Constant height mode Constant force mode Force: van der Waals force, electrostatic force, Pauli repulsive force, etc laser detection cantilever Revealing

Constant height mode

Constant force mode

Force: van der Waals force, electrostatic force, Pauli repulsive

force, etc

laserdetection

cantilever

Position sensitive Photodiode array Laser beam

Bending

Torsion

LOAD

FRICTION

Light Beam DeflectionPosition sensitive Photodiode array Laser beam

Bending

Torsion

LOAD

FRICTION

Position sensitive Photodiode array Laser beam

Bending

Torsion

LOAD

FRICTION

Light Beam Deflection

Revealing surface energy with atomic force microscopy (AFM)

EEW508VI. Mechanical Properties at Surfaces

Measurement of adhesion force between AFM tip and sample with force-distance curve

-500

-400

-300

-200

-100

0

100

-100 0 100 200 300

distance (nm)

No

rmal

for

ce (

nN)

A

B

A

B

At the point A, the tensile load is the same with the adhesion force (FAB corresponds to the adhesion force)



Schematic of force-distance curve

The arrow on the curve indicates loading and unloading process

(i) Tip is far away(ii) Tip is moved closer to

the sample, and the attractive force between tip and sample begins the tip down.

(iii) Repulsive region – the sample is pressed by the tip, which causes the elastic and plastic deformation.

(iv) The sample moves in the opposite direction, the tip and the sample surfaces maintains the contact.


Tip-sample forces

1. Van der Waals force -- is caused by fluctuations in the electric dipole moment of atoms and their mutual polarization

2. Electrostatic force -- When the tip and sample are both conductive and have an electrostatic potential difference V, electrostatic forces are important.

3. Capillary force – forces caused by water bridge formed at the tip-sample contact

4. Chemical force - chemical interaction between the tip and sample


-40

0

40

80

120

160

-50 -30 -10 10 30

z (nm)

F (

nN

)

0V

-5V

Fo (pulloff force)

Fo + Fe

0

10

20

30

40

50

-6 -4 -2 0 2 4 6Vs(V)

adh

esio

n f

orc

e (n

N) p stripe

n region

Electrostatic force and van der Waals force

Force-distance curves measured in the n region silicon surface with the sample biases of 0 and −5 V.

Plot of the pull-off force as a function of sample bias for both p and n regions

J. Y. Park et al. PHYSICAL REVIEW B 76, 064108 (2007)

Force-volume mapping : three dimensional mapping of adhesion force

CdSe tetrapod

Adhesion force (nN)

35

30

25

20

15

10

5

0

30252015105

18nN

28nN

ConductiveAFM

Au(111) or Si

A

Vs

A

Vs

tetrapod

topography Adhesion mapping

L. Fang, J. Y. Park, et al. Journal of Chemical Physics (2007)


Adhesion and stiction are important issues in reliability of MEMS(Microelectromechanical) systems devices


Influence of F-based etching on surface adhesion

Zhang, Park, Huang, and Somorjai, Appl. Phys. Lett (2008)


Real contact area between the AFM tip and the surface

The model system for the elastic continuum contact theories. The AFM tip is modeled by a small sphere with a radius R. After applying a load F, the sphere and the surface deform elastically, and the contact area increases.

There are four models within the framework of the elastic continuum contact mechanics. The simplest model is Hertz model. The contact area A is given by

3/2

K

RFA

Where K is the reduced Young’s modulus. Because the tip and the surface can be elastically deformed,

t

t

s

s

EEK

22 11

4

31

Where Et, Es , t, s are Young’s moduli and the Poisson ratios of the flat surface and the tip


EEW508Mechanical Properties at Surfaces

JKR (Johnson-Kendall-Roberts) model

JRK theory neglects long range forces outside the contact area and considers only the short range force inside the contact region.

3/2

2/12)3(6(3

RWRWRWFK

RA

Where W is the work of adhesion, which can be calculated as

Fad can be obtained from the force-distance curve. JKR is applicable to the contact between the tips with a large radius and highly adhesive and soft materials.

R

FW ad

3

2

cont

act

are

a [n

m ]

A2

-150

externally applied load [nN]Fl

-100 -50 0 50

2000

4000

6000

Friction at the single asperity


DMT (Derjaguin-Muller-Toporov) model

JRK theory neglects the adhesion force and the long range adhesion force outside the contact area is considered.

3/2

2

RWFK

RA

Where W is the work of adhesion, which can be calculated as

Fad can be obtained from the force-distance curve. DMT is suitable for the contact between tips with a small radius and less adhesive surface.

R

FW ad

2

Intermediate model – Maugis theory

Deals with the intermediate regime between DMT and JKR model.


Which model is more suitable? DMT or JKR model?

An empirical nondimensional parameter (Tabor parameter, )

3/1

30

2

2

9

16

zK

RW

Where W is the work of adhesion, and z0 is the equilibrium spacing of two surfaces (roughly an atomic distance)

If >5, JKR model is a good approximation, while DMT is more appropriate when is less than 0.1


J. Y. Park et al. Appl. Phys. Lett (2005)

Wear track Rotating

disk

Weight: 1N

Elastic arm

Friction force sensor

atomic/friction force microscopy

AFM and pin-on-disk tribometer on the sample specimen

Tools for tribological study


AB

DC

AB

DC

AB

DC

xyz actuator

4 quadrant photodiode

laser

cantilever

sample

V(A+C)-(B+D)

Lateral distance

quadrantphotodiode

Friction signal

A B

C D

A B

C D

Principle of friction force microscopy

AFM invented by Binnig, Quate, and Gerber in 1986AFM has a sharp tip with a radius between 10-100 nm, and the resolutions for the displacement and force sensing can be up to 0.01 nm and 0.1 pA.

Stick <-- slip


Topographical and friction images of SAM molecules on silicon

AFM topography friction

C16 silane

n typesilicon

SAM molecules are common lubricating materials to reduce friction on silicon devices



Atomic scale friction and adhesion

Factors that affect friction force

1.Surface layer – oxide, hydrocarbon2.Contact regime – plastic or elastic deformation3.Atomic structure4.Electrical property5.Dislocation, defects

The influence of surface oxidation on surface energy – 10-fold Al-Ni-Co surface

before After (2L dosing)

2f surface

1nm

LEED 10f surface

0

100

200

300

400

0 200 400 600

Oxygen dosing (L)

Fri

ctio

n f

orc

e (

nN

)

0

100

200

300

400

0 200 400 600

Oxygen dosing (L)

Fri

ctio

n f

orc

e (

nN

)

0

100

200

300

400

0 200 400 600

Oxygen dosing (L)

Fri

ctio

n f

orc

e (

nN

)

0

100

200

300

400

0 200 400 600

Oxygen dosing (L)

Fri

ctio

n f

orc

e (

nN

)

0

200

400

600

800

1000

1200

Ad

he

sio

n fo

rce

(n

N)

Air oxide

Air oxide

Adhesion force

Frictionforce


0

20

40

60

80

100

0 500 1000 1500

Load (nN)

adhe

sion

forc

e (

nN)

0

20

40

60

80

100

0 500 1000 1500

Load (nN)

adhe

sion

forc

e (

nN)

0

20

40

60

80

100

0 500 1000 1500

Load (nN)

adhe

sion

forc

e (

nN)

Elastic regime

plasticregime

intermediateregime

0

50

100

150

200

250

0 500 1000 1500 2000 2500

Load (nN)

Fric

tion

(nN

)

experimentalfriction data

DMT fitting

JKR fitting

Inelasticcontribution

0

50

100

150

200

250

0 500 1000 1500 2000 2500

Load (nN)

Fric

tion

(nN

)

experimentalfriction data

DMT fitting

JKR fitting

Inelasticcontribution

Elastic regime

Plastic regime

Adhesion force friction force

Ethylene passivated 10-fold Al-Ni-Co surface

Indented areaby applying the high load (>700 nN)

Jeong Young Park et al. Phys. Rev. B 71, 144203 (2005).

The influence of plastic deformation on surface energy


Atomic scale stick-slip motion

(a) 6nm x 6 nm friction images of KF(001) cleaved and imaged in UHVWith a silicon nitride tip and (b) friction loop from the single line of the image shown in (a).

Stick-slip motion with the periodicity of the KF surface unit cell is observed.


Friction and atomic structure – commensurability

Commensurate contact – Superlubricity of Graphite

Dienwiebel et al. Phys. Rev. Lett (2004).

Graphite flake

Graphite

Commensurate contact-high friction

Incommensurate contact-low friction


Friction anisotropy ~ 3 R. Carpick et al. Tribol. Lett.

(1999)

Silicon nitride

Polydiacetylene

Friction anisotropy

LFM image of a thiolipid monolayer on a mica surface

“Friction Anisotropy and Asymmetry of a Compliant Monolayer Induced by a Small Molecular Tilt”Science, Vol. 280. no. 5361, pp. 273 - 275


d-Al-Ni-Co surface Adhesion

force(N) Work of adhesion (J/m2)

Mechanical regime

10 – fold (clean) 0.7 ± 0.2 0.7 (DMT) ~0.9(JKR) Plastic 2 – fold (clean) 0.35 ± 0.08 0.35 (DMT) ~0.5(JKR) 10 – fold (200 L oxygen in-situ) 0. 4 ± 0. 1 0.4 (DMT) ~0.5(JKR) 10 – fold (ethylene passivated) 0.07 ± 0.01 0.07 (DMT) ~ 0.09

(JKR)

Pt (111) (clean)

10 12(DMT)~16(JKR)

2-fold (clean surface- with passivated probe)

0.17 ± 0.03

0.18(DMT)~ 0.22(JKR)

Elastic

10 – fold (ethylene passivated) 0.013 ± 0.002 ~0.013 (DMT) 10- fold (short air oxidized) 0.04 ± 0.012 ~0.04 (DMT) 2-fold (short air oxidized) 0.045 ± 0.01 ~0.045(DMT) 10- fold (long air oxidized) 0.02 ± 0.004 ~0.02(DMT) 2-fold (long air oxidized) 0.02 ± 0.004 ~0.02(DMT)

Case study: Adhesion force and work of adhesion for several complex metal alloy surfaces

Adhesion forces and work of adhesion of decagonal Al-Ni-Co surfaces in both plastic and elastic regime against a TiN-coated tip. Work of adhesion is estimated with DMT or JKR model, and tip radius of 150 nm.


Singleasperity

Real contact

AFM

cont

act

are

a

[nm

]

A2

-150

externally applied load [nN]Fl

-100 -50 0 50

2000

4000

6000

Friction at the single asperity

Friction at the Macroscopic scale

Ff

Fn

F

L

Elementary mechanisms

DMT: Derjaguin-Müller-Toporon JKR:Johnson, Kendall and Roberts

Frictions at the different scale (nano versus macroscale)


Case study- Role of aperiodicity on low

friction force of quasicrystal surfaces

Jeong Young Park, D. F. Ogletree, M. Salmeron, R. A. Ribeiro, P. C. Canfield, C. J. Jenks, and P. A. Thiel, “High Frictional Anisotropy of Periodic and Aperiodic Directions on a Quasicrystal Surface “ Science 309, 1354 (2005).

Quasiperiodicity and Golden Mean

Leonardo da Vinci’s ‘Annunciation’

Quasi-periodicity Fibonacci sequence

fn+1 = fn + fn-1

LSLLSLSLLSLLS..

0-1-1-2-3-5-8-13-21-34-…

Quasicrystals: Intellectual Beauty meets Practical Application

Quasicrystal

Rotational symmetryBut no translational periodicity

Mechanical properties of quasicrystal

Low friction coefficients High hardness

Low surface energy Good wear-resistance

Good oxidation-resistance

“New prospects from potential applications

of quasicrystallinematerials”

J. M. DuboisMat. Sci. Eng. (2000)

A progression of numbers which are sums of the previous two termsf(n+1) = f(n) + f (n-1),

Quasiperiodicity – Fibonacci sequence

n

n

n f

f 1lim

LSLLSLSLLSLLSLSLLSLSL

721

LSLLSLSLLSLLS

613

LSLLSLSL58

LSLLS45

LSL33

LS22

L11

S01

Golden string

nF(n)

LSLLSLSLLSLLSLSLLSLSL

721

LSLLSLSLLSLLS

613

LSLLSLSL58

LSLLS45

LSL33

LS22

L11

S01

Golden string

nF(n)

(Golden Mean, 1.618..)

Fibonacci rabbit sequence

L: a pair of adult rabbitsS : a pair of baby rabbits

Lnext term

L S

next termS L

The Parthenon in Athens

13-3-2-21-1-1-8-5Fibonacci in fiction

Golden Mean – Fibonacci sequence

Fibonacci in nature: spirals

Fibonacci in body: fingers

Tribology of quasicrystals(historical overview)

J. M. Dubois groupQuasicrystals exhibit anomalously low coefficients of friction when sliding against diamond and steel

Is low friction due to the aperiodicity of quasicrystals ?

Leonardo La Vince

frictionGolden Mean

Tribology of quasicrystals(historical overview)

Mancinelli, Gellman, Jenks, Thiel

Al-Pd-Mn approximant and quasicrystals

UHV tribometer

Insight on low friction of quasicrystals

1. Atomic structure should be checked

2. Plastic deformation of clean and reactive surface

surface sensitive atomic probe

Bulk structure of decagonal quasicrystal

4Å

Icosahedral: Aperiodic in 3D

10 fold axis(periodic) 10f surface

Stack of 10-foldAperiodic planes

2f surface

Atomic structure of 2-fold Al-Ni-Co surface

L =13Å S=8Å

L (13Å) S(8Å)

L18Å

S15Å

L18Å

L25Å

L25Å

S23Å

S23Å

L25Å

L

SL

LSL1

L1

L1

L1

L1

S1

S1

S1

S2

S2

S2

S2

L2

S2L2

L2

L2L2

L2

L2L2

L=12.80.4 Å, S=7.80.3 ÅL2 = 5.00.4 Å, S2 = 2.90.2 Å

L/S ~ L1/S1 ~ L2/S2

~ (Golden mean =1.618..)

d (4Å)

Periodicd (4Å)

Periodic

L

SL

L

L

S

S

L

L

S

L1

L1

L1

L1

L1

L1

L1

L1

L1

S1

S1

S1

S1

S1

S1L1

S2

S2

S2

S2

S2

S2

S2

S2

S2

S2

L2L2

L2

L2 L2

L2

L2 L2

L2 L2

L2

L2

L2

L2 L2

L2

Quasiperiodic

(Fibonacci sequence)

L

SL

L

L

S

S

L

L

S

L1

L1

L1

L1

L1

L1

L1

L1

L1

S1

S1

S1

S1

S1

S1L1

S2

S2

S2

S2

S2

S2

S2

S2

S2

S2

L2L2

L2

L2 L2

L2

L2 L2

L2 L2

L2

L2

L2

L2 L2

L2

Quasiperiodic

(Fibonacci sequence)

Atomic structure of two fold Al-Ni-Co surface

Golden string n Fn

S 0 1

L 1 1

LS 2 2

LSL 3 3

LSLLS 4 5

LSLLSLSL 5 8

LSLLSLSLLSLLS

6 13

L1S1L1L1S1L1S1L1

L1S1L1L1S1L1S1L1

L1S1L1S1L1

7 21

S2L2L2S2L2S2L2L2

S2L2L2S2L2S2L2

L2S2L2S2L2L2S2

L2L2S2L2S2L2L2

S2L2L2S2L2

8 34

Atomically clean surface – highly reactive

Pulloff force~ 1 NPark et al.

TrobologyLetters (2004)

Adhesion force for Al-Ni-Co

10 fold surface : 1 N2 fold surface : 0.4 N(cf. W2C-Pt(111): 12 NM. Enachescu et al. )

Passivated tip-passivated 10f(ethylene) : 14 nNPassivated tip – clean 2f :200nN

Typical contact imaging(metallic probe – metallic surface)

Unstable, irreversibletopography current friction

STM images before and after contact measurement

Contact imaging in elastic regime (alkylthiol passivated probe – clean quasicrystal surface)

topography current friction

Taking three images at the same time with the passivated probe

Alkylthiol molecules

2f surfaceSTM image 10-fold

before After friction

-300

-200

-100

0

100

200

300

-400 -350 -300 -250 -200

z (nm)

Fn (n

N)

-600

-400

-200

0

200

400

600

I (nA

)

normal force

current

Passivated probe

Unpassivated probe

-1

-0.5

0

0.5

1

-2 -1 0 1 2

Vs(V)

I(uA

)

Evidence of elastic regime

Force & current versus distanceContact I-V curve

Applied load = 0nN Sample bias = 1V

Passivated probe

Friction anisotropy in decagonal quasicrystal

peri

odic

peri

odic

aperiodicaperiodic

Park, Ogletree, Salmeron, Ribeiro, Canfield, Jenks, Thiel, Science (2005)

0

20

40

60

80

100

-150 -100 -50 0 50 100applied load (nN)

-4

0

4

8

12

Fric

tion

anis

otro

py

Friction anisotropy

Friction (periodic)

Friction (aperiodic)Tor

sion

al r

espo

nse

(nN

)

0

0.1

0.2

0.3

-100 -50 0 50 100

applied load (nN)fr

ictio

n (

a.u

.)

periodic

aperiodic

Low friction of quasicrystals in macroscopic scale(no friction anisotropy in air-oxidized surface)

periodic

aperiodic

Contact AFM images of air-oxidized 2f surface Friction of air-oxidized surface

The presence of oxide (amorphous and isotropic)significantly reduces electronic and phononic frictions

The role of surface oxide as the lubricant layer is more importantThe high hardness of bulk quasicrystal leads to low contact area, thus low friction.

(Also, bulk hardness is isotropic; 10f-11.1GPa, 2f-10.7GPa)

Macro and nanoscale friction anisotropyon decagonal quasicrystals

Wear track Rotating

disk

Weight: 1N

Elastic arm

Friction force sensor

atomic/friction force microscopy

periodic

(10 fo

ld d

irectio

n) aperiodic

(2 fold direction)

AFM and pin-on-disk experiments on oxidized Al-Ni-Co decagonal quasicrystals


0

0.05

0.1

0.15

0.2

0.25

0.3

-1000 0 1000 2000 3000 4000applied load (nN)

fric

tion

(a.u

.)aperiodic(2 fold)periodic(10 fold)

Breakingoxide

10-f

old

dire

ctio

n

Trench

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500

x (nm)

z (n

m)

Length: 200 nm

depth2 nm

AFM images on oxidized Al-Ni-Co decagonal quasicrystals before and after breaking through oxide layer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 0.01 0.03 0.04

Distance (m)

fric

tion

co

effi

cie

nt

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

pin

po

sitio

n (

a.u

.)

fric

tion

for

ce (

N)

Pin

pos

ition

(a.

u.)

Breaking oxide

2 periodicity periodicity

Cycles [2x(mm)/a]0 2

2 periodicity

1 3 4 5 6


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.0123 0.0246 0.0369

distance (m)

fric

tion

co

effi

cie

nt

0

1

2

3

4

5

Breaking oxide

aperiodic

periodic

Normal force (N)

F n

(N)

Fri

ctio

n c

oef

ficie

nt

Cycles [2x(mm)/a]

0 21 3 4 5 6

Pin-on-disk measurement on oxidized Al-Ni-Co decagonal quasicrystals before and after breaking through oxide layer

Friction anisotropy is revealed after breaking through the oxide

Friction coefficient along this periodic direction is 0.45 ± 0.06, whereas that along the aperiodic direction is 0.30 ± 0.05, i.e., larger by a factor of 1.5.

Conclusion

1. The fundamental question of whether or not the desirable properties of quasicrystals are a direct result of quasiperiodic atomic structure were investigated with a combined atomic force microscopy / scanning tunneling microscopy.

2. Strong friction anisotropy were observed when sliding along the two directions: high friction along the periodic direction, and low friction along aperiodic direction.

3. This feature can be associated with (i) Electronic contribution due to anisotropic electrical conductance(ii) phononic contribution

4. The unique friction properties of decagonal Al-Ni-Co quasicrystals are an intrinsic property of their peculiar crystallographic structure.

Slippery atoms

L LLL LS SSL LLL LS SS

(c)L =12.3Å

L2L2L2

S =7.5Å

S2S2

(b)

2.1Å

(a)

Atomic models of Al-Ni-Co surface (ii)

Documents

Constant height mode Constant force mode Force: van der Waals force, electrostatic force, Pauli repulsive force, etc laser detection cantilever Revealing