<100> Axially oriented Copper Nanowires

We present results of calculations for atomic relaxations of Cu nanowires with the cross-sectional orientation of (100), employing a many-body, semi-empirical interaction potential based on the embedded atom method. The influence of reduced symmetry and size of the nanowires on local atomic relaxations is examined. Relaxations of the atoms near the outer walls are found to exhibit characteristic behaviors with varying cross-sectional area of the wires. Metallic nanowires have been the focus of a broad range of experimental and theoretical works as they exhibit quite distinctive mechanical, electrical, thermal, and magnetic characteristics compared to their bulk counterparts [1]. For structures with a high surface-to-volume ratio like nanowires the key question concerning the equilibrium configuration of the crystal is closely related to the rearrangement of electronic and ionic structure induced by loss of symmetry. For nanowires, this effect is expected to be dramatic in radial direction. As a result of this charge redistribution [2], the force fields in the vicinity of outer wall of the wire may be modified and thus different characteristics in atomic relaxations in these specific local regions are more likely. In this study it is our aim to explore any size effect, if there is, on atomic relaxations of Cu nanowires. Our main interest here lies in a comperative study of Cu nanowires with the axial direction of <100>. In our model systems for examining the size effect on atomic relaxations, the <100> axially oriented copper nanowires are constructed by top-down fabrication process, involving extraction of the nanowire from a slab with the associated axial orientation. Each suppercell representing the nanowire contains 24 layers of atoms along the axial direction. We allow the atoms in computational cells to interact through a semi-empirical and many-body type potential obtained from the embedded atom method (EAM)[3]. After being Figure: (a) Cross-sectional view of the nanowire with the <100> axial orientation. The arrows indicate the atomic displacements from the bulk terminated positions. Displacements are magnified by a factor 7. (b) Computational cell for 5x5 nanowire. 5x5 refers to the number of atoms along the diagonals of the cross-sectional plane. (c) Atomic displacements on the left corner of the 15x15 nanowire. Displacements are magnified by a factor of 45. constructed in their bulk terminated geometries, the nanowires are allowed to relax to their minimum energy or 0oK equilibrium configuration, using the standard conjugate gradient method. Periodic boundary conditions are applied along the axial direction to diminish the end effects. Table: Calculated percentage change in bond-lengths of the atoms of nanowires. Here dbond=100x{[(xi-xj)+(yi-yj)]-dbulk}/dbulk To examine the influence of varying cross-sectional area of the nanowire on atomic relaxations, we have investigated the structural properties of the nanowire ranging from 3x3 to 19x19, containing from 108 to 4332 atoms. In the above Table, we present the calculated percentage changes in the bond-lengths of B1-B2, B1-B3, A1-A3, and A2-A3 with respect to the corresponding interatomic separations in the bulk. The largest change occurs for A1-A3. Significant changes are found for several other interatomic separations as well. As seen in the Table, the general outcome of the results is that the relaxation effect on the interaomic distances diminishes with the increasing cross-sectional area of the nanowire. It is also interesting to note that the percentage wise change of the bond-length of B1-B2 shows prominent charcteristics with varying cross-sectional area of the nanowire. We would like to remind that the authors in Ref. 4 also investigated the atomic relaxations on the same copper nanowires and defined the multilayer relaxations on these systems. Since the local atomic environment for each atom on the axial surface of the nanowire is rather different (this effect is even more pronounced on the nanowire with smaller crosssectional area), during the energy minimization procedure each atom will relax accordingly. We therefore find it rather problematic to define multilayer relaxations for nanowires. In short, we have calculated the atomic relaxations on the <100> axially oriented copper nanowires and established that multilayer relaxations on nanowires cannot be defined. On the nanowires one need to study individual relaxations of the atoms instead. This work was partially supported by TUBITAK under Grant No. TBAG-106T567. *Corresponding author: [email protected] [1] H. Hegger, B. Huckestein, K. Hecker, M. Janssen, A. Freimuth, G. Reckziegel, and Rüdiger Tuzinski, Phys. Rev. Let. 77, 3885 (1996); B. Wang, S. Yin, G. Wang, A. Buldum, and J. Zhao, Phys. Rev. Let. 86, 2046 (2001); J.W. Kang, and H.J. Hwang, Inst. Phys. Pub., Nanotech. 13, 524 (2002). [2] F. Kassubek, C.A. Stafford, and H. Garbert, Phys. Rev. B 59, 7560 (1999). [3] S. M. Folies, M.I. Baskes, M.S. Daw, Phys. Rev. B 33, 7983 (1986); M.S Daw, S.M. Foiles. M.I. Baskes, Mater. Sci. Rep. 9, 251 (1993). [4] F. Ma and K. Xu, Solid State Comm. 141, 273 (2007); F. Ma and K. Xu, Solid State Comm. 140, 487 (2006). Bonds 3x3 5x5 7x7 9x9 11x11 13x13 15x15 17x17 19x19 dB1-B2 -1.4 -0.15 -0.11 -0.99 -1.42 -1.34 -0.49 -0.32 -0.32 dB1-B3 -2.14 -1.81 -0.91 -0.62 -0.37 -0.13 -0.08 -0.08 dA1-A3 -6.18 -5.81 -5.55 -4.61 -4.22 -3.22 -1.18 -0.76 -0.76 dA2-A3 -0.62 -0.45 -0.67 -0.50 -0.32 -0.11 -0.07 -0.07