addition, coverage. Numerous Kr isotherms were recorded on mono-
post data acquisition measurements of the rms roughness of layer and bilayer C60 isotherms:19 In no case was the solid-
C60 samples were performed using an in-air STM. The aver- liquid transition observed for adsorption on the bilayer. In
age rms roughness was 4.5 nm for an image size of contrast, the transition was always present for Kr monolayers
104 nm⫻ 104 nm, which represents very little out of plane condensing on a monolayer. Note two representative samples
variation in height for large lateral extents. We expect that for Kr sliding on monolayer and bilayer C60 are shown in the
this value places an upper limit on the roughness, since the figures. There are variations in dissipation and hence slip
characterization took place in air after the UHV data had time between these samples, which we attribute to variations
been acquired. Note that the frequency shift data for the in the in-plane ordering of the C60 layers. Prior reports have
Cu共111兲 sample under-represent the actual mass of the ad- indicated a high sensitivity of slip times to the in-plane or-
sorbed film on account of film slippage effects 关see Eq. 共1兲兴. dering of the substrate, for example, Krim and colleagues
The slip times for krypton on Cu共111兲, Ag共111兲, Ni共111兲, measured the slip time for monolayer Kr on 共111兲 gold sur-
and C60 are shown in Figs. 5–7, as a function of coverage as faces 共depicted as triangles in Fig. 1兲 to be 2 – 10 ns spanning
estimated via Eq. 共1兲. At frequency shifts near one mono- the liquid solid transition,4 Mak and Krim measured 2 – 5 ns
layer 共near 30 Hz兲 there are “jumps” in the slip time for for 共111兲 films prepared in slightly higher vacuum
conditions20 and Bruschi and colleagues reported the slip
FIG. 4. Frequency and inverse quality factor shifts for krypton
adsorbed on bilayer C60 for sample A 共inverted triangles兲 and FIG. 6. QCM slip time data for krypton sliding on monolayer
sample B 共diamonds兲. C60 for sample A 共inverted triangles兲 and sample B 共diamonds兲.
235414-3T. COFFEY AND J. KRIM PHYSICAL REVIEW B 72, 235414 共2005兲
as was previously observed for krypton/Au共111兲 surfaces
共sol / liq = 5.0, see Table I兲.4 One possibility is that the elec-
tronic friction of a system is linked to the chemical reactivity
of the adsorbate-substrate system. This may explain the large
jump in slip time for Kr/ Au共111兲 as compared to the sur-
faces studied here; the electronic friction for the surfaces
studied here may be higher. As suggested by Robbins and
Muser,8 this may reduce the height of the jump in slip time
due to the liquid-solid phase transition.
The slip time for liquid and solid krypton monolayers is
slightly longer atop C60 bilayer films than C60 monolayer
films. One possible explanation may be a changing coeffi-
cient of electronic friction for a monolayer vs a bilayer C60
film. Electronic friction is present only for conductors; for
FIG. 7. QCM slip time data for krypton sliding on bilayer C60 insulators, only phononic friction is present. C60 is more in-
for sample A 共inverted triangles兲 and sample B 共diamonds兲. sulating than silver; so as the thickness of the C60 coating
increases, the substrate becomes less conducting, hence less
electronic friction and a longer slip time.
time of presumably liquid Kr monolayers on gold 共111兲 sur-
face to be 1 – 2 ns.13 In a separate study of the impact of One of the most interesting results of this study is that the
in-plane surface disorder on slip time, Mak and Krim and “jump” in slip time due to the two-dimensional liquid-solid
colleagues reported an increase of the slip time to 5 – 50 ns phase transition in krypton is present for monolayer
arising from in-plane disorder of the gold substrate.20,21 Out C60 / Ag共111兲 films but disappears for bilayer films of
of plane disorder in the form of step edges would presum- C60 / Ag共111兲. If the electronic friction is higher for the liquid
ably lower the slip time, as considered theoretically by To- phase of krypton and the reduced slip time for C60 monolay-
mossone and Sokoloff.22 The slip times for the liquid and ers vs bilayers is due to electronic friction, then the slip times
solid phases of krypton at given monolayer coverage are for liquid krypton on monolayers of C60 would be lower than
shown in Table I. the slip times for liquid krypton on C60 bilayers. If the elec-
tronic friction is much reduced for a solid phase of krypton,
then the slip times for solid krypton for C60 monolayers vs
IV. DISCUSSION bilayers would depend mostly on phononic contributions to
For the metal共111兲 surfaces, a jump in the slip time, at- friction, and might be very similar.
tributable to the liquid-solid phase transition, is observed. Krypton sliding atop Au共111兲 was modeled as a thin, elas-
However, the jump is not as large in the systems studied here tic krypton sheet atop a rigid, periodic Au共111兲 potential.7 In
the liquid phase, the krypton atoms were more mobile and
could deform to fill in the low potential sites in the Au共111兲
TABLE I. Slip times for the liquid 共liq兲, solid 共sol兲 phases of
substrate. This caused high phononic friction and short slip
krypton at given monolayer coverage 共⌰兲 and the ratio of the slip
times. In the solid phase, however, the krypton atoms were
time of liquid and solid phases for the various substrates. The su-
perscripts for the C60 substrates indicate the number of C60 mono-
more rigidly bound to each other, and thus could not as eas-
layers. The Au共111兲 data has been previously published in two in- ily deform to fill the low potential sites. Thus, the solid phase
dependent experiments; however, both experiments gave the same had lower phononic friction and longer slip times than the
ratio of solid to liquid slip times 共Ref. 4兲. liquid phase. C60 has much larger lattice spacing than
Au共111兲. It might therefore be more difficult for the liquid
liq 共ns兲 sol 共ns兲 krypton monolayer to deform and fill the low potential sites.
Substrate 共⌰ in monolayers兲 共⌰ in monolayers兲 sol liqⲐ Therefore the phononic contribution for liquid vs solid kryp-
ton monolayers may be similar, leaving only differences in
Cu共111兲 7.0 11 1.6 electronic friction to explain the jump in slippage for mono-
共0.89兲 共1.0兲 layer C60.
Ag共111兲 2.1 2.7 1.3 It is also possible that the differences in both the structure
共0.9兲 共1.0兲 and magnitude of the Kr slip time curves between monolayer
Au共111兲3 2.0; 1.0 10.0; 5.0 5.0 and bilayer C60 are attributable to variations in the in-plane
共0.85兲 共1.0兲 ordering, or perfection of the C60 layer, as noted previously
Ni共111兲 0.26 0.78 3.0 for studies of Kr sliding on disordered gold substrates.20,21
共0.8兲 共1.0兲 However, for past studies of Kr sliding on smooth gold vs
C60共1兲 / Ag共111兲 1.6 2.7 1.7 共out-of plane兲 rough silver surfaces,4 the slip times for the
共0.93兲 共1.0兲 smooth surfaces were significantly larger than for the rough
C60共2兲 / Ag共111兲 3.1 3.3 1.1 surfaces, and the slip time jumps disappeared for the rough
共0.93兲 共1.0兲 surfaces vs smooth surfaces. Therefore differences in surface
roughness alone do not seem to be sufficient to explain both
235414-4QUARTZ-CRYSTAL MICROBALANCE STUDIES OF THE… PHYSICAL REVIEW B 72, 235414 共2005兲
the higher slip times and lack of the phase transition jump for rugation is not known for all of these systems, they are ideal
the bilayer C60 surfaces vs monolayer C60 surfaces. for further study and future modeling.
V. CONCLUSIONS ACKNOWLEDGMENTS
We have observed that for metal共111兲 substrates, there is a This work has been supported in part by the NSF Grant
jump in the slip time at solid monolayer krypton coverage, No. DMR0320743, DOE Grant No. FG02-01ER45936 and
attributable to the liquid-solid phase transition. This jump is AFOSR Grant No. F49620014-0132. S.M. Winder is
also present for krypton slipping atop monolayers, but not thanked for useful discussions, technical assistance, and data
bilayers, of C60. Although the damping and atomic scale cor- collection.
12
*Currently at Department of Physics and Astronomy, Appalachian B. Borovsky, B. L. Mason, and J. Krim, J. Appl. Phys. 88, 4017
State University, CAP Bldg., 525 Rivers St., Boone, NC 28608. 共2000兲.
1
E. Watts, J. Krim, and A. Widom, Phys. Rev. B 41, 3466 共1990兲. 13
L. Bruschi, A. Carlin, and G. Mistura, Phys. Rev. Lett. 88,
2 J. Krim and A. Widom, Phys. Rev. B 38, 12184 共1986兲; A. Wi-
046105 共2002兲.
dom and J. Krim, ibid. 34, 1403 共1986兲. 14 Research grade krypton 共99.999% pure兲 was purchased from
3
L. Bruschi and G. Mistura, Phys. Rev. B 63, 235411 共2001兲.
4 J. Krim, D. H. Solina, and R. Chiarello, Phys. Rev. Lett. 66, 181 Airco Industrial Gases.
15 G. Z. Sauerbrey, Phys. Verh. 8, 113 共1957兲.
共1991兲, C. Mak and J. Krim, Phys. Rev. B 58, 5157 共1998兲. 16 M. Chester, L. C. Yang, and J. G. Stephens, Phys. Rev. Lett. 29,
5 J. Krim, J. G. Dash, and J. Suzanne, Phys. Rev. Lett. 52, 640
共1984兲. 211 共1979兲.
6 A. Thomy and X. Duval, in Adsorption at the Gas-Solid And 17 V. Panella and J. Krim, Phys. Rev. E 49, 4179 共1994兲.
18 G. Palasantzas and J. Krim, Phys. Rev. Lett. 73, 3564 共1994兲.
Liquid-Solid Interface, edited by J. Rouquerol and K. S. W. Sing
共Elsevier, Amsterdam, 1982兲. 19 T. Coffey, Ph.d. thesis, 2004.
7
M. Cieplak, E. D. Smith, and M. O. Robbins, Science 265, 1209 20
C. Mak and J. Krim, Faraday Discuss. 107, 389 共1997兲.
共1994兲. 21 Y. Braiman, H. G. E. Hentschel, F. Family, C. Mak, and J. Krim,
8 M. O. Robbins and J. Krim, Mater. Res. Bull. 23, 23 共1998兲.
Phys. Rev. E 59, R4737 共1999兲.
9 B. N. J. Persson, Phys. Rev. B 44, 3277 共1991兲.
22
M. S. Tomassone and J. B. Sokoloff, Phys. Rev. B 60, 4005
10
S. M. Lee and J. Krim, Thin Solid Films 489, 325 共2005兲.
11 K. K. Kakati and H. Wilman, J. Phys. D 6, 1307 共1973兲. 共1999兲.
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