2063-20 ICTP/FANAS Conference on trends in...
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2063-20
ICTP/FANAS Conference on trends in Nanotribology
MEYER Ernst
19 - 24 October 2009
University of BaselCondensed Matter Division Institute of Physics
Klingelbergstrasse 82, CH-4056Basel
SWITZERLAND
Atomic friction: ways to determine the elastic and viscous properties ofnano-contacts
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Atomic Friction: Ways to determine elastic and viscous properties of nano-contacts
Ernst MeyerInstitute of PhysicsUniversity of Basel, Switzerland
• Atomic-scale stick slip- loading dependence- multiple slips and estimation of damping
• Simultaneous measurement of normaland lateral contact stiffnes
• Control of friction-actuation of nano-contacts
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Acknowledgement
Thilo Glatzel Enrico Gnecco Bartosz Such Alexis Baratoff
Lars Zimmerli(Glas Troesch)
Sascha Koch Akshata Rao Pascal Steiner Raphael Roth Monika Schönenberger
Anisoara Socoliuc(Nanonis)
Oliver Pfeiffer(Individual Computing)
Sabine Maier(LBL)
Jonas Gessler(Antarctic)
Roland Bennewitz(Saarbrücken)
ESF-NatriboEUROCORE-FANAS
Shigeki Kawai
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UHV-Force microscope with in-situ preamplifier
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Friction on the Nanometer-scale: Atomic-Stick Slip
FN = 0.44 nN
Ediss = 1.4 eV
(per slip)
Atomic stick-slip Friction loop
KBr(001)-crystal
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Observation of defects and superstructure of KBr on NaCl(001)
Contact size ist smaller than 10 atomsContact stiffness is about 1N/m Fmax≈ 0.1nN
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Monte Carlo Simulations of KBr/NaCl(001)
J. Baker and P.A. Lindgard, Phys. Rev. B 54, R 11137 (1996)
17% misfit leads to superstrucutre6 KBr-units fit on 7 NaCl-units
Rumpling of NaCl-interface is observed on the KBr-surface (0.01nm for 2ML)
Agreement with Helium scattering data; Duan et al. Surf. Sci. 272, 220 (1992)
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FN=0.01 nN
FN=-0.31 nNClose to jump-off
0 2 4 6 8 10
-0.1
0.0
0.1
fric
tio
n f
orc
e (
nN
)
distance (nm)
0 2 4 6 8 10
-0.1
0.0
0.1
fric
tio
n f
orc
e (
nN
)
distance (nm)
Loading dependence of atomic friction: KBr/NaCl(001) superstructure
Superstructure is less pronounced at lower loadsInfluence of the buried interface?
10x10nm2: Friction force map at 2 loads
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η>1 stick-slipη<1 smooth sliding
Modification of the Tomlinson Model
12
3 4
56
7
Fmax
kexp
S. Maier et al., Phys. Rev. B 78, 045432 (2008).
� Modulation of the stiffness k or energy corrugation E0
E0
kE0
k
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Modified 1D Tomlinson ModelComparison with Experimental Results
Experiment Tomlinson Model
Parameters: E0*=0.144 eV, αααα=0.45, k=0.75N/m, v=10nm/s, a=0.66nm
⇒It is possible to observe areas in the superlubricityregime (η<1) and areas with stick slip (η>1) due to thelarge variations of energy barriers
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Atomistic Simulations: KBr/NaCl(001)
Tip (9000 atoms)KBr/NaCl (70‘000 atoms)
-Superstructureobserved
-small topographic changes
-Interface leads to strongvariations of atomicfriction
A. Ghasemi, S. Goedekker, Uni Basel
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Loading dependence of Friction on NaCl(001)UHV FFM with sharp tip vs. Prandtl-Tomlinson model
kx = 29 N/m, kz = 0.05 N/m, vx = 3 nm/s, const. zScans along [100] showing maximum variation
Stick-slip Continuous sliding in contact!
η η η η > 1 ηηηη < 1 mean load FN = Fz + 0.7 nN A. Socoliuc et al., Phys. Rev. Lett. 92, 134301 (2004)
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1d-Prandtl-Tomlinson-Model
20 )(2
12cos
2st
t xxka
xEU −+
−= πPotential energy:
Stability criterion:
η < 1: unique sliding solutionη > 1: instabilities
2
22
02
2
0
2
ka
E
ka
Eπ
πη ==
02cos2
02
2
2
2
>+
=
∂
∂k
a
xE
ax
U t
t
ππ
η > 1 η < 1
η = 3 η = 1
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Multiple Slips
S. Medyanik, W. Liu, I. Sung, R. Carpick, Phys. Rev. Lett. 97, 136106 (2006).
Silicon tip on graphite in airTransitions for η= 1 / 4.604 / 7.788 / 10.95 / 12.66 ...
... but this is only valid for the quasi-static limit (and 1 dimensional).
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Variation~5.1 nN→quadruple slip
Variation~1.1 nN→ single slip
Variation~3.8 nN→ triple slip
Variation~1.2 nN→ single slip
Variation~2.4 nN→ double slip
Variation~2.3 nN→double slip
load=91 nN load=39 nN
Multiple slips do happen at relatively high loads, but they are quite rare (single events)
Experiments on NaCl(001) in UHV
R. Roth et al., Trib. Lett. (09)
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single slip
double slip
triple slip
quadruple slip
a
Force-variation= 1/2 a x kcont ~ 1.2 nN
Force-variation= 1 a x kcont ~ 2.4 nN
Force-variation= 3/2 a x kcont ~ 3.6 nN
Force-variation= 2 a x kcont ~ 4.8 nN
depends on load~4.6-5.4 N/m
These jumps are
nothing special,
they also occur at
low loads
We are looking for these
jumps!
etc... PS: Force variations are upper limits, since jump distance is actually smaller than multiples of a/2
Classification of multiple slips on NaCl(001)
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load=13 nNη=5.6
load=39 nNη=8.2
load=78 nNη=12.8
double triple quadruple & higher
double
double
triple
triple
quadruple & higher
quadruple & higher
Statistics of multiple slips on NaCl(001)
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damping=0.3 x
critical
Same slip-recognition program run with output of 2D thermal Tomlinson simulation program:
Onset of
multiple slips!
double
double
double
triple
triple
triple
quadruple & higher
quadruple & higher
quadruple & higher
damping=0.7 x
critical
damping=0.5 x
critical
Damping < 0.5 x
critical
Simulation parametersE0=3.3 eVkx=ky=5 N/mT=293 Kv=10 nm/sm_tip=1e-12 kgdt=1e-8 s
Comparison with simulations (η=8.2)
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damping=2 x
critical
Onset of
multiple slips!
double
double
double
triple
triple
triple
quadruple & higher
quadruple & higher
quadruple & higher
damping=10 x
critical
damping=5 x
critical
Damping < 5 x
critical
Same slip-recognition program run with output of 2D thermal Tomlinson simulation program:
Simulation parametersE0=5 eVkx=ky=5 N/mT=293 Kv=10 nm/sm_tip=1e-12 kgdt=1e-8 s
Comparison with simulations (η=12.5)
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Multiple slips: An indicator for damping
m
γΓ tip =
m
kcrit 2=Γ
critγγ 5.0<
d2xtip/dt2 + ΓΓΓΓtip dxtip/dt + ωωωωtip2 (xtip – xs) = - (ππππE0/a) sin (2ππππxtip/a)
Critical damping:
Observation of multiple slips indicate that the slightlyunderdamped case is present for intermediate loadings (39nN):
At high loads (78nN), there seems to occur a transition to theoverdamped case.
m
kωtip =
critγγ 5<
-1.5e-009
-1e-009
-5e-010
0
5e-010
1e-009
1.5e-009
0 5e-010 1e-009 1.5e-009 2e-009 2.5e-009 3e-009 3.5e-009
'friction21b' using 1:2
R. Roth et al., Trib. Lett. (09)
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Dependence of Tomlinson Parameters
π
max
0LaF
E =
12
exp
max
−=ak
FLπη
exp
1kk
η
η +=
E0: linear increasewith normal forces
k: rather independent(contact area const.?)
max
LF
expk−
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Lateral contact stiffness
contacttiplever kkkk
1111++=
R. Carpick et al, Appl. Phys. Lett. 70, 1548-1550 (1997)
Here: klever=29N/m » k ⇒ kcontact ≈ 1-2N/m
Continuum model :
kcontact= 8 a G ⇒ a < 1Å ?
⇒ Atomistic model needed
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Contact resonance frequencies and normal stiffness k*
U. Rabe in Applied Scanning Probe Methods II, p. 39ffEds. H. Fuchs, B. Bhushan, Springer-Verlag, Berlin
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Contact mode imaging with excitation of NaCl(001) on Cu(111) and amplitudemeasurement at contact resonance
Fixed frequency: 56.2kHz Lock-In measurement of amplitude
⇒Local variations of normal contact stiffness
Topography Lock-in amplitude at 56.2kHz
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Contact Resonances
Free cantilever: 11325Hz; In Contact: 55.3kHz and 55.5kHz
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Imaging of contact resonance by PLLNaCl(001) on Cu(111)
Topography Frequency shiftmeasured by PLLAmplitude=400pm
Contrast between copper and NaCl: 195HzFree cantilever: 11325Hz; In Contact: 55.3kHz and 55.5kHz
CuNaCl
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Simultaneous determination of lateral and normal contact stiffness
P. Steiner et al., to appear in Nanotechnology
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Determination of normal contact stiffness
kN=0.095N/mf1=49.5kHz f10=10.2kHz R. Roth et al.
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Contact resonance frequencies as a function of normalized contact stiffness
U. Rabe in Applied Scanning Probe Methods II, p. 39ffEds. H. Fuchs, B. Bhushan, Springer-Verlag, Berlin
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Comparison of lateral and normal contact stiffness
R. Roth et al.
k cont lat k cont normlatcont
normcont
k
k
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Comparison of lateral and normal contact stiffness
Normal contact stiffness determined from contactresonances:k*=13-40N/mRatio of normal to lateral contact stiffness:k*/kL=6-15
Normal contact stiffness is larger than lateral contact stiffnessFrom continuum models a ratio of E/G=2-4 is expected!
Lateral contact stiffness underatomic stick slip condition (FN=0.1-1nN; η=3-5): kL=1-3N/m
R. Roth et al.
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Normal and lateral contact stiffness
B. Luan and M. Robbins, Phys. Rev. E 74, 026111 (2006).
-Normal contact stiffness in reasonable agreeementwith continuum models-Lateral contact stiffness differs from the continuum modelfor small radii
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Contact area from normal contact resonancefrequencies measurements
==*E
k2a normcont
−+
−=
sample
sample
tip
tip
EE
22 11
*E
1 νν
kcont, norm=32N/m on NaCl(001)/Cu(111)kcont. norm=40N/m on Cu(111)
Application of Continuum model (flatpunch):
Etip=169GPa νtip=0.33Esample=40GPa/120GPa νsample=0.25/0.34
0.9nm / 0.5nm
⇒Area from normal contact stiffness seems in agreement with resolution
NaCl (2 layers)
Cu
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Simultaneous imaging of lateral forces and normal contact stiffness: NaCl(001) on Cu(111)
Lowest friction on Cu(111)Contact stiffness on NaCl k*(NaCl)=32N/mContact stiffness on Cu(111) k*(Cu)=40N/mContact diameter: 2a=k*/E*=0.9nm (0.5nm)Contact stiffness rather independent of number of layers
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Simultaneous measurement of atomic stick slipand normal contact resonances on NaCl(001)
Friction
Contactresonance Defect observed
⇒Maximum normal contact resonance is observed for FL=0P. Steiner et al., to appear in Nanotechnology
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• Observation of atomic-scale stick slip withsingle molecular and single atomic resolution
•Observation of multiple slips: A toolto estimate damping coefficients
•Simultaneous determination of normal and Lateral contact stiffness by contact resonance frequency measurements
Conclusions