POLITEHNICA UNIVERSITY OF TIMIŞOARA -...

POLITEHNICA UNIVERSITY OF TIMIŞOARA

MECHANICAL ENGINEERING FACULTY

DIPLOMA PROJECT

COORDINATORS:

CONF. PHD. ENG. MIRCEA DREUCEAN

LECTURER / PROJECT ENG. ANSSI SUHONEN

PHD. MIKKO LAASANEN

PHYSICIST ARI HALVARI

STUDENT:

CRISTINA FLOREA

TIMIŞOARA

2008

POLITEHNICA UNIVERSITY OF TIMIŞOARA

IN COLLABORATION WITH

SAVONIA UNIVERSITY OF APPLIED SCIENCES

DIPLOMA PROJECT

Nanoindentation of microstructures with an

atomic force microscope

COORDINATORS:

CONF. PHD. ENG. MIRCEA DREUCEAN

LECTURER / PROJECT ENG. ANSSI SUHONEN

PHD. /PROJECT ENG. MIKKO LAASANEN

PHYSICIST ARI HALVARI

STUDENT:

CRISTINA FLOREA

SPECIALIZATION: MEDICAL ENGINEERING

TIMIŞOARA

2008

Acknowledgements

As an international student, lost in the new country and surroundings, I was welcomed in the

Information Technology R&D Unit of the Savonia University of Applied Sciences, Kuopio,

Finland. I would first and foremost like to thank my teacher Mircea Dreucean for the opportunity

to study one semester in Finland and accomplish my diploma project. I would like to take this as

an opportunity to thank to Mikko Laasanen, Project Manager at Savonia University of Applied

Sciences, for his support and guidance in finishing this diploma project. I would also like to

sincerely thank to lecturer Anssi Suhonen and to physicist Ari Halvari at Savonia University of

Applied Sciences for patiently hearing to all my queries and teaching me how to use the AFM

software and helping me with the nanoindentation measurements. Furthermore, I want to thank

Sarianne Pääkkö, University of Kuopio for help with the bones samples. Last but not the least I

would like to thank to Asmo Jakorinne for helping me with the LabVIEW program. I would like

to thank to all of you for this wonderful contribution of time and effort. Any project would be

incomplete for me without support from my mother. So I would like to thank her for

understanding and loving support.

Cristina Florea

Timisoara, 10 June 2008

Rezumat

Microscopul de forţã atomicã (AFM) foarte rapid a devenit unul dintre cele mai

rãspândite metode pentru studierea proprietãţilor volumelor foarte mici de material. Recent,

nanoindentarea a apãrut ca un puternic instrument pentru mãsurarea la nivel nano- şi micro a

proprietãţilor mecanice a biomaterialelor.

Scopul acestei lucrãri a fost validarea metodei de mãsurare prin nanoindentare,

identificarea materialelor care sunt cele mai potrivite pentru calibrarea sistemului în vederea

analizãrii diferitelor materiale (dure sau moi), mãsurarea şi compararea modulului lui Young a

diferitelor materiale la nivel micro- (metale, polimeri, oase) cu modulul lui Young a materialului

în formã brutã. Modelul lui Hertz a fost folosit pentru calcularea modulului lui Young din partea

de descãrcare a curbei forţã-deplasare.S-a dovedit cã aceastã tehnicã de nanoindentare dã

rezultate bune pentru materiale moi (polimeri, oase). Modulul lui Young pentru polyimidã a fost

gãsit ca fiind 1.9 GPa ± 0.3, valoare apropiatã de cea prescrisã de producãtor. Modulul lui Young

s-a situat între 4.19 GPa ±2.55 pentru osul cortical de vitã şi 4.31 GPa ±4.91 pentru osul

trabecular de vitã.

Acest proiect cu caracter experimental, în urma rezultatelor experimentale obţinute

propune câteva îmbunãtãţiri a tehnicii de mãsurare rezolvând astfel o problemã de autodotare a

laboratorului.

Cuvinte Cheie: Microscop de forţã atomicã, nanoindentare, modulul lui Young, os trabecular şi

cortical

Abstract

The atomic force microscope (AFM) has rapidly become one of the most widely used

instrument for the investigation the surface topography for very small volumes of material. In

addition, the AFM can be used for analyzing material mechanical properties.(nanoindentation)

Recently, nanoindentation has emerged as a powerful tool for measuring nano- and microscale

mechanical properties, especially in biomaterials.

The main goal of this thesis was to verify the validity of the nanoindentation method for

solid materials. More specific objectives were to determine which material (hard or soft

materials) is most suitable for calibration of the system in order to analyze bones structures and to

use nanoindentation for comparing the Young’s modulus of different materials (metals,

polymers, bones) in microstruture state and bulk state. The Hertz model was used to calculate the

Young’s modulus from the unloading force-displacement curve. It was found that this

nanoindentation technique gives good results for soft materials (polyimide and bone). The

Young’s modulus for polyimide was found to be 1.9 GPa ± 0.3, close to the values provided by

the manufacturer. The Young’s modulus ranged from 4.19 GPa ± 2.55 for bovine cortical bone to

4.31 GPa ± 4.91 for bovine trabecular bone.

This experimental study, based on the experimental results achieved, suggests several

improvements for the measurement technique and for the equipment involved.

Key Words: Atomic force microscope, nanoindentation, Young’s modulus, trabecular cortical

bone

Table of contents

Plan tematic

Fişa de evaluare a proiectului de diplomă

Acknowledgements

Rezumat în limba română

Abstract

Pag.

1.Introduction.............................................................................................................. 1

2.Mechanical testing of elastic materials.................................................................. 4

2.1. Material deformation ............................................................................................. 4

2.1.1 Elastic deformation................................................................................... 5

2.1.2.Plastic deformation................................................................................... 5

2.2. Basic measurement geometries.............................................................................. 6

2.3. Young’s modulus and Poisson’s ratio.................................................................... 8

2.4. Hertz’s model for indentation geometry.................................................................

10

3.Atomic force microscope..........................................................................................

13

3.1. Brief history............................................................................................................ 13

3.2. Comparison of AFM to other microscopes…………………………………….... 14

3.3. AFM images........................................................................................................... 15

3.4. Interactive forces.................................................................................................... 16

3.5. Operation Principles............................................................................................... 17

3.6. Scan modes............................................................................................................ 18

3.6.1. Contact-AFM 18

3.6.2. Vibrating mode........................................................................................ 19

3.6.3. Non-contact mode 20

3.6.4. Resonant frequency................................................................................. 22

3.6.5.Advantages and disadvantages of C-AFM and-AFM.............................. 23

3.7.AFM Probe.............................................................................................................. 24

3.8.Force curve measurements...................................................................................... 25

3.9.AFM Application in biology……………………………………………………...

26

4. Nanoindentation ......................................................................................................

27

5. Materials and methods............................................................................................

33

5.1.Park System of XE-100 AFM............................................................................... 33

5.1.1. Primary components of XE-100 system.................................................. 33

5.1.2. XE-100 Stage........................................................................................... 34

5.1.3. XE-100 Head........................................................................................... 34

5.1.4. Cantilever movement detection mechanism used in XE-100.................. 36

5.1.5. XE Software............................................................................................. 38

5.1.6. Tips.......................................................................................................... 40

5.2. Materials................................................................................................................. 41

5.3. Technique used....................................................................................................... 45

5.4. Description of LabVIEW program 54

5.4.1.Calibration of AFM

cantilever..................................................................

55

5.4.2. Calculating the Young’s modulus of the analyzed material....................

58

6. Results.......................................................................................................................

63

7. Discussion and future directions............................................................................

67

References..................................................................................................................... 69

Appendix

Nanoindentation of microsctructures with an atomic force microscope

1

1. Introduction

In many aspects of technology, there is a drive for smaller and smaller components. As

the volumes of material decrease, the response of the material to characterization techniques may

be different from their bulk form. One explanation for the change in behavior is the increased role

of the surface. On the macro-scale the surface is such a small portion of the overall subject, it is

often ignored. When the volume is reduced sufficiently the surface becomes a large fraction of

the overall quantity of material.[1]

The mechanical characterization of tissue and other biological materials is of utmost

importance in clinical medicine and the field of biomaterials. Bone regeneration presents a major

challenge to orthopedic medicine. Current methods for the treatment of massive bone loss are

essentially dependent on artificial prostheses. Prostheses cannot be used in every case due to the

limitation of movement and biocompatibility issues. Similarly, the prosthesis can fail in the long

term and result in the loss of function and possibly morbidity. New nanoscale analysis applied in

bones and other mineralized biological materials enables a new window into the fine details of

mechanical behaviour at extremely small scales.[2]

The elastic properties of bone have been measured at the microstructural level in many

investigations. Some of the microstructural features of interest include individual trabeculae,

single osteons and the thin cortical shell. For many years, it was assumed that the elastic modulus

of these microstructural components are similar to those of dense cortical bone. However, recent

investigations have suggested that this may not be the case, rather the modulus of some of the

components may be smaller.

In addition, it appears that significant variations in Young’s modulus may exist within a

given microstructural component. For example, Young’s modulus for individual trabeculae

reported in the literature range from 1 to 14 GPa.[3-4] It should be noted, however, that even the

largest of these values is still smaller than the frequently quoted modulus for dense cortical bone,

E=17.1 GPa.[3] Observation of specimen size influences on the measured modulus also suggest

that the elastic modulus of the individual microstructural components of the bone may not be the


2

same as the macroscopically measured values. Choi et al [5] and Lotz et al.[6] found that

Young’s modulus for cortical bone obtained from micro-bending tests (5.4 and 12.5 GPa,

respectively) is considerably smaller than that obtained by others in tensile tests of large

specimens (17.1 GPa [7])

One explanation for these observations is that the elastic properties of the microstructural

components of the bone are not the same as the macroscopic values. More recently, a

nanoindentation technique was developed that allows measurement of some mechanical

properties within a bone. The nanoindentation technique has several advantages over

conventional microhardness measurement methods, such as the Vickers and Knoop techniques.

Major benefits arise from the accurate positioning capability and the high resolution load and

depth-sensing capabilities which enable relatively small areas of material to be tested and

measured.

Rho et al.[8] found that Young’s modulus for human vertebral trabeculae obtained using

nanoindentation is 13.5GPa ± 2.0. Furthermore, Hengsberger et al [9] found that Young’s

modulus ranged from 18GPa ± 1.7 for human cortical bone to 22.5GPa ± 3.1 for a human

trabecular bone. Zysset et al.[10] found that the elastic modulus ranged from 6.9GPa ± 4.3 in

trabecular tissue from the femoral neck of a 74 year old female up to 25.0GPa ± 4.3 in interstitial

tissue from the diaphyseal cortex of a 69 year old female. Makoto et al [11] reported that the

averages for the longitudinal elastic modulus for bovine plexiform and Haversian bone specimens

were 17.9GPa ±4.1 and 10.0GPa ±4.0, respectively. The average elastic modulus measured for

pig plexiform bone was 14.6GPa ±3.9, and the average for pig Haversian bone was 8.3GPa ± 3.3.

Previous nanoindentation studies characterized the dependence of the elastic modulus of the

cortical and trabecular bone with age, anatomical site, microstructural orientation and tissue

preparation.

AFM based nanoindentation involves a probe tip lowered into contact with the sample,

then indented into the surface, and finally lifted off the sample surface. Concurrently, a

measurement of the probe tip deflection is produced through an optical lever detection system, in

which a laser beam is reflected off the top of the probe and onto a segmented photodiode. A plot

of this tip deflection signal as a function of the vertical displacement of the piezo scanner is

called a force curve. With this new measurement technique, loads as small as tenths of

micronewtons and depths as small as fractions of nanometers, are measurable.


3

This thesis is organized into seven chapters:

The first Chapter is this introduction, discussing the relevant literature and the

background for bone nanoindentation

Chapter 2 starts with a discussion of mechanical testing of elastic materials. There

is an introduction to contact mechanics starting with elastic deformation and Hertz

model for indentation geometry

In Chapter 3, atomic force microscope (AFM), the main instrument used in this

thesis, is introduced

Chapter 4 presents 2 main nanoindentation techniques : depth-sensing

nanoindentation and AFM based nanoindentation

Chapter 5 presents all the experimental procedures, describes the instrumentation

aspects of the microscope and the materials and also the LabVIEW program used

for analyzing the experimental datas

Chapter 6 is devoted to the experimental results

General conclusions and the ideas for the future research are given in Chapter 7

The experiments were carried out in Microsensorlaboratory of Savonia University of

Applied Sciences, Information Technology R&D Unit, Kuopio, Finland. Microsensorlaboratory

provides resources for testing and fabrication of micro- and nanoscale sensors and structures.

Education, technical surveys and customization of commercial sensors are the most important

side activities.


4

2. Mechanical testing of elastic materials

2.1 Material deformation

“In engineering mechanics, deformation is a change in shape due to an applied force.

This can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or

torsion (twisting). Deformation is often described in terms of strain.”[12]

The engineering measures of stress and strain, denoted in this module as ζe and εe respectively,

are determined from the measured the load (P) and deflection (δ)using the original specimen

cross-sectional area A0 and length L0 as :

0A

Pe (2.1)

0L

e

(2.2)

The image below shows the engineering stress vs. strain diagram for a typical ductile material

such as steel:

Figure 2.1.Stress vs. strain diagram

http://en.wikipedia.org/wiki/Engineering_mechanics

http://en.wikipedia.org/wiki/Force_%28physics%29

http://en.wikipedia.org/wiki/Tensile_strength

http://en.wikipedia.org/wiki/Compressive_strength

http://en.wikipedia.org/wiki/Simple_shear

http://en.wikipedia.org/wiki/Bending

http://en.wikipedia.org/wiki/Torsion

http://en.wikipedia.org/wiki/Strain_%28materials_science%29


5

Depending on the type of material, size and geometry of the object, and the forces applied,

various types of deformation may result. The most common types of deformation are introduced

in the following chapters.

2.1.1 Elastic deformation

“This type of deformation is reversible. Once the forces are no longer applied, the object

returns to its original shape. Soft thermoplastics and metals have moderate elastic deformation

ranges while ceramics, crystals, and hard thermosetting plastics undergo almost no elastic

deformation. Elastic deformation is governed by Hooke's law which states:

E (2.3)

ζ is the applied stress

E is a material constant called Young's modulus

ε is the resulting strain.

This relationship only applies in the elastic range and indicates that the slope of the stress vs.

strain curve can be used to find Young's modulus.”[12]

2.1.2 Plastic deformation

“This type of deformation is not reversible. However, an object in the plastic deformation

range will first have undergone elastic deformation, which is reversible, so the object will return

part way to its original shape. Soft thermoplastics have a rather large plastic deformation range as

do ductile metals such as copper, silver, and gold. Steel does, too, but not iron. Hard

thermosetting plastics, rubber, crystals, and ceramics have minimal plastic deformation ranges.

Under tensile stress plastic deformation is characterized by a strain hardening region and a

necking region and finally, fracture (also called rupture). During strain hardening the material

becomes stronger through the movement of atomic dislocations. The necking phase is indicated

by a reduction in cross-sectional area of the specimen. Necking begins after the ultimate strength

is reached. During necking, the material can no longer withstand the maximum stress and the

http://en.wikipedia.org/wiki/Thermoplastic

http://en.wikipedia.org/wiki/Metal

http://en.wikipedia.org/wiki/Ceramic

http://en.wikipedia.org/wiki/Crystal

http://en.wikipedia.org/wiki/Thermosetting_plastic

http://en.wikipedia.org/wiki/Hooke%27s_law

http://en.wikipedia.org/wiki/Stress_%28physics%29

http://en.wikipedia.org/wiki/Young%27s_modulus

http://en.wikipedia.org/wiki/Strain

http://en.wikipedia.org/wiki/Thermoplastics

http://en.wikipedia.org/wiki/Copper

http://en.wikipedia.org/wiki/Silver

http://en.wikipedia.org/wiki/Gold

http://en.wikipedia.org/wiki/Steel

http://en.wikipedia.org/wiki/Iron

http://en.wikipedia.org/wiki/Strain_hardening

http://en.wikipedia.org/wiki/Necking_%28engineering%29

http://en.wikipedia.org/wiki/Dislocation


6

strain in the specimen rapidly increases. Plastic deformation ends with the fracture of the

material.”[12]

2.2. Basic measurement geometries

Mechanical properties of materials can be characterized by determining the load-

deformation behavior. [13] For this purposes there are three different commonly accepted

measurement geometries:

indentation

unconfined compression

confined compression

Figure 2.2.During indentation, the sample is compressed with a plane-ended or spherical ended,

impermeable or permeable indenter. Indentation is possible in situ or in vivo


7

Figure 2.3.In unconfined compression the sample is compressed between two smooth frictionless

impermeable platens

Figure 2.4.In confined compression the sample is compressed with a permeable piston. The

sample is placed in a confining chamber

In all geometries the compression is made under load or displacement (creep or stress-

relaxation). In the stress-relaxation test, a constant deformation is induced in the sample and

relaxation of the load is recorded. In the creep test, a constant stress is exposed on the sample and

the time-dependent deformation of the sample is registered.


8

2.3 Young’s modulus and Poisson’s ratio

Elastic modulus is sometimes called Young's modulus after Thomas Young who

published the concept back in 1807. Young’s modulus (E) refers to the stiffness or elasticity of a

material and is defined by it’s resistance to elastic deformation. The ratio of an applied normal

stress, to the resultant normal strain, in the direction of loading:

E (2.4)

The relation applies only for strains up to an elastic limit, which is of order of 0.1-1.0% for most

materials. Values of E range from ~0.01 GPa for rubbers, through ~1-10 GPa for ceramic (fibres)

and 1000 GPa for diamond.

Modulus of elasticity is the slope of the straight line portion of a stress-strain diagram.

Tangent modulus of elasticity is the slope of the stress-strain diagram at any point. Secant

modulus of elasticity is stress divided by strain at any given value of stress or strain. Tangent and

secant modulus of elasticity are equal, up to the proportional limit of a material.

Specifying how stress and strain are to be measured, including directions, allows for many types

of elastic moduli to be defined. The three primary ones are:

Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform

along an axis when opposing forces are applied along that axis; it is defined as the ratio of

tensile stress to tensile strain. It is often referred to simply as the elastic modulus.

The shear modulus or modulus of rigidity (G or μ) describes an object's tendency to shear

(the deformation of shape at constant volume) when acted upon by opposing forces; it is

defined as shear stress over shear strain. The shear modulus is part of the derivation of

viscosity.

The bulk modulus (K) describes volumetric elasticity, or the tendency of an object's

volume to deform when under pressure; it is defined as volumetric stress over volumetric

strain, and is the inverse of compressibility. The bulk modulus is an extension of Young's

modulus to three dimensions.

http://en.wikipedia.org/wiki/Young%27s_modulus

http://en.wikipedia.org/wiki/Elasticity_%28physics%29

http://en.wikipedia.org/wiki/Tensile_stress

http://en.wikipedia.org/wiki/Tensile


http://en.wikipedia.org/wiki/Shear_modulus

http://en.wikipedia.org/wiki/Shear_stress

http://en.wikipedia.org/wiki/Shear_strain

http://en.wikipedia.org/wiki/Viscosity

http://en.wikipedia.org/wiki/Bulk_modulus

http://en.wikipedia.org/wiki/Stress_%28physics%29#Stress_deviator_tensor

http://en.wikipedia.org/wiki/Compressibility


9

Poisson's ratio (ν), named after Simeon Poisson, is the ratio of the relative contraction

strain, or transverse strain (normal to the applied load), divided by the relative extension strain, or

axial strain (in the direction of the applied load).

xx

yy

(2.5)

Tensile deformation (εyy) is considered positive and compressive deformation (εxx) is considered

negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a

positive ratio. The Poisson ratio for most metals falls between 0.25 to 0.35. Rubber has a

Poisson’s ratio close to 0.5 and is therefore almost incompressible. Theoretical materials with a

Poisson’s ratio of exactly 0.5 are truly incompressible, since the sum of all their strains leads to a

zero volume change. The Poisson's ratio is bounded by two theoretical limits:

it must be greater than -1, and less than or equal to 0.5

(2.6)

The proof for this stems from the fact that E, G, and K are all positive and mutually dependent.

However, it is rare to encounter engineering materials with negative Poisson’s ratios. Most

materials will fall in the range, [14]

(2.7)

http://en.wikipedia.org/wiki/Simeon_Poisson


http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/elastic_constants_G_K.cfm#shearmod

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/elastic_constants_G_K.cfm#bulkmod

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/elastic_constants_G_K.cfm#shearmod


10

2.4 Hertz’s model for indentation geometry

“The Hertz model of contact mechanics [15] was the first attempt to provide a theoretical

basis for the physics of contacts between solids. Although it has been extended and refined, most

notably by Johnson, Kendall, and Roberts (JKR) and Derjaguin, Muller, and Toporov (DMT), the

Hertz model remains a useful and simple method for estimating some of the properties of

materials during contact. In particular, it does not account for either short-range (modeled by

JKR) or long-range (modeled by DMT) pre-contact attractive interactions, which may cause

deformation of one or other of the surfaces in contact. The Hertz model has proven sufficient for

modeling of AFM data on soft biological samples (Laney et al., 1997).” [16]

Indentation is the act of bringing two bodies into contact, one being a probe, extremely

stiff and minimally altered by the interaction, the second is the specimen whose properties we are

interested in quantifying. It is the response to this applied load that provides an indication of the

mechanical properties. In order to understand and interpret what is measured during indentation

testing, its necessary to start with the theories that describe the influence of force on materials.

Hertz first theorized about idealized material contact when working with distortion due to

contacting lenses in 1882. The contact distorted the lenses and caused fringes to be formed in the

transmitted light. In order to understand the nonpermanent change in the lens shape he began to

investigate elasticity. His theory of elasticity can also be applied to the initial portion of point

contact loading.[17]

He demonstrated that the radius of contact (a) is related to the combined radius of the

objects (R), the force applied (F), and the materials elastic properties (E*) in the following

manner:

*

3

4

3

E

RFa

(2.8)

Figure is a cross-section of a flat surface and a rigid spherical indenter. The indenter

radius is R, the radius of contact is a, and ht is the total depth of penetration. The other two depths

indicated are the distance from the free surface to the radius of contact (he), and the distance from

the radius of contact to the total depth (hp).


11

Figure 2.5.Schematic of the interaction between a rigid spherical indenter

(with radius = R) and a flat surface

The quantity E* combines the modulus of the indenter and the specimen and is given by:

i

i

m

m

EEE

)1()1(122

*

(2.9)

E* - the reduced modulus

Em , Ei- Young’s modulus for the sample material and the indenter

vm , vi - materials Poisson’s ratio of the material and indenter, respectively

It is a composite modulus property used to account for the non-rigid tip interaction, or the

elastic interactions of the tip and the surface. An efficient method of combining the two moduli is

to assume that the two materials behave as springs in series.

If both contacting bodies have a curvature, then R in the above equations is their relative

radii given by:

21

111

RRR (2.10)

R1 , R2 are the radii of the two contacting bodies

In the previous equation the radius of the indenter is set to be positive always, and the

radius of the specimen to be positive if its center of curvature is on the opposite side of the lines

of the contact between two bodies.


12

It is important to realize that the deformation at the contact are localized and the Hertz

equations are concerned with these and not the bulk deformations and stresses associated with the

method of support of the contacting bodies. The deflection h of the original free surface in the

vicinity of the indenter is given by:

)2(42

3

*

12

2

a

r

a

F

Eh ar (2.11)

In this equation r is the radial distance from the axis of symmetry. This equation helps to define

that of the total elastic displacement pictured in Figure 2.5.

It can be easily shown that the depth of the circle of contact beneath the specimen free surface is

half of the total elastic displacement. That is, the distance from the specimen free surface to the

depth of the radius of the circle of contact at full load is ha=hp=ht/2.

The distance of mutual approach of distant points in the indenter and specimen is calculated

from:

R

F

E

22

*

3 )4

3( (2.12)

Substituting Eq.(2.12) into Eq.(2.8) , we can express the distance of mutual approach as:

R

a 2

(2.13)

For the case of a non-rigid indenter, if the specimen is assigned a modulus of E*

,then the contact

can be viewed as taking place between a rigid indenter of radius R. δ in Eq.(2.11) becomes the

total depth of penetration ht beneath the specimen free surface. Rearranging Eq (2.12) slightly,

we obtain:

23

21

*

3

4thREF (2.13)

From Eq.(2.13) ,Young’s modulus is given by :

2

3

4

)1(3

R

FE

(2.14)


13

3. Atomic force microscope

3.1 Brief history

Scanning probe microscopy (SPM) techniques have developed into important tools for

surface physics and the characterization of surface structures in recent years. The different types

of scanning probe microscopes provide the possibility of investigating electrical, topographic,

optical, magnetic and many other types of surface properties with atomic resolution.[18]

The atomic force microscope (AFM) or scanning force microscope (SFM) is a very

high-resolution type of scanning probe microscope, with demonstrated resolution of fractions of a

nanometer, more than 1000 times better than the optical diffraction limit. The precursor to the

AFM, the scanning tunneling microscope STM, was developed by Gerd Binnig and Heinrich

Rohrer in the early 1980s, a development that earned them the Nobel Prize for Physics in 1986.

Binnig, Quate and Gerber invented the first AFM in 1985. Their original AFM consisted of

a diamond shard attached to a strip of gold foil. The diamond tip contacted the surface directly,

with the interatomic van der Waals forces providing the interaction mechanism. Detection of the

cantilever’s vertical movement was done with a second tip - an STM placed above the cantilever.

Figure 3.1.The world's first atomic force microscope on display in the Science Museum in

London, UK [19]

http://en.wikipedia.org/wiki/Scanning_probe_microscopy

http://en.wikipedia.org/wiki/Nanometer

http://en.wikipedia.org/wiki/Diffraction_limited

http://en.wikipedia.org/wiki/Scanning_tunneling_microscope

http://en.wikipedia.org/wiki/Gerd_Binnig

http://en.wikipedia.org/wiki/Calvin_Quate

http://en.wikipedia.org/w/index.php?title=Christoph_Gerber&action=edit&redlink=1


14

3.2 Comparison of AFM to other microscopes

“The Atomic Force Microscope (AFM ) is being used to solve processing and materials

problems in a wide range of technologies affecting the electronics, telecommunications,

biological, chemical, automotive, aerospace, and energy industries. The materials being

investigating include thin and thick film coatings, ceramics, composites, glasses, synthetic and

biological membranes, metals, polymers, and semiconductors. The AFM is being applied to

studies of phenomena such as abrasion, adhesion, cleaning, corrosion, etching, friction,

lubrication, plating, and polishing. By using AFM one can not only image the surface in atomic

resolution but also measure the force at nano-newton scale.”[20]

In comparison, with other forms of microscopy the AFM is better or comparable.

AFM versus Scanning Electron Microscope:

Compared with Scanning Electron Microscope, AFM provides extraordinary topographic

contrast, direct height measurements and unobstructed views of surface features ( no

coating is necessary).

AFM versus Transmission Electron Microscope :

Compared with Transmission Electron Microscope, the three-dimensional AFM images

are obtained without expensive sample preparation and yield far more complete

information than two-dimensional profiles available from cross-sectioned samples.

AFM versus Optical Microscope:

Compared with Optical Interferometric Microscope, the AFM provides unambiguous

measurement of step heights, independent of reflectivity differences between materials.

There are some significant advantages of AFM as an imaging tool in biology and physics

when compared with complementary techniques. Not only does AFM achieve molecular

resolution but can be performed under fluids permitting sample to be imaged in near native

conditions. The fluid may be exchanged or modified during imaging and therefore there is the

potential for observing biological processes in real time, something which electron microscopy is

not currently able to achieve.


15

3.3 Atomic force microscope images

“Typically, when we think of microscopes, we think of optical or electron microscopes.

Such microscopes create a magnified image of an object by focusing electromagnetic radiation,

such as photons or electrons, on its surface. Optical and electron microscopes can easily generate

two dimensional magnified images of an object’s surface, with a magnification as great as 1000X

for an optical microscope, and as large as 100,000X for an electron microscope. Although these

are powerful tools, the images obtained are typically in the plane horizontal to the surface of the

object. Such microscopes do not readily supply the vertical dimensions of an object’s surface, the

height and depth of the surface features.

Unlike traditional microscopes, the AFM does not rely on electromagnetic radiation, such

as photon or electron beams, to create an image. An AFM is a mechanical imaging instrument

that measures the three dimensional topography as well as physical properties of a surface with a

sharpened tip.

In AFM, a microscale cantilever with a sharp tip (probe) is scanned across a surface ,left,

and by monitoring the motion of the tip (probe) from each pass across the surface, a 2-D line

profile is generated. Then the line profiles are combined to create a three dimensional image of

the surface, right. (Figure 2)

Figure 3.2. AFM image [21]

The sharpened tip (probe) is positioned close enough to the surface such that it can

interact with the force fields associated with the surface. Then the probe is scanned across the

surface such that the forces between the probe remain constant. An image of the surface is then

reconstructed by monitoring the precise motion of the probe as it is scanned over the surface.

Typically the probe is scanned in a raster-like pattern.”[21]


16

3.4 Interactive forces

The main difference between different types of microscopy and the AFM is, as the name

suggests, interactive forces between the sample and the tip. The force most commonly associated

with atomic force microscopy is an interatomic force called the van der Waals force. The relation

between this force and distance is shown in next figure.

Figure 3.3.Van der Waals force vs. distance

In the contact region, the cantilever is held less than a few angstroms (10-10

m) from the

sample surface, and the interatomic force between the cantilever and the sample is repulsive.

In the non-contact region, the cantilever is held on the order of tens to hundreds of

angstroms from the sample surface, and the interatomic force between the cantilever and sample

is attractive.

Different scanning modes operate in different regions of this curve: Non–contact in the

attractive region, contact mode in the repulsive and intermittent or tapping mode fluctuates

between the two.

At the right side of the curve, the atoms are separated by a large distance. As the atoms

are gradually brought together, they first weakly attract each other. This attraction increases until

the atoms are so close together that their electron clouds begin to repel each other

electrostatically. This electrostatic repulsion progressively weakens the attractive force as the

distance continues to decrease. Following the graph, the force goes to zero when the distance


17

reaches a couple of angstroms. Anything closer than this, the total van der Waals force becomes

positive (repulsive). This distance will not change, therefore any more attempt to force the

sample and tip closer will result in deformation or damage to the sample or the tip.

There are two other forces that arise during the scan:

a capillary force that is caused by a build-up of water, which is normally present without

an inert environment, on the tip;

the force caused by the cantilever itself, which is like a force caused by a compressed

spring.

3.5 Operation Principles

The principal behind the operation of an AFM is shown in Figure 4. The AFM tip is first

brought (manually) close to the sample surface, and then the scanner makes a final adjustment in

tip–sample distance based on a setpoint determined by the user. The tip is scanned across the

sample under the action of a piezoelectric actuator, either by moving the sample or the tip relative

to the other. A laser beam aimed at the back of the cantilever–tip assembly reflects off the

cantilever surface to a split photodiode, which detects the small cantilever deflections. A

feedback loop, shown schematically in Figure 4, maintains constant tip–sample separation by

moving the scanner in the z direction to maintain the setpoint deflection. Without this feedback

loop, the tip would “crash” into a sample with even small topographic features (although this

phenomenon can happen even with careful AFM operation).

By maintaining a constant tip-sample separation and using Hooke’s Law the force

between the tip and the sample is calculated:

F = -kx (3.1)

F –force

k- spring constant

x - cantilever deflection

Finally, the distance the scanner moves in the z direction is stored in the computer relative

to spatial variation in the x-y plane to generate the topographic image of the sample surface.


18

Figure 3.4.Principle of operation [22]

3.6 Scan modes

3.6.1 Principle of Contact Mode AFM (C-AFM)

The contact mode where the tip scans the sample in close contact with the surface is the

common mode used in the force microscope.At the lower end of Z scanner, there is a typical

cantilever of very tiny dimensions: 100 µm long,10 µm wide and 1 µm thick, which is

manufactured by means of micromachining techniques. At the free end of the cantilever, there is

a very sharp cone-shaped or pyramid-shaped tip. As the distance between the atoms at this tip and

the atoms on the surface of the sample becomes shorter, these two sets of atoms will interact with

each other. As shown in Figure 3.3, when the distance between the tip and the surface atoms

becomes very short, the interaction force is repulsive due to electrostatic repulsion, and when the

distances gets relatively longer, the interatomic force becomes attractive due to the long-range

van der Waals forces.


19

The interatomic force between atoms can bend or deflect the cantilever, and the amount of

the deflection will cause a change in the reflection angle of the laser beam that is bounced off the

upper surface of the cantilever. This change in laser path will in turn be detected by the PSPD

(Position Sensitive Photo Detector), thus enabling the computer to generate a map of the surface

topography.

Figure 3.5.Contact mode AFM.

In contact mode AFM the probe makes “soft contact” with the sample surface, and the

study of the sample’s topography is then conducted by utilizing the repulsive force that is exerted

vertically between the sample and the probe tip as shown in Figure 3.5. Even though the

interatomic repulsive force in this case is merely 1~10 nN, the spring constant of the cantilever is

also sufficiently small (less than 1N/m) , thus allowing the cantilever to react very sensitively to

very minute forces. The AFM is able to detect even the slightest amount of cantilever’s deflection

as it moves across a sample surface. Therefore, when the cantilever scans a convex area of a

sample, it will deflect upward, and when it scans a concave area, it will deflect downward. This

probe deflection will be used as a feedback loop input that is sent to an actuator (z-piezo). In

order to produce an image of the surface topography, the z-piezo will maintain the same

cantilever deflection by keeping a constant distance between the probe and the sample.[23]

3.6.2 Principle of Vibrating Mode

The cantilever in an AFM can be vibrated using a piezoelectric ceramic. When the

vibrating cantilever comes close to a surface, the amplitude and phase of the vibrating cantilever

may change. Changes in the vibration amplitude or phase are easily measured and the changes

can be related to the force on the surface. This technique has many names including non-contact

mode, and intermittent contact mode. It is important that the tip not "tap" the surface because the


20

probe may be broken or the sample may be damaged. However, in same cases the sample is

carefully tapped on purpose, which is called the tapping mode.

Figure 3.6. Vibrating mode.

3.6.3 Principle of Non-contact Mode AFM (NC-AFM)

There are two major forces, the static electric repulsive force and attractive force, existing

between atoms a short distance apart. The static electric repulsive forces (Fion ) between ion cores

and the static electric attractive forces (F el) between valence electrons and ion cores. When the

distance between the atoms at the end of the probe tip and the atoms on the sample surface

becomes much shorter, the repulsive forces between them become dominant, and the force

change due to the distance change becomes greater and greater. Therefore, contact AFM measure

surface topography by utilizing the system’s sensitive response to the Repulsive Coulumb

Interactions that exist between the ion cores when the distance between the probe tip and the

sample surface atoms is very small. However, as shown in Figure 5, when the distance between

the probe tip and the sample atoms is relatively large, the attractive force Fel becomes dominant.

Ion cores become electric dipoles due to the valance electrons in the other atoms, and the force

induced by the dipole-dipole interaction is the Van der Waals force. Non contact AFM (NC-

AFM) measures surface topography by utilizing this attractive atomic force in the relatively

larger distance between the tip and a sample surface.


21

Figure 3.7.Concept diagram of Contact mode and Non-contact mode

Figure 3.7 compares the movement of the probe tip relative to the sample surface for

images being acquired between in contact AFM and in non-contact AFM. Contact AFM uses the

“physical contact” between the probe tip and the sample surface, whereas non-contact AFM does

not require this contact with the sample. In Non-contact mode, the force between the tip and the

sample is very weak so that there is no unexpected change in the sample during the measurement.

Therefore, Non-contact AFM is very useful when a biological sample or other very soft sample is

being measured. The tip will also have an extended lifetime because it is not abraded during the

scanning process. On the other hand, the force between the tip and the sample in the non-contact

regime is very low, and it is not possible to measure the deflection of the cantilever directly. So,

Non-contact AFM detects the changes in the phase or the vibration amplitude of the cantilever

that are induced by the attractive force between the probe tip and the sample while the cantilever

is mechanically oscillated near its resonant frequency.[23]


22

3.6.4.Resonant frequency

A cantilever used in Non-Contact AFM typically has a resonant frequency between 100

kHz and 400 kHz with vibration amplitude of a few nanometers. Because of the attractive force

between the probe tip and the surface atoms, the cantilever vibration at its resonant frequency

near the sample surface experiences a shift in spring constant from its intrinsic spring constant

(k0) .This is called the effective spring constant (keff), and the following equation holds:

keff=k0-F’ (3.2)

When the attractive force is applied, keff becomes smaller than k0 since the force gradient

F’(=∂F/∂) is positive. Accordingly, the stronger the interaction between the surface and the tip (in

other words, the closer the tip is brought to the surface), the smaller the effective spring constant

becomes.

A bimorph is used to mechanically vibrate the cantilever. When the bimorph’s drive

frequency reaches the vicinity of the cantilever’s natural/intrinsic vibration frequency (f0),

resonance will take place, and the vibration that is transferred to the cantilever becomes very

large. This intrinsic frequency can be detected by measuring and recording the amplitude of the

cantilever vibration while scanning the drive frequency of the voltage being applied to the

bimorph. Figure 3.8 displays the relationship between the cantilever’s amplitude and the

vibration frequency. From this output, we can determine the cantilever’s intrinsic frequency.

Figure 3.8. Resonant frequency of the cantilever


23

3.6.5 Advantages and Disadvantages of C-AFM and NC- AFM

Contact Mode AFM

Advantages:

High scan speeds (throughput)

Rough samples with extreme changes in vertical topography can sometimes be scanned

more easily in contact mode

Disadvantages:

Lateral (shear) forces can distort features in the image

The forces normal to the tip-sample interaction can be high in air due to capillary forces

from the adsorbed fluid layer on the sample surface

The combination of lateral forces and high normal forces can result in reduced spatial

resolution and may damage soft samples (i.e., biological samples, polymers, silicon) due

to scraping between the tip and sample

Non-contact mode AFM

Advantage:

No force exerted on the sample surface

Disadvantages:

Lower lateral resolution, limited by the tip-sample separation

Slower scan speed than Contact Mode to avoid contacting the adsorbed fluid layer which

results in the tip getting stuck

Non-contact usually only works on extremely hydrophobic samples, where the adsorbed

fluid layer is at a minimum. If the fluid layer is too thick, the tip becomes trapped in the

adsorbed fluid layer causing unstable feedback and scraping of the sample


24

3.7 AFM Probe Selection

The final AFM image is virtually a composite or “convolution” between the geometric

properties of the tip and the sample surface. Undoubtedly, one of the most important controllable

parameter for AFM imaging, either in ambient air of fluid, is proper selection of scanning tips.

The AFM scanning “tip” typically consists of a sharp microfabricated barb or spike mounted at

the end of a “cantilever” to form a unified “probe”. Although these terms are sometimes used

interchangeably, only the microstructured component at the end of the cantilever is the part that

actually indents the sample surface during the AFM scanning.

A wide variety of AFM scanning tips are currently available, differing in geometry,

material properties and chemical composition. Tips are broadly defined by their aspect ratio

(length to with), opening angle and/or radius of curvature.

The typical geometry of an AFM cantilever:

w-width

t- thickness

L-length

h-the tip height from the cantilever middle to the tip

Figure3.9.Cantilever’s geometry

Relatively rough sample surfaces, in the range of micrometers, should be scanned using

high-aspect-ratio tips, which combine small opening angles with a long tip. However, low-

aspect-ratio tips, corresponding with high opening angles, are more suitable for scanning

relatively flat specimens. A special type of low-aspect-ratio tip exist where the very end is shaped

into a high-aspect-ratio peak with overall low-aspect-ratio configuration of the tip. These tips are


25

referred to as “sharpened tips” and ensure greater scan depth with improved resolution when

scanning relatively flat samples. Radius of curvature of the AFM tip reflects the nanometric

sharpness of the tip’s peak. Typical radius of curvature of sharpened tips is less 20 nm, while that

of unsharpened tips ranges from 20-50 nm. Oxide sharpened silicone nitride tips are widely

utilized in the AFM scanning of living cells and various other biological structures due to their

high versatility and ability to combine high resolving power with physical tolerance on soft

sample surface.

The tip-cantilever assembly is most commonly made of crystal silicone or silicone nitride,

which are both suitable for microfabrication due to their stiffness and wear resistance. Silicone

nitride tips are more suitable for contact mode imaging due to their flexibility and “forgiveness”

on the sample surface compared to the stiffer crystal silicone probes. Such forces, although

micro- and nano-scale in nature, might be strong enough to deform the surface of the soft sample.

Therefore, considerable attention to the selection of the scanning tip should be taken, especially

when imaging delicate samples. By contrast, when scanning harder samples or using tapping

mode AFM, stiffer crystal silicone probes are likely more appropriate. However, increased

brittleness of the crystal silicone tips due to their greater stiffness mandates considerable care

during handling and preparation for the scanning session.

Several recent efforts are directed toward substituting the silicone and the silicone nitride with

more characterized materials for the fabrication of enhanced AFM probes. Carbon nanotubes are

gaining rising popularity to the backbone structural material for the second generation of AFM

probes. Additional advantages offered by the carbon nanotubes include their well-characterized

structure, mechanical robustness, and unique chemical properties that allow well-defined surface

modification without jeopardizing the AFM scanning resolution. [24]

3.8 Force Curve Measurements

In addition to topographic measurements, the AFM can also provide much more

information. The AFM can also record the amount of force felt by the cantilever as the probe tip

is brought close to - and even indented into - a sample surface and then pulled away. This

technique can be used to measure the long range attractive or repulsive forces between the probe


26

tip and the sample surface, elucidating local chemical and mechanical properties like adhesion

and elasticity, and even thickness of adsorbed molecular layers or bond rupture lengths.

Force curves ( force-versus-distance curve) typically show the deflection of the free end of the

AFM cantilever as the fixed end of the cantilever is brought vertically towards and then away

from the sample surface. Experimentally, this is done by applying a triangle-wave voltage pattern

to the electrodes for the z-axis scanner. This causes the scanner to expand and then contract in the

vertical direction, generating relative motion between the cantilever and sample. The deflection

of the free end of the cantilever is measured and plotted at many points as the z-axis scanner

extends the cantilever towards the surface and then retracts it again. By controlling the amplitude

and frequency of the triangle-wave voltage pattern, the researcher can vary the distance and speed

that the AFM cantilever tip travels during the force measurement.[25]

3.9 Biological Applications of AFM

One of the advantages of AFM is that it can image the non-conducting surfaces. So it was

immediately extended to the biological systems..

Applications of AFM in the biosciences include:

DNA and RNA analysis;

underlying cytoskeleton;

Protein-nucleic acid complexes;

Chromosomes;

Bones;

Cellular membranes;

Proteins and peptides;

Molecular crystals;

Polymers and biomaterials;

Ligand-receptor binding.

Bio-samples have been investigated on lysine-coated glass and mica substrate, and in buffer

solution. By using phase imaging technique one can distinguish the different components of the

cell membranes. The process of image acquisition is such that the AFM can also measure forces

at the molecular level. In addition, the AFM can interact with the sample, thereby manipulating

the molecules in a defined manner-nanomanipulation.[25]


27

4. Nanoindentation

Indentation testing is a simple method that consists essentially of touching the material of

interest whose mechanical properties such as elastic modulus and hardness are unknown with

another material whose properties are known. The technique has its origins in Mohr’s hardness

scale of 1822 in which materials that are able to leave a permanent scratch in another were ranked

harder material, with diamond assigned the maximum value of 10 on the scale.

Nanoindentation is simply an indentation test in which the length scale of the penetration

is measured in nanometres (10-9

m) rather than microns (10-6

m) or millimetres (10-3

m), the later

being common in conventional hardness tests.

In conventional indentation tests, the area of contact is calculated from direct measurements of

the dimensions of the residual impression left in the specimen surface upon the removal of the

load.

Figure 4.1.Conventional indentation

In nanoindentation tests, the size of the residual impression is of the order of microns and

too small to be conveniently measured directly. Thus, it is customary to determine the area of

contact by measuring the depth of penetration of the indenter into the specimen surface. This,

together with the known geometry of the indenter, provides an indirect measurement of contact

area at full load.

It is not only hardness that is of interest to material scientists, the indentation techniques can also

be used to calculate elastic modulus, strain-hardening exponent, fracture toughness (for brittle

materials) and viscoelastic properties.[17]


28

Load-displacement curves

In nanoindentation the measured data are extracted from the load-displacement response

shown in figure 4.2. [15]

Figure 4.2.Schematic load-displacement plot of the Oliver and Pharr (1992) model

This type of data is obtained when an indenter, shaped as a sphere, is placed into contact with the

flat surface of the specimen with a steadily increasing load. Both load and depth of penetration

are recorded at each load increment. Following the attainment of the maximum load, in the

material shown in figure 4.3., the load is steadily removed and the penetration depth recorded.

Figure 4.3.Schematic representation of the indentation process, in which S is dP/dh,

hc is the contact depth, hf is the final penetration depth, h is the penetration depth and hmax

is maximum penetration depth


29

The loading part of the indentation cycle may consist of an initial elastic contact, followed

by plastic flow, or yield, within the specimen at higher loads. Upon unloading, if yield has

occurred the load displacement data follow a different path until at zero applied load, a residual

impression is left in the specimen surface. The maximum depth of penetration for a particular

load, together with the slope of the unloading curve measured at the tangent to the data point at

maximum load, lead to a measure of both hardness and elastic modulus of the specimen material.

In some cases, it is possible to measure elastic modulus from not only the unloading portion, but

also the loading portion of the curve. For a viscoelastic material, the relationship between load

and depth of penetration is not so straight forward. That is, for a given load, the resulting depth of

penetration may depend upon the rate of application of load as well as the magnitude of the load

itself. For such materials, the indentation test will be accompanied by “creep”, and this manifests

itself as a change in depth for a constant applied load.[17]

Nanoindentation technologies

The two most known nanoindentation technologies both developed in the 1980s and both

available commercially are:

the depth-sensing nanoindenter (DSN)

the atomic force microscope (AFM) based nanoindentation

Advantages of one system over the other are dependent on its basic design and control

scheme. The depth-sensing system, with its basis in electromagnetic or electrostatic force

actuation, permits either load-controlled or displacement-controlled indentation and the

application of a force perfectly normal to the sample surface.

In commercial AFM’s, fine displacement control in all three axes is typically achieved via

piezoelectric actuation. This feature of the AFM contributes to its high-resolution imaging

capability. Drawbacks of using the AFM in nanoindentation are chiefly associated with the

necessity to match the bending stiffness of the cantilever with the stiffness of the indented sample

[18]. For hard surfaces, it may be difficult to achieve adequate penetration depths even with the

stiffest cantilevers. Conversely in very soft materials, it may be difficult to generate adequate

deflection of the cantilever for accurate force measurements.


30

1. Depth sensing nanoindentation (DSN)

One of the most known machines based on depth sensing nanoindentation is the Hysitron

Triboscope. It is a unique and powerful instrument because it is a quantitative nanoindentation

system and it has the ability to image the surface before and after indentation. It does not utilize

the piezo feedback nor the Atomic Force Microscope (AFM) cantilever to perform its tests. The

nanoindenter can be attachment (accessory) to a scanning probe microscope or the system can be

totally stand alone type.

The Triboscope itself has three main parts:

the transducer

the transducer controller

separate data acquisition system

The Scanning Probe Microscope (SPM) software is used to interpret the voltage signal from the

transducer, and the microscope piezos enable displacement control when imaging. The transducer

holds the indenter tip which doubles as a probe for imaging. The resolution of the image is not as

good as those obtained with an AFM or STM tips due to the bluntness of the indenter. It does

give sufficient resolution to identify desired surface features and to choose optimal areas to

indent.

The Triboscope uses a simple three-plate capacitor system for its force-displacement

transducer. Figure 4.4. is a sketch of the transducer configuration.

Figure 4.4 Schematic of a three of a plate capacitor force-displacement transducer of the Hysitron

Triboscope


31

The two outer plates (the drive plates) are fixed and the middle plate is spring mounted

and therefore free to move. This middle plate has a screw, which is where the tip attaches. To

perform an indentation an electrostatic force is generated between a drive plate and the pick up

electrode. The area of the plates and the distance between them determines this electrostatic force

constant. Once calibrated the instrument determines the appropriate voltage profile to apply the

required force profile for the specified indentation test. For displacement sensing, the two outer

electrodes are driven by AC voltage that is 180° out of phase.

This results in an electrostatic field whose potential varies linearly with lateral

displacement, due to the close proximity of the plates. In the center this field is zero, because the

two fields cancel each other out. At the location of either plate the field is proportional to the

voltage applied. The middle plate or pick-up electrode assumes the potential of the position

relative to the drive plates. The displacements are measured by changes in the capacitance of the

stack of plates. This enables the displacement and applied load to be measured simultaneously.[1]

2. AFM based nanoindentation

The principle of nanoindentation by using AFM is shown in the figure 4.5.

Figure 4.5.AFM based nanoindentation

When the cantilever is moved by a piezoelectric scanner and the tip of the cantilever

comes in contact with a sample, the cantilever starts to deflect. The deflection of the cantilever is

detected by optical detector which is composed of a laser, a mirror and a photodiode detector,

where these signals are then transformed digitally into force image. Force curves are generated

automatically by selecting particular points on the force-volume image within its scanning field.

Force curves typically consist of approaching and retraction phases, representing the arrival and

departure motions of the AFM scanning tip over the sample surface.


32

As the AFM probing tip approaches the sample surface, a number of interactive events

take place before the tip makes an actual contact with the surface. Electrostatic forces between

the scanning tip and the sample surface can be either repulsive or attractive, depending upon the

electric charge of both the tip and sample surface. These repulsive or attractive forces are the first

interactive forces between the material surface of the scanning tip and the outer most layer of the

sample surface. As the tip moves closer to the sample surface the Van der Waals attractive forces

start to take effect between the molecules and atoms of the tip and the scanned surface. Finally,

when the tip makes its way down to the sample surface, a nanoindentation on the surface is

produced. By this measurement, the relationship between the movement of the cantilever z by the

piezoelectric scanner and the cantilever deflection d was obtained. The force applied to the

sample can be calculated by multiplying the cantilever deflection d by the spring constant of the

cantilever.

The Hertz model is the most straight forward mathematical derivation for describing the

elastic responses of an indented sample by the tip of the AFM.


33

5. Materials and methods

5.1 Park System XE-100 AFM

5.1.1 Primary components of XE-100 system

All the experiments were carried out with XE-100 atomic force microscope (Park Systems, Santa

Clara, CA, USA). The XE-100 system consists of four primary components: the XE-100 Stage,

the XE-100 Control Electronics, a computer and monitor, and a video monitor.

Video Monitor XE-100 Stage Computer and Monitor XE-100 Control Electronics

Figure 5.1.The XE-100 System

The XE-100 Stage is where actual measurements are made, and the XE-100 Control Electronics

controls the movement of the XE-100 Stage according to the commands from the computer.

The Video Monitor, which displays the image from the optical microscope that is mounted on the

XE-100 Stage , is used to locate the exact spot that is to be measured on the sample surface. It is

also used to view the cantilever that will be used to make the measurement.

Computer and Monitor

Software in the computer is used for acquiring and displaying AFM images. Also, software for

processing and analyzing AFM images typically resides in the computer.

Control Electronics


34

The control electronics generate the electronic signals required for moving stage components

such as the Z motors and the XYZ scanner. The control electronics also digitize the images

measured in the stage so that they can be displayed by the computer.

5.1.2 XE-100 Stage

Figure 5.2. shows overall structure of the XE-100 Stage with the acoustic enclosure open.

The following explains the individual components in detail.

Figure 5.2. Park System XE -100 AFM

The XE-100 is extremely sensitive to external vibrations. Thus, it is important to isolate all

possible vibrations from the equipment’s surroundings. So, the whole XE-100 system is placed

on a marble table suspended by thick ropes. Vibration level of the stand is 0.018 nm, as measured

by the service engineer of the XE-100.

CCD Camera

Optical Microscope

Frame

Objective Lens

XY Scanner

XE Head

Z Stage

XY Stage

AFM Frame


35

5.1.3 XE-100 Head

The XE-100 head is the component which actually interacts with the sample and takes

measurements. A unique characteristic of the XE-100 compared to that of conventional SPM is

that the Z scanner, which controls the vertical movement of the AFM tip, is completely separated

from the X-Y scanner which moves in horizontal direction on the sample.(Figure 5.3)

Figure5.3.Z scanner separated from X-Y scanner

XE-100 Head Components:

Probe Head: Interchangeable head slips into place on the XY translation; different heads

have certain scan mode capabilities, houses laser and photodiode

XY Translation Stage: Holds probe head, movable in XY direction by XY translation

screws and in Z direction by controls in software

Position Sensitive Photo detector (PSPD): Detects laser deflections, which is then

converted into a topographical map

PSPD adjustment screws: controls position of PSPD; screw on left controls up and down

adjustment; screw on right controls left right adjustment

Laser Beam Steering Screws: controls position of laser on back of cantilever

Laser Intensity and Position Indicators: Lights represent laser position and intensity on

photo detector

This structural change provides several operational advantages.


36

The Z scanner, being separate from X-Y scanner, is designed to have a higher resonant

frequency than conventional piezoelectric tube scanners. This enables the tip to precisely

follow the topography of a sample surface at faster rate and increases the speed of the

measurement, and protects the tip, resulting in the ability to acquire clear images for an

extended period of time.

Physical separation of the XY-scanner from the Z-scanner completely removes

background curvature from the fundamental level, and effectively eliminates the cross-

talk and non-linearity problems that are intrinsic to conventional piezoelectric tube based

AFM systems.

This XE scan system increases the data collecting speed by at least 10 times compared to

a conventional piezoelectric tube type scanner and improves the error due to the inherent

non-linearity of the scanner itself.

5.1.4 Cantilever movement detection mechanism used in XE-100

Figure 5.4 shows a diagram that explains the cantilever movement detection mechanism used in

the XE series. This laser beam/PSPD configuration, which permits the acquisition of stable

images at high measurement speeds, is a remark of the XE- series and it also satisfies the

following two important imaging conditions:

At first, the PSPD should be able to measure only the deflection of the cantilever

without interference from the Z scanner.

Secondly, to improve the response rate in the Z direction, the weight of the Z scanner

must be minimized.


37

Figure 5.4 Laser beam path related to the cantilever’s movement

The cantilever and the PSPD move together with the Z scanner while the laser beam, a

steering mirror, and a fixed mirror in front of the PSPD are fixed relative to the scanner frame.

The laser beam, positioned at the one side of the scanner, is aimed at a prism that is situated

above the cantilever. The prism reflects the laser beam downward and onto the back surface of

the cantilever. The laser beam will always hit the same spot on the cantilever’s surface since the

Z scanner only moves vertically. Therefore, once the laser beam is aligned, there is no need to

realign the laser beam, even after the Z scanner has been moved up and down to change samples.

The steering mirror, located at the front of the Z scanner assembly, adjusts the reflection angle of

the laser beam that is reflected off the cantilever’s surface. The steering mirror reflects the laser

beam to a fixed mirror which, in turn, reflects the beam at once to the PSPD. Another feature of

this alignment design is that as a result as a result of placing the second (fixed) mirror next to the

PSPD, it allows changing the Z scanner position without having to readjust the position of the

PSPD. Therefore, only the deflection of the cantilever will be detected, independent of the Z

scanner movement.

Since there is nothing obstructing the view above the cantilever in the structure like Figure 5.5,

the optical microscope is located on the same axis as the laser beam that is reflected at the prism

as shown in Figure 5.4.

Figure 5.5 shows the cantilever with the laser beam focused on it, as it is displayed on the

video monitor. Since the CCD camera is aligned directly with the cantilever with nothing


38

blocking its view, it is very convenient to focus on or to observe the sample while moving the

camera up and down..

Figure 5.5 Captured optical microscope image of cantilever and gold surface

The red “spot” is from the laser that is used in the light lever force sensor. Upon scanning

ranges greater than 1 micron, it is possible to see the AFM cantilever move in the video

microscope image.Furthermore, the computer is equipped Windows XP operating system.

5.1.5 XE Software

XEP is a data acquisition program that communicates with the XE Control Electronics in

order to control the XE-series system. The XEP interface allows a user to investigate and analyze

a sample surface. That is, XEP controls and operates the XE system to collect sample data. XEP

supports all the standard and advanced measurement modes.

XEP has full windows multi-tasking capability with Windows XP based data acquisition

and imaging processing programs. It can acquire up to 16 images simultaneously in both forward

and reverse scan with real time auto-tilt, auto-contrast and auto-curvature. XEP provides arbitrary

data pixel size in both X and Y directions, up to 4096 × 4096. All images are originally in TIFF

format, and can be exported as PNG, JPEG and Text files.

Figure 5.6. shows an example of the XEP program completed with safety functions and various

measurement capabilities that are required to perform advanced applications.


39

Figure 5.6.XEP Data Acquisition Program of the Park System XE-100 AFM

XEI provides user-friendly and dynamic tools for image processing, quantitative analysis

and statistics, and exporting and printing of processed images and measurement results. XEI

supports all the standard imaging processing such as Fourier power spectrum editor, low pass

filter and deglitch, and 1st-2nd order polynomial surface fit. Its analysis functions include but are

not limited to user selectable Profile Tracer and Region, Line Measurement of Height, Line

Profile, Power spectrum, Line Histogram, Region Measurement of Height, Average Roughness,

Volume, Surface Area, Histogram, Bearing Ratio, Ry, Rz, Grain Analysis Functions, and many

more. Figure 5.7. shows an example of the XEI program that is used to convert acquired data into

an image and to perform various analyses of images.


40

Figure 5.7.Image Processing Program XEI of the Park System XE-100

5.1.6 Tips

The probe tip is a very important part of indentation testing. The geometry and the

material it is made from can dramatically influence the raw data. The experiments have been

done with an Non contact/Tapping Probe made out of single crystal silicon. The reflex coating

is an approximately 30 nm thick aluminium coating on the detector side of the cantilever which

enhances the reflectivity of the laser beam by a factor of 2.5 .

Figure 5.8.NCHR AFM Tip (Savonia University of Applied Sciences, JEOL JSM 840 SEM )


41

Table 5.1.Showing Cantilever NCHR specifications

Technical data

Length,l±5μm 125

With,w±3μm 30

Thickness, μm 4

Resonant frequency,kHz 320

Force constant k, N/m 42

5.2 Materials

The materials examined in this study were fused silica, copper, nickel, titanium, thin films of

polyimide (Kapton) and bovine bones (cortical and trabecular).

Fused silica

Fused silica is used as a standard specimen for calibration in nanoindentation, because it

has almost the same Young’s modulus as the tip used for the measurements.

Fused silica (amorphous SiO2) has several properties that make it an ideal standard:

Inexpensive and easily obtained in bulk form

Smooth surface with no oxidation

Amorphous

Isotropic

Mid-range mechanical properties

No significant time dependence

The nominal elastic modulus of fused silica is 71.7GPa

Poisson’s ratio 0.16


42

Copper

A single crystal copper consists of a few microns of small crystals. In this form of crystal

(c), the yield stress is high and crystal undergoes a large amount of elastic deformation before

going into the plastic deformation region. The plastic deformation region has an unpredictable

outcome. The plastic deformation of polycrystal is similar to mild steel. Copper has a high

ductility and will continue to elongate as stress is applied.

Copper is malleable and ductile, a good conductor of heat and, when very pure, a good conductor

of electricity.

Biomedical applications:

As a biostatic surface in hospitals, and to line parts of ships to protect against barnacles

and mussels, originally used pure, but superseded by Muntz Metal. Bacteria will not grow

on a copper surface because it is biostatic. Copper doorknobs are used by hospitals to

reduce the transfer of disease, and Legionnaires' disease is suppressed by copper tubing in

air-conditioning systems.

Copper-62-PTSM, a complex containing radioactive copper-62, is used as a Positron

emission tomography radiotracer for heart blood flow measurements.

Table 5.2.Showing Mechanical Properties of Copper[26]

Mechanical Properties Values

Young’s Modulus 128GPa

Yield Strength 100MPa


Nickel

Nickels are low cost components with high strength stiffness, fracture toughness,

hardness, and modulus of elasticity. Nickel is hard, malleable, and ductile metal. It is of the iron

group and it takes on a high polish. It is a fairly good conductor of heat and electricity.

The major use of nickel is in the preparation of alloys. Nickel alloys are characterized by

strength, ductility, and resistance to corrosion and heat. Mechanical properties of nickel are

shown in Table 5.3

http://www.chemeurope.com/lexikon/e/Ductile

http://www.chemeurope.com/lexikon/e/Conductor_of_heat

http://www.chemeurope.com/lexikon/e/Biostatic

http://www.chemeurope.com/lexikon/e/Positron_emission_tomography



http://www.lenntech.com/Periodic-chart-elements/Fe-en.htm


43

Table 5.3.Showing Mechanical Properties of Nickel [26]


Young’s Modulus 204 GPa

Yield Strength 0.5 GPa


Titanium

Titanium is a light, strong metal with low density that, when pure, is quite ductile,

corrosion resistant.Because it is biocompatible (non-toxic and is not rejected by the body),

titanium is used in a gamut of medical applications including surgical implements and implants,

such as hip balls and sockets (joint replacement) that can stay in place for up to 20 years.

Titanium has the inherent property osseointegrate, enabling use in dental implants that can

remain in place for over 30 years. This property is also useful for orthopedic implant applications.

Mechanical properties of titanium are shown in Table 5.4

Table5.4. Showing Mechanical Properties of Titanium [26]


Young’s Modulus 115 GPa

Yield Strength 400 MPa


Polyimide

Polyimides are a very interesting group of chemical resistant polymers. Their strength and

heat and chemical resistance are so great that these materials often replace glass and metals, such

as steel, in many demanding industrial applications.

Polyimide it’s used in Bio-MEMS and implantable intracortical electrode array. Polyimide is a

proven biocompatible material and an excellent choice for neuroprosthetic applications.

Mechanical properties of Polyimide are shown in Table 5.5

http://en.wikipedia.org/wiki/Joint_replacement

http://en.wikipedia.org/wiki/Dental_implants


44

Table 5.5.Showing Mechanical Properties of Polyimide [26]


Young’s Modulus 2.5 GPa

Yield Strength 400 MPa


Copper (99.5% pure), nickel (99.9% pure) and titanium (99.6% pure) samples used in this study

are actually sputtering targets. The samples were polished by grinding to 2500 grit.

Polyimide (IM 301450) sample thickness was 125 µm and 50 μm.(Goodfellows)

Bovine cortical and trabecular bone

As a structural material, bone is unique when compared with other engineering materials

because of its well-known capacity for self-repair and adaptation to changes in mechanical usage

patterns.Cortical bone is dense and forms the surface of the bones, contributing 80% of the

weight of the weight of a human skeleton. It is extremely hard, formed of multiple stacked layers

with few gaps.Trabecular (cancellous) bone is spongy and makes up the bulk of the interior of

most bones, including vertebrae.[27] At nanoscale dimensions, bone is composed of type-I

mineralized collagen fibers (up to 15 mm in length and 50–70nm in diameter) bound and

impregnated with carbonated hydroxylapatite nanocrystals (tens of nm in length and width, 2–

3nm in thickness).Bovine cortical and trabecular bones used in the experiments were not

polished.


45

Figure 5.9.Trabecular bone (Savonia University of Applied Sciences SEM)

5.3 Technique Used

The nanoindentation process is straightforward:

1. First, engage on the surface in Non-Contact Mode AFM. The sample surface is beeing

imaged to find the desired location for the nanoindentation. Once the area of interest is

located, lift the cantilever slightly off the surface and switch to Contact-Mode and select

Nanoindentation.

2. Then, select the desired indentation parameters and execute the nanoindentation. The

cantilever oscillation is now turned off, and the scanner lowers the tip towards the surface

where the tip is forced into the sample surface until the cantilever deflects a specified

amount. The tip is then retracted until it reaches the initial position above the surface.

While indenting, a force displacement curve is recorded utilizing the DC displacement of

the cantilever versus the extension of the scanner.

Imaging steps:

After switching on XEC and XEP, the program automatically chooses the operation

frequency for Non-contact cantilever. Adjusts “drive” so that within 2.5 kHz the

eigenfrequency curve decreases approximately 600 nanometers;

Laser adjustment

Adjust the laser beam (red dot) in the middle of the photo detector using smaller knobs so

that A-B and C-D is smaller than 0.5. Also the total intensity of the beam A+B should be

bigger than 2.


46

Figure 5.10.Photo detector

Place the sample on the sample stage;

Adjust the scan area to 0 micrometers;

Drive the cantilever 1 mm above the sample ,clicking on Z Stage area (lower part)

Uncross the “Focus follow” box and focus on the sample;

Figure 5.11 Z stage and Focus

Drive the cantilever close to the sample so that the shape of the cantilever can be seen;

Using the micrometer screws of the sample stage find the target to be scanned;

After closing the AFM door, drive the cantilever into contact by pressing the button

“Approach”;

Taking a picture

1. Adjusting Scan Parameters

In the Scan Controls panel, set the initial Scan Size to 1 μm, X and Y Offsets to 0, and

Scan Angle to 0;

set Z-servo gain (amplification of the feedback 5 ,when finding some regular pattern)

In the actual scanning the value is between 1 and 3;

set Scan Rate to 0.2-1.0 Hz;

Set point (the amplitude of the cantilever vibration)


47

Figure 5.12.Scan Control

2. Checking to see if Trace and Retrace are tracking each other well (i.e. look similar). If they

are tracking, the lines should look the same, but they will not necessarily overlap each other.

If they are tracking well, then the tip is scanning on the sample surface. You may want to try

keeping a minimum force between the tip and sample by clicking on Setpoint and using the

right arrow key to increase the Setpoint value gradually, until the tip lifts off the surface (at

this point the Trace and Retrace will no longer track each other). Then decrease the Setpoint

with the left arrow key until the Trace and Retrace follow each other again. Decrease the

Setpoint one or two arrow clicks more to make sure that the tip will continue to track the

surface.

If they are not tracking well, adjust the Scan Rate and Setpoint to improve the tracking. If

Trace and Retrace look completely different, you may need to decrease the Setpoint one or

two clicks with the left arrow key until they start having common features in both scan

directions.

Figure 5.13. Scanning to the right and left should match (blue and yellow)


48

3. “Scan control/ Scan here” takes the picture

Topography data is acquired by raster-scanning the tip or the sample and continuously

recording the height data. A typical AFM image size is 256 pixels by 256 pixels (256×256). For a

10 μm×10 μm scan area, a pixel in a 256×256 image corresponds to an area of 39.1 nm×39.1 nm.

The height data is averaged over a pixel area to avoid aliasing effects. As the gathered data is

three-dimensional (3D) surface topography, it is natural to present the data in 3D. AFM data

acquisition is slow. Because of the long acquisition time, AFM data often contain noise related to

thermal drifts.

Before the nanoindentation, all the samples were first imaged using the steps described above.

Figure 5.14.Fused silica Topography and Scanning parameters


49

Figure 5.15.Copper Topography and Scanning parameters

Figure 5.16. Nickel Topography and Scanning parameters


50

Figure 5.17.Titanium Topography and scanning parameters

Figure 5.18.Polyimide Topography and scanning parameters


51

Figure 5.19.Trabecular bone (collagen fibers) and scanning parameters

Nanoindentation

The experiments were carried out using following nanoindentation parameters :

Figure 5.20 Scan Control Window


52

All indentation tests had a down speed of 0.38 μm/sec and a up speed of 0.38 μm/sec and

also indentation depth of min.-10 μm and max. 10 μm. All indents had a maximum load of 5000

nN.

The measurements were first calibrated by using fused silica .Fused silica is often used

for calibration in nanoindentation testing because its relatively low modulus-to-hardness ratio,

E/H, leads to a large amount of elastic recovery during unloading, and this improves

measurement accuracy.[28]

For the metals and polyimide experiments were made in displacement control test and the

load (force) was recorded. For the trabecular and cortical bone the experiments were carried out

in both load and depth control. While indenting, a force-deformation curve is recorded utilizing

the DC displacement of the cantilever versus the extension of the scanner.

Figure 5.21 Fused silica Force vs. deformation

Figure 5.22 Titanium Force vs. deformation


53

Figure 5.23 Copper Force vs. deformation

Figure 5.24 Nickel Force vs. deformation

Figure 5.25 Polyimide Force vs. deformation


54

5.4 Description of LabVIEW program

AFM control unit stores several parameters while indenting material. Following custom made

LabVIEW program does not control the AFM, but it employs the collected indentation data such

as Time (s), Z-scan (µm) and Force (nN) and use these parameters to calibrate the AFM tip with

known material, such as fused silica, and after calibration to calculate the analyzed material

Young’s modulus.

Figure.5.26 .Front panel of the custom made LabVIEW program which is used to first calibrate

the AFM tip with known material and second calculating analyzed material Young’s modulus


55

5.4.1 Calibration of the AFM cantilever tip

Deformation (Z-scan) stored in to file during AFM nanoindentation consist in two separate parts.

First part the deformation of the material under pressure and second part the deformation of the

cantilever tip. Calculation of the material deformation relative to certain force F is possible

using the Hertz model equation (5.1), when calibration material, Poisson’s ratio and Young’s

Modulus are known.

(5.1)

Where F is force data point from the selected area of the curve, υ is Poisson’s ratio of the

calibration material (fused silica 0.16), R is the radius of the AFM tip and E is the Young’s

modulus of the calibration material (fused silica 71.7 GPa).

After calculating the material deformation using equation (5.1) cantilever deformation d is

obtained simply by substracting material deformation δ from the original deformation Z-scan

gained during AFM indentation.

(5.2)

Figure.5.27. Calibrated Force vs. Deformation graph.


56

White line indicates original data Z-scan, red line is deformation of the calibration material δ

calculated using the Hertz model, Equation (5.1) and Green line indicates cantilever deformation

d obtained from equation (5.2) Slope k of the cantilever force vs. deformation curve is obtained

using linear fit. Slope k is later used for calculating the deformation of the analyzed material. It’s

assumed that cantilever spring constant behaves linear with respect to force F:

(5.3)

Respectively cantilever spring constant is obtained by taking the slope k2 of the linear fit from

cantilever deformation vs. Force curve. Calculated cantilever spring constant is needed to

compare to the spring constant provided by the manufacturer.

5.4.2 Calculating the Young’s modulus of the analyzed material

After taking into consideration the calibration of the AFM cantilever tip using calibration

material calculation of Young’s modulus of analyzed material takes place. Deformation (Z-scan2)

collected during nanoindentation of analyzed material still consists of two separate parts. First

material deformation (δ2) and second cantilever deformation d2. By using equation (5.3) with

force values gained in analyzed material indentation and with cantilever linear fit slope value k

from calibration, it’s possible to calculate material deformation δ2 subtracting cantilever

deformation d2 from the complete deformation data Z-scan2.


57

Figure 5.28. Force vs. Deformation graph in analyzation of material

White line indicates the measured deformation during AFM indentation. Green line is the

cantilever deformation gained with equation (5.3). Red line is the result of equation (5.2 )which

indicates the analyzed material deformation. Again, slope K from the material deformation curve

is gained using linear fit. Young’s modulus E of the analyzed material is calculated with

following equation:

(5.4)

To be able to use the slope K for calculating analyzed material Young’s modulus it is needed to

write relation of the force F and the deformation D as in equation (5.3). Equation (5.4 ) can now

be written in the following form:

(5.5)

and further

(5.6)


58

Where υ is Poisson’s ratio of the analyzed material, R is the radius of the AFM tip, K is the slope

of the analyzed material deformation curve and D is the maximum deformation of the unknown

material curve.

6.Results

By using only the calibration part LabVIEW program it was possible to determine

cantilever’s spring constant using different stiff materials.The materials were fused silica,

titanium, nickel and copper. The results are close to the nominal values provided by the

manufacturers.(42 N/m)

Table6.1.Spring constant of the NCHR tip cantilever as determined by using different

materials

Material Fused silica Titanium Nickel Copper

Tip1 41.2709 41.2372 42.7342 41.8831

Tip2 39.1455 38.4004 41.2569 40.2415

Tip3 38.9034 38.4587 40.1548 39.1542

Figure 6.1.Spring constant of the NCHR tip cantilever as determined by using different

materials


59

Young’s modulus of the materials was presumed and if there is variation in the presupposition, as

compared to the real values, it may explain the variation.

Determination of the Young’s modulus of hard materials (titanium, copper, nickel) was

unsuccessful.

The metals and polyimide were measured also with Hysitron at the Helsinki University of

Technology using three-sided pyramidal Berkovich. Measurements were performed in series of

25 independent indentations for each type of test.

The determined Young’s modulus for the metals was close to bulk Young’s modulus.

Unfortunately, the polyimide seemed not to be suitable with the nanoindenter, because of the

sticky surface of coating material. Even if there are some reasonable result it’s extremely hard to

extract correct contribution of proper specimen.

Table 6.2.Depth, Reduced Young’s modulus and hardness for metals and polyimide

Data is reported as mean±standard deviation

No. Specimen Series Depth [nm] Er [GPa] H [GPa]

1 Cu

5 – 5 – 5 s 100.58± 2.32 123.4 ±5.5 2.18 ±0.10

0.26 – 5 – 0.26 s 99.73 ±1.90 122.6 ±7.4 2.22 ±0.08

0.26 – 0.26 s 101.26 ±1.83 131.2 ±5.2 2.46 ±0.09

DC 0.26 – 5 – 0.26 s 99.10 ±0.64 119.7 ±8.8 1.97 ±0.15

2 Ti

5 – 5 – 5 s 99.92± 2.12 137.3 ±7.8 3.50 ±0.13

0.26 – 5 – 0.26 s 100.77± 1.33 129.9 ±3.6 3.51 ±0.10

0.26 – 0.26 s 100.20 ±1.90 140.4 ±4.1 4.24 ±0.16

DC 0.26 – 5 – 0.26 s 98.79 ±0.42 122.2 ±6.4 2.76 ±0.21

3 Ni

5 – 5 – 5 s 99.93± 2.29 227.0 ±11.0 3.79 ±0.18

0.26 – 5 – 0.26 s 100.77 ±1.79 221.7 ±10.4 3.75 ±0.13

0.26 – 0.26 s 99.82 ±1.99 217.3 ±9.8 3.78 ±0.14

DC 0.26 – 5 – 0.26 s 99.14 ±0.98 206.9 ±12.2 3.31 ±0.24

4 Polyimide

125m

5 – 5 – 5 s 100.12 ±1.37 3.91 ±0.11 0.305 ±0.010

0.26 – 5 – 0.26 s 100.73 ±2.09 4.40 ±0.28 0.305 ±0.011

DC 0.26 – 5 – 0.26 s 98.59 ±1.11 3.99 ±0.32 0.289 ±0.018

5 Polyimide

50m

5 – 5 – 5 s 99.38 ±1.26 1.330 ±0.037 0.225 ±0.012

0.26 – 0.26 s 100.13 ±1.09 1.444 ±0.032 0.248 ±0.011

DC 0.26 – 5 – 0.26 s 99.24 ±0.56 1.371 ±0.056 0.178 ±0.008


60

Tomasetti et al [29] calculated the Young’s modulus of eight polymers, determined using

AFM and bulk values of Poisson’s ratio. They used a very small 10 nm radius cylindrical tip.

Their results show differences in the measured Young’s modulus between the AFM and the more

traditional DSN method for these copolymers. It can be attributed this, possibly to the

copolymers having phase separated at the nanoscale .Therefore at this scale only one phase is

measured whereas at the bulk for DNS analysis, these values are averaged.

Using the AFM based nanoindentation, mean Young’s modulus of 125 μm polyimide

was 1.9 GPa ± 0.3. Reproducibility of the measurements as indicated by the coefficient of

variation CV(%) was 14. Poisson’s ratio was assumed to be 0.25. Results are close to “Dupont

Kapton Polyimide Film General Specifications, Bulletin GS-96-7” –Young’s modulus 2.5 GPa

The cortical and trabecular bones were indented in both load and position control. In load

control, the user specifies the maximum test force and the displacement is recorded. In position

control, the user specifies the maximum depth of penetration. There is a linear correlation

between Young’s modulus determined in load control and the one determined in the position

control.

Figure 6.2.Linear correlation was found between the load and position control measurements

of the bovine bone


61

The Young’s modulus for the cortical bone in load control was 4.19 GPa ± 3.11 and in

position control was 4.19 GPa ± 2.5, respectively.

Figure 6.3.Young’s modulus for cortical bone

The Young’s modulus for the trabecular bone in load control was 2.32 GPa ± 1.70 and in

position control 4.31 GPa ± 4.91, respectively.

Figure 6.4.Young’s modulus for trabecular bone

The Young’s modulus of trabecular bone was slightly lower in load control measurents than

the Young’s modulus of cortical bone.The obtained values are consistent with previous

studies.


62

7. Discussion and future directions

Nanoindentation has proven itself to be a powerful technique for the measurement of

mechanical properties in diverse materials ranging from metals to mineralized tissues and soft

materials. The results of this thesis indicate that it is possible to succesfully make

nanoindentation using the proposed method, but it is necessary to take in account the factors that

affect nanoindentation. Control of experimental conditions and use of proper technique are

essential for obtaining accurate and reproducible results, particularly with the AFM.

The results for the metals were not reliable because it may be difficult to achieve adequate

penetration depths even with the stiffest cantilevers.[30] Using AFM based nanoindentation good

results were obtained using soft materials.(polyimide and bones)

In general uncertainties of the AFM nanoindentation are arising from a lack of calibration

of key components, use of manufacturer’s nominal values for cantilever spring constants and tip

radii or from the use of incorrect models.[31]

Piezoelectric scanner

The AFM requires a calibrated piezoelectric scanner to obtain accurate z movement. Piezoelectric

scanners exhibit hysteresis, non-linearity and creep with errors as large as 25 % unless calibrated.

The calibration is either via software or hardware or both.

Spring constant

Many manufacturers provide data sheets for their cantilevers giving general values of the spring

constant, k, the geometry and the resonant frequency .These are only nominal values and can be

up to 100% in error compared to their true value.

For indentation using AFM for good sensitivity, it is important to match the cantilever’s spring

constant k to the Young’s modulus E of the sample under test. In practice, this means selecting a

cantilever whose stiffness approximately matches that of the sample stiffness. If a cantilever is

chosen that is too stiff for a given sample, there will be a little sensitivity because the cantilever

gives insufficient deflection. On the other hand, if the cantilever is too compliant, no indentation

will occur. In this work, it was found that in the case of stiff materials, only the cantilever

deformation occurred. So, determination of the cantilever spring constant can be done with nickel

(>200 GPa) or titanium (~ 130 GPa).


63

Tip shape and radius

For the direct measurement of elastic modulus, the tip shape and radius has to be known.

Manufacturer’s values for the tip radius are nominal values and the true tip shape and size may

deviate significantly from those given. These parameters may also change during the use of the

tip.The method to determine tip radius uses the indentation of a reference material of known

modulus, Fused silica is widely used as a reference. It is assumed that the modulus of this

reference material does not vary with depth. By, knowing the other parameters (cantilever spring

constant k, Young’s modulus and Poisson’s ratio of fused silica, force and material deformation)

it’s easy to determine tip radius.

Using this improvements in the measurement method and also in the analyses program

and a better knowledge of the tip-sample contact area and interactions, will contribute to more

accurate measurements. These improvements will open the possibility to study the viscoelastic

behavior of biological samples, especially bones structures in more detail.


64

References:

[1] Martha M. McCann, Nanoindentation of gold single crystals, PhD work, Virginia

Polytechnic Institute and State University, 2004

[2] CSM Instruments, Nanoscale analysis and nanoindentation used to study the effects of

osteoporosis and its treatments on bone tissue quality by CSM Instruments,

http://www.azonano.com/Details.asp?ArticleID=1931, cited 10.06.2008

[3] Clifford C.A, Seah M.A , Quatification issues in the identification of nanoscale regions of

homopolymers using modulus measurement via AFM naoindentation, Applied Surface Science

252 (2005)1915

[4] Choi K.,Kuhn J.L., Ciarelli M.J.and Goldstein S.A.,The elastic moduli of human subchondral

trabecular and cortical bone tissue and the size-dependency of cortical bone modulus,Journal of

Biomechanics,1990,23,1103-1113

[5] Choi K.,Kuhn J.L., Ciarelli M.J.and Goldstein S.A.,The elastic moduli of human

subchondral trabecular and cortical bone tissue and the size-dependency of cortical bone

modulus,Journal of Biomechanics,1990,23,1103-1113

[6] Lotz, J.C.,Gerhart, T.N. and Hayes, W.C., Mechanical properties of methaphyseal bone in the

proximal femur, Journal of Biomechanics,1991,24,317-329

[7] Reilly D.T., Burstein A.H, Frankel, V.H., The elastic modulus of bone, Journal of

Biomechanics,1974 ,7, 271-275

[8] Rho J.-Y., Ting Y.T., Pharr G.M., Elastic properties of human cortical and trabecular lamellar

bone measured by nanoindentation, Biomaterials 18 (1997) 1325-1330

[9] Hengsberger S., Kulik A., Zysset P. , A combined atomic force microscopy and

nanoindentation technique to investigate the elastic properties of bone structural units, European

Cells and Materials,2001,12-17

[10]. Zysset, P. Guo,X.E Hoffler,C.E Moore,K.E Goldstein,S.A, Elastic modulus and hardness

of cortical and trabecular bone lamellae measured by nanoindentation in the human femur,

Journal of Biomechanics 32 (1999) 1005-1012

[11] Makoto S., Kenji S., Kobayashi K., Measurements of mechanical properties of cortical bone

using nanoindentation tests , Proceedings of Annual Meeting of Japanese Society for Orthopaedic

Biomechanics, 2003,1-5

http://www.azonano.com/Details.asp?ArticleID=1931


65

[12] Wikipedia, Deformation (engineering), http://en.wikipedia.org/wiki/Deformation, cited

10.06.2008

[13] Korhonen, R., Experimental analysis and finite element modeling of normal and degraded

articular cartilage, Phd thesis, Kuopio, 2003

[14] Wikislice, Poisson’s ratio, http://wikislice.webaroo.com/external/Poisson's_ratio, cited

10.06.2008

[15] Hertz, H., On contact of elastic solids, J. Reine Angew. Math,1881

[16] Round A.N., Yan B., Dang S., Estephan R., Stark R.E., Betteas J.D., The influence of water

on the nanomechanical behavior of the plant biopolyester cutin as studied by AFM and solid-state

NMR, Biophys J, 2000, 79, 2761-2767

[17] Fisher-Cripps, Anthony C., Nanoindentation, USA, Springer-Verlag New York,2002

[18] Waser R., Nanoelectronics and information technology, Wiley-VCH Verlag, 2003

[19] Wikipedia, Atomic force microscope

http://en.wikipedia.org/wiki/Atomic_force_microscope, cited 10.06.2008

[20] Univeristy of Guelph, http://www.chemistry.uoguelph.ca/educmat/chm729/afm/, cited

10.06.2008

[21] Paul E.West, Introduction to Atomic force microscopy, USA, Pacific Nanotechnology

[22] Digital Instruments, Scanning probe microscopy training notebook, version 3.0, Digital

Instruments, Veeco Metrology Group, 2000

[23] http://nanoparticles.pacificnano.com/atomic-force-microscope.html

[24] Yourek G., Al-Hadlaq A., Patel R., McCormick S., Reilly G.C., Mao J.J., Nanophysical

properties of living cells, in book “Biological nanostructures and applications of nanostructures

in biology”, Springer

[25] http://www.chembio.uoguelph.ca/educmat/CHM729/afm/force.htm

[26] L. Xiaodong, B. Bharat, A review of nanoindentation continuous stiffness measurement

technique and its applications, Materials Characterization 48, 11(2002)

[27] Wikipedia, Cortical bone and trabecular bone, http://en.wikipedia.org/wiki/Cortical_bone

[28] Oliver,W.C. and Pharr,G.M.,An improved technique for determining hardness and elastic

modulus using load and displacement sensing indentation experiments, Journal of Materials

Research, 7, 1992,1564-1583

http://en.wikipedia.org/wiki/Deformation

http://wikislice.webaroo.com/external/Poisson%27s_ratio

http://en.wikipedia.org/wiki/Atomic_force_microscope

http://www.chemistry.uoguelph.ca/educmat/chm729/afm/introdn.htm

http://nanoparticles.pacificnano.com/atomic-force-microscope.html

http://www.chembio.uoguelph.ca/educmat/CHM729/afm/force.htm

http://en.wikipedia.org/wiki/Cortical_bone


66

[29] E.Tomasetti, R.Legras, B.Nysten, Quantitative approach towards the measurement of

polypropylene (ethylene-propylene) copolymer blends surface elastic properties by AFM,

Nanotechnology 9 (1998) 305

[30] David C.Lin, K.Dimitriadis, F.Horkay, Advances in the mechanical characterization of soft

materials by nanoindentation,Recent Res.Devel.Biophysic,5(2006)

[31] Walters D.A, Cleveland J.P,Thomson N.H.,Hasma P.K, Wendman M.A., Gurley G., Elings

V. , Rev. Sci.Instrument 67 (1996) 3583

POLITEHNICA UNIVERSITY OF TIMIŞOARA -...

Documents

Transcript of POLITEHNICA UNIVERSITY OF TIMIŞOARA -...