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Simultaneously enhancing strength and ductility of metals and alloys has been a tremendous challenge. Here, we investigate a CoCuFeNiPd high-entropy alloy (HEA), using a combination of Monte Carlo method, molecular dynamic simulation, and density-functional theory calculation. Our results show that this HEA is energetically favorable to undergo short-range ordering (SRO), and the SRO leads to a pseudo-composite microstructure, which surprisingly enhances both the ultimate strength and ductility. The SRO-induced composite microstructure consists of three categories of clusters: face-center-cubic-preferred (FCCP) clusters, indifferent clusters, and body-center-cubic-preferred (BCCP) clusters, with the indifferent clusters playing the role of the matrix, the FCCP clusters serving as hard fillers to enhance the strength, while the BCCP clusters acting as soft fillers to increase the ductility. Our work highlights the importance of SRO in influencing the mechanical properties of HEAs and presents a fascinating route for designing HEAs to achieve superior mechanical properties., The strength-ductility trade-off has been a long-standing problem for alloy development. Here the authors present a route for designing high-entropy alloys to overcome this trade-off via short-range ordering shown by combined Monte Carlo, molecular dynamic, and density-functional theory simulations.

Lattice structures, defect structures, and deformation mechanisms of high-entropy alloys (HEAs) have been studied using atomistic simulations to explain their remarkable mechanical properties. These atomistic simulation techniques, such as first-principles calculations and molecular dynamics allow atomistic-level resolution of structure, defect configuration, and energetics. Following the structure–property paradigm, such understandings can be useful for guiding the design of high-performance HEAs. Although there have been a number of atomistic studies on HEAs, there is no comprehensive review on the state-of-the-art techniques and results of atomistic simulations of HEAs. This article is intended to fill the gap, providing an overview of the state-of-the-art atomistic simulations on HEAs. In particular, we discuss how atomistic simulations can elucidate the nanoscale mechanisms of plasticity underlying the outstanding properties of HEAs, and further present a list of interesting problems for forthcoming atomistic simulations of HEAs.

Deformation twinning has been frequently observed in body-centered cubic (BCC) high entropy alloys (HEAs), however, the underlying mechanism remains elusive. We perform molecular dynamics simulations on a representative BCC HEA nanopillar under high-symmetry compression, describe atomic details of deformation twinning, and propose a mechanism of twin nucleation from the surface. We find that twinned regions are formed by partial dislocations and that chemical heterogeneity can reduce local fault energy and promote stacking faults and twins. These results help to understand the propensity for stacking fault formation and twinning in HEAs and may guide the design of novel HEAs through control of active twinning mechanisms.

The predictability of molecular dynamics simulations on the plasticity and fracture behaviors of metals is critically dependent on the accuracy of the employed interatomic potential. Here we present an approach to fitting modified embedded-atom method (MEAM) interatomic potentials to several key properties obtained from first-principles calculations and literature data that govern the continuous mechanistic processes in pure unary fcc Ni, Al, and Cu metals. Along with the commonly used lattice and elastic properties, our MEAM potentials are fitted to the cohesive energy curve, the decohesive energy curve, and the generalized stacking fault energy curve, which are the key properties governing the lattice response to volumetric, fracture, and shear deformations. We further demonstrate that these potentials are able to accurately predict the experimental values for a range of other mechanically relevant properties. Importantly, the potentials presented here outperform all existing EAM/MEAM interatomic potentials readily available from the literature and thus enable more accurate simulations of plasticity and fracture behavior of unary fcc metals.

The interaction of crystalline defects leads to strain hardening in bulk metals. Metals with high stacking fault energy (SFE), such as aluminum, tend to have low strain hardening rates due to an inability to form stacking faults and deformation twins. Here, we use in situ SEM mechanical compressions to find that colloidally synthesized defect-free 114 nm Al nanocubes combine a high linear strain hardening rate of 4.1 GPa with a high strength of 1.1 GPa. These nanocubes have a 3 nm self-passivating oxide layer that has a large influence on mechanical behavior and the accumulation of dislocation structures. Post-compression TEM imaging reveals stable prismatic dislocation loops and the absence of stacking faults. MD simulations relate the formation of dislocation loops and strain hardening to the surface oxide. These results indicate that slight modifications to surface and interfacial properties can induce enormous changes to mechanical properties in high SFE metals., Comment: 10 pages, 7 figures

The demonstration of high entropy alloys (HEAs), or more generally multi-principal-element alloys (MPEAs), which display a greater resistance to softening at elevated temperatures and embrittlement at cryogenic temperatures, has offered an accessible alternative alloying process for materials scientists and engineers. Although solidification is a fundamental process in synthesis of alloys which strongly affects their microstructure and properties, a firm understanding of this process in HEAs is scarce. Here, using molecular dynamics (MD) simulations, we study the rapid solidification of the multi-principal-element CoFeNiPd alloy as a prototypical single-phase HEA. Our simulations reveal an intense competition between fcc and bcc structures during homogenous nucleation in this alloy. According to our numerical analyses, the crystalline fcc phase is thermodynamically the most stable structure in this alloy, which is in agreement with the experimental observations. We show that formation of the fcc structure can be facilitated through heterogeneous nucleation by including a pre-existing fcc seed in the liquid phase. Interestingly, we illustrate that altering the crystal structure of the seed from fcc to bcc leads to obtaining a single phase bcc alloy. Our detailed analyses confirm that the tendency of HEA systems to undergo crystallization (rather than amorphisation) at fast cooling rates is owing to the neutral chemical affinity and similar atomic size of their constitutive elements. Our findings suggest that rapid solidification accompanied with heterogeneous (e.g. seed-assisted) nucleation could be a promising processing route to control the microstructure and properties of the HEAs.

Recently, atomic segregation, short-range ordering, and cluster formation have been observed experimentally in high-entropy alloys (HEAs). Differences in the atomic size and electronegativity of constituent elements were proposed to be the underlying cause of such ordering. Here, we investigated two HEAs, CoCuFeNiPd and CoCuFeNiTi, using a combination of Monte Carlo and molecular dynamic simulations. Our results show that the CoCuFeNiPd HEA exhibits much stronger atomic segregation and short-range ordering than the CoCuFeNiTi HEA, despite the larger differences in the relative atomic size and electronegativity of Ti with other constituent elements, as compared to those of Pd, suggesting that the differences in the atomic size and electronegativity alone are insufficient to explain the simulation results. We find that it is the chemical-affinity disparity and exclusivity between Ti (Pd) with the remaining species that lead to the different clustering behavior in these two HEAs. Specifically, three conditions for strong atomic segregation and short-range ordering are identified: 1. a large chemical-affinity disparity amongst the chemical elements; 2. a high chemical-element exclusivity in low-, medium-, and high-energy clusters; and 3. a net energy reduction associated with low- and medium-energy-cluster formation that compensates for the energy increase associated with high-energy-cluster formation. Our findings are in agreement with experimental results reported in literature, and highlight the importance of chemical-affinity disparity and exclusivity in influencing the microstructure of HEAs, explain the origin of high-energy-cluster formation in HEAs, and provide guidelines for designing HEAs with excellent properties.

Previous studies have shown that a small variation in the chemical composition of metallic glasses (MGs) can drastically alter their strength and ductility. However, the underlying structural origin and atomistic mechanisms remain unclear. Using large-scale molecular dynamics simulations, we studied the effect of chemical composition and affinity on the microstructure and deformation behaviour of Zr50Ni50 − xAlx MG by varying the value of x in the range of 5 ≤ x ≤ 25 (at.%). We show that an increase in x is able to strengthen and embrittle the material. In particular, a ductile (homogeneous deformation) to brittle (shear banding) transition occurs at x ~ 15. To reveal the structural origin, we performed both short- and medium-range order (SRO/MRO) analyses on the MG. By varying the cooling rate while maintaining a constant composition, our structural analyses identify the Al-centred full-icosahedron (Al-FI) as the key structural motif responsible for the strengthening and embrittlement. Then, our analyses of SRO and MRO reveal an increase in both the fraction and connectivity of Al-FI by increasing x from 5 to 25 at.%. We also show that chemical affinities among different atomic species are strongly correlated with the structural attributes, which in turn strongly affect the mechanical behaviour of the MGs. Our findings highlight the importance of chemical composition and affinity in influencing the microstructural features of MGs at different length scales and their mechanical properties.

We conducted in situ three-point bending experiments on beams with roughly square cross-sections, which we fabricated from the frustule of Coscinodiscus sp. We observe failure by brittle fracture at an average stress of 1.1 GPa. Analysis of crack propagation and shell morphology reveals a differentiation in the function of the frustule layers with the basal layer pores, which deflect crack propagation. We calculated the relative density of the frustule to be ∼30% and show that at this density the frustule has the highest strength-to-density ratio of 1,702 kN⋅m/kg, a significant departure from all reported biologic materials. We also performed nanoindentation on both the single basal layer of the frustule as well as the girdle band and show that these components display similar mechanical properties that also agree well with bending tests. Transmission electron microscopy analysis reveals that the frustule is made almost entirely of amorphous silica with a nanocrystalline proximal layer. No flaws are observed within the frustule material down to 2 nm. Finite element simulations of the three-point bending experiments show that the basal layer carries most of the applied load whereas stresses within the cribrum and areolae layer are an order of magnitude lower. These results demonstrate the natural development of architecture in live organisms to simultaneously achieve light weight, strength, and exceptional structural integrity and may provide insight into evolutionary design.

We conducted uniaxial compression of single crystalline Mg alloy, AZ31 (Al 3% wt. and Zn 1% wt.) nanopillars with diameters between 300–5000 nm with two distinct crystallographic orientations: (1) along the [0001] c-axis and (2) at an acute angle away from the c-axis, nominally oriented for basal slip. We observe single slip deformation for sub-micron samples nominally oriented for basal slip with the deformation commencing via a single set of parallel shear offsets. Samples compressed along the c-axis display an increase in yield strength compared to basal samples as well as significant hardening with the deformation being mostly homogeneous. We find that the “smaller is stronger” size effect in single crystals dominates any improvement in strength that may have arisen from solid solution strengthening. We employ 3D-discrete dislocation dynamics (DDD) to simulate compression along the [0001] and [1122] directions to elucidate the mechanisms of slip and evolution of dislocation microstructure. These simulations show qualitatively similar stress strain signatures to the experimentally obtained stress-strain data. Simulations of compression parallel to the [1122] direction reveal the activation and motion of only -type dislocations and virtually no dislocation junction formation. Computations of compression along [0001] show the activation and motion of both and dislocations along with a significant increase in the formation of junctions corresponding to the interaction of intersecting pyramidal planes. Both experiments and simulation show a size effect, with a differing exponent for basal and pyramidal slip. We postulate that this anisotropy in size effect is a result of the underlying anisotropic material properties only. We discuss these findings in the context of the effective resolved shear stress relative to the unit Burgers vector for each type of slip, which reveal that the mechanism that governs size effect in this Mg-alloy is equivalent in both orientations.

Here we examine the role of anharmonicity in the elastic constants of bulk metallic glasses and develop an anharmonic model to consider the effects of both pressure and temperature across the glass transition. By comparing against reported experimental data and elastic constants obtained from molecular dynamics simulations, we show that the model is able to capture reported elastic constants from cryogenic temperatures through the glass transition and under hydrostatic pressures up to 18 GPa. Microstructural indicators based on short-range order analysis also display strong correlations with the bulk and shear moduli across the range of pressures and temperatures studied. These results not only greatly expand our understanding in the physical origins of elastic properties of bulk metallic glasses but are also of practical interest for application to processing routes for bulk metallic glass materials.

Significant theoretical efforts have been made to understand the Hall-Petch and inverse Hall-Petch relations of nanocrystalline pure metals, metallic glasses and binary alloy systems. However, only a few studies have investigated the Hall-Petch or inverse Hall-Petch relations in high-entropy alloys. In this work, phase stability of single-crystalline CoNiFeAlxCu1-x and uniaxial compression of polycrystalline CoNiFeAlxCu1-x are investigated by molecular dynamics simulation. Calculations of cohesive energies indicate that FCC structured CoNiFeAlxCu1-x is more stable at low Al concentrations (x ≤ 0.4) and BCC structured CoNiFeAlxCu1-x is more stable for high Al concentrations (x > 0.4). Based on the phase stability, FCC structured polycrystalline CoNiFeAl0·3Cu0.7 and BCC structured polycrystalline CoNiFeAl0·7Cu0.3 are constructed to perform uniaxial compression. Hall-Petch and inverse Hall-Petch relations are observed in both FCC and BCC structured polycrystalline CoNiFeAlxCu1-x. The microstructural evolutions of polycrystalline CoNiFeAlxCu1-x reveal that the dominant deformation mechanisms in the Hall-Petch regime of FCC structures are dislocation slip and deformation twinning due to relatively low stacking fault energy and that of BCC structures is phase transformation plasticity. For the inverse Hall-Petch relation, the dominant deformation mechanisms for both FCC and BCC HEAs are the rotation of grains and migration of grain boundaries. It indicates that FCC and BCC HEAs exhibit similar Hall-Petch and inverse Hall-Petch relations with the conventional polycrystalline materials, but its grain size exponent and gradient are quite different from those of pure metals.

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 nature of dislocation sources in small-scale metals is critical to understanding and building models of size-dependent crystalline strength at the nanoscale. Pre-existing dislocations with one pinning point can be readily described as truncated Frank–Read sources, and modeling their operation strengths is straightforward. In contrast, simple and accurate models describing surface dislocation nucleation processes remain elusive. Here, we develop a computationally simple model of heterogeneous dislocation nucleation from free surfaces by combining a continuum description of the nucleation process with the atomistic inputs where accuracy is critical. This model is used to derive the upper strength limits of single-crystalline face-centered cubic nanopillars as a function of size, material and crystal orientation for uniaxial compression and tension. The output parameter space of this model is critically compared against direct atomistic simulations, as well as experiments on tension of pristine gold nanowires and compression of copper nanopillars to highlight its virtues and limitations.

Our current understanding of size-dependent strength in nano- and microscale crystals is centered around the idea that the overall strength is determined by the stress required to propagate dislocation sources. The nature and type of these dislocation sources is the subject of extensive debate, however, one commonality amongst these theories is that the ability of the free surface to absorb dislocations is a necessary condition for transition to a source controlled regime. In this work we demonstrate that atomic layer deposition (ALD) of conformal 5–25 nm thick TiO_2/Al_(2)O_3 coatings onto electroplated single crystalline copper pillars with diameters ranging from 75 nm to 1 μm generally inhibits the ability of a dislocation to vanish at the free surface. Uniaxial compression tests reveal increased strength and hardening relative to uncoated pillars at equivalent diameters, as well as a notable recovery of plastic strain during unloading, i.e. the Bauschinger effect. Unlike previous reports, these coated pillars retained the stochastic signature in their stress–strain curves. We explain these observations within the framework of a size-dependent strength theory based on a single arm source model, dislocation theory, and microstructural analysis by transmission electron microscopy.

Heat Flow in Graphene Unsupported graphene sheets show exceptional thermal transport properties, but are these properties maintained when a graphene sheet is in contact with a substrate? Seol et al. (p. 213 ; see the Perspective by Prasher ) measured the thermal conductivity of graphene supported on silicon dioxide and found that, while the conductivity was considerably lower than that of free-standing graphene, it was still greater than that of metals such as copper. A theoretical model suggested that the out-of-plane flexing vibrations of the graphene play a key role in thermal transport. Thus, graphene may help in applications such as conducting heat away from electronic circuits.

Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the supported graphene. In this paper, we theoretically analyze the morphological stability of a graphene monolayer on an oxide substrate, subject to van der Waals interactions and in-plane mismatch strains. First, we define the equilibrium separation and the interfacial adhesion energy as the two key parameters that characterize the van der Waals interaction between a flat monolayer and a flat substrate surface. By a perturbation analysis, a critical compressive mismatch strain is predicted, beyond which the graphene monolayer undergoes strain-induced instability, forming corrugations with increasing amplitude and decreasing wavelength on a perfectly flat surface. When the substrate surface is not perfectly flat, the morphology of graphene depends on both the amplitude and the wavelength of the surface corrugation. A transition from conformal (corrugated) to non-conformal (flat) morphology is predicted. The effects of substrate surface corrugation on the equilibrium mean thickness of the supported graphene and the interfacial adhesion energy are analyzed. Furthermore, by considering both the substrate surface corrugation and the mismatch strain, it is found that, while a tensile mismatch strain reduces the corrugation amplitude of graphene, a corrugated substrate surface promotes strain-induced instability under a compressive strain. These theoretical results suggest possible means to control the morphology of graphene monolayer on oxide substrates by surface patterning and strain engineering., Comment: 25 pages, 9 figures, submitted for review on March 3, 2010

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.