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Atomic-sized metal nanowires: novel structures, physical properties, and nanodevices Jijun Zhao State Key Laboratory 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

Outline • Experimental background and computational methods • Gold nanotubes and multi-shell helical nanowires 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

Experimental synthesis of metal nanowires Recently, atomic-sized metal nanowires have been fabricated using the 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

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

Observation of helical nanotubes and nanowires Gold Takayanagi, Phys. Rev. Lett. 91, 205503(2003) Platinum 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)

Structural optimization of nano systems For a nano system with N atoms, the potential Structural optimization of nano systems For a 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 3 N dimensional potential energy surface (PES): NP-hard problem kinetic energy simulated annealing SA is hard to overcome high barriers on PES, could be very computational costly.

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

Implement of GA in low-dimensional nanostructures Successful example: C 60 buckyball from scratch “cut Implement of GA in low-dimensional nanostructures Successful example: C 60 buckyball from scratch “cut and splice” crossover operation Deaven and Ho, PRL 75, 288 (1995). For details, see our recent review: J. Comput. Theor. Nanosci. 1, 117(2004).

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

Helical multi-shell nanowires from GA simulation Implement of GA into 1 -D, unbiased search 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)

Structural evolution towards bulk fcc in Au nanowire • • • Phys. Rev. Lett. Structural evolution towards bulk fcc in Au nanowire • • • Phys. Rev. Lett. 86, 2046 (2001) A 1 -A 3: noncrystalline structures without definite bond angle. A 4 -A 9, three peaks at 60 o, 90 o, 120 o (bond angle in the bulk fcc) are gradually forming. Atomic cross-section projection: crystalline structure in A 9 and the transition starts from the core region (A 7, A 8).

Vibrational properties of helical gold nanowires • A 9 wire is similar to bulk Vibrational properties of helical gold nanowires • A 9 wire is similar to bulk gold. • The first peak ~ 2. 3 THz do not sensitively change from A 3 -A 9. • Additional peak ~ 4. 2 THz in A 4 - A 8 wires: the noncrystalline curved outer surface. • Thinnest A 1 and A 2 wires: many discrete vibrational bands. The maximal frequency are comparable those calculated for monatomic chains and dimer. Phys. Rev. Lett. 86, 2046 (2001)

Electronic density of states of gold nanowires • Thin wire (A 2): molecule-like, sharp Electronic density of states of gold nanowires • Thin wire (A 2): molecule-like, sharp and discrete peaks. • In A 3, discrete levels overlap and form continuous bands. • The shape of DOS of A 3 - A 9 wires (1. 0 ~ 3. 0 nm) does not sensitively depend on size. The band width narrows as wire become thicker. • A 9 wire (3 nm) is already quite close to the bulk and like the average of the bulk DOS. Phys. Rev. Lett. 86, 2046 (2001)

Conductance of gold nanowire: size effect DFT band structures of A 2: two conduction Conductance of gold nanowire: size effect DFT band structures of A 2: two conduction channels In general, wire conductance increases linearly with diameters, while geometric structure has certain influence (like A 5). Phys. Rev. Lett. 86, 2046 (2001)

Structural growth sequences of helical nanowires Empirical potentials + unbiased GA search, →complete structural 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)

Shell effects in metal clusters Electron shell Atomic shell Electron shells in Na clusters: Shell effects in metal clusters Electron shell Atomic shell Electron shells in Na clusters: W. D. Knight, PRL 52, 2141(1984).

Alkali-metal nanowires: observation of shell effects “The quantum states of a system of particles 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)

Crystalline and helical structures in Na nanowires Unbiased GA search with empirical potential + 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

Crystalline vs. helical: binding energy of Na nanowires • Binding energies of helical wires 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. 4 nm). Phys. Rev. B, submitted

Crystalline vs. helical: conductance of Na nanowires • Conductance is not simply proportional to 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.

Crossover from electronic to atomic shells in Na nanowires Approximately, nanowire radius is linearly 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/G 0)1/2 fall into two distinct slopes. electronic shell atomic shell C 1 -7 wire from GA Yanson, Phys. Rev. Lett. 87, 216805 (2001). Phys. Rev. B, submitted

Structures and conductance of Cu nanowires: experiments Observation of highly stable pentagonal copper nanowire Structures and conductance of Cu nanowires: experiments Observation of highly stable pentagonal copper nanowire with a diameter of 0. 45 nm and 4. 5 G 0. Gonzalez et al. , Phys. Rev. Lett. 93, 126103 (2004).

Atomistic simulation of Cu nanowires Wire Symmetry Eb (e. V/atom) G (G 0) 3 Atomistic simulation of Cu nanowires Wire Symmetry Eb (e. V/atom) G (G 0) 3 a 2. 38 D 3 d 2. 439 3 3 b 2. 14 C 2 2. 262 2 4 a 3. 24 D 4 d 2. 602 3 4 b 2. 86 C 2 2. 473 3 4 c 2. 74 D 2 d 2. 563 4 5 -1 a 4. 10 C 5 v 2. 814 6 5 -1 b 3. 70 C 5 2. 725 4 5 -1 c 3. 52 C 5 v 2. 735 5 6 -1 a 4. 86 C 6 v 2. 816 4 6 -1 b 4. 56 C 6 2. 815 4 6 -1 c 4. 24 C 2 2. 757 4 6 -1 d 4. 20 C 3 v 2. 831 4 9 -3 6. 78 C 1 2. 991 5 9 -4 6. 92 C 2 2. 997 8 12 -6 -1 Experiment: D=4. 5Å, G~4. 5 G 0 D (Å) 9. 36 C 2 3. 104 10 Nanotechnology 17, 3178 (2006).

Band structures and conductance of Cu nanowires Quadratic fitting: G=2. 0+0. 12 D 2 Band structures and conductance of Cu nanowires Quadratic fitting: G=2. 0+0. 12 D 2 D=4. 5Å→G=4. 43 G 0 (experiment: ~4. 5 G 0) Number of bands crossing Fermi lever determines quantum conductance of nanowires Nanotechnology 17, 3178 (2006).

Nanocable with BN tube sheaths and Cu nanowire cores Macroscopic coaxial cable Cu@BN: a Nanocable with BN tube sheaths and Cu nanowire cores Macroscopic coaxial cable [email protected]: 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 e. V per Cu atom (GGA) Yu et al. Chem. Commun. , 2704 (2005). J. Phys. Chem. B 110, 2529 (2006).

Nanocable with BN tube sheaths and Cu nanowire cores Cu wire Cu@BN BN tube Nanocable with BN tube sheaths and Cu nanowire cores Cu wire [email protected] 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 [email protected] nanocables: clearly a superposition of individual BN tubes and Cu wires J. Phys. Chem. B 110, 2529 (2006).

Ultrathin single-crystalline silver nanowires: experiments Hong et al. , Science 294, 348 (2001). Ultrathin 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?

Electronic states and conductance of ultrathin Ag wire Long Ag wire, 4 -atoms cross 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)

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

Conductance of Ag nanowire with multiple defects Two-atoms vacancy • Multiple single-atom vacancies One 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)

Quantum interference between two separated defects Conductance at EF D G (2 e 2/h): Quantum interference between two separated defects Conductance at EF D G (2 e 2/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)

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

Conductance of Ag nanobridge: experiment vs. theory Experiment: Rodrigues, Phys. Rev. B, 2002 Computational Conductance of Ag nanobridge: experiment vs. theory Experiment: Rodrigues, Phys. Rev. B, 2002 Computational simulation on Ag nanobridge: ~2 nm long, 7 -atoms cross section, 5 conduction channels Quantization of conductance for Ag nanobridge q Global histogram of conductance for 500 randomly generated finite nanowires with defects reproduce experimental peaks: 1 G 0, 2. 4 G 0, 4 G 0 q 1 1 2. 4 4 2. 6 4 Nanotechnology 14, 501 (2003)

Melting behavior of titanium nanowires Helical wire: D=1. 71 nm • • Diffusion start Melting behavior of titanium nanowires Helical wire: D=1. 71 nm • • Diffusion start at 950~1000 K, before melting Transformation into bulk structure before overall melting Melting temperature: 1150 K Phys. Rev. B 67, 193403 (2003)

Size dependence of melting temperature • Melting temperature for hexagonal nanowires (6 -1, 12 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=1542 K 682 K·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)

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

Mechanical properties of Ni nanowires fcc crystalline structure helical multi-shell structure (6 -1 9 Mechanical properties of Ni nanowires fcc crystalline structure helical multi-shell 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).

Elastic deformation under uniaxial loading • Periodic oscillation within elastic limit • Keeping helical Elastic deformation under uniaxial loading • Periodic oscillation within elastic limit • Keeping helical multi-shell structure A 3 wire Tension: Chin. Phys. Lett. 22, 1195(2005). A 1 (6 -1) A 3 (12 -6 -1) Diameter 0. 76 nm 0. 94 nm 1. 18 nm Tensile stress 2. 85 GPa 3. 38 GPa 3. 48 GPa Compressive stress Compression: Physica E 30, 45 (2005). A 2 (9 -3) 13. 01 GPa 9. 09 GPa 9. 17 GPa Yield strength of Ni nanowires is about one order of magnitude larger than macroscopic strength

Plastic deformation under uniaxial compression C 1, A 1: 1. 2 n. N (4. Plastic deformation under uniaxial compression C 1, A 1: 1. 2 n. N (4. 5 GPa) C 2, A 2: 2. 0 n. N (4. 7 GPa) C 3, A 3: 3. 7 n. N (5. 5 GPa) • • • 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.

Plastic deformation under uniaxial compression Two different kinds of deformation mechanisms: • C 1, Plastic deformation under uniaxial compression Two different kinds of deformation mechanisms: • C 1, C 2, C 3: (reiterative) crystalline • A 1, A 2, A 3: helical multi-shell amorphous crystalline distorted crystalline Pair distribution functions g(r) of C 3, A 3 nanowires at different MD time steps Physica E 30, 45 (2005).

Summary • Helical multi-shell structures found for atomic-sized nanowires of different metals. Transition towards Summary • Helical multi-shell structures found for atomic-sized nanowires of different metals. Transition towards bulk-like crystalline structure ~ 3 nm. • 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.

Acknowledgements Collaborators: • Dr. B. L. Wang, Dr. J. L. Wang, Prof. G. H. 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!