On the impact of capillarity for strength at the nanoscale

The interior of nanoscale crystals experiences stress that compensates the capillary forces and that can be large, in the order of 1 GPa. Various studies have speculated on whether and how this surface-induced stress affects the stability and plasticity of small crystals. Yet, experiments have so far failed to discriminate between the surface contribution and other, bulk-related size effects. In order to clarify the issue, we study the variation of the flow stress of a nanomaterial while distinctly different variations of the two capillary parameters surface tension and surface stress are imposed under control of an applied electric potential. Our theory qualifies the suggested impact of $\textit{surface stress}$ as not forceful and instead predicts a significant contribution of the surface energy, as measured by the $\textit{surface tension}$. The predictions for the combined potential- and size dependence of the flow stress are quantitatively supported by the experiment. Previous suggestions, favoring the surface stress as the relevant capillary parameter, are not consistent with the experiment

Anomalous compliance and early yielding of nanoporous gold

We present a study of the elastic and plastic behavior of nanoporous gold in compression, focusing on molecular dynamics simulation and inspecting experimental data for verification. Both approaches agree on an anomalously high elastic compliance in the early stages of deformation, along with a quasi immediate onset of plastic yielding even at the smallest load. Already before the first loading, the material undergoes spontaneous plastic deformation under the action of the capillary forces, requiring no external load. Plastic deformation under compressive load is accompanied by dislocation storage and dislocation interaction, along with strong strain hardening. Dislocation-starvation scenarios are not supported by our results. The stiffness increases during deformation, but never approaches the prediction by the relevant Gibson-Ashby scaling law. Microstructural disorder affects the plastic deformation behavior and surface excess elasticity might modify elastic response, yet we relate the anomalous compliance and the immediate yield onset to an atomistic origin: the large surface-induced prestress induces elastic shear that brings some regions in the material close to the shear instability of the generalized stacking fault energy curve. These regions are elastically highly compliant and plastically weak

Nanoporous-gold-based composites : toward tensile ductility

We report on mechanical tests on interpenetrating-phase nanocomposite materials made by vacuum impregnation of nanoscale metal networks with a polymer. The metal component is nanoporous gold made by dealloying, whereas two epoxy resins and polyurethane are explored as the polymer component. The composites are strong and deformable in compression. Although previous observations invariably indicate tensile brittleness for nanoporous gold, composite samples made from cm-sized nanoporous samples enable macroscopic tensile and four-point bending tests that show ductility. This implies that the high strength of individual metal objects such as nanowires can now be incorporated into a strong and ductile material from which macroscopic things can be formed. In fact, a rule-of-mixture-type analysis of the stresses carried by the metal phase suggests quantitative agreement with data reported from separate experiments on small-scale gold nanostructures

Measurement of local crystal lattice strain variations in dealloyed nanoporous gold

Reversible macroscopic length changes in nanoporous structures can be achieved by applying electric potentials or by exposing them to different gases or liquids. Thus, these materials are interesting candidates for applications as sensors or actuators. Macroscopic length changes originate from microscopic changes of crystal lattice parameters. In this report, we show spatially resolved measurements of crystal lattice strain in dealloyed nanoporous gold. The results confirm theory by indicating a compression of the lattice along the axis of cylindrically shaped ligaments and an expansion in radial direction. Furthermore, we show that curved npAu surfaces show inward relaxation of the surface layer. (Figure presented) IMPACT STATEMENT We show spatially resolved measurements of strain in nanoporous gold confirming theory: Crystal lattice is compressed along the axis of cylindrical ligaments and expanded in radial direction, surfaces relax inward

3D stochastic bicontinuous microstructures: Generation, topology and elasticity

Motivated by recent experimental investigations of the mechanical behavior of nanoporous metal we explore an efficient and robust method for generating 3D representative volume elements (RVEs) with strikingly similar behavior. Our approach adopts Cahn's method of generating a Gaussian random field by taking a superposition of standing sinusoidal waves of fixed wavelength but random in direction and phase. In its theory part, our study describes closed-form expressions for how the solid volume fraction affects the binarization level, mean structure size, specific surface area, averages of mean and Gaussian curvature, and the scaled topological genus. Based on numerical studies we report on criteria for achieving representative realizations of the structure by proper choice of the number of waves and element size. We also show that periodic structures are readily created. We analyze the mechanical properties considering linear and infinitesimal elasticity and evaluate the residual anisotropy (which can be made small) and the effective values of the Young's modulus and Poisson's ratio. The numerical results are in excellent agreement with experimental findings for the variation of stiffness with solid fraction of nanoporous gold made by dealloying. We propose scaling relations that achieve naturally a perfect agreement with the numerical and experimental data. The scaling relation for the stiffness accounts for a percolation-to-cluster transition in the random field microstructure at a finite solid fraction. We propose that this transition is the origin of the previously reported anomalous compliance of nanoporous gold

Adsorption–strain coupling at solid surfaces

This brief review inspects how chemistry or electrochemistry at a solid–vapor or solid–electrolyte interface couple to the mechanics of the solid. Emphasis is on the complementarity of two at first sight unrelated phenomena: on the one hand, adsorption or electric charging change the local tangential stresses in the solid surface; on the other hand, a tangential strain of the surface changes the adsorption enthalpy and the chemical or electric potential. One and the same materials parameter underlies these phenomena. The phenomenology and the Maxwell relations behind that observation are discussed and the underlying microscopic mechanisms addressed, with particular attention to symmetry and sign of the coupling coefficients. © 2019 The AuthorThis work was supported by the German Research Foundation (DFG) , grant We1424/16-1

Stress-charge coupling coefficient for thin-film polypyrrole actuators – Investigation of capacitive ion exchange in the oxidized state

This work quantifies the actuation behavior of thin electrodeposited polypyrrole films on rigid substrates. During in situ cantilever bending experiments in aqueous perchloric acid, the films remain clamped to their substrate and the film stress is inferred from a small bending of the cantilever. The potential range under study is 0.4–0.8 V versus the standard hydrogen electrode. Within this potential region, the film is in the oxidized state and the actuation arises from capacitive electrode processes. For the volumetric capacitance, c*, we find 0.24±0.01F/mm3. The stress-charge coupling coefficient, ξ, which is defined as the stress variation per volumetric charge density, emerges as −153±11mV. The results are robust, reproducible and independent of the film thickness or the potential scan rate. The experimental value of ξ is supported by an independent estimate, based on a micromechanical model in combination with literature data for the partial molar volume of solvated perchlorate anions and the elastic constants of polypyrrole.This work was supported by the German Research Foundation (DFG) via SFB 986 M 3 , project B2

Imaging the deformation-induced accumulation of defects in nanoporous gold

Nanoporous gold (NPG) provides a model material for studying small-scale deformation and the mechanical behavior of network solids. We report a transmission electron microscopy study of the defect structure in electron-transparent NPG leaf deformed by rolling. The results confirm that plastic deformation significantly enhances the defect density. Specifically, twins are formed on several sets of crystallographic planes, and their interaction forms Lomer-Cottrell locks. This inhibits dislocation escaping from NPG, thus avoiding the dislocation starvation scenario that is often considered in the ‘smaller is stronger' context of small-scale plasticity. Instead, strain hardening is apparently linked to accumulation and interaction of twins