Constant height mode Constant force mode Force: van der Waals force, electrostatic force, Pauli repulsive force, etc laser detection cantilever Revealing surface energy with atomic force microscopy (AFM) EEW508 VI. Mechanical Properties at Surfaces

Measurement of adhesion force between AFM tip and sample with force-distance curve At the point A, the tensile load is the same with the adhesion force (F AB corresponds to the adhesion force) EEW508 VI. Mechanical Properties at Surfaces

EEW508 VI. Mechanical Properties at Surfaces 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.

EEW508 VI. Mechanical Properties at Surfaces 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

EEW508 VI. Mechanical Properties at Surfaces 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, (2007)

Force-volume mapping : three dimensional mapping of adhesion force CdSe tetrapod topography Adhesion mapping L. Fang, J. Y. Park, et al. Journal of Chemical Physics (2007) EEW508 VI. Mechanical Properties at Surfaces

Adhesion and stiction are important issues in reliability of MEMS(Microelectromechanical) systems devices EEW508 VI. Mechanical Properties at Surfaces

Influence of F-based etching on surface adhesion Zhang, Park, Huang, and Somorjai, Appl. Phys. Lett (2008) EEW508 VI. Mechanical Properties at Surfaces

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 Where K is the reduced Young’s modulus. Because the tip and the surface can be elastically deformed, Where E t, E s, t, s are Young’s moduli and the Poisson ratios of the flat surface and the tip EEW508 VI. Mechanical Properties at Surfaces

EEW508 Mechanical 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. Where W is the work of adhesion, which can be calculated as F ad 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. Friction at the single asperity

EEW508 Mechanical Properties at Surfaces DMT (Derjaguin-Muller-Toporov) model JRK theory neglects the adhesion force and the long range adhesion force outside the contact area is considered. Where W is the work of adhesion, which can be calculated as F ad can be obtained from the force-distance curve. DMT is suitable for the contact between tips with a small radius and less adhesive surface. Intermediate model – Maugis theory Deals with the intermediate regime between DMT and JKR model.

EEW508 Mechanical Properties at Surfaces Which model is more suitable? DMT or JKR model? An empirical nondimensional parameter (Tabor parameter,  ) Where W is the work of adhesion, and z 0 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

EEW508 Mechanical Properties at Surfaces J. Y. Park et al. Appl. Phys. Lett (2005)

atomic/friction force microscopy AFM and pin-on-disk tribometer on the sample specimen Tools for tribological study EEW508 VI. Mechanical Properties at Surfaces

Principle of friction force microscopy AFM invented by Binnig, Quate, and Gerber in 1986 AFM has a sharp tip with a radius between nm, and the resolutions for the displacement and force sensing can be up to 0.01 nm and 0.1 pA. Stick  <-- slip  EEW508 VI. Mechanical Properties at Surfaces

Topographical and friction images of SAM molecules on silicon AFM topography friction C16 silane n type silicon SAM molecules are common lubricating materials to reduce friction on silicon devices EEW508 VI. Mechanical Properties at Surfaces

EEW508 VI. Mechanical Properties at Surfaces Atomic scale friction and adhesion Factors that affect friction force 1.Surface layer – oxide, hydrocarbon 2.Contact regime – plastic or elastic deformation 3.Atomic structure 4.Electrical property 5.Dislocation, defects

The influence of surface oxidation on surface energy – 10-fold Al-Ni-Co surface EEW508 VI. Mechanical Properties at Surfaces

The influence of plastic deformation on surface energy EEW508 VI. Mechanical Properties at Surfaces

Atomic scale stick-slip motion (a) 6nm x 6 nm friction images of KF(001) cleaved and imaged in UHV With 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. EEW508 VI. Mechanical Properties at Surfaces

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 EEW508 VI. Mechanical Properties at Surfaces

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 no. 5361, pp EEW508 VI. Mechanical Properties at Surfaces

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. EEW508 VI. Mechanical Properties at Surfaces

Single asperity Real contact AFM Friction at the single asperity Friction at the Macroscopic scale DMT: Derjaguin-Müller-Toporon JKR:Johnson, Kendall and Roberts Frictions at the different scale (nano versus macroscale) EEW508 VI. Mechanical Properties at Surfaces

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 f n+1 = f n + f n-1 LSLLSLSLLSLLS … Quasicrystals: Intellectual Beauty meets Practical Application Quasicrystal Rotational symmetry But 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 quasicrystalline materials” J. M. Dubois Mat. Sci. Eng. (2000)

A progression of numbers which are sums of the previous two terms f(n+1) = f(n) + f (n-1), Quasiperiodicity – Fibonacci sequence (Golden Mean, ) Fibonacci rabbit sequence L : a pair of adult rabbits S : a pair of baby rabbits L next term LS S L

The Parthenon in Athens Fibonacci in fiction Golden Mean – Fibonacci sequence       Fibonacci in nature: spiralsFibonacci in body: fingers

Tribology of quasicrystals (historical overview) J. M. Dubois group Quasicrystals 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 4Å4Å Icosahedral: Aperiodic in 3D 10 fold axis (periodic) 10f surface Stack of 10-fold Aperiodic planes 2f surface

Atomic structure of 2-fold Al-Ni-Co surface L =13Å S=8Å L (13Å) S(8Å) L1 8 Å S1 5 Å L1 8 Å L2 5 Å L2 5 Å S2 3 Å S2 3 Å L2 5 Å L S L L S L1 S1 S2 L2 S2 L2 L=12.8  0.4 Å, S=7.8  0.3 Å L 2 = 5.0  0.4 Å, S 2 = 2.9  0.2 Å L/S ~ L 1 /S 1 ~ L 2 /S 2 ~  (Golden mean = )

Atomic structure of two fold Al-Ni-Co surface Golden stringn Fn S01 L11 LS22 LSL33 LSLLS45 LSLLSLSL58 LSL LSLSLLSLL S 613 L1S1L1L1S1L1S1L1L1S1L1L1S1L1S1L1L1S1L1S1L1L1S1L1L1S1L1S1L1L1S1L1L1S1L1S1L1L1S1L1S1L1 721 S2L2L2S2L2S2L2L2S2L2L2S2L2S2L2L2S2L2S2L2L2S2L2L2S2L2S2L2L2S2L2L2S2L2S2L2L2S2L2S2L2L2S2L2L2S2L2S2L2L2S2L2S2L2L2S2L2L2S2L2S2L2L2S2L2L2S2L2 834

Atomically clean surface – highly reactive Pulloff force ~ 1  N Park et al. Trobology Letters (2004) Adhesion force for Al-Ni-Co 10 fold surface : 1  N 2 fold surface : 0.4  N (cf. W2C-Pt(111): 12  N M. Enachescu et al. ) Passivated tip-passivated 10f (ethylene) : 14 nN Passivated tip – clean 2f :200nN Typical contact imaging (metallic probe – metallic surface) Unstable, irreversible topographycurrent 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 surface STM image 10-fold before After friction

Evidence of elastic regime Force & current versus distance Contact I-V curve Applied load = 0nNSample bias = 1V Passivated probe

Friction anisotropy in decagonal quasicrystalperiodic aperiodic Park, Ogletree, Salmeron, Ribeiro, Canfield, Jenks, Thiel, Science (2005)

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 important The 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 anisotropy on decagonal quasicrystals atomic/friction force microscopy periodic (10 fold direction) aperiodic (2 fold direction) AFM and pin-on-disk experiments on oxidized Al-Ni-Co decagonal quasicrystals

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

Macro and nanoscale friction anisotropy on decagonal quasicrystals 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

(c) L =12.3Å L2L2 L2L2 L2L2 S =7.5Å S2S2 S2S2 (b) 2.1Å (a) Atomic models of Al-Ni-Co surface (ii)