Magic Structures of Helical Multi-shell Zirconium Nanowires

The structures of free-standing zirconium nanowires with 0.6−2.8 nm in diameter are systematically studied by using genetic algorithm simulations with a tight-binding many body potential. Several multi-shell growth sequences with cylindrical structures are obtained. These multi-shell structures are composed of coaxial atomic shells with the threeand four-strands helical, centered pentagonal and hexagonal, and parallel double-chain-core curved surface epitaxy. Under the same growth sequence, the numbers of atomic strands in innerand outer-shell show even-odd coupling and usually differ by five. The size and structure dependence of angular correlation functions and vibrational properties of zirconium nanowire are also discussed. 61.46.+w, 68.65.+g, 73.61.-r Typeset using REVTEX Corresponding author, E-mail: [email protected], Fax: +86-25-3595535. 1 In the past decade, there has been tremendous interests on ultrathin metal nanowires from both fundamental low-dimensional physics and technological applications such as nanoelectronic devices1–14. Most of the previous studies are based on the tip-surface contact1–5 or mechanically controllable break junctions, which can be seen as very short metal nanowire. In recent experiments, Takayanagi’s group has successfully fabricated stable gold wires with various diameter of sufficient length suspended between two stands8–10, and the helical multishell structures are observed in those ultrathin wires. On the theoretical side, the noncrystalline structures, melting behavior, and electronic properties of ultrathin free standing Pb, Al, Ag nanowires have been investigated by Tosatti and co-workers11–14. By using molecular dynamics-based (MD) genetic algorithm (GA) simulations, our group has studied structural, vibrational, electronic, magnetic properties of gold, titanium, and rhodium nanowires15–17. However, the current knowledge on the detailed structural characters and growth sequences of the metal nanowires is still quite limited. In this paper, we report systematical multi-shell structural growth sequence of zirconium nanowires and their vibrational properties. In our simulations, the zirconium nanowires with diameters from 0.6 to 2.8 nm are modeled by a supercell with one-dimensional (1D) periodical boundary condition along the wire axis direction. For the most zirconium nanowires studied, the length of 1-D supercell is chosen to be 1.413 nm, which is a reasonable compromise between discovering the helicity in 1D direction and avoiding the nanowires breaking into clusters upon relaxation. To match the periodicity of the multi-shell structures with pentagonal symmetry, several different supercell lengths, i.e., 1.177 nm for S5-1, S5-2 wires (see Fig.1), 1.648 nm for S5-3, S5-4 wires, have been used. The “effective diameter”, which can be controlled by adjusting the number of atoms in the supercell, is used to denote the cross section area of the nanowires12,15–17. To search the most stable structure of nanowire, we adopt the genetic algorithm (GA) based on MD relaxation15–17. The vibrational densities of states can be then calculated by diagonalizing the dynamical matrix for the optimized configurations. The interaction between zirconium atoms is described by a tight binding (TB) many body potential, which has successfully reproduced the high-temperature hcp-bcc transition in 2 bulk zirconium. To further check the validity of TB potential in low-dimensional systems with reduced coordination number (CN), we have performed density functional calculations on small zirconium clusters (Zr7, Zr13, Zr15, Zr19) and bulk zirconium solid by using a DMol package within local density approximation (LDA). In both TB and LDA calculations, the cluster structures are optimized and the similar equilibrium configurations are obtained. Typically, the discrepancy for interatomic distance obtained from tight-binding potential and LDA calculation are within 0.1 Å. The comparison of LDA and TB results on the binding energies of small clusters with equilibrium structures are given in Table I. The satisfactory agreement between LDA and TB results on Zr clusters in Table I demonstrates the validity of the TB potential in the other low-dimensional systems like nanowire.