Christopher R. Weinberger

Discrete plasticity in sub-10-nm-sized gold crystals

Although deformation processes in submicron-sized metallic crystals are well documented, the direct observation of deformation mechanisms in crystals with dimensions below the sub-10-nm range is currently lacking. Here, through in situ high-resolution transmission electron microscopy (HRTEM) observations, we show that (1) in sharp contrast to what happens in bulk materials, in which plasticity is mediated by dislocation emission from Frank-Read sources and multiplication, partial dislocations emitted from free surfaces dominate the deformation of gold (Au) nanocrystals; (2) the crystallographic orientation (Schmid factor) is not the only factor in determining the deformation mechanism of nanometre-sized Au; and (3) the Au nanocrystal exhibits a phase transformation from a face-centered cubic to a body-centered tetragonal structure after failure. These findings provide direct experimental evidence for the vast amount of theoretical modelling on the deformation mechanisms of nanomaterials that have appeared in recent years.

Surface-controlled dislocation multiplication in metal micropillars

Understanding the plasticity and strength of crystalline materials in terms of the dynamics of microscopic defects has been a goal of materials research in the last 70 years. The size-dependent yield stress observed in recent experiments of submicrometer metallic pillars provides a unique opportunity to test our theoretical models, allowing the predictions from defect dynamics simulations to be directly compared with mechanical strength measurements. Although depletion of dislocations from submicrometer face-centered-cubic (FCC) pillars provides a plausible explanation of the observed size-effect, we predict multiplication of dislocations in body-centered-cubic (BCC) pillars through a series of molecular dynamics and dislocation dynamics simulations. Under the combined effects from the image stress and dislocation core structure, a dislocation nucleated from the surface of a BCC pillar generates one or more dislocations moving in the opposite direction before it exits from the surface. The process is repeatable so that a single nucleation event is able to produce a much larger amount of plastic deformation than that in FCC pillars. This self-multiplication mechanism suggests a need for a different explanation of the size dependence of yield stress in FCC and BCC pillars.

Plasticity of metal nanowires

The mechanisms of plasticity in metal nanowires with diameters below 100 nm are reviewed. At these length scales, plasticity in face-centered-cubic metals subjected to uniaxial loading is dominated by dislocation nucleation from free surfaces, which has been studied extensively by molecular dynamics. These simulations show that nanowires can deform in a variety of ways including slip via perfect dislocations, partial dislocations and deformation twins. The competition between these mechanisms can be explained primarily through the Schmid factor and material properties, although surface orientation and roughness also contribute. The strength of these materials is very high and can be described by classical nucleation theory which predicts strong temperature and geometry dependence as well as a weak strain rate dependence. Additionally, nanowires exhibit, through twinning or phase transformation, pseudo-elastic and shape-memory behaviors which are attributed to their small size and the surface stress. The plasticity of nanowires subject to torsion and bending as well as those composed of body-centered-cubic metals are also summarized.

Slip planes in bcc transition metals

Abstract Slip in face centred cubic (fcc) metals is well documented to occur on {111} planes in 〈110〉 directions. In body centred cubic (bcc) metals, the slip direction is also well established to be 〈111〉, but it is much less clear as to the slip planes on which dislocations move. Since plasticity in metals is governed by the collective motion and interaction of dislocations, the nature of the relevant slip planes is of critical importance in understanding and modelling plasticity in bcc metals. This review attempts to address two fundamental questions regarding the slip planes in bcc metals. First, on what planes can slip, and thus crystallographic rotation, be observed to occur, i.e. what are the effective slip planes? Second, on what planes do kinks form along the dislocation lines, i.e. what are the fundamental slip planes? We review the available literature on direct and indirect characterisation of slip planes from experiments, and simulations using atomistic models. Given the technological importance of bcc transition metals, this review focuses specifically on those materials.

Application of generalized non-Schmid yield law to low-temperature plasticity in bcc transition metals

In this work, a generalized yield criterion that captures non-Schmid effects is proposed and implemented into a finite element crystal plasticity model to simulate plastic deformation of single and polycrystals. The parameters required for the constitutive formulation were calibrated to deformation experiments on single crystals. This model is used to investigate the effects of non-Schmid effects on the predictions of the stress–strain response and texture evolution in body-centered-cubic (bcc) metals. The non-Schmid contributions are required to accurately predict the stress–strain response of single crystals, and the concomitant non-associativity of the flow also increases the tendency of localization in polycrystal deformations.

Modelling dislocations in a free-standing thin film

We present a set of efficient numerical algorithms to accurately compute the forces on dislocations in free-standing thin films. We first present a spectral method for computing the image stress field of dislocations in an isotropic elastic half space and a free-standing thin film. The traction force on the free surface is decomposed into Fourier modes by a discrete Fourier transform and the resulting image stress field is obtained by superimposing analytic solutions in the Fourier space. Dislocations intersecting free surfaces are discussed, including the use of virtual segments and the associated uniqueness of their solutions. The efficiency of the algorithm is enhanced by incorporating the analytical solutions for straight dislocations intersecting free surfaces. A comprehensive algorithm, including a flow diagram, is formulated and the numerical convergence of these algorithms discussed. As a benchmark, we compute the equilibrium orientation of a threading dislocation in a free-standing thin film. Good agreement is observed between the predictions from the dislocation dynamics model and those from molecular static simulations and the line tension model.

Orientation-Dependent Plasticity in Metal Nanowires under Torsion: Twist Boundary Formation and Eshelby Twist

We show that the plastic deformation of nanowires under torsion can be either homogeneous or heterogeneous, regardless of size, depending on the wire orientation. Homogeneous deformation occurs when 110-oriented face-centered-cubic metal wires are twisted, leading to the nucleation of coaxial dislocations, analogous to the Eshelby twist mechanism. Heterogeneous deformation is predicted for 111 and 100 wires under torsion, localized at the twist boundaries. These simulations also reveal the detailed mechanisms of twist boundary formation from dislocation reactions.

Improved modified embedded-atom method potentials for gold and silicon

The modified embedded-atom method interatomic potentials for pure gold and pure silicon are improved in their melting point and latent heat predictions, by modifying the multi-body screening function and the equation of state function. The fitting of the new parameters requires rapid calculations of melting point and latent heat, which are enabled by efficient free-energy methods. The results provide the basis for constructing a cross-potential that will be fitted to the binary gold–silicon phase diagram.

Grain Boundary Sliding in Aluminum Nano-Bi-Crystals Deformed at Room Temperature

Room-temperature uniaxial compressions of 900-nm-diameter aluminum bi-crystals, each containing a high-angle grain boundary with a plane normal inclined at 24° to the loading direction, revealed frictional sliding along the boundary plane to be the dominant deformation mechanism. The top crystallite sheared off as a single unit in the course of compression instead of crystallographic slip and extensive dislocation activity, as would be expected. Compressive stress strain data of deforming nano bicrystals was continuous, in contrast to single crystalline nano structures that show a stochastic stress strain signature, and displayed a peak in stress at the elastic limit of ~ 176 MPa followed by gradual softening and a plateau centered around ~ 125 MPa. An energetics-based physical model, which may explain observed room-temperature grain boundary sliding, in presented, and observations are discussed within the framework of crystalline nano-plasticity and defect microstructure evolution.

The mechanical behavior and deformation of bicrystalline nanowires

The competition between free surfaces and internal grain boundaries as preferential sites for dislocation nucleation during plastic deformation in aluminum bicrystalline nanowires is investigated using molecular dynamics simulations at room temperature. A number of nanowires containing various minimum energy interfaces are studied under uniaxial compression at a constant applied strain rate to provide a broad, inclusive look at the competition between the two types of sources. In addition, we conduct a detailed study on the role of the grain boundaries to act as a source, sink, or obstacle for lattice dislocations, as a function of grain boundary structure. This work compares the behavior of bicrystalline nanowires containing both random high-angle boundaries and a series of symmetric tilt grain boundaries to further elucidate the effect of interface structure on its behavior. The results show that grain boundaries in nanowires can be preferred nucleation sites for dislocations and twin boundaries, in addition to efficient sinks and pinning points for migrating dislocations. Plastic deformation behavior at high imposed strains is linked to the underlying deformation processes, such as twinning, dislocation pinning, or dislocation exhaustion/starvation. We also detail some important reactions between lattice dislocations and grain boundaries observed in the simulations, along with the activation of a single-arm source. This work suggests that the cooperation of numerous mechanisms and the structure of internal grain boundaries are crucial in understanding the deformation of bicrystalline nanowires.