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1 Liquid-like peudoelaticity of ub-10-nm crytalline ilver particle Jun Sun 1,*, Longbing He 1,*, Yu-Chieh Lo 2,5*, Tao Xu 1, Hengchang Bi 1, Litao Sun 1, Ze Zhang 3, Scott X. Mao 2,4, Ju Li 2 1 SEU-FEI Nano-Pico center, Key Lab of MEMS of Minitry of Education, Southeat Univerity, Nanjing, , China 2 Department of Nuclear Science and Engineering and Department of Material Science and Engineering, Maachuett Intitute of Technology, Cambridge, Maachuett 02139, USA 3 Department of Material Science, State Key Lab of Si Material, Zhejiang Univerity, Hangzhou, Zhejiang, , China 4 Department of Mechanical Engineering and Material Science, Univerity of Pittburgh, 3700 O Hara Street, Pittburgh, Pennylvania 15261, USA 5 Center for Element Strategy Initiative for Structural Material (ESISM), Kyoto Univerity, Sakyo, Kyoto , Japan *Thee author contributed equally to thi work. NATURE MATERIALS 1

2 Correpondence and requet for material hould be addreed to L.S. ( J.L. ( or Z.Z. ( 1. Experimental etup Figure S1 how the experimental etup of the STM-TEM holder. The piezotube i three dimenional movable and the movement accuracy i 20 pm in X and Y direction and 2.5 pm in Z direction (toward the ample end). Figure S1 Experimental etup of STM-TEM holder. The ample i fixed onto the STM- TEM holder at one end, the counter end i a chemical-etched W tip fixed onto a movable piezotube. 2. Structure characterization of the Ag NC Figure S2 how a high-reolution image of initial crytal tructure of the Ag NC. The marked pot (0.24 nm) correpond to the lattice pacing of (111) crytal plane. The hemiphere NC how a featured geometry with a planar facet parallel to the (111) crytal plane on the top. The tructure of the NC i table and remain inge-crytalline. Figure S3 how the crytal tructure of the NC during compreion. 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION Figure S2 High-reolution image of the Ag NC under normal TEM imaging. The tructure remain ingle-crytal and quite table under electron beam irradiation during normal imaging. Figure S3 High-reolution image of the Ag NC during queezing. The tructure alo repreent ingle-crytal tructure without any dilocation. 3. Recoverable hape evolution during compreion and elongation Pleae find the attached GIF file named Video S1, Video S2 and Video S3 NATURE MATERIALS 3

4 4. Splitting the Ag NC into two maller NC The obtained two mall nanocrytal alo preent uperelatic propertie. Pleae find the attached GIF file named Video S4. 5. Surface recontruction during deformation Pleae find the movie named Video S5.wmv and Video S6.wmv 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION 6. Shrinkage of a harp Ag tip due to urface tenion Pleae find the movie named Video S7.wmv 7. MD imulation of liquid-like urface diffuion for a 10 nm Ag particle at 800 K (Movie S8) NATURE MATERIALS 5

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7 SUPPLEMENTARY INFORMATION 8. MD imulation of liquid-like urface diffuion for a 10 nm Ag particle at 900 K (Movie S9) 9. MD imulation of liquid-like urface diffuion for a 10 nm Ag particle at 1000 K (Movie S10) NATURE MATERIALS 7

8 10. Illutration of curvature-driven urface diffuion An atom in the urface layer perform random walk, but drift with average peed v M. ( x) R( x) [J]: chemical potential x [m] : poition 2 [~ 1 J/m ] : urface energy 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION 3 [~ 1e-29 m ] : atomic volume R [m] : radiu of curvature v M v [m/]: average drift peed of atom in urface layer [J/m] : thermodynamic driving force for drift [m] : arc length along urface M 2 [m //J] : urface mobility Eintein relation: M D kt B D 2 [m /] : urface diffuivity J X X D v kt B J [#atom/m/] : number of atom croing urface cut per length per time X [dimenionle] 1 : olubility of diffuing atom in urface liquid layer 3 1/ [1/m ]: number denity of atom inide urface layer Depoition rate: h J 0 h t t [m/] : peed of urface height increae J 2 [#atom/m /] : divergence of urface flux X D X D 1 h kt kt R () 2 2 t B B Ue the final radiu of curvature R 0 a an order of magnitude etimate of the magnitude of radiu of curvature during the hape evolution NATURE MATERIALS 9

10 []: timecale of the hape evolution h t ~ R0 : height change neceary to accomplih the hape change ~ R () R 3 0 R X D ~ kt B R0 11. Table SI A ummary of activation energy barrier (ev) of diffuion event on Ag urface from Kim et al databae 21,22 Diffuion mechanim (001) (110) out-channel (110) in-channel (111) Single atom Two atom Three atom Four atom Acending adatom Decending adatom NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION Leaving the corner Approaching the corner Table SII Tranition time (pico econd) of adatom diffuion on (001) and (111) urface calculated by train boot and bond boot method 29,30 Temperature t(001) trainboot t(001) bondboot t(111) MD 300 K K K K K K K K Enthalpy (ev) Enthalpy Surface formation energy Surface formation energy (J/m 2 ) Temperature (K) Figure S4 Enthalpy and urface formation energy of Ag particle a a function of temperature. NATURE MATERIALS 11

12 g(r) Crytalline phae 800 K 1000 K 1200 K 1250 K 1300 K Liquid phae r (nm) Figure S5 Radial ditribution function of Ag particle a a function of temperature. 12. The extrapolation of time cale in MD imulation Since our MD imulation howed that the particle urface motly conited of (111), (001) facet, we applied accelerated MD method to etimate the tranition rate of adatom diffuion on (001) and (111) urface at different temperature and lited the reult in Table SII 29,30. The average tranition time of adatom diffuion on (001) and (111) urface at 300 K are 10 and 3 p, repectively. The ditribution of average tranition time at different temperature how a traight-line behavior in the Arrheniu plot (Figure 5). The time cale of diffuion event between 300 and 800 K how only light difference on (111), but varie by 5~6 order for adatom diffuion on (001) urface, due to the larger activation energy. The enthalpy of 10 nm Ag particle preent a linear relationhip between 300 K and 800 K (Figure S4), which implie no phae tranformation during the temperature range. Therefore, mot diffuion procee occurring at 800 K may be extrapolated to 300 K directly in the Arrheniu fahion. According to the data in table SII, we extrapolated the time cale of the MD hape-change at 300 K by t (MD imulation time at 800K) 10 5~6 (difference of time 800K cale). Then we concluded that the approximation of hape evolution at room temperature 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION hould be 0.01 ~ 0.1 for the imulated geometry, which ha a radiu of curvature about half of that of the experiment. Moreover, melting of the nanoparticle will occur only at the temperature above 1200 K baed on the radial ditribution function of nanoparticle in Fig. S5. The tip of nanoparticle may locally melt at 1100 K before the nanoparticle change to a emi-phere hape. Below 1000 K the nanoparticle of 10 nm in ize alway tay highly crytalline. Conequently, the effect of melting can be eliminated from thi work. 13. The melting point of metal NC One may upect that the Ag NC might have a melting point reduced to room temperature due to ize effect, and it liquid-like deformation behavior i the reult of uch ize dependent melting. However, both calculation and previou experimental work 8,9,32-36 how that the melting point of Ag, Au, Al, Cu and etc. at ize cale of 5 nm are till high above RT. The Ag NC here clearly how crytal tructure before and during deformation. It therefore indicate a new mechanical behavior rather than melting. 14. The beam effect on temperature The e-beam heating effect in our experiment i not a primary factor in thi liquid-like behavior of Ag nanocrytal. It i ure that urface diffuion can be influenced by electron beam irradiation. To reduce thi influence, we ued very weak beam intenity (around 3.8 A/cm 2 ) for imaging. Thi beam intenity i far lower than the publihed literature below. 1) D. J. Smith et al Nature (1985) 317, 5 and Science (1986) 233, 872: 20-40A/cm 2 2) S. Iijima et al PRL (1986) 56, 6: around 200 A/cm 2 3) P.M. Ajayan and L.D. Mark PRL (1989) 63, 3: A/cm 2 4) D. Ugarte et al PRL (2000) 85, 4124: 120A/cm 2 5) Z.W. Wang & R. E. Palmer PRL (2012) 108, : >48 A/cm 2 In our experiment, the Ag nanocrytal maintained it tructure well under thi weak beam current. Atom hopping and diffuion became activated only when the nanocrytal wa under compreion or relaxation after deformed. So the acceleration of urface diffuion by e-beam NATURE MATERIALS 13

14 i not oberved in our experiment under above condition. We alo tried to queezing the Ag nanocrytal with e-beam blocked. The Ag nanocrytal could till recover back imilar to it initial geometry, indicating that the e-beam effect hould not play a critical role. A hown in Figure R1, we firt took an image of the Ag nanoparticle, then we turned off the e-beam and performed the ame compreing and detaching procee in the following 148 econd. At lat, we turn on the e-beam and took another image. The reult howed that the Ag nanoparticle had recovered it original hape. Since the e-beam wa turned off, the heating effect could alo be excluded. Theoretically, the e-beam induced temperature rie could be etimated by Fiher model [Radiat. Eff. (1970) 5, 239]: ( ) where T i the maximum temperature rie caued by an electron beam, k i the thermal conductivity of tungten, I i the beam current, E i the total energy lo per electron in a ample of thickne d, b i the radiu of the heat ink, and r 0 i the beam radiu. The eence of Fiher model i that the heat generation (in an incident beam of diameter d) i balanced by heat lo due to radial conduction. Becaue energy loe in the ample were mall compared to the initial energy (200 kev), the term E/d wa equal to the topping power of electron, de/dx, which wa calculated from the Bethe-Bloch equation[j. Appl. Phy. (1995) 78, 974]: where Z i the atomic number of the target element, ρ i the atomic denity, ε 0 i the dielectric contant, m i the electron ret ma, ν i the electron velocity, c i the peed of light, E i the electron energy, I e i the average excitation energy of electron in the target, and β=ν/c. In our tudy, the acceleration voltage i 200 kv; thu, β= and ν= m/., m= kg, e= C, ε 0 = F/m, I=4.8 na, b=1.5mm, and r 0 =0.2 μm. The firt tep i to determine the range of temperature rie of tungten probe. 14 NATURE MATERIALS

15 SUPPLEMENTARY INFORMATION For W, Z=74, I e =8.8 Z=651.2 ev, ρ= m -3 (the ma denity i kg m -3 ), and thermal conductivity of tungten k=173 Wm -1 K -1. It i found that the maximum temperature increae of tungten probe wa etimated to be 0.079K, i.e. the tungten could be een at room temperature. It i an obviou dicrimination compared with nanoparticle located on low thermal conductivity ubtrate (e.g. amorphou carbon film) [Appl. Phy. Lett. (1987) 50, 1760]. The econd tep i analyzing the temperature of ilver nanoparticle. The heat injection per unit time on ilver nanoparticle by electron irradiation could be ummarized a: (I/e) E, where i the heat injection, I i the beam current on ilver nanoparticle, E i the average energy lo per inelatic colliion [J. Appl. Phy. (1995) 78, 974;Micron (2004) 35, 399]. Conidering that the electron energy lo in the ample i negligible compared to the initial energy, (de/dx) can be aumed contant, o E could be obtained by the following:, Where d i the thickne of ilver nanoparticle, could be obtained by aforementioned Bethe-Bloch equation. For Ag, Z=47, ρ= m -3 (the ma denity i kg m -3 ) and I e =8.8 Z=413.6 ev. According to above parameter, we could found the heat injection per unit time on ilver nanoparticle by electron irradiation i J/. The injected energy would tranport heat acro the interface between Ag and tungten and induce a temperature gradient. To determine the temperature difference between the Ag nanoparticle and the W tip, the interface i taken into account. Since mot phonon mediated interface (dielectric-dielectric and metal-dielectric) have thermal conductance between 80 and 300 MWm -2 K -1 [ our Ag-W interface hould have a conductance in the range of 10 2 MW m -2 K -1 (conidering a thin oxide layer formed). Taking into account the contacting area, the interface thermal conductance G i etimated to be 10-8 W/K. According to the definition of thermal reitance,, the temperature difference between Ag nanoparticle and W ubtrate i in the range of 10-3 K, which i extremely mall. In concluion, the electron beam denity i 3.8 A/cm -2 and very mall, the thermal conductivitie of W ubtrate and W-Ag interface are high and in the range of 10 2 W/m/K. So NATURE MATERIALS 15

16 the e-beam induced heating effect i not a primary factor. Alo, many literature [J. Phy. Chem. B (2005) 109, 9703; Appl. Phy. Lett. (1987) 50, 1760] upport thi concluion that the temperature rie i very mall when the electron beam denity i mall and the thermal conductivity i good. William et al [Appl. Phy. Lett. (1987) 50, 1760] have reported that the irradiation induced Au nanoparticle temperature rie occur only at low thermal conductivity ubtrate. 15. The difference between peudoelatic and reverible platic In thi paper, the 'peudoelatic' we mentioned i not jut reverible platic. See illutration Figure S6 below for the tandard definition of peudoelaticity and platicity. While both peudoelaticity and platicity involve diipation, and indeed mot platic train i reverible, the latter require impoing a negative load, while the former return completely at till poitive load. Thi i fundamental, becaue peudoelatic deformation cannot have platic train ( locked in even at zero tre). And platic train i of coure what make platic forming poible. Figure S6. Illutration of peudoelatic deformation and reverible platic deformation. During compreion, the Ag nanoparticle deform platically due to W tip queezing. However, during detaching, the hape recover i driven by urface energy. The Vander Waal force in t the driving force. 16 NATURE MATERIALS

17 SUPPLEMENTARY INFORMATION 16. Laterally queezing a Ag nanoparticle how perfect recovery from it deformed form Sometime, laterally queezing a Ag nanoparticle can how the poibility of perfect recovery of the deformed form, a hown in Figure S7. The Ag nanoparticle demontrate the exactly ame height of 41 atomic layer and ame top ize of 2.4 nm before (Figure S7a) and after (Figure S7h) compreion. Figure S7. An image equence of queezing a ub-10nm ized Ag nanoparticle. The white triangle i an anchor point. The white arrow how the moving direction of the W tip (bottom). NATURE MATERIALS 17