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SPECIAL SECTION ON NANOMATERIALS AND NANOMECHANICS

# Pseudoelasticity of Single Crystalline Cu Nanowires Through Reversible Lattice Reorientations

[+] Author and Article Information
Wuwei Liang

The George W. Woodruff School of Mechanical Engineering  Georgia Institute of Technology, Atlanta, GA 30332-0405 USA

Min Zhou1

The George W. Woodruff School of Mechanical Engineering  Georgia Institute of Technology, Atlanta, GA 30332-0405 USA

1

Author to whom correspondence should be addressed; Email: min.zhou@me.gatech.edu

J. Eng. Mater. Technol 127(4), 423-433 (Mar 07, 2005) (11 pages) doi:10.1115/1.1928915 History: Received January 02, 2005; Revised March 07, 2005

## Abstract

Molecular dynamics simulations are carried out to analyze the structure and mechanical behavior of Cu nanowires with lateral dimensions of 1.45–2.89 nm. The calculations simulate the formation of nanowires through a “top-down” fabrication process by “slicing” square columns of atoms from single-crystalline bulk Cu along the [001], [010], and [100] directions and by allowing them to undergo controlled relaxation which involves the reorientation of the initial configuration with a $⟨001⟩$ axis and {001} surfaces into a new configuration with a $⟨110⟩$ axis and {111} lateral surfaces. The propagation of twin planes is primarily responsible for the lattice rotation. The transformed structure is the same as what has been observed experimentally in Cu nanowires. A pseudoelastic behavior driven by the high surface-to-volume ratio and surface stress at the nanoscale is observed for the transformed wires. Specifically, the relaxed wires undergo a reverse transformation to recover the configuration it possessed as part of the bulk crystal prior to relaxation when tensile loading with sufficient magnitude is applied. The reverse transformation progresses with the propagation of a single twin boundary in reverse to that observed during relaxation. This process has the diffusionless nature and the invariant-plane strain of a martensitic transformation and is similar to those in shape memory alloys in phenomenology. The reversibility of the relaxation and loading processes endows the nanowires with the ability for pseudoelastic elongations of up to 41% in reversible axial strain which is well beyond the yield strain of the approximately 0.25% of bulk Cu and the recoverable strains on the order of 8% of most bulk shape memory materials. The existence of the pseudoelasticity observed in the single-crystalline, metallic nanowires here is size and temperature dependent. At 300 K, this effect is observed in wires with lateral dimensions equal to or smaller than $1.81×1.81nm$. As temperature increases, the critical wire size for observing this effect increases. This temperature dependence gives rise to a novel shape memory effect to Cu nanowires not seen in bulk Cu.

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## Figures

Figure 10

(Color) The configuration of a Cu nanowire with initial lateral dimensions of 2.17×2.17nm (6×6 lattice constants): (a) external view; (b) section view; (c) defects (twin boundaries) only. Atoms are colored according to their centrosymmetry values

Figure 11

Comparison of the potential energy of the wires with ⟨001⟩∕{001} and ⟨110⟩∕{111} configurations at 300 K

Figure 12

Surface-stress-induced stress in the axial direction when wires are just “sliced” out of a bulk Cu crystal, the solid curve indicates the critical stress σcr and temperature Tcr for a wire of a certain size to fully reconstruct

Figure 13

The stress-strain relation of a ⟨110⟩∕{111} reconstructed wire with an initial dimension of 1.81×1.81nm (5×5 lattice constants) during tensile loading and unloading at 300 K

Figure 14

(Color) Lattice orientations on the cross sections of a Cu nanowire with initial dimensions of 1.81×1.81nm (5×5 lattice constants) at a strain of 0.24; (a) a sectional view along the wire axis and the ⟨110⟩ diagonal of the cross section, (b) elongated hexagonal lattice in the ⟨110⟩∕{111} region, (c) a cross section in the transition region containing both the ⟨001⟩∕{001} and the ⟨110⟩∕{111} configurations, (d) square lattice on the cross section in the ⟨001⟩∕{001} region. Atoms are colored according to their centrosymmetry values

Figure 15

(Color) Twin boundary between the ⟨001⟩ and ⟨110⟩ lattices during the reorientation process, the details of a (110) lattice section which is part of Sec. A-A in Fig. 1 is shown. γ denotes the misorientation angle between the lattices on both sides of the twin boundary. The atoms are colored according to their centrosymmetry values

Figure 16

An illustration of the shape-memory effect in Cu nanowires, Tcr is the critical temperature for a Cu nanowire of a certain size to fully reconstruct or show the effect

Figure 1

The structure of a 1.81×1.81nm (5×5 lattice constants) Cu nanowire before relaxation: (a) {001} square lattice on square cross sections; (b) external view of the nanowire; (c) {001} square lattice on lateral surfaces

Figure 2

Computational model for the tensile deformation of Cu nanowires, boundary atoms are colored blue

Figure 3

(Color) The progression of the structural transformation in a 1.81×1.81nm (5×5 lattice constants) Cu nanowire at 300 K

Figure 4

Axial strain ε1 after relaxation as a function of wire size

Figure 5

Pair correlation functions for Cu nanowires before and after reconstruction and bulk Cu crystal at 300 K

Figure 6

The reconstructed structure of a Cu nanowire with initial dimensions of 1.81×1.81nm (5×5 lattice constants): (a) ⟨110⟩ elongated hexagonal lattice on a rhombic cross section; (b) external view of the reconstructed nanowire; (c) {111} hexagonal lattice on lateral surfaces

Figure 7

A schematic illustration of the projections of two (110) planes (black and gray atoms) in a fcc structure observed along the [110] directions; the (110) plane is characterized by elongated hexagonal lattice with α=70.5deg and β=109.5deg (Ref. 21)

Figure 8

A schematic illustration of the deformation of a wire associated with the lattice transformation; the gray dash lines indicate the wire configuration before the transformation, the solid lines denote the configuration after the transformation

Figure 9

Lattice rotation associated with the structural transformation during relaxation, (a) a (110) atomic plane containing the original wire axis ([001]) and a diagonal ([1¯10]) of the (001) square cross section of the original wire before reconstruction [Sec. 1-1 in Fig. 1], (c) a (110) atomic plane containing the new wires axis [11¯0] and the long diagonal ([001]) of the transformed cross section (110) plane [Sec. 2-2 in Fig. 6]

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