Diameter- and Loading Mode Effects of Modulus in ZnO Nanowires

Diameter- and Loading Mode Effects of Modulus in ZnO Nanowires In Situ Measurements & Theoretical Understanding Mo-rigen H, CQ Chen, Y Shi, YS Zhang, W Zhou, JW Chen, YJ Yan, J Zhu* Beijing National Center of Electron Microscopy Department of Materials Science and Engineering Tsinghua University, Beijing, China 2009. 08. 25 Jing Zhu s Group, BNCEM, DMSE, TsingHua Univ.

Outline Introduction In Situ Bending and Tension Dual Probe System Electric Field Induced Resonance Uniaxial Stress-strain Curve Experimental Results for ZnO Nanowires Theoretical Studies Structural Relaxation and Core-Shell Model Diameter Dependence and Loading Mode Effect Summary Jing Zhu s Group, BNCEM, DMSE, TsingHua Univ.

Nano-Mechanics? Strength of α-al 2 O 3 whisker Space-ladder made of CNT Decreasing the Size Mechanical properties? Yacobson BI. American Scientist. July-August (1997) Levitt AP. Whisker Technology. New York: Wiley (1970)

Nanomanipulator in SEM Electrochemical-etched tungsten nano-tip Degree of Freedom: X, Y, Z, Θ piezotube X Θ Z Y V DC,V AC NW W tip Applying forces and electric field to individual nanowire Free transverse vibration of Euler-Bernoulli beam: EI 3 Z y ( xt, ) + ρ Ayxt (, ) = 0 Bending Modulus vs. Fundamental frequency: E ρ A = L ω 1.875 IZ 4 2 3 4 1 Yan YJ, Zhu J, et al. J. Chin. Electr. Microsc. Soc. 23: 484 (2004) Nayfeh AH, Mook DT. Nonlinear Oscillations. New York: Wiley (1979)

Electric Field Induced Resonance Experimentally, resonance can be stimulated by three frequencies (Ω), which are double each other. F() t [ Δ V + V + V cos Ωt] AC = F + F + F (0) (1) (2) cos Ωt 2 cos 2Ωt DC u + Forced Resonance 2μ u + ω = t 2 1 u F() Parametric Resonance u + 2μu + ε F() t u = 0 F(t) F(t) Poncharal P, Wang ZL, et al. Science. 283: 1513 (1999) Shi Y, Zhu J, et al. Nanotechnology. 18: 075709 (2007)

In Situ Tensile Testing Uniaxial tension and stress-strain curve: the best method for bulk samples Comprehensiveness Easiness Difficulties Confronted in Nanoscale: Manipulation Dual-Probe Testing System: Clamping Alignment Loading Measurement Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

Nano-piezomotor in SEM Step-by-step (min.~10nm) actuation: Computer-controlled voltage signal Carrying a pair of AFM cantilevers Φ Calibration: Resonance Method Degree of Freedom: X, Y, Z, Φ Chen DM, et al. Rev. Sci. Instrum. 72: 4398 (2001) Sader JE, et al. Rev. Sci. Instrum. 70: 3967 (1999) Zhou W. BS Thesis. Tsinghua Univ. (2006) Shi Y. MS Thesis. Tsinghua Univ. (2007)

Methodologies Uniaxial Tensile Testing: (Quantitative) Manipulation: Tungsten tip Clamping: Electron Beam Induced Deposition of amorphous carbon Alignment: Rotation of tungsten tip (horizaontal) specimen stage (uniaxial) Loading: Stepwise driving nanopiezomotor Measurement of stress and strain = 4 K δ σ D 2 π Δ ε = L Δ δ Y. Shi. MS Thesis. Tsinghua Univ., 2007

Uniaxial Stress-Strain Curve Linear Elasticity Before Fracture Modulus: Diameter Dependence ZnO NW Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

ZnO Nanowires Sample:High-Quality ZnO Nanowires (CVD) Morphology Large range in diameter ~20nm--2um Free standing High aspect ratio root [0001] [0001] Crystallography Free of extended defect Uniformly [0001]-oriented; {1010} faceted Elastically anisotropic E 3 =1/S 33 =140GPa (bulk value) Zhang YS, Zhu J, et al. J. Phys. Chem. B 109: 13091 (2005)

Diameter Dependence of Modulus Tensile Modulus Bending Modulus 550nm>D>120nm, modulus slightly depends on diameter and tends to (the same) bulk value 120nm>D>17nm, modulus dramatically increases with decreasing D Chen CQ, Zhu J, et al. Phys. Rev. Lett. 96: 075505 (2006) Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

Equilibrium Relaxation of Nanowires Surface Relaxation of bulk ZnO{1010}: Contraction of Zn-O dimers along [0001] direction Relaxation of nanowires: Radial-distributed Diameter-dependent ε(ρ,d) Determined by minimization of total elastic energy: U Elastic [ε(ρ,d)]= U Bulk +U Surface +U Gradient Meyer B, Marx D. Phys. Rev. B. 67: 035403 (2003) Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

Energetic Analysis D 1 2 2 Bulk strain energy UB[ ε( ρ, D) ] = E 0 Bε ( ρ, D) 2πρdρ 2 [ D Surface strain energy U S ε( ρ, D) ] = τε (, D) π D 2 D Strain gradient energy 1 ε( ρ, D) 2 2 UG[ ε( ρ, D) ] = η[ ] 2πρd ρ 0 2 ρ Strain damping under surfaces: η = χ -1 μ 2-6 -7 11 3311 ~(10-10 )N Nonlocal electro-mechanical effect χ 11 (Remarkable in nanoscale) : polarizability; μ 3311 : flexoelectricity Modulus: highly sensitive to equilibrium inter-atomic distance (Bulk:) E[ ε( ρ, D)] d ~[1 + ε( ρ, D) ] 4 4 Mindlin RD, Int. J. Solids Struct. 1: 417 (1965) Kogan SM, Sov. Phys. Solid State. 5: 2069 (1964)

Core-Shell Approximation Stiffening of core and shell: LS ES( D) = ESC(1 + ) ESC = E( ε SC ) D L0 E0( D) = E0C (1 + ) E0C = EB D (Both the surface and core are size-dependently relaxed) Governing parameter for elastic response: Uniaxial tension: EA (tensile rigidity) Lateral bending: EI (flexural rigidity) Solution of min U E [ε(ρ,d)]: rs( D) = rsc rsc εs( D) = εsc(1+ 2 ) 2r D SC ε0( D) = εsc D r SC L S = η E B ε de SC < B L0 EBdε = Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted τ E B 2 τ η E B

Diameter Dependence A0 AS L0 2rSC 2 LS 2rSC 2 TM ( D) = E0 + ES = E0C(1 + )(1 ) + ESC(1 + )[1 (1 ) ] A A D D D D I0 IS L0 2rSC 4 LS 2rSC 4 BM ( D) = E0 + ES = E0C(1 + )(1 ) + ESC(1 + )[1 (1 ) ] I I D D D D Size dependence: sign (±) of surface tension along NW axis. Loading mode effect: difference in contributions from core and shell. For the same D: E S (D)>E 0 (D)>E B BM(D)>TM(D)>E B Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

D>120nm: BM and TM converge to E B. Negligible contribution from the stiffened surfaces. 120nm>D>30nm: Relaxed surfaces contribute to BM more than TM. TM increases slower than BM with decreasing D. Loading Mode Effect D<30nm: The core modulus remarkably increases, and the NW tends to be uniformly relaxed. TM increases more rapidly and gets close to BM. D<2r S ~9nm: Current model may no longer work. Mo-rigen H, Zhu J, et al. Appl. Phys. Lett. accepted

Summary In situ dual-probe mechanical testing system; Bending modulus: resonance method; Tensile modulus: stress-strain curves; Modulus in ZnO nanowires: diameter- and loading mode dependence; Relaxation in nanowires: energetic analysis Continuum mechanics: works above 10nm (in ZnO NWs), with the surface and nonlocal elastic effect considered. Core-shell model: universal for various relaxation states and loading modes. Jing Zhu s Group, BNCEM, DMSE, TsingHua Univ.

Thanks for your attention! Jing Zhu s Group, BNCEM, DMSE, TsingHua Univ.