June 29, 2012 1

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Quantitative Nano-Mechanical Characterizationof Composites and Thin Films

‐Combo TMT/AFM Webinar on Nanoindentation and Peak‐force on June 26‐

Ilja Hermann Ben Ohler

• Motivation• Theory of Nano‐indentation• Experimental aspects • Example Results• Conclusion

Outline

MotivationWhy do we need mechanical properties ? 

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Mechanical Properties

Failure Analysis Virtual Tests

Materials design Tribology

Wear

Understand and prevent irreversible deformation

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MotivationFundamentals of mechanical properties  

Stress and Strain :

AF

Normal Stress

ll

Normal Strain

AF

Shear Stress

ll

tan

Shear Strain

... mnklijklmnklijklij SS

Constitutive Equation :

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MotivationMeasuring mechanical properties

Test & specimen:•Uniaxial tension/compression •Bending•Accoustic wave

=> Mechanical properties on macroscopic scale

Hooke:

11

12

11

11

E

klijklij S

homogenious, isotropic:

Properties:• E, , K, G, • Y0, K1

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MotivationHardness test

28544.1dFHV

[Applied load] = kgf

[Diagonal] = mm

VICKERS-Hardnessnumber

23

32

21

1 015.0c

FHE

laK

Fracture-

Toughness

F…Applied load (N)H…Hardness (Gpa)E…Young’s Modulus (Gpa)c,a,l…distances from img (m)

Pros:• Simple application• Small specimen• Easy to scale

Cons:• HV difficult co-relate to physical properties• Scaling limited by imaging resolution• No elastic properties

Concept: 1. Apply load. 2. Analysis of residual imprint after load removal

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MotivationInstrumented indentation

Concept: 1. Accurate measurement of compliance curve 2. Elastic analysis of tri-axial stress-state in contact

Nano-indentation QNM

Elastic-plastic Elastic

Typical load: ~10 mN ~1 nN

Typical depth: ~100 nm ~10 nm

Property access:  E, H, Y, K1, Rep(Rep) E, E(x,y)=>Mechanical properties on mesoscopic scale

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Theory of Nano‐indentation

Fundamentals of contact mechanics

p(r,)

i, i

drdrpE

uz ),(1 2

Point-contact solution

Superposition

Obtaining contact stress field and surface deformation

, = ?

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Theory of Nano‐indentation

Elastic surface deformation

Contact Geometry

Pressure distribution

Mean pressure Surface Deflection (r=0)

Surface Deflection (r=a)

Flat Punch Sneddon:

Sphere(Hertz)

Cone(Sneddon) 2

12

tan21

rEFh

21

2

2

123

ar

pm

z

ra

pm

z 1cosh

21

2

2

121

ar

pm

z FaE

hr2

1 2

32

43

REFh

r he FS

pm HB 4Er

3

aR

f (r) Brn

m 1 1

m(2m 2)

m(2m1)

with

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Theory of Nano‐indentation

Hertzian contact stress

222222 *621

zyxzxyzzxxyyzzyyxxMisesvon

Prin

cipa

l stre

ss

1(a

.u.)

Von

Mis

es S

tress

(a.u

.)

Tensile stress Von Mises stress

Hertzian cone fracture Residual imprint by sub-surface plasticity

Related material failure modes

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Theory of Nano‐indentation

Elastic-plastic indentation

i R

aR cos()

Ideal cone/Pyramid: elastic-plastic transition occurs instantly

0.07 0.5

Stress field during unloading altered by elastic constraint plastic zone

hc hmax FS f(r)=Brn

r

“Effective indenter”

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Theory of Nano‐indentation

Oliver & Pharr

AFH

F a(hh0 )m

1.2 m 1.6

hc hmax FS

hR FS

Ac Ac (hc )

1rE

1 i2

iE

1 p2

pE

Er

2 Ac

S

Young’s modulus E

S dFdh Fmax

2 Ac

Er

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Experimental aspects

Typical setup an test

Calibrations:• Tip-shape• Frame compliance• Offset in-line toolsSpecimen:• Smooth• Alignment • Bonding

Nano-HeadMicro-Head

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ResultsLoading types

• Constant• Linear• Parabolic• Harmonic• Combinations

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ResultsRaw-data post processing - Zero-point correction

F=c(h-h0)3/2

h0i

1. Hertzian fit for small depths2. Auto-correction applied to all curves

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Experimental aspects

Raw-data post-processing - other automatic corrections

• Thermal drift

• Frame Compliance: hframe F

Si (F)

hth ht driftholdtime

t

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Hardness and Young’s Modulus on SiO2NanoHead results at 10 different surface positions

Force-Displacement curve (raw-data)

Oliver&Pharr analysis results:

Experimental aspects

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Results

Hardness of steel SRM 724HV1

Ac,AFM 1 AC

AC

Ac,OP

HV 725.011.4 Kpmm2 H 7.110.11 GPaStatic :

Instrumented : H 9.82 0.17 GPaPoor agreement !

Topographical pile-up analysis

Correction:

AC

AC

26%StaticIIT

Excellent agreement with static test after pile-up – correction

-V +V -Ac

June 29, 2012

Results

Stress-strain curve

rep HB2.88

rep 0.2 aR

Tabor:

Load-multiple-partial-unload test(LMPU) with 12.5 um radius tip

Micro-structure – oriented positioning structure-sensitive mechanical response

Insights into constitutive curve

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Results

Hardness of 100 nm DLC on Steel

H Hs

H f

Hs

1

1B hd

D

Hu-Lawn:

H=(32.4+12.7) GPa

Rms>50nm

June 29, 201221

[1] D. S. Harding, W. C. Oliver and G. M. Pharr: Mat. Res. Soc. Symp. Proc., 356, 1995, 663.[2] R. Dukino and M.V. Swain, J. Am. Ceram. Soc. 75 12, 1992, 3299

Step 2: Produce a series of indentations at different loads and surface locationsStep 3: Image indents to find critical load for fully developed set of lead corner radial cracks

AFM

Step 4: Calculate Fracture toughness :

These parameters must be known:E…Young’s modulus H…hardnessP…test loada, c, l….distances from image

Berkovich [2]:

Cube Corner [1]:

Example: Si02 K1=0.604 Mpa m1/2

Results

Fracture toughness

Step 1: Measure Hardness and Young’s modulus of the specimen

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ResultsSoft materials

• 9 indents on polycarbonate can be clearly distinguished from each other on an are of 5x5 um

• The required test force was under 10 uN, and all resulting Force-displacement curves are nicely repeatable

• 16 Scratches:  1xMarker + 15 Scratches 0.1‐4mN in Fused silica• Repeatable scratch test over 40 um length• The deepest scratch is <50 nm ; the shallowest is just 1.2 nm deep

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3‐D view (AFM‐topography) 

Results

Nano-Scratch

Application: Sclero-hardness measurement on very thin films

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Results

Zig-Zag-Scratch

Application: Adhesion study

Conclusions

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• Nano-Indentation is a tool for quantitative characterization of elastic, plastic, and brittle behavior of thin films and composites

• Nano-indentation accuracy depends on a careful consideration of the most important parasitic influences

• Nano-indentation is an ideal tool to test new contact mechanical models, which will expand the field of applications for contact tests in the future.

Introduction to PeakForce QNM Ben Ohler

PeakForce QNM: Quantitative Nanomechanics

• PeakForce QNM is an AFM-based technique for high-resolution mapping of quantitative nanomechanical properties

• PeakForce QNM can measure: • Topography • Young’s modulus (~10 kPa - ~100 GPa) • Adhesion (pN-µN) • Deformation (nm) • Dissipation (eV)

• PeakForce QNM enables:

• High-resolution property mapping (true nanoscale resolution) • High-speed property mapping (normal AFM imaging rates) • Non-destructive operation (typically avoid plastic deformation)

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Atomic Force Microscopy

• Imaging technique based on the mechanical interactions between a very sharp microfabricated probe and sample surface.

• Probe raster scans, line by line, across the surface, tracing its topography

Different AFM modes differ in how the surface is detected:

• Contact mode • Probe drags in contact with the

surface at a constant force • TappingMode

• Probe oscillates at its resonance, intermittently contacting the surface. Amplitude held constant.

• Peak Force Tapping mode

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PeakForce QNM uses Peak Force Tapping

• Peak Force Tapping is a new Bruker AFM imaging technology • Probe is oscillated, but sub-resonance (typically 2 kHz) • Probe intermittently contacts the surface • Full force-distance interaction for each tap is measured • Feedback based on the peak force

• PeakForce QNM analyzes these force-distance interactions • Calculate modulus based on indentation models: DMT or Sneddon • Other properties measured directly from the force-distance data

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PeakForce QNM enables truly nanoscale nanomechanical measurements

• Typical instrumented nanoindenters • Indents 100’s nm deep and ~µm wide • Plastic deformation common

• Typical AFM-based nanoindentation

• Indents 10’s nm deep and 10’s or 100’s nm wide

• Plastic deformation common • Non-normal load results in asymmetric

pile-up around indents

• PeakForce QNM • Indentations several nm deep and

several nm wide • Deformation typically remains elastic • Also, mapping vs. discrete points

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0.5µm

Why? Sharper tips and lower loads

• Typical Berkovich nanoindentation tip • Included angle 142.3° • Typical apex end radius >100nm • Loads typically in mN range

• Conventional AFM-based nanoindentation probe • Included angle 90° • Typical end radius ~40nm • Loads typically in µN range

• Typical PeakForce QNM probe • Half angle <20° • Typical end radius <10nm • Loads can vary from pN to µN range

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TappingMode Phase Imaging

• Phase contrast is proportional to energy dissipation: • Low tapping force, phase contrast dominated by adhesion • At higher tapping forces, the elasticity may dominate

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Harder tapping

Lighter tapping

Lighter tapping

PeakForce QNM vs. Phase Imaging

• Comparison of the adhesion and phase images clearly shows that the phase contrast is primarily due to adhesion, whereas one might more commonly assume that it reflects modulus variations

• Section plot illustrates ability to measure the modulus across the polymer layers

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PeakForce QNM can quantitatively and unambiguously identify modulus and

adhesion variations. Phase imaging and multifrequency imaging techniques cannot.

PFQNM-Height

PFQNM-Adhesion

PFQNM-Modulus

Tapping-Height

Tapping-Phase

Multilayered polymer film, 10 µm scans Left: PeakForce QNM Right: TappingMode

A typical example: polymer blend

• Many polymer materials are blends of two or more components, formulated to obtain more desirable properties than those attainable with a single component.

• PeakForce QNM can assist with identifying components in microtomed sections of the blends

• Here, a polymer blend clearly shows three components: • Two higher modulus

polymers, ~1.8 GPa and 2.6 Gpa.

• A softer, rubbery material, ~200 Mpa.

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Modulus map of a multi-component polymer blend imaged using PeakForce QNM. There are three different components clearly present, the light blue component (A), the darker blue component (B), and the red/black component (C). (7 µm scan)

Nanoscale Tribofilm Properties

• PeakForce QNM reveals complex nanoscale structure in both topography and modulus data

• Nanoindentation measures only discreet points, averaging over a much larger volume and missing the bigger picture

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Samples: Tribofilms with wear scars PeakForce QNM modulus maps overlaid on topography, 2µm scan areas

Nanoscale mechanical properties at polymer interphases

• Example: Three layer polymer film used for heat sealed bags • Barrier layer: provides strength and gas impermeability • Sealant layer: adheres during heat sealing • Tie layer: preserves adhesion between Barrier and Sealant layers

• What’s happening in the interphase regions? 6/29/2012 11

Barrier layer: Nylon

Tie layer: Ultra low density

polyethylene

Sealant layer: Metallocene polyethylene/

LLDPE blend (85-15)

PeakForce QNM clearly visualizes interphase properties

• Compatibility of polymer layers has a strong influence on interphase properties

• Barrier-Tie interphase • Lamella do not cross the

interface, but grow epitaxially from the Barrier layer into the Tie layer.

• Main modulus transition occurs over ~100 nm, but the whole interphase is ~330 nm wide.

• Tie-Sealant interphase • Lamella from Tie layer act as

nucleation sites or penetrate into the Sealant layer resulting in a more ordered region ~1 µm from the interface.

• Main modulus transition occurs over ~250 nm, but the whole interphase is ~1 µm wide. 6/29/2012 12

DMTModulus DMTModulus

Tie-Sealant interphase (more compatible polymers)

Barrier-Tie interphase (less compatible polymers)

Bar

rier

Tie

Tie

Seal

ant

PeakForce QNM combined with other techniques for a more complete picture

• SEM, EDS and PeakForce QNM can be used together to understand the composition and structure of nanocomposite materials • EDS clearly shows the carbon-rich epoxy filled voids and the

calcium-rich calcium hydroxide regions • PeakForce QNM reveals that the calcium hydroxide regions

vary from ~30 GPa to ~50 GPa

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Cement paste sample (epoxy embedded)

PeakForce QNM

SEM / EDS

AFM- Topography AFM- Modulus AFM- Adhesion

SEM EDS- Carbon EDS- Calcium Modulus overlaid on SEM

Modulus of calcium hydroxide regions

Trtik et al. Cement and Concrete Research. 42:215-21 (2012).

Conclusions

• PeakForce QNM is a powerful technique for characterizing nanomechanical properties on a variety of sample types • Unambiguously separates modulus, adhesion, dissipation variations • Wide modulus operating range: 10 kPa – 100 GPa • True nanoscale lateral resolution: same as normal AFM • Fast and convenient: same as normal AFM

• PeakForce QNM can be complementary to nanoindentation • Enables mapping instead of measurements at discrete points • Enables investigation at length scales too small for nanoindentation

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