Presentation at National Center for Theoretical Sciences & National Cheng Kung University

1. Atomic-sized metal nanowires: novel structures, physical properties, and nanodevices Jijun Zhao State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams & College of Advanced Science and Technology Dalian University of Technology Presentation at National Center for Theoretical Sciences & National Cheng Kung University 8/26/2006

2. Outline • Experimental background and computational methods • Gold nanotubes and multi-shell helical nanowires • Atomic and electronic shells in sodium nanowires • Copper nanowires and nanocables • Crystalline silver nanowires • Melting behavior and thermal stability of metal wires • Summary

3. Experimental synthesis of metal nanowires Recently, atomic-sized metal nanowires have been fabricated using the following methods: Electron-beam lithograph & irradiation Electrochemical etching STM/AFM based tip-surface contacts Mechanically controllable break junction (MCBJ) One-dimensional template-aid synthesis

4. Novel 1-D structures from folding 2-D slab/sheet Single-layer sheet => nanotube Multi-layer slab => helical wires

5. Observation of helical nanotubes and nanowires Gold Takayanagi, Phys. Rev. Lett. 91, 205503(2003) Platinum Kondo, Science 289, 606 (2000) Oshima, Phys. Rev. B 65, 121401 (2002)

6. kinetic energy simulated annealing Structural optimization of nano systems Fora nano system with N atoms, the potential energy is function of the atomic coordinates {xi,yi,zi} (i=1,N): E=E(xi,yi,zi,). Optimizing the lowest-energy configuration is a global minimization problem in 3N dimensional potential energy surface (PES): NP-hard problem SA is hard to overcome high barriers on PES, could be very computational costly.

7. Genetic algorithm as a global search method GA can efficiently skip from trap by local minima and hop in potential energy surface crossover mutation Only the fittest candidates can survive (to mimic Darwinian evolution process)

8. Implement of GA in low-dimensional nanostructures Successful example: C60 buckyball from scratch “cut and splice” crossover operation Deaven and Ho, PRL75, 288 (1995). For details, see our recent review: J. Comput. Theor. Nanosci. 1, 117(2004).

9. Electron density ρ ion ion ion ion ion ion ion ion ion ion EAM-type many-body potentials used for metal nanowires Ion i embedded in the electron density ρifrom other ions j + repulsion V between ions i and j F(ρ) was usually chosen as: Some typical many-body potentials used in our atomistic simulations • Glue potential: Phys. Rev. Lett. 57, 719 (1986). • Sutton-Chen potential: Philos. Mag. Lett. 61, 139 (1990). • Gupta-type tight-binding potential: Phys. Rev. B 23, 6265 (1981); Phys. Rev. B 48, 22 (1993); Phys. Rev. B 57, 15519 (1998).

10. Helical multi-shell nanowires from GA simulation Implement of GA into 1-D, unbiased search from scratch (glue potential + MD) Helical multi-shell structures were obtained in ultrathin gold nanowires, while crystalline-like structure was found in nanowire with 3 nm. Phys. Rev. Lett. 86, 2046 (2001)

11. Structural evolution towards bulk fcc in Au nanowire • A1-A3: noncrystalline structures without definite bond angle. • A4-A9, three peaks at 60o, 90o, 120o (bond angle in the bulk fcc) are gradually forming. • Atomic cross-section projection: crystalline structure in A9 and the transition starts from the core region (A7, A8). Phys. Rev. Lett. 86, 2046 (2001)

12. Vibrational properties of helical gold nanowires • A9 wire is similar to bulk gold. • The first peak ~ 2.3 THz do not sensitively change from A3-A9. • Additional peak ~ 4.2 THz in A4 - A8 wires: the noncrystalline curved outer surface. • Thinnest A1 and A2 wires: many discrete vibrational bands. The maximal frequency are comparable those calculated for monatomic chains and dimer. Phys. Rev. Lett. 86, 2046 (2001)

13. Electronic density of states of gold nanowires • Thin wire (A2): molecule-like, sharp and discrete peaks. • In A3, discrete levels overlap and form continuous bands. • The shape of DOS of A3 - A9 wires (1.0 ~ 3.0 nm) does not sensitively depend on size. The band width narrows as wire become thicker. • A9 wire (3 nm) is already quite close to the bulk and like the average of the bulk DOS. Phys. Rev. Lett. 86, 2046 (2001)

14. Conductance of gold nanowire: size effect DFT band structures of A2: two conduction channels In general, wire conductance increases linearly with diameters, while geometric structure has certain influence (like A5). Phys. Rev. Lett. 86, 2046 (2001)

15. Structural growth sequences of helical nanowires Empirical potentials + unbiased GA search, →complete structural growth sequences obtained for Au and Zr nanowires. Phys. Rev. B 65, 235406 (2002)

16. Shell effects in metal clusters Electron shell Atomic shell Electron shells in Na clusters: W.D.Knight, PRL52, 2141(1984).

17. Alkali-metal nanowires: observation of shell effects “The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or closelying levels, called shells. In fermionic systems, this gives rise to a local minimum in the total energy when all the states of a given shell are occupied.” Yanson et al., Nature 400, 144 (1998). Correlation between radius and conductance: Shell structure in conductance count Na wire studied by mechanically controllable break junction (MCBJ)

18. Crystalline and helical structures in Na nanowires Unbiased GA search with empirical potential + DFT optimization of 1-D supercell length and internal coordinates Simultaneous observation of helical and bulk-like bcc structures in Na nanowires Two formation mechanisms: wall-by-wall and facet-based Phys. Rev. B, submitted

19. Crystalline vs. helical: binding energy of Na nanowires • Binding energies of helical wires usually higher than crystalline ones, in particular for those small wires (R<0.4 nm). • Eb for two series of structures become closer for the thicker wires (R0.4nm). Phys. Rev. B, submitted

20. Crystalline vs. helical: conductance of Na nanowires • Conductance is not simply proportional to area of cross section of nanowires • Conductance sensitively depends on wire geometry. Crystalline wire typically have more conduction channels than helical one due to higher symmetry. • Several nanowires with different structures and radii can have identical conductance: undistinguishable in experimental conductance histograms.

21. electronic shell atomic shell Crossover from electronic to atomic shells in Na nanowires Approximately, nanowire radius is linearly proportional to the square root of conductance. We use a sequentially numbered index to characterize different wires according to their conductance values. The plot of (G/G0)1/2 fall into two distinct slopes. C1-7 wire from GA Yanson, Phys. Rev. Lett. 87, 216805 (2001). Phys. Rev. B, submitted

22. Structures and conductance of Cu nanowires: experiments Observation of highly stable pentagonal copper nanowire with a diameter of 0.45 nm and 4.5 G0. Gonzalez et al., Phys. Rev. Lett. 93, 126103 (2004).

23. Atomistic simulation of Cu nanowires Experiment: D=4.5Å, G~4.5G0 Nanotechnology 17, 3178 (2006).

24. Band structures and conductance of Cu nanowires Quadratic fitting:G=2.0+0.12D2 D=4.5Å→G=4.43G0 (experiment: ~4.5G0) Number of bands crossing Fermi lever determines quantum conductance of nanowires Nanotechnology 17, 3178 (2006).

25. Nanocable with BN tube sheaths and Cu nanowire cores Macroscopic coaxial cable Cu@BN: a true nanocable with metallic core and insulating sheath? Experiment: coaxial Ag/C nanocables Tube-wire interaction mainly van der Waals type: equilibrium distance 3.5Å, binding energy -0.04 eV per Cu atom (GGA) Yu et al. Chem. Commun., 2704 (2005). J. Phys. Chem. B 110, 2529 (2006).

26. Nanocable with BN tube sheaths and Cu nanowire cores Cu wire Cu@BN BN tube Conduction electrons localized on inner Cu wire; electron transport occurs only through Cu wires; BN nanotubes serve as insulating cable sheaths Band structures for Cu@BN nanocables: clearly a superposition of individual BN tubes and Cu wires J. Phys. Chem. B 110, 2529 (2006).

27. Ultrathin single-crystalline silver nanowires: experiments Hong et al., Science 294, 348 (2001). Ultrathin single-crystalline silver nanowires (0.4 nm width, m length) arrays are grown in pores of template. Conducting wire in nanoelectonics? Effect of defect and strain?

28. Electronic states and conductance of ultrathin Ag wire Long Ag wire, 4-atoms cross section, experimentally synthesized s electron approximation, neglecting of low-lying d electrons Three s-bands cross Fermi level  three conduction channels s-orbital TB model: Phys. Stat. Sol. (b)188, 719 (1995)

29. lower coordinate higher coordinate Conductance of crystalline Ag nanowires with defect Infinite nanowire, 4-atom cross section • Three conduction channels for perfect nanowire • One conduction channel disrupted by a single-atom defect, independent of defect geometry Nanotechnology 14, 501 (2003)

30. Conductance of Ag nanowire with multiple defects Two-atoms vacancy Multiple single-atom vacancies • One or two conduction channels can be disrupted by two-atoms vacancy defect, depending on the site coordinate • Ballistic conduction of fcc ultrathin wire is very robust (one channel at least remains open at Fermi energy): good for nanoelectronics Nanotechnology 14, 501 (2003)

31. D Quantum interference between two separated defects Conductance at EF G (2e2/h): Quantum interference leads to strong oscillation of conductance vs. distance between two separated single-atom defects, related to Fermi wavelength. Similar effects observed in carbon nanotubes. Nanotechnology 14, 501 (2003)

32. Conductance of silver nanowires: strain effect • The original three channels of Ag wire remain robust under substantial strain (up to ~5%). • Larger strain can reduce conductance. Conductance of silver as function of energy and strain Nanotechnology 14, 501 (2003)

33. 1 1 2.4 4 2.6 4 Conductance of Ag nanobridge: experiment vs. theory Computational simulation on Ag nanobridge: ~2nm long, 7-atoms cross section, 5 conduction channels Experiment: Rodrigues, Phys. Rev. B, 2002 • Quantization of conductance for Ag nanobridge • Global histogram of conductance for 500 randomly generated finite nanowires with defects reproduce experimental peaks: 1 G0, 2.4 G0, 4 G0 Nanotechnology 14, 501 (2003)

34. Melting behavior of titanium nanowires Helical wire: D=1.71nm • Diffusion start at 950~1000K, before melting • Transformation into bulk structure before overall melting Melting temperature: 1150 K Phys. Rev. B 67, 193403 (2003)

35. Size dependence of melting temperature • Melting temperature for hexagonal nanowires (6-1, 12-6-1, 17-12-6-1) fit well to a linear dependence of 1/D: Tm=1542K682K·nm/D • Nanowires with 3 or 4 atomic strands in internal shell (9-3, 14-9-3, 9-4, 15-9-4) have lower melting temperature than wires with one atomic strand in the center • Melting temperature of nanowire higher than nanoclusters with comparable size Phys. Rev. B 67, 193403 (2003)

36. Interior melting behavior of gold nanowires Starting melting temperature: 300K Overall melting temperature: 1100K 18-12-6-1 nanowire • 3501000K: core atoms begin to diffuse along wire axis and become wet; surface atoms remain solid-like. • 10001150K: surface atoms involve in melting • Surface melting represents the overall melting in the ultrathin multi-shell nanowires Phys. Rev. B 66, 085408 (2002)

37. Mechanical properties of Ni nanowires helical multi-shell structure fcc crystalline structure (6-1 9-3 12-6-1) Parrinello-Rahman variable-cell MD algorithm in 1-D: constant compressive/tensile force • Within elastic limit, elastic deformation, oscillation of 1-D supercell • Beyond elastic limit, plastic deformation, lose initial configurations Physica E 30, 45 (2005).

38. A3 wire Elastic deformation under uniaxial loading • Periodic oscillation within elastic limit • Keeping helical multi-shell structure Tension: Chin. Phys. Lett.22, 1195(2005). Yield strength of Ni nanowires is about one order of magnitude largerthan macroscopic strength Compression: Physica E 30, 45 (2005).

39. Plastic deformation under uniaxial compression C1, A1: 1.2 nN (4.5GPa) C2, A2: 2.0 nN (4.7GPa) C3, A3: 3.7 nN (5.5GPa) • Helical multi-shell structure enhance the elasticity and strength of Ni nanowires. • Mechanisms of plastic deformation different; final structures are resemblant and crystalline. • Coexistence crystalline and noncrystalline phases, related to superplasticity.

40. Plastic deformation under uniaxial compression Two different kinds of deformation mechanisms: • C1, C2, C3: crystalline amorphous crystalline (reiterative) • A1, A2, A3: helical multi-shell distorted crystalline Pair distribution functions g(r) of C3, A3 nanowires at different MD time steps Physica E 30, 45 (2005).

41. Summary • Helical multi-shell structures found for atomic-sized nanowires of different metals. Transition towards bulk-like crystalline structure ~ 3nm. • For alkali-metal nanowires, atomic and electronic shells are observed. • Wire conductance sensitively depends on size, geometry and defect. • Ultrathin crystalline silver wires show robust conductivity, even with multiple defects and can be excellent candidates in nanoelectronics. • BN nanotube could be good sheath for constructing true nanocable. • Interior melting behavior earlier than overall melting is found for metal nanowires. Melting temperatures of nanowire depend on atomic geometry and are lower than nanoclusters of comparable size. • Both elastic and plastic deformation observed for nanowire under uniaxial loading with either compression or tension. Helical multi-shell wires show enhanced yield strength than bulk solids.

42. Acknowledgements • Collaborators: • Dr. B.L. Wang, Dr. J.L. Wang, Prof. G.H.Wang (Nanjing Univ.) • Mr. J.M. Jia, Prof. D.N. Shi (Nanjing Univ. of Aeronautics & Astronautics) • Dr. C. Buia, Prof. J.P. Lu (UNC-Chapel Hill) • Prof. W. Lu, Prof. X.S. Chen (CAS, Shanghai) • Prof. P.R. Schleyer, Prof. R. B. King, Dr. Z.F. Chen (Univ. of Georgia) • Prof. Z. Zhou (Nankai Univ.) Thank you for your attentions!