Wuwei Liang

Pseudoelasticity of Single Crystalline Cu Nanowires Through Reversible Lattice Reorientations

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 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 diffusion less 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 X 1.81 nm. 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.

Response of copper nanowires in dynamic tensile deformation

Molecular dynamics (MD) simulations with an embedded atom method (EAM) potential are carried out to analyse the size and strain rate effects in the tensile deformation of single-crystal copper nanowires. The cross-sections of the wires are squares with dimensions of between 5 and 20 lattice constants (or 1.8-7.2nm). Deformations under constant strain rates between 1.67 × 107 and 1.67 × 1010s−1 are analysed. It is found that the yield stress decreases with specimen size and increases with loading rate. On the other hand, ductility increases with specimen size and strain rate. The influence of specimen size is due to enhanced opportunities for dislocation motion at larger sizes. The influence of strain rate is due to the dynamic wave effect or phonon drag which impedes the motion of dislocations. The analysis also focuses on the variation in deformation mechanisms with specimen size and strain rate. Slip along alternating (111) planes is observed in small wires, while multiple cross-slips are primarily responsible for the progression of plastic deformation in larger wires. As strain rate is increased, a transition of the deformation mechanism from sequential propagation of slip along well-defined and favourably oriented slip planes to cross-slip, and then to amorphization, is observed.

Discovery, characterization and modelling of novel shape memory behaviour of fcc metal nanowires

Novel shape memory behaviour was discovered recently in single-crystalline fcc nanowires of Cu, Ni and Au with lateral dimensions below 5 nm. Under proper thermomechanical conditions, these wires can recover elongations up to 50%. This phenomenon only exists at the nanoscale and is associated with reversible lattice reorientations within the fcc lattice structure driven by surface stresses. Whereas the propagation of partial dislocations and twin planes specific to fcc metals are the required mechanism, only materials with higher propensities for twinning (e.g. Cu and Ni) show this behaviour and those with lower propensities for twinning (e.g. Al) do not. This paper provides an overview of this novel behaviour with a focus on the transformation mechanism, driving force, reversible strain, size and temperature effects and energy dissipation. A mechanism-based micromechanical continuum model for the tensile behaviour is developed. This model uses a decomposition of the lattice reorientation process into a reversible, smooth transition between a series of phase-equilibrium states and a superimposed irreversible, dissipative propagation of a twin boundary. The reversible part is associated with strain energy functions with multiple local minima and quantifies the energy conversion process between the twinning phases. The irreversible part is due to the ruggedness of the strain energy landscape, associated with dislocation nucleation, gliding and annihilation, and characterizes the dissipation during the transformation. This model captures all major characteristics of the behaviour, quantifies the size and temperature effects and yields results which are in excellent agreement with data from molecular dynamics simulations.

Modeling and Simulation of the Mechanical Response of Nanowires

We present here a contemporary review of the hitherto computational analyses of the mechanical deformation of nanowires. The bulk of the research reported in the literature concern metallic nanowires made of copper, gold, nickel, and their alloys and carbon nanotubes. Research has also been reported for nanowires with molecules having long chain structures (e.g., Silicon Diselenide (SiSe2)). Calculations have primarily focused on discrete simulations using molecular dynamics (MD). In some cases, ab initio and first principle calculations have also been carried out [1, 2]. Recently, some researchers have attempted to use continuum formulations to obtain macroscale interpretations of the results of molecular simulations [3, 4]. Interatomic potentials used for modeling interactions between the atoms/molecules in these nanowires include empirical two-body potentials such as the Lennard-Jones potential and many-body potentials such as the embedded atom method (EAM) potential [5, 6]. Issues analyzed include structural changes under loading [7–10], the formation and propagation of defects [11–13], and the effect of the magnitude of applied loading on deformation mechanisms [2, 8, 10]. Efforts have also been made to correlate results of simulations with experimental observations. However, direct comparisons are difficult since most simulations are carried out under conditions of extremely high strain rates due to computational limitations. In some cases, excellent results have been reported and clear understandings have been obtained. However, this area of research is still in a nascent stage and significant work lies ahead in terms of problem formulation, interpretation of results, identification and delineation of deformation mechanisms, and constitutive characterization of behavior. We first present an introduction to commonly adopted methods in the studies of the deformation of nanowires, followed by an overview of findings concerning the mechanics of nanowires. We will also present some recent results from our own work with an emphasis on the effects of strain rate and wire size on the stress-strain relations of nanowires. One interest is to reach down to lower strain rates (107 s−1 at this time) and avoid artificial schemes necessitated by computational limitations. We will conclude by offering some thoughts on future directions in the rich and largely under-explored territory of the computational mechanics of nanowires.

Shape Memory Effect and Pseudoelasticity in Cu Nanowires

We report the discovery of a novel pseudoelastic behavior in single-crystalline Cu nanowires through atomistic simulations. Under tensile loading and unloading, the nanowires are capable of recovering elongations up to 51%, well beyond the typical recoverable strains of 5–8% for most bulk shape memory alloys (SMAs). This phenomenon is associated with a reversible crystallographic lattice reorientation driven by the high surface-stress-induced internal stresses due to high surface-to-volume ratios at the nanoscale. The temperature-dependence of this behavior leads to a shape memory effect (SME). This behavior is well-defined for wires between 1.76 and 3.39 nm in size over the temperature range of 100–900 K.

Surface-Stress-Driven Pseudoelasticity and Shape Memory Effect at the Nanoscale

The pseudoelastic deformation of some shape memory alloys (SMAs) such as Au-Cd, Au-Cu-Zn, Cu-Zn-Al, and Cu-Al-Ni proceeds through the reversible movement of twin boundaries (Ren and Otsuka [1]). The behavior of these materials is commonly referred to as rubber-like due to its resemblance to the behavior of soft and pseudoelastic rubber (Otsuka and Wayman [2]). A similar behavior and a shape memory effect (SME) are discovered in single-crystalline Cu nanowires with lateral dimensions between 1.76 and 3.39 nm through molecular dynamics simulations. This behavior at the nanoscale is due to reversible crystallographic lattice reorientations through the movement of twin boundaries within the FCC crystalline structure (Fig. 2), allowing Cu nanowires to exhibit recoverable strains of up to more than 50% which are well beyond the recoverable strains of 5–8% of most SMAs. The reorientation is driven by high internal stresses resulting from the surface stress and high surface-to-volume ratios of the nanowires. This phenomenon only occurs in nanowires within the size range of 1.76–3.39 nm and is not observed in bulk Cu. Furthermore, it is temperature-dependent and hence gives rise to an SME. Specifically, the critical temperature for spontaneous reorientation upon unloading increases from 100 to 900 K as the wire size increases from 1.76 to 3.39 nm, making it possible to design nanoscale components of varying sizes for operation over a wide range of temperature. Such an objective is more difficult to achieve with conventional bulk SMAs since their transition temperatures (martensite start and finish temperatures, austenite start and finish temperatures) only vary with material structures and composition, not size. Moreover, the nanowires have very short response times which are on the order of nanoseconds due to their extremely small dimensions compared with bulk SMAs.

Deformation Mechanisms of Copper Nanowires under Tensile Loading

Molecular dynamics (MD) simulations with an embedded atom method (EAM) potential are carried out to analyze the deformation mechanisms and the size and strain rate effects in the tensile deformation of single-crystal Cu nanowires. The cross-sections of the wires are squares with dimensions between 5 and 20 lattice constants (or 1.8 to 7.2 nm). Deformations under constant strain rates between 1.67◊10 5 s -1 and 1.67◊10 10 s -1 are analyzed. The analysis focuses on the variation of deformation mechanisms with specimen size and strain rate. It is observed that in small wires stacking faults are formed along alternating (111) planes through the motion of a single dislocation, while the formation of networks of stacking faults, local HCP structure, and twins through nucleation and motion of multiple dislocations are primarily responsible for the progression of plastic deformation in larger wires. As strain rate is increased, dislocation speed increases to accommodate the plastic deformation. However, when the dislocation speed approaches the shear wave speed of the material, a transition of deformation mechanism from sequential propagation of stacking faults through dislocation motion to amorphization is observed. The influences of specimen size and strain rate on the behavior are also discussed.