UNIVERSITA’ DEGLI STUDI DI PADOVA
FACOLTA’ DI SCIENZE MM.FF.NN.
PH.D. IN PHYSICS
PH.D. THESIS
Depinning transition in the nanofriction of thin
films sliding on metallic surfaces
Thesis Advisors: Prof. Lorenzo Bruschi
Dott. Giampaolo Mistura
Candidate: Alessandro Carlin
ACADEMIC YEAR 2003/2004
Contents
Abstract (English)
iii
Abstract (Italiano)
v
Introduction
ix
1 Theoretical models
1.1 The Frenkel-Kontorova monodimensional model . . . . .
1.2 The Langevin equation . . . . . . . . . . . . . . . . . . .
1.2.1 1-dimensional brownian model . . . . . . . . . . .
1.2.2 Meaning of η ∗ and f . . . . . . . . . . . . . . . .
1.3 Simulation of 2-dimensional models . . . . . . . . . . . .
1.3.1 Role of defects . . . . . . . . . . . . . . . . . . .
1.3.2 The depinning transition in computer simulations
1.4 Electronic and phononic contributions to sliding friction .
1.4.1 Adsorbate-induced resistivity . . . . . . . . . . .
1.4.2 Theoretical explanations of DAK experiment . . .
1.4.3 Phononic friction . . . . . . . . . . . . . . . . . .
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2 Quartz crystal microbalance (QCM)
2.1 Equations of motion . . . . . . . . . . . . . . . . . . .
2.2 Microbalance in presence of a fluid . . . . . . . . . . .
2.3 The acoustic impedance . . . . . . . . . . . . . . . . .
2.3.1 Separation of acoustic impedance contributions.
2.4 Mechanical impedance measurement . . . . . . . . . .
2.5 Pre-existing analysis . . . . . . . . . . . . . . . . . . .
2.6 Electric behaviour of the QCM . . . . . . . . . . . . .
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3 Experimental apparatus
3.1 UHV system . . . . . .
3.1.1 Main chamber .
3.1.2 Jacket . . . . .
3.1.3 Fast entry lock
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ii
CONTENTS
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surface
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5 Data analysis
5.1 Analysis of vapour contribution . . . . . . . . . . . . . . . . . . .
5.1.1 Correction of the measured frequency . . . . . . . . . . . .
5.1.2 Amplitude correction . . . . . . . . . . . . . . . . . . . . .
5.2 Error extimate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Nanofriction measurements for the system Kr/Au : the depinning
transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Performances of the new UHV apparatus . . . . . . . . . . . . . .
5.4.1 Necessity of UHV environment . . . . . . . . . . . . . . .
5.4.2 Temperature and pressure limits . . . . . . . . . . . . . . .
5.4.3 Detection of the superconducting transition . . . . . . . .
5.4.4 Stability of the QCM . . . . . . . . . . . . . . . . . . . . .
5.4.5 Cleaning of the quartz electrode surface by ion sputtering
5.4.6 Control of the gas deposition . . . . . . . . . . . . . . . . .
5.5 First measurements performed in UHV around 7K . . . . . . . . .
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6 Conclusions and perspectives
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A C++ program for data analysis
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Bibliography
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3.2
3.3
3.4
3.5
3.1.4 UHV suitcase . . . .
3.1.5 Baking system . . . .
3.1.6 Cooler . . . . . . . .
The sample holder . . . . .
3.2.1 Mechanical mounting
Gas system . . . . . . . . .
Thermoregulation . . . . . .
QCM electronics . . . . . .
4 Preparation of the adsorption
4.1 Commercial gold surface . .
4.2 Lead on gold . . . . . . . .
4.3 Lead on quartz . . . . . . .
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of the crystal
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Abstract (English)
The investigation of friction on atomic scale is a recent discipline, carried out
using experimental techniques such as Surface Force Apparatus (SFA), Atomic
Force Microscope (AFM) and Quartz Crystal Microbalance (QCM). In particular, the last one is a powerful technique to investigate nanofriction of thin films
physisorbed on macroscopic surfaces and sliding along them [1], [2].
The quartz crystal microbalance was and is extensively used as a balance in
many scientific fields from chemistry to biology [3], and many important results
have been reached in physics research [4], [5], [6] thanks to its sensitivity and
stability. But what is a QCM? Of course we will describe it in detail in the third
chapter, but let me introduce here the basic idea. It is a mechanical resonator
characterized by high Q-values (Q ≈ 105 ) and very high stability ( δF
> 107 ),
F
which is electrically driven at one of its own resonant frequencies, typically some
megahertz. A change in the inertial mass of this object, whose surfaces act as
adsorption substrates, for example due to the deposition of molecules on it, causes
a shift in its resonant frequency, and so it can be used this way as a very sensitive
balance.
The application of this object to the field of nanotribology involves a deeper
analysis of the interaction between the surface and the adsorbate. In fact, a
possible energy loss due to dissipation of the film sliding with respect to the substrate can be detected by analyzing the decrease in the Q-value of the resonator.
Therefore, the simultaneous detection of frequency and Q-value shifts are the
input we need to analyze the behaviour of the adsorbate and to quantify its mass
and its motion.
The first measurements we performed were carried out using krypton films
physisorbed on gold surfaces at 77÷85K, in conditions of high vacuum (10−6 T orr)
and showed a depinning transition, similar to the phenomena observed in many
other physical fields in the recent past years [7], [8], [9]. Because of the problems due to the non ultra-high vacuum environment we decided to improve our
apparatus, and constructed in the last two years a totally new UHV chamber,
whose features will be described in the third chapter of this thesis. In particular,
by using this new facility, we are able to perform experiments under extremely
controlled conditions, at pressures < 10−10 T orr, without exposing the surfaces to
air, from 4 to 400K. The main goal of this new work, together with an exhaustive
iii
iv
Abstract (English)
characterization of the depinning transition, is the measurement of the electronic
contribution to sliding nanofriction. The idea is very simple: by substituting
the traditional gold substrates with lead ones, evaporated using state-of-art techniques, we are interested in performing measurements of sliding friction around
its superconductive transition. This experiment was proposed by Persson, who
suggested that if the magnitude of the electronic contribution to energy loss is
of the same order of the phononic one, then a decrease in dissipation had to be
observed as the substrate became superconductive. A similar experiment, carried
out by Krim and coworkers in 1998 [10] showed a sudden drop in sliding friction
of N2 molecules sliding on Pb as the transition took place, but so far nobody was
able to build a theory which accounts for the data, and nobody was even able to
reproduce the same experiment too! The conclusion was that probably the uncontrolled conditions under which the experiment was conducted greatly affected
the measurements. To reproduce the Krim experiment, and to understand the
real contribution of electronic friction, is one of the motivations behind this work.
This thesis is organized as follows:
• In the first chapter I will describe what theory predicts for a model system
similar to those investigated in real experiments. In particular I will present
the main conclusions of theorists about electronic and phononic friction and
the computational simulations which predicted the depinning transition.
• Chapter two will rigorously report the physics of the microbalance sensor
(i.e. the quartz crystal). In particular it will treat the solution of the
Navier-Stokes equations for our system.
• The third chapter will describe the experimental set-up built expressely for
this kind of experiments.
• The preparation and characterization of the Pb adsorption surfaces are
illustrated in chapter four.
• In chapter five I will present the experimental data, from the analysis of
vapour contribution to total impedance and the testing of the new apparatus to sliding friction measurements concerning the characterization of the
depinning transition for the system Kr/Au in high vacuum.Data relative
to krypton physisorbed on lead are not avaible yet.
• Conclusions and perspectives.
Abstract (Italiano)
Lo studio dell’attrito su scala atomica è una disciplina piuttosto recente, cha da
un punto di vista sperimentale viene affrontata soprattutto utilizzando tecniche
moderne quali SFA (Surface Force Apparatus), AFM (Atomic Force Microscope)
e QCM (Quartz Crystal Microbalance). Quest’ultima in particolare rappresenta
un potente strumento di indagine per quanto riguarda la dissipazione energetica
dovuta all’attrito di films di spessore monoatomico adsorbiti su di una superficie
e in movimento relativamente ad essa [1], [2]. Tale tecnica è stata ed è tuttora
usata diffusamente in svariati campi, dalla chimica alla biologia [3] e alla fisica [4],
[5], [6], in quanto il quarzo rappresenta una microbilancia estremamente stabile
e sensibile.
La tecnica QCM verrà descritta dettagliatamente nel terzo capitolo, ma il
principio su cui si basa il suo funzionamento è molto semplice. Il sensore consiste
in un oscillatore meccanico caratterizzato da alti fattori di merito (Q ≈ 105 )
e altissima stabilità ( δF
> 107 ), che viene pilotato su una delle sue risonanze,
F
tipicamente a frequenze dell’ordine di qualche megahertz. Un alterazione della
massa di questo oggetto, ad esempio causato dalla presenza di un sottile film
sulla superficie, da luogo ad uno shift nella frequenza di risonanza facilmente
misurabile.
L’applicazione di questa tecnica al campo della nanotribologia coinvolge una
più profonda analisi dell’interazione tra substrato e adsorbato. Infatti, un eventuale dissipazione di energia dovuta allo scivolamento del film rispetto alla superficie del sensore può essere rilevata misurando le variazioni del fattore di merito
della microbilancia rispetto al valore in assenza di adsorbato. Quindi attraverso
la misura diretta di variazioni di frequenza e di fattore di merito è possibile sia
dedurre la massa adsorbita sulle superfici che stimare la forza di attrito su scala
atomica.
Le prime misure eseguite hanno riguardato films di krypton fisisorbiti su oro a
temperature dell’ordine di 80K, in condizioni di alto vuoto (10−6 T orr), ed hanno
condotto alla scoperta di una transizione di depinning, simile a fenomeni simili
osservati finora in sistemi fisici completamente differenti [7], [8], [9]. A causa di
problemi dovuti al non eccezionale livello di vuoto che si rifletteva in contaminazione delle superfici e compromissione di molte misure è stato deciso un salto
di qualità nell’apparato sperimentale; una camera da ultra alto vuoto completav
vi
Abstract (Italiano)
mente nuova, largamente descritta nel terzo capitolo della tesi, è stata disegnata,
costruita e testata negli ultimi due anni. In particolare utilizzando questo nuovo
strumento è possibile effettuare esperimenti con tecnica QCM in condizioni estremamente controllate, a pressioni < 10−10 T orr da 4 a 400K. Lo scopo principale
del progetto, assieme ad un più accurato e completo studio della transizione di
depinning, consiste nella misura del contributo elettronico al nanoattrito. L’idea
di base è piuttosto semplice: sostituendo il tradizionale substrato di oro con uno
di piombo, evaporato in maniera estremamente regolare e controllata grazie a moderne tecniche di fisica delle superfici, è possibile effettuare misure di nanoattrito
a cavallo della transizione superconduttiva del metallo che ha luogo alla temperatura di circa 7K, perfettamente raggiungibile dalla nuova strumentazione. Un
esperimento di questo tipo era stato proposto da Persson, il quale intuì che, se la
dissipazione energetica dovuta a canali elettronici è significativa, una variazione
di attrito avrebbe dovuto essere osservata in corrispondenza della transizione superconduttiva del substrato. L’esperimento vero e proprio, condotto da Krim e
collaboratori nel 1998 [10], mostrò un improvviso calo nell’attrito di molecole di
azoto adsorbito su piombo proprio alla transizione, ma fino ad oggi nessuno è
stato in grado di produrre una teoria in grado di spiegare quantitativamente il
risultato sperimentale, e allo stesso tempo nessuno è stato in grado di ripetere
l’esperimento. La conclusione è che probabilmente le condizioni non ideali in cui
l’esperimento è stato condotto possono aver compromesso i risultati delle misure.
Riprodurre l’esperimento in questione e comprendere la reale importanza del
contributo elettronico all’attrito su scala atomica e uno dei principali obiettivi di
questo lavoro.
La tesi è organizzata come segue:
• Nel primo capitolo sarà illustrato ciò che la teoria predice per un sistema
simile a quello da noi investigato sperimentalmente. In modo particolare
saranno esposte le principali conclusioni circa attrito elettronico e fononico
e le simulazioni al computer che hanno predetto l’esistenza della depinning
transition.
• Il capitolo due descriverà la fisica della microbilancia a cristallo di quarzo,
e in particolare saranno risolte le equazioni di Navier-Stokes per il sistema
quarzo-film-vapore.
• Nel terzo capitolo sarà analizzato nel dettaglio il nuovo apparato sperimentale costruito espressamente per questo tipo di misure.
• La preparazione e la caratterizzazione dei films di Piombo che costituiscono
i substrati d’adsorbimento saranno illustrati nel quarto capitolo.
• Nel capitolo quinto saranno esposti i dati sperimentali, dall’analisi dell’impedenza
del vapore alla descrizione dei test relativi alle prestazioni del nuovo apparato, per finire con le misure di attrito relative alla caratterizzazione della
vii
transizione di depinning per il sistema Kr/Au in condizioni di alto vuoto. I
primi dati relativi invece a krypton su piombo non sono ancora disponibili
allo stato attuale del lavoro.
• Conclusioni e prospettive future.
Introduction
From a practical point of view, sliding friction is one of the most important
phenomena in physics. It has been recently estimated that only in the USA
economic losses due to ignorance about tribology phenomena amount to about 6%
of the gross national product, that is over $400 billion every year [11], since such
a phenomenon has been discovered, in its basic principles, thousands years ago.
We can try to understand how important the knowlwdge of tribology is by just
thinking that in every mechanical system it is the main cause of wear and damage.
In particular modern technologies can produce smaller and smaller mechanical
components, and accordingly their surface/volume ratio increases continuously.
In this situation friction, which is a typical interfacial phenomenon, becomes
crucial as a limiting factor in the development of new nanoscopic devices. Without
friction it would be impossible to make experience of almost all we can actually
do, from walking to playing a violin. Sometimes we try to minimize friction, for
example to reduce wear in mechanical devices, other times we want to maximize
it, such as in adhesion between pneumatics and roads. Nevertheless many aspects
of friction are still not well understood and the studying of friction at an atomic
scale is just starting to emerge.
Figure 1: Leonardo Da Vinci’s notes about friction.
The first practical aspects of friction can be discovered in prehistory, when
hominids started chipping stone tools. 200000 years ago Neanderthals were able
ix
x
Introduction
to correctly use friction between wood and wood to generate fire. The importance
of lubricants was appreciated by Sumerians and Egyptians about 2400 years B.C.
as they started using simple lubricants as mud or grease to transport building
blocks; after 800 years they learned how to use wooden logs for the same purpose.
The first systematic study of tribology is due to Leonardo da Vinci, who performed experimental studies of friction and wear, and invented ingenious schemes
for rolling-element bearings. He surely measured the force of friction between objects on both horizontal and inclined surfaces, and firstly introduced the concepts
of "normal force" and "apparent area of contact" [12]. He introduced the friction
coefficient, defined as the ratio between frictional resistence and weight, and argued that for flat and clean surface its value is 0.25. This is not generally correct,
but is quite realistic for materials which were used in bearings at the end of the
Middle Ages.
In 1687, the publication of Newton’s "Principia" gave the basis for all the
subsequent studies on sliding friction, in particular that carried out by Charles
Coulomb. Surely he is very famous for his contributions in the field of electricity
and magnetism, but Coulomb also systematically studied the influence of the five
main factors upon friction (nature of materials, extent of surface area, normal
force, length of time the surfaces remained in stationary contact and ambient
conditions). Thanks to many experimental data, he constructed empirical relations, in particular F = µL (L is the normal load), finding that µ doesn’t depend
on L, on sliding velocity and on contact area. Similar conclusions were carried
out in by Guillame Amontons in the last years of XVII century [13].
The basis of hydrodynamic lubrication is given by the equations of motion of
viscous fluids, developed by Euler, Poiseuille, Bernoulli, Navier and Stokes in the
period 1730-1850. From a practical point of view, during industrial revolution
many excellent lubricants were discovered.
In 1847 Gustav Adolph Hirn performed an exhaustive study of lubrication,
in particular he found that while at high sliding velocity µ ∝ v, when velocity
is reduced lubricant can be expelled from the interface resulting in enormous
friction.
In 1922 the biologist W.B. Hardy discovered that even atomically thin films
are able to make two glass surfaces slide over each other with very low friction. He
firstly introduced the concept of boundary lubrication, and show that in this case
what determines lubrication is not the viscosity but the chemical constitution of
the fluid; in particular fluids adsorbed by the surfaces are excellent lubricants.
The explanation of the proportionality between µ and L was given around
1940 by Tabor and Bowden, in terms of the crucial difference between apparent and real area of contact, due to the surface roughness [15]. Also the nondependence of µ on velocity was explained in the same period (Tomlinson 1929)
[16]. Since late 80’s new powerful experimental techniques, such as Atomic Force
Microscope (AFM) and Surface Force Apparatus (SFA) have succesfully been applied to the study of sliding friction and boundary lubrication. At a nanoscopic
xi
Figure 2: In some cases it is necessary to maximize friction, for example
between pneumatics and road.
scale, it has been discovered that the main process which causes energy dissipation is due to phononic excitations: kinetic translational energy is converted into
energy of the inernal degrees of freedom of the bodies [17]. Another important
contribution is given by interaction between conduction electrons, but this aspect is still not clear to the scientific community. In particular in 1998 Krim and
co-workers, while measuring the sliding friction of a N2 monolayer physisorbed
on lead, found an abrupt change of sliding friction across the superconductive
transition of the substrate, at about 7K [10].This experiment has not still any
clear theoretical explanation [19], [20], [21], [22], and nobody (nor Krim herself)
was able to reproduce it convincingly [18], [23]. One of the main goals of INFM
PRA-Nanorub is to repeat such an experiment under more controlled conditions,
in order to better understand the role of electronic contribution to sliding friction.
This project involves four italian research groups:
- Trieste (SISSA): theoretical study of sliding friction and electronic contribution
- Modena university: computer simulation of the sliding friction of simple
molecules adsorbed on crystalline surfaces
- Genova university: preparation of the lead surfaces by means of state-of-art
techniques in thin film evaporation
- Padova university: measurement of the sliding friction of simple-gases molecules physisorbed on lead and gold using the Quartz Crystal Microbalance
(QCM) technique
The main topic of this thesis is the work carried out in Padova in the last
three years, from the setting up of the totally new UHV experimental apparatus
to the analysis of the data collected so far. The technique used is the same
which has been succesfully applied to sliding friction studies by Krim and co-
xii
Introduction
workers known as QCM technique [2]. The first measurements we will present are
relative to krypton films sliding on gold substrates at liquid nitrogen temperature,
carried out in high vacuum. Analysing the behavior of this system we found the
first experimental evidence of depinning transition in tribological systems, but
also understood the necessity to upgrade our facilities. The new UHV system
allowed us to reach lower pressures (10−10 T orr), lower temperatures (4K) and in
particular to observe the superconductive transition of the lead substrate.