While metal nanoparticles are widely used, their small size makes them mechanically unstable. Extensive prior research has demonstrated that nanoparticles with sizes in the range of 10-50 nm fail by the surface nucleation of dislocations, which is a thermally activated process. Two different contributions have been suggested to cause the weakening of smaller particles: first, geometric effects such as increased surface curvature reduce the barrier for dislocation nucleation; second, surface diffusion happens faster on smaller particles, thus accelerating the formation of surface kinks which nucleate dislocations. These two factors are difficult to disentangle. Here we use in situ compression testing inside a transmission electron microscope to measure the strength and deformation behavior of platinum particles in three groups: 12 nm bare particles, 16 nm bare particles, and 12 nm silica-coated particles. Thermodynamics calculations show that, if surface diffusion were the dominant factor, the last two groups would show equal strengthening. Our experimental results refute this, instead demonstrating a 100% increase in mean yield strength with increased particle size and no statistically significant increase in strength due to the addition of a coating. A separate analysis of stable plastic flow corroborates the findings, showing an order-of-magnitude increase in the rate of dislocation nucleation with a change in particle size and no change with coating. Taken together, these results demonstrate that surface diffusion plays a far smaller role in the failure of nanoparticles by dislocations as compared to geometric factors that reduce the energy barrier for dislocation nucleation.
The mechanical behavior of nanostructures is known to transition from a Hall-Petch-like "smaller-is-stronger" trend, explained by dislocation starvation, to an inverse Hall-Petch "smaller-is-weaker" trend, typically attributed to the effect of surface diffusion. Yet recent work on platinum nanowires demonstrated the persistence of the smaller-is-stronger behavior down to few-nanometer diameters. Here, we used in situ nanomechanical testing inside of a transmission electron microscope (TEM) to study the strength and deformation mechanisms of platinum nanoparticles, revealing the prominent and size-dependent role of surfaces. For larger particles with diameters from 41 nm down to approximately 9 nm, deformation was predominantly displacive yet still showed the smaller-is-weaker trend, suggesting a key role of surface curvature on dislocation nucleation. For particles below 9 nm, the weakening saturated to a constant value and particles deformed homogeneously, with shape recovery after load removal. Our high-resolution TEM videos revealed the role of surface atom migration in shape change during and after loading. During compression, the deformation was accommodated by atomic motion from lower-energy facets to higher-energy facets, which may indicate that it was governed by a confined-geometry equilibration; when the compression was removed, atom migration was reversed, and the original stress-free equilibrium shape was recovered.
The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.
While it is well established that nanoparticle shape can depend on equilibrium thermodynamics or growth kinetics, recent computational work has suggested the importance of thermal energy in controlling the distribution of shapes in populations of nanoparticles. Here, we used transmission electron microscopy to characterize the shapes of bare platinum nanoparticles and observed a strong dependence of shape distribution on particle size. Specifically, the smallest nanoparticles (<2.5 nm) had a truncated octahedral shape, bound by ã111ã and ã100ã facets, as predicted by lowest-energy thermodynamics. However, as particle size increased, the higher-energy ã110ã facets became increasingly common, leading to a large population of non-equilibrium truncated cuboctahedra. The observed trends were explained by combining atomistic simulations (both molecular dynamics and an empirical square-root bond-cutting model) with Boltzmann statistics. Overall, this study demonstrates experimentally how thermal energy leads to shape variation in populations of metal nanoparticles, and reveals the dependence of shape distributions on particle size. The prevalence of non-equilibrium facets has implications for metal nanoparticles applications from catalysis to solar energy.
Understanding the size- and shape-dependent properties of platinum nanoparticles is critical for enabling the design of nanoparticle-based applications with optimal and potentially tunable functionality. Toward this goal, we evaluated nine different empirical potentials with the purpose of accurately modeling faceted platinum nanoparticles using molecular dynamics simulation. First, the potentials were evaluated by computing bulk and surface properties-surface energy, lattice constant, stiffness constants, and the equation of state-and comparing these to prior experimental measurements and quantum mechanics calculations. Then, the potentials were assessed in terms of the stability of cubic and icosahedral nanoparticles with faces in the {100} and {111} planes, respectively. Although none of the force fields predicts all the evaluated properties with perfect accuracy, one potential-the embedded atom method formalism with a specific parameter set-was identified as best able to model platinum in both bulk and nanoparticle forms.
