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D 03657

E DE BRUXELLES nces Appliquées

Sen^ice Matières et Matériaux

ULB

Characterization and

modification of the mechanical and surface properties at the

nanoscale

Académie year 2009—2010

PhD Director: Professor Marie-Paule Delplancke Author: Enrico Tarn

Université Libre de Bruxelles ain the title of Philosophical Doctor ering Sciences

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UNIVERSITE LIBRE DE BRUXELLES Faculté des Sciences Appliquées

Service Matières et Matériaux

ULB

Characterization and

modification of the mechanical and surface properties at the

nanoscale

Academie year 2009—2010

PhD Director: Professer Marie-Paule Delplancke Author: Enrico Tam

Dissertation presented in order to obtain the title of Philosophical Doctor (PhD) in Engineering Sciences

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Consultation

AUTORISEE

(biffez la mention inutile)

Signature

”La pensée ne doit jamais se soumettre, ni à un dogme, ni à un parti, ni à une passion, ni à un intérêt, ni à une idée préconçue, ni à quoi que

ce soit, si ce n’est aux faits eux-mêmes, parce que, pour elle, se soumettre, ce serait cesser d’être.”

Henri Poincaré (Fêtes du LXXVe anniversaire de l’ULB, 21 novembre 1909)

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Acknowledgments

The writing of a dissertation is a very challenging expérience which is obviously not possible without the Personal and practical support of numerous people. Therefore, I would here like to express my gratitude to the people who contributed to the accom- plishment of this thesis.

First and foremost I wish to thank Prof. Marie-Paule Delplancke-Ogletree for giving me the chance to participate in this project and for giving me aU the resources I needed to succesfully accomplish this work. Her oral and written comments were cdways extremely perceptive, helpful, and appropriate.

Then, my sincere gratitude goes to ail the members of the MiniMicroNano project:

Prof. Philippe Bouillard, Prof. Alain Delchambre, Prof. Frank Ogletree, Prof. Pierre Lambert, Prof. Tliierry Massart, Dr Marion Sausse Lhernould et Dr Peter Berke.

Many people on the faculty and staff of the Chemicals and Materials department assisted and encouraged me in varions ways during my Works. I especially wish to thank them for ail the enjoyable lunches and coffee breaks we had.

During the PhD studies I had the great opportunity to spend 6 months at the Lawrence Berkeley National Laboratory. I would like to express my deepest gratitude to ail the Molecular Foundry staff. In particular, I am greatful to Prof Miquel Salmeron, Prof.

Frank Ogletree and Dr Paul Ashby for their critical comments and discussions, which were very important for my Personal and scientific development.

During these last years spent working abroad (Belgium and USA) I hâve been fortunate to corne across many exceptional friends, without whom life would be bleak. I would like to thank ail of them for always supporting me and for ail the nice moments we shared together. They were my real source of energy.

This whole thesis would not look Uke it is without the precious help of some proof- readers. I more than appreciate their help.

My gratitude also goes to the french coimnunity of Belgium since this work would not hâve been possible without their financial support.

Last but not least, Fm particularly greatful to my family who, through my childhood and study career, hâve always encouraged me to follow my heart and my adventurous mind in any direction this bas taken me.

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Abstract

In the past two décades much effort bas been put in tbe cbaracterization of tbe mecbanical and surface properties at tbe nano-scale in order to conceive reliable N/MEMS (Nano and Micro ElectroMecbanical Systems) appbcations. Techniques like nanoinden

tation, nanoscratcbing, atomic force microscopy bave become widely used to measmre tbe mecbanical and surface properties of materials at sub-micro or nano scale. Nev- ertbeless, many pbenomena sucb us pile-up and pop-in as well as surface anomalies and rougbness play an important rôle in tbe accurate détermination of tbe materials properties. Tbe first goal of tbis report is to study tbe infulence of tbese sources of data distortion on tbe experimental data. Tbe results are discussed in tbe first experimental cbapter.

On tbe otber band, conceptors would like to adapt/tune tbe mecbanical and surface properties as a function of tbe required application so as to adapt tbem to tbe industrial need. Coatings are usually applied to materials to enbance performances and reliability sucb as better bardness and elastic modulus, cbemical résistance and wear résistance.

In tbis Work, tbe magnetron sputtering technique is used to deposit biocompatible thin layers of different compositions (titanium Carbide, titanium nitride and amorphous carbon) over a titanium substrate. The goal of tbis second experimental part is the study of the déposition parameters influence on the resulting mecbanical and surface properties.

New materials sucb as nanocrystal superlattices bave recently received considérable attention due to their versatile electronic and optical properties. However, tbis new class of material requires robust mecbanical properties to be useful for technological applications. In the third and last experimental cbapter, nanoindentation and atomic force microscopy are used to characterize the mecbanical behavior of well ordered lead sulfide (PbS) nanocrystal superlattices. The goal of tbis last cbapter is the understanding of the deformation process in order to conceive more reliable nanocrystal superlattices.

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Introduction

1.1 The MiniMicroNano Project

Tho development of NEMS and MEMS (Nano and Micro Electro Mechanical Systems) is a very big challenge for today’s society. Silicon technology thanks to its easy intégration between mechanical and electronic components gave tremendous advance to the microelectronics business over the last forty years.

The object of the Mini-Micro-Nano project is to focus on complementary approaches to N/MEMS development using more conventional engineering materials (métal alloys, ceramics, polymers). Such an approach btings new opportunities and a much wider array of materials properties becomes available.

With new opportunities corne new challenges. Critical components such as microassem- blers and movable microstructures (i.e. for human implanted devices) require charac- teristics like smaller dimensions, lighter weight, and increased résistance to wear and deformation. Thus, a better understanding of phenomena taking place at sniall scale, new techniques, and multifunctional materials are needed. These new challenges can only be handled by a niultidisciplinary engineering approach.

The main and long terni goal of this project is to build a center of excellence at the ULB (Université Libre de Bruxelles) in the field of micromechanical engineering, combining fundamental and applied research simultaneously. Its development is based on the expertise of three ULB partners:

• Chemicals and MaterieJs Department: Surface characterization and modi

fications

• BATir: Simulation of the mechanical behavior at microscale

• BEAMS: Design and production of micro components

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Introduction

The Chemicals and Materials department was in charge of the experimental task in order to characterize and niodify the mechanical and surface properties of materiels at micro and nanoscales so as to understand the phenomena taking place at the nanoscale.

This constitutes the subject of this thesis. A more exhaustive introduction about the undertaken works and experiments performed in this context is given in the next section.

The B ATir department main task was the development of a simulation tool characterizing the deformation involved during the depth sensing nanoindentation experiments.

This becomes particularly useful to understand the mechanical behavior of materials at a very small scale.

The BEAMS department focused on the understanding and modeling of surface forces (such as electrostatic forces) at the nanoscale. Those forces can be neglected at the macroscale but are of great practical impact at a micro or nanoscale.

The main interactions between the three departments are shown in image 1.1.

Figure 1.1: Main interactions between the three departments involved in the mini-micro-nano project.

The Project, financially supported by the "Communauté Française de Belgique”, spanned over five years and involved three PhD students attached to the relative departments for four years. Four DEA (Diplôme d’études approfondies) [1-4] and 2 PhD thesis [5,6]

were alredy obtained in the frame of this project.

An international collaboration with the Lawrence Berkeley National Laboratory (Cal

ifornia, USA) was also provided thanks to Prof. D.F.Ogletree. This consisted of a 6 montlis stage at the Molecular Foundry department of the above mentioned laboratory.

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1.2. Présent Work

1.2 Présent Work

This thesis constitutes a dissertation of the study conducted during the four academie years spanning from 2005 to 2009 at the Chemicals and Materials Department of the Université Libre de Bruxelles in order to obtain the title of Philosophical Doctor in Engineering (PhD).

The long-term aims of this work are to lay the scientific basis leading to the design of a microscale gripper capable of manipulating microscopie objects in various environments. The importance of various phenomena taking place at the micro and nanoscale can be totally different from what we expect at the macroscale. For instance, when two objects axe brought into contact and then separated, electrostatic forces (which are usually neglected at the macroscale) can play an important rôle. As a resuit, the con

ception of reliable micromanipulation Systems able to work in different environments is possible only if those phenomena are miderstood and controlled.

Various issues hâve to be taken into account to reach this goal. On the one hand, the mechanical properties of the material used to conceive the manipulator tool are of great importance in order to provide reliability. On the other hand, the manipulation by contact of objects at the microscale (generally between Ipm and 1mm) is often disturbed by pertmbations related to adhesive surface forces between the manipulated object and the gripper. For example, high surface energies are unwanted since they induce high pull-ofî forces and can make it impossible to release the manipulated object.

In this optic, controlling the electrostatic forces (in fimction for instance of the intrinsic surface roughness resulting from different machining techniques) would provide new important design solutions for the conception of new micromanipulators devices.

To reach the aim of the project, an integrated approach combining simulation and experimental work has been conducted. The major techniques used to characterize the surface properties at the nanoscale (nanoindentation, nanoscratching, atomic force microscopy, etc...) were deeply studied. The simulation of the nanoindentation and of the surface forces (mainly electrostatic forces) were provided by the interaction with the BATir and BEAMS departments respectively.

Understanding the phenomena taking place at the nanoscale is, of course, a major and important task but the real challenge would be the modification of the mechanical and surface properties in order to adapt them to the required application. In this context, big efforts were also put in the modification of the surface properties through the déposition of spécifie thin layers over a bulk substrate.

As a conséquence, the efforts done to complété this work are divided into two directions.

Firstly, it was important to understand the nanoscale phenomena and the resulting surface properties associated with them. Secondly, the attention was focused on the modification of the surfaces (for instance by physical vapor déposition) in order to control properties like surface energy and electrostatic forces which, as already stated, are primordial in the manipulation of small objects.

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Introduction

Since the use of micromanipulation tools (and more generally of MEMS) for hmnan implanted devices is consistently growing, it was decided to take into account mainly biocompatible materials. Bulk titanium was chosen as 'base’ material for its well known biocompatibility and good mechanical properties. Titanium Carbide, titanium nitride, titEuiium oxide and carbon layers, ail known to bave biocompatible behaviors (even if the extent should be verified) were chosen to be the main coating materials. Bulk nickel was aJso studied because of its wide utilization in the conception of micromanipulation tools.

Figure 1.2: Main steps foUowed during the accompUshement of the mioi-micro-nano Project. The simulation of the surface forces and of the nanoindentation was provided by the

collaboration with the BEAMS and BATir departments of the ULB.

The main steps of the PhD work are illustrated on figure 1.2 while the current disser

tation is divided in the following 9 chapters:

The first Chapter is dedicated to the introduction and to the présentation of the Mini-Micro-Nano project.

The second Chapter introduces the main surface characterization techniques, the theory behind it, the properties derived from it and the instrumentation used to perform the tests. Mechanical property values such as modulus and hardness are calculated from nanoindentation experiments based on the idealized elastic contact the

ory and load-displacement data. Nanoindentation is slightly different from macroscale hardness tests and requires a number of signiflcant assumptions. In some circumstances these assumptions can lead to signiflcant sources of error. In order to understand why the resulting data may be inaccirrate, some of the common sources of data distortion that need to be corrected (such as pile-up and roughness) are discussed.

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1.2. Présent Work

Nanoscratching, which allows deriving properties such as the coefficient of friction and the délamination résistance is aJso presented and discussed. Then, the basic theory behind the atomic force inicroscopy (AFM) is presented. AFMs were mainly used to characterize the electrostatic forces as a function of the tip/sample séparation distance.

Finally, some information about the surface energy characterization teclmique and the residual stresses détermination rire presented.

Chapter three introduces the techniques utilized to modify the surface properties.

The Physical Vapor Déposition technique (by magnetron sputtering), which was used in oiur study to deposit thin layers over bulk substrate (titanium Carbide, titanium nitride, and carbon layers), is presented. The process parameters to control, the ad- vantages and the main application of the magnetron sputtered films are extensively discussed.

Ail experimental procedures and materials taken into account during the experimental part are introduced in Chapter four. Any of the additional instrumentation aspects and procedures involved in the characterization and modification of the surface prop

erties are given in this chapter.

Chapter flve deals with the characterization of bulk materials (titanium and nickel).

Elastic modulus and hardness were measured using the nanoindentation technique.

The influence of parameters like the holding time at maximum load and the loading rate was investigated. The efîects of roughness and grain size was also taken into accoimt at this stage. Electrostatic forces determined by AFM are derived and the effect of factors like roughness is studied. Then, the results of the nanoscrathing experiments and the surface energy détermination are shown and discussed.

Chapter six introduces and discusses the resuit of the modification of the surface prop

erties. The déposition procedure of thin titanium oxide, titanium Carbide, titanium nitride and carbon layers is given and discussed. At the same time, the mechanical properties (modulus and hardness) and their évolution across the layer are studied.

This is doue by many different characterization techniques such as nanoindentation, nanoscrathing, atomic force microscope, XPS, RBS, XRD, contact angle measurement.

Chapter seven complétés the experimental part and concerns the study of lead sulfide (PbS) nanocrystal superlattices. This advanced material received considérable interest due to its enhanced electronic and optical properties. Nanocrystal superlattices are characterized by an organized structure and are composed of an inorganic nanoparticles core with organic ligands bound to the surface of each core. This new class of material combines the unique properties of the organic nanocrystal core with the properties arising from the interaction between neighboring nanocrystals in the superlattice. The knowledge acqulred during the characterization of bulk material and thin layers was necessary to study this new kind of advanced material.

Chapter eight présents the major and most importcmt conclusions and gives some perspectives for future works.

Finally the last Chapter is dedicated to the annexes in which the major publications realized in the mini-micro-nano project frame are reported.

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Chapter 2

Literature Survey (Section A):

Surface Properties Characterization

2.1 Introduction

The study of the mechanical properties at the micro and nanoscale is of great practicle importance for the development of M-NEMS in order to provide the reliability of the conceived Systems. For more than a century, researchers in material sciences hâve tried to develop techniques and experimental tools able to dérivé the mechanical properties of materials at small scales. In the past two décades, however, a véritable révolution has occurred thanks to the development of new sensors and actuators. This chapter présents an overview of the main techniques to characterize the surface properties at the nanoscale.

Depth sensing nanoindentation provides a highly powerful method for ineasuring the localized Young’s modulus and hardness, and there has been considérable progresses in the measurement of other mechanical properties such as the hardening/softening behavior, the creep efîect, and the residual stresses. The nanoindentation technique current rôle and some of the physical phenomena connected with it are presented here, with spécial emphasis on the post treatment methods.

Thin layers are of great practical importance nowadays, thus, the problems associeted with the nanoindentation of thin layers are also discussed in this chapter. Nano- scratching, which is a powerful technique to study, for instance, the délamination of thin layers, is also presented and discussed.

On the other hand, the interaction and adhesion of surfaces brought into contact is primordial in the conception of micromanipulator tools. AFM can be utilized to dérivé the attractive forces between two approaching objects. Surface energy, which is connected with the adhesion between two bodies, can also be measured with surface angle measurements. Those techniques are described and illustrated in the last part of the chapter.

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Literature Survey (Section A): Surface Properties Characterization

2.2 Mechanical Properties by Nanoindentation

2.2.1 Generalities about Nanoindentation

Ncinoindentation is a novel technique developed in the pa.st two décades to measure the mechanical properties of materials [7-24]. This technique is based on high-resolution instruments that continuously monitor the loads and displacements of an indenter as it is pushed into and withdrawn from a material. The load-displacement data (see figure 2.1) obtained from the indentation process, which is often referred to a load-penetration depth curve of indentation, can be used to dérivé varions mechanical properties of materials, most commonly, hardness and Young’s modulus. In addition, the load-displacement curve may contain other information about properties such as the hardening exponents [25-28], creep parameters [29-31] and residual stresses [32-35].

An obvions advantage of depth-sensing indentation test over conventional hardness test is that the contact area of an imprint can be directly determined from the load- penetration depth curve knowing the geometry of the indenter. This feature makes the depth-sensing indentation test particularly suitable for measuring the mechanical properties of materieJs at small scales where accurate détermination of the contact area would be an extremely difficult task for conventional hardness test.

In general, load-displacement curves provide a lot of information but care shoidd be given to the conditions in which these properties were derived. Several adaptations to the basic nanoindentation set-up could be applied to obtain additional information about the processes that occur dming nanoindentation testing. For example, in-situ measurements of acoustic émissions and contact résistance can indicate if a phase transformation, fracture or delanrination occurred in the sample [36-46]. Environmen- tal control can also be used to examine the effects of température and surface chemistry on the mechanical behavior of nanocontacts.

As can be seen, nanoindentation is in continuing development and the aim of the following paragraphe is to summarize the state of the art about this useful mechanical properties characterization technique.

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2.2. Mechanical Properties by Nanoindentation

An idéal load-penetration cnrve* obtained after a nanoindentation experiment consista of two parts, loading and unloading, as shown in figure 2.1. The loading part normally 2.2.2 Young’s Modulus and Hardness by Oliver & Pharr

Figure 2.1: Schematic of a load-displaœment curve as obtained from a single nanoindentation test and the principal parameters eniployed in the Oliver and Pharr

technique. [8]

includes the elastic-plastic deformation of the material [7,8,10] and can be expressed as

P = AhT' (2.1)

where P is the indentation load, h is the pénétration depth measured from surface, m and A are two constants that are dépendent on the geometry of the indenter and the mechanical properties of the material. The relationship in Eq. 2.1 has been confînned by the experiments of Hainsworth et al. 1996 [10]. According to Oliver and Pharr [7,8,10] the unloading part of the indentation process, which is mainly elastic, can be described by

P = Bh'^ (2.2)

where hg is the elastic depth of the pénétration, B is a constant that is related to the elastic properties of materials and the geometry of indenter, and m is a constant, which equals 1, 1.5, and 2 for a fiat cylinder punch, sphere or parabola of rotation, and cône, respectively. Experiments conducted on a variety of materials hâve revealed that the imloading curve is well-described by équation 2.2. Rewriting hg as h — hf one finds

P = B{h-h}Y' (2.3)

where hf is the final pénétration depth after complété unloading.

^Also called load-displacement curve

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P

II

Figure 2.2: Schematic oian indentation cross-section and the parameters used during the détermination of the Young’s modulas and hardness. [8j

To obtain reliable indentation results accurate knowledge of the area of contact is crucial. In order to détermine the projected contact area two factors must be known.

One is the geometry of the indenter, i.e. the area function, A = f(h), that relates the cross-sectional area of the indenter to the distance from its tip. This area function can be determined by direct measurement^ or can be derived using the calibration method suggested by Oliver and Pharr [8].

A general fonn that is often used to describe the area function is

A = Cih^ + Cih + Czh}!'^ + + ... (2.4) where the number of terms is chosen to provide a good fit over the entire range of calibration.

The other parameter needed for the calculation of the projected contact area is the contact depth at peak load. As shown in Fig. 2.2, the contact depth at peak load is given by

hc — hnmx fis (2’^)

where hc is the so called contact depth, hmax is the maximum pénétration depth, which can be directly determined from the load-penetration curve and fis is the defiection of the surface at the perimeter of the contact. It is given by Sneddon’s équation.

fis=e^ (2.6)

where £ is a géométrie constant and e = 0.72 for cône, £ = 0.75 for paraboloid of révo

lution, and e = 1 for fiat punch while S is the contact stiffness at the initial unloarling.

^This approach is particularly inconvénient, especially at very low loads where direct imaging is difficult to perform.

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The contact stiffness, S, is cletermined in two steps: firstly, a fraction of the unloading curve (normally the unloading data from 20-95% is considered) is fitted with équation 2.3. Secondly, the unloading curve fit is differentiated analytically to déterminé the slope at maximum load

5 = ^(W

dh (2.7)

The contact depth is then determined by recombining équations 2.5, 2.6 and 2.7

hc — hmax £ (2.8)

and the projected contact area can consequently be calculated from the relation

Ac = f(hc) (2.9)

The relation connecting the contact area to the contact depth can be directly derived by imaging the indenter tip by atomic force microscopy (AFM), which is the most reliable way, or can be indirectly derived. This second way implies performing several indentations at different increasing maximum load in a material of known Young’s modulus and the final Ac = f(hc) relation is found by deriving the contact area for which the experimental Young’s modulus match the expected one.

Now, assuming that indenter and specimen behave like springs in sériés [14], the elastic deformation of both can be characterized by a single ’reduced modulus’

l _l-uf 1 - i/|

Er Ei Es (2.10)

where Er is the so-called reduced modulus due to a non-rigid indenter, Ei (known) is the Young’s modulus of indenter, Es is the Young’s modulus of the specimen, i/i (known) and i/g (known) are the Poisson’s ratio of the indenter and the specimen, respectively.

Introducing the équation

Er \pïï s

(2.11) which is derived from the Sneddon’s solution (1965) for the elastic deformation of an isotropie elastic material with a flat-ended cylindrical punch, one finds the unknown specimen Young’s modulus Es which is the only unknown parameter remaining.

In addition to the Young’s modulus of the specimen, the data obtained using this method can be used to déterminé the hardness, H. We define the hardness as the mean pressure the material will support under load. With this définition, the hardness is computed from

H = (2.12)

■^C

where Ac is the projected ruea of contact at peak load evaluated from équation 2.9.

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idéal elastic

déplacement

I

elrnfic zone

ngid-plastic

rigid zone

elastoplastic

strain

displacemeni

I

elastic zone

Figure 2.3: Schematic présentation of stress-strain diagrains, load-displacement curves, and surface profiles at maximum load (full Unes) and after complets unloading (dotted Unes)

for idéal elastic (left), rigid-plastic (middie), and elastoplastic materials (right) [47].

Figure 2.3 shows the stress-strain diagrams, the load-displacement curves and the surface profiles at maximum load for an idéal elastic, rigid plastic and elastoplastic material.

Note 1:

Hardness measured using this définition may be different from that obtained from the more conventional définition in which the area is determined by direct measurement of the size of the residual hardness impression. This is because, in few materials, a portion of the contact area under load may not be plastically deformed, and as a resuit, the contact area measured by observation of the residual hardness impression may be less than that at peak load.

Note 2:

The Poisson’s coefficient is necessary to dérivé the Young’s modulus of the indented sample (see équation 2.10). Thus, in the experimental chapters, Young’s modulus will be derived when indenting on materials with known Poisson’s coefficient (bulk titanium and nickel) while the only ’reduced modulus’ will be calculated for materials with unknown Poisson’s coefficient (thin layers). Nevertheless, Young’s modulus and reduced modulus values are similar.

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In order to improve the characterization of the Young’s modulus and hardness of a given material many authors proposed a different approach based on energetic considérations [48-54],

2.2.3 Young’s Modulus and Hardness by the Energetic Approach

P.

O,

rtO J

Figure 2.4: Energetic load-diaplacement curve. [48]

hf K,

Displacement h

The principle of the energetic approach was first introduced by Stilwell and Tabor in 1961. In this work, it was shown that the conventional estimation of hardness (maximum applied load divided by the projected contact area H = Pmax!Acontact) is équivalent to the plastic work divided by the plastically deformed volume [50], This hardness characterization method was nevertheless not useful due to the lack of préci

sion of the measurement techniques.

Starting from the conventional expression of hardness one can write:

^conventional —

Pdh dWrpi

dh dl4_pi (2.13)

where Wpi and Vpi are the plastic work and the plastic volume respectively.

Integrating this last expression for pénétration h ranging from 0 to hmax one find:

, J^”‘"Pdh f^-'^^dWpi Wpi

(2.14) which is the expression for the energetic hardness. As a conséquence, for purely elastic indentation, one obtains lien = g and the hardness value is then undefined.

The plastic work as well as the elastic work involved during an indentation experiment can easily be derived from the load-displacement curve (see figure 2.4).

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The other paranieter necessary to the energetic hardness détermination is the plastic volume Vpi. Wolf et. al [55] hâve proposed the calculation of Vpi by using the contact area determined by the tip area fmrction (see previous sections for more details). It was shown previously that the aurea of contact can be expressed as a function of the pénétration:

A{h) = Cih^ + C2h + + ... (2.15)

and the contact volume can then be derived integrating this latter équation:

, 2C3/i3/2 ,

V{h) = j A{h)dh=^- + —^ +--------- +-------- + ... (2.16) which correspond to the volume of the tip pressed into the sample under load. Dming the unloading, a part of the deformation is relaxed. In a first order approximation, it can be assumed that this elastic relaxation occurs mainly in the vertical direction, whereas the latéral relaxation is negligible. The plastic volume of the remaining imprint can then be calculated as follow:

V{pl) = * V{hc) (2.17)

hjQ

Cheng and Chen [56] demonstrated that the ratio Wpi/{Wpi + Wei) can be linked to the material constitutive behavior such as ratio of hardness to reduced modulus H/Er-

Wpi Wtot

(2.18) where Wtot = Wpi + Wei-

The value x can be derived by indenting in a sample of known Young’s modulus, for instance using the standard sample (fused quartz) used during the area function calibration.

Knowing the hardness, it is now possible to dérivé the reduced modulus associated with the material (and consequently the Young’s modulus).

xHo

1 - Wpi/Wtot (2.19)

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Continuous Stiffness Measurement (CSM) is a recent and extremely powerful technique [16] that ofîers a significant improvement in nanoindentation testing. The CSM allows the measurement of the contact stiffness at any point along the loading curve and not just at the point of unloading as described in the preceding section. This is accomplished by imposing a harmonie force P = Pos, which is added to the nominally increasing load on the indenter, as shown in figure 2.5.

2.2.4 Continuous Stiffness Measurement

Figure 2.5: Schematic of the Contact Stiffness Measurement (CSM) loading cycle. [16j

By continuously measuring the displacement response h(u>) during the loading of the indenter at the excitation frequency and the phase angle between the two, it is possible to solve the in-phase and out-of-phase portions of the response results. This permits an explicit détermination of the contact stiffness, S, as a continuous function of depth.

Considering the masse m of the indenter, the spring constant. Kg, of the leaf springs that support the indenter, the stiffness of the indenter frame Kf = 1/C/ (where Cf is the compliance of the load frame) and the damping coefficient, C, due to the air in the gaps of the capacitor plate displacement sensing System, combined with the contact stiffness. S, it is possible to schematize the overall response as shown in figure 2.6.

As a resuit, knowing the imposed driving force P = Pose^'“^^^ and the displacement response of the indenter h(m) = the schematic of figure 2.6 can be solved for the contact stifiFness S passing from the détermination of the displacement signal,

= + Ks- rnut^y + (2.20)

or from the phase angle between the force and the displacenient signal.

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taii((ÿ) = ^ùj^C (2.21)

(5-1 + +/f. - mu2 where u> is the frequency of the oscillation.

Solving équations 2.20 and 2.21 for the contact stifihess, S, and for the damping due to the air in the gaps between the capacitor plates wC one finds (the damping of the contact itself is regarded to be negligible):

This technique makes possible the measurement of mechanical properties of materials such as hardness and Young’s modulus as a continuons function of depth from a single indentation experiment. It makes also possible to obtain data at very small pénétration depths. This makes CSM a powerful tool for measuring mechanical properties of nanometric films.

5 = ¹ (2.22)

(2.23)

S Kf= 1/Cf

Mass - m

Figure 2.6: Schematic of the dynainic indentation model. [8j

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In addition, treating non uniform materials in which the microstructm'e and tiie me- chanicai properties change with indentation depth becomes possibie. Furthermore, utiiizing the continuons stiffness technique, creep measurement on the nanoscale can be performed by monitoring changes in dispiacement and stress reiaxation.

Moreover, CSM is iess sensitive to thermai drift because it is carried out at frequencies greater than 40 Hz. This aiiows the accurate observation of creep in smaii indents to be carried out over a iong time period. Aiso, the performance of fatigue tests at the nanoscaie is permitted tiurough ioad cycies of a sinusoidai shape at high frequencies.

The fatigue behavior of tiiin fiinis and microbeains can be studied by monitoring the change in contact stiffness because it has been demonstrated that the contact stiffness is sensitive to damage formation.

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2.2.5 Fracture Toughness Characterization

Fracture toughness is a term that quantitatively describes the material’s résistance to fracturing in the presence of a crack. Large values of fracture toughness mean that the material will probably undergo ductile fracture while low values of fracture toughness indicate that the material will probably face brittle friture.

To explain the fracture toughness, one can assume that the stabiUty of the crack is assessed as follow [57-60]. For simplicity, the displacement at a defined load can be considered constant and the problem can be simphfied characterizing the crack by its area A. Increasing the load will lead to a larger crack (area A+dA), and the strain energy released rate can be evaluate with respect to the change in crack area.

If the displacement is constant, the force level is dictated by the stiffness (or com- phance) of the indented body. Thus, when the crack increases in size, the stiffness decrease and that leads to a decreasing of the force level. The fact that the force level decrease under the same displacement indicates that the elastic strain energy stored in the body is decreasing (is being released). Generally, the higher the load, the higher the cracks and the higher the elastic strain energy released.

When the released strain energy exceeds a critical value, the crack will grow spon- taneously. For brittle material, the crack will grow (in an unstable manner) if the the elastic energy released by the crack is greater than the critical energy required to increeise the crack surface. For ductile materials, the energy associated with the plastic deformation must be taken into account. In this case, the energy involved in the propagation of the crack can be much larger than the one observed for brittle ma

terials since the work necessary for the plastic deformation can be much greater than the surface energy.

In practice, if the elastic energy released is higher than the sum of the surface energy and plastic deformation energy, the crack will propagate.

Nanoindentation can be used to evaluate the fracture toughness of materials and inter

faces by measuring the residual crack after complété unloading. This can be doue for instance by taking some AFM or high resolution SEM images of the residual imprint.

The type of the created cracks, as well as their formation mechanism, varies according to the nature of the material and the indenter geometry. The two main crack geometry régimes for sharp indenters are described by the Half-Penny and the Palmqvist model depending on the crack formation évolution [61,62].

Half-Penny models are connected with both médian and radial cracks. Médian cracks consist of penny shaped cracks which lie perpendicular to the indented surface while radial cracks are cracks propagating radially from the tip center. Palmqvist models are developed for shallow radial créicks occurring on the specimen surface at the edge of the plastic contact impression, usually at the indentation corner.

It was demonstrated by Palmqvist that the length of cracks, which emanate from the corner of an indent, can be empirically related to the toughness of the investigated material [62].

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Figure 2.7: Crack deformation processes: a) médian cracks b) shallow radiai cracks c) latéral cracks [63j.

Attention is usually given to the length of the radial cracks as measm-ed froni the corner of the indentation and then radiaJly outward along the specimen surface as shown in figure 2.8.

Figure 2.8: Crack parameters for a Berkovich indenter when measuring the fracture toughness.

The nunierical values of the fracture toughness in the case of both Palmqvist and Half-Penny models can then be derived measuring the length of the radial cracks and applying the Laugier’s équations [64,65]:

Where Kc is the fracture toughness, a,c,l describe the length of radial cracks (see image 2.8), E the Young’s modulus, H the hardness, x„P and XyHP two constants (usually 0.015).

(2.24)

(2.25)

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Latéral cracks can also be présent. They are usually generated below the surface regardless of whether the threshold for médian crack initiation is exceeded or not. If the applied load is too high for the given specimen then these latéral cracks tend to divert upwards toward the surface, and can resuit in material removal at the surface.

This process is ailso called "chipping” [60].

Table 2.1 sumniarizes the fracture toughness for the most common materials.

Material Fracture Toughness

[MPa mi/2]

Metals Aluminium alloy 36

Steel alloy 50

Titanium alloy 44-66

Ceramics Aluminium oxide 3-5

Silicon Carbide 0.7-0.8

Concrète 0.2-1.4

Polymers Polymethyl méthacrylate 1

Polystyrène 0.8-1.1

Table 2.1: Typical fracture toughness values for the most common materials.

It is important to mention that the presence of residual stresses can influence the fracture résistance. From the theoretical point of view, the apparent surface crack length is a combination of both the intrinsic fracture toughness of the material and the pre-existing residual stresses. Compressive stresses will lead to a diminution of the surface crack length relative to the equilibrium length in the absence of stresses.

Tensile stresses will do the opposite [66].

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2.2.6 Indentation of Thin Layers

Measuring the mechanical properties of bulk materials has been the subject of the prececling paragraphs. This chapter will deal with the use of nanoinclentation in the measurement of mechanical properties of thin films. Any ineasurement performed on the whole sample will inevitably be dominated by the bulk substrate. Nanoindentation, since it allows to perform indentation at a very small depth, offers a possible solution to avoid the substrate influence and to the problem of measuring exclusively the properties of the film.

However, the problems cornes in part from the presence of an interface between the film and substrate. The quality of the interface can be afîected by many variables, resulting in a range of efîects on the apparent elastic and plastic properties of the film.

In particular, when the deformation région around the indent approaches the interface, the indentation curve may exhibit features due to the thin film, the bulk, the interface, or a combination of ail three. As a direct conséquence of these complications, models for thin-film behavior must attempt to tcike into account not only the properties of the film and substrate, but also the interface between them.

If the standard nanoindentation analysis routines are to be used and only the thin film properties has to be measured, it is essential that the plastic zone and the elastic strain field are both confined to the film and do not reach the substrate.

Recently published ISO and ASTM standards (ISO: 14577-4 and ASTM: E 2546-07) State strong rules to conduct indentation tests on thin films:

• the surfaces must be smooth enough compared to the pénétration depth which means that the indentation depth should be at least 20 times greater than the Ra average roughness of the tested material;

• the maximum indentation depth should not exceed 10% of the thickness of the film to avoid the influence of the substrate.

As a resuit, when indenting films of a micron of thickness, the pénétration depth must be less than 100 run, and the surface roughness must be less than 5 nm. Clearly, this is difficult to achieve in practice.

In addition, these rules are questionable. There are film/substrate combinations for which 10% is very conservative, while for other combinations even 5% may be too deep. GeneraUy, for a very soft film on a hard substrate, nanoindentations of 50% of the film thickness can be al-right, but less than 10% can be necessary when indenting a hard film on a soft substrate. For a very hard film on a soft substrate, the surface film behaves like an elastic membrane or a bending plate.

Due to ail of these complications, the use of nanoindentation to study thin film me

chanical properties should be a danger if the interprétation of the resulting data is not done correctly. It can be easy to misguidedly take the values of E and H obtained during nanoindentation testing to be absolute values and discover later that those values contained significant errors.

Disponible à / Available at permalink :

D 03657

ULB

Characterization and

modification of the mechanical and surface properties at the

nanoscale

ULB

Characterization and

modification of the mechanical and surface properties at the

nanoscale

AUTORISEE

Acknowledgments

Abstract

Contents

Introduction

Literature Survey (Section A):

Surface Properties Characterization

I

I