Strengthening Mechanism of a Single Precipitate in a Metallic Nanocube

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Strengthening Mechanism of a Single Precipitate in a Metallic Nanocube Mehrdad T Kiani, Yifan Wang, Nicolas Bertin, Wei Cai, and Xun Wendy Gu Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03857 • Publication Date (Web): 11 Dec 2018 Downloaded from http://pubs.acs.org on December 13, 2018

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Strengthening Mechanism of a Single Precipitate in a Metallic Nanocube Mehrdad T. Kiania, Yifan Wangb, Nicolas Bertinb,c, Wei Caib, X. Wendy Gub*

aDepartment

of Materials Science and Engineering, bDepartment of Mechanical

Engineering, Stanford University, Stanford, CA 94305, United States, cLawrence Livermore National Laboratory, Livermore, CA 94550, United States

Abstract

Nano-precipitates play a significant role in the strength, ductility and damage tolerance of metallic alloys through their interaction with crystalline defects, especially dislocations. However, the difficulty of observing the action of individual precipitates during plastic deformation has made it challenging to conclusively determine the mechanisms of the precipitate-defect interaction for a given alloy system, and presents a major bottleneck in the rational design of nanostructured alloys. Here we demonstrate the in situ compression

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of core-shell nanocubes as a promising platform to determine the precise role of individual precipitates. Each nanocube with a dimension of ~85 nm contains a single spherical precipitate of ~25 nm diameter. The Au-core/Ag-shell nanocubes show a yield strength of 495 MPa with no strain hardening. The deformation mechanism is determined to be surface nucleation of dislocations which easily traverses through the coherent Au-Ag interface. On the other hand, the Au-core/Cu-shell nanocubes show a yield strength of 829 MPa with a pronounced strain hardening rate. Molecular dynamics and dislocation dynamics simulations, in conjunction with TEM analysis, have demonstrated the yield mechanism to be the motion of threading dislocations extending from the semi-coherent Au-Cu interface to the surface, and strain hardening to be caused by a single-armed Orowan looping mechanism. Nanocube compression offers an exciting opportunity to directly compare computational models of defect dynamics with in situ deformation measurements to elucidate the precise mechanisms of precipitate hardening.

Keywords: Coherent interface, semi-coherent interface, precipitate, strain hardening, compression, in-situ scanning electron microscopy


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Introduction Nanoscale precipitates play a critical role in controlling the strength, ductility, and damage tolerance of metallic alloys through interactions with crystalline defects. Classical, continuum models for precipitation hardening have been used extensively to predict the effect of lattice mismatch, and precipitate size and density on mechanical properties.1 However, these models have difficulties in explaining the behavior of nanoprecipitates in superalloys2, micron-sized shape memory alloys3, and alloys in extreme environments of temperature4, radiation5, and environmental corrosion.6 The role of the atomistic structure of metallic interfaces in defect nucleation, propagation, and annihilation is increasingly recognized. Experiments and simulations on metallic multilayers show that faceting, crystallographic orientation and initial misfit dislocation structure at a bimetallic interface can determine strength, strain hardening, and slip transmission versus interfacial sliding.7–10 A similar level of understanding for individual


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metallic precipitates, connecting dislocation activities and microstructure changes with the stress-strain responses, would be a significant step forward for the design of nanostructured alloys. However, such observations have been very challenging to achieve. In-situ transmission electron microscope (TEM) mechanical testing on thin films enables high-resolution imaging of dislocation-precipitate interactions, but cannot quantify the mechanical properties due to an individual precipitate.11,12 Mechanical tests have been performed on metallic micropillars containing precipitates,13,14 but it has not been possible to separate the effect of a single precipitate from the aggregated response of many precipitates. Here, we perform in situ scanning electron microscope (SEM) compression tests on bimetallic core-shell nanocubes with dimensions ~85 nm, each containing a single spherical precipitate with dimensions of ~25 nm. The small size of the nanocubes allows for TEM imaging without further thinning of the specimen. The cubic geometry is designed to maintain a constant cross-sectional area for mechanical testing and imaging. Previous studies show that the density and network structure of misfit and threading dislocations within core-shell nanocrystals can be tuned through the lattice mismatch between the


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core and the shell.15,16 To probe these microstructural effects on strength and ductility, Au-core/Ag-shell (Au@Ag) nanocubes with 0.2% lattice mismatch17 and Au-core/Cushell (Au@Cu) nanocubes with 12% lattice mismatch17 are synthesized and compressed inside an SEM. Au@Ag nanocubes show a yield strength of 495 ± 150 MPa with no strain hardening, while Au@Cu nanocubes show a yield strength of 829 ± 268 MPa with pronounced strain hardening. Transmission electron microscopy (TEM) is used to analyze strain and dislocations both before and after compression. Molecular dynamics (MD) and discrete dislocation dynamics (DDD) simulations are used in conjunction with experiments to determine the deformation mechanisms. The plastic flow of Au@Ag nanocubes is caused by the motion of surface-nucleated dislocations, which cut across the coherent Au/Ag interface easily. On the other hand, yield of Au@Cu nanocubes is caused by the motion of threading dislocations connecting between the semi-coherent Au/Cu interface and the surface, similar to the single-arm source mechanism in micropillar compression experiments. However, the threading dislocations wrap around the Cu precipitate, similar to the Orowan looping mechanism, and resulting in a strain hardening behavior that is not observed in single-crystal micropillars.


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Au@Ag and Au@Cu nanocubes were synthesized in a two-step process using colloidal methods in aqueous solutions.15,18 Single crystalline Au nanospheres are first synthesized through an iterative growth process (Figure S1),19 onto which a Ag or Cu shell is subsequently grown (Figure 1).15,18 The cubic geometry is achieved by using a surfactant (cetyltrimethylammonium chloride) that selectively binds to {100} faces, such that crystal growth occurs more rapidly along other faces (e.g. {110}, {111}) and only {100} faces remain at the end of synthesis.15,18,20 The Au@Ag nanocubes have a core diameter of 26.4 ± 0.7 nm and a cube size of 87.0 ± 2.8 nm, while the Au@Cu nanocubes have a core diameter of 23.8 ± 0.4 nm and a cube size of 86.4 ± 5.1 nm. The Au core is in the center of the Au@Ag nanocube but is 0 to 20 nm off-center in the Au@Cu nanocubes. The eccentric structure of Au@Cu nanocubes may be attributed to preferential attachment of Cu atoms to {100} over {111} faces, according to first principles studies,21 but stress relaxation has also been proposed as an alternative mechanism for the uneven shell growth.22 Au@Ag nanocubes have sharp cube corners and edges, with a radius of curvature of 7.5 ± 2.1 nm, while Au@Cu nanocubes have more rounded edges with a radius of curvature of 15.1 ± 2.7 nm.


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Bright field transmission electron microscopy (TEM) indicates that as-synthesized Au@Ag nanocubes are single crystalline and do not contain dislocations or twin boundaries (Figure 1A). The majority of nanocubes showed uniform contrast, although some nanocubes showed alternating bands of contrast that are attributed to thickness fringes. High-resolution TEM images of the Au/Ag interface revealed continuous lattice fringes across the core-shell interface, indicating a coherent interface (Figure 1B, C). Xray diffraction (XRD) was used to investigate the average defect density within an ensemble of Au@Ag nanocubes with better statistics than is possible with TEM (Figure S2). Our XRD analysis showed that the nanocubes on average contained fewer than one dislocation per cube, in agreement with our TEM observations. On the other hand, TEM images of Au@Cu nanocubes show discontinuous lattice fringes across the Au/Cu interface (Figure 1D), and defects at the interface (Figure 1F), corresponding to misfit dislocations. Lines of dark contrast are observed to extend from the core-shell interface to the surface. These are threading dislocations which are the result of incomplete relaxation of the misfit strain between the core and the shell.16 Although dislocations in an FCC metal can exist on twelve slip systems,23 not all


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dislocations may be observed simultaneously under a given TEM imaging condition. For 𝑎

example, one-third of the 2〈110〉{111} dislocations do not satisfy the 𝑔 ∙ 𝑏 criterion and are invisible when imaged along a 〈100〉 zone axis. Tilting the nanocube by 30° revealed these missing dislocations, which indicates that the threading dislocations in the Cu shell 𝑎

have a Burgers vector of 2〈110〉 and reside on the {111} plane (Figure S3). Figure 1E shows Moiré fringes at the Au core in the Au@Cu nanocubes. These features are due to the superimposition of Au and Cu atomic columns, which leads to a periodic interference pattern.24 Misfit dislocations are identified as discontinuous lattice fringes at the core-shell interface, which can be related to the periodicity of the Moiré fringes (Figure 1E). The relationship between misfit dislocation spacing (𝑑Misfit) and Moiré fringe spacing (𝑑Moire) is provided by:25 𝑑Misfit = 𝑑Moire +

𝑑Au ― 𝑑Cu 4

Eq. 1

where 𝑑Au and 𝑑Cu are the Au and Cu lattice spacing in the nanocube, respectively. 𝑑Au ― 𝑑Cu ≪ 𝑑Moire, so 𝑑Misfit ≈ 𝑑Moire. Using this expression, 𝑑Misfit can be estimated as 1.6 ± 0.2 nm from Figure 1F. The Burgers vectors of the misfit dislocations can be identified


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𝑎

as either 2〈110〉 or 𝑎〈100〉. TEM images of the Au@Cu nanocube at 30° tilt also show Moiré fringes along a different direction (Figure S3), which indicates that a network of misfit dislocation loops aligned in different directions surrounds the Au core. A misfit dislocation spacing of 1.8 – 2 nm is estimated from the Matthews-Blakeslee model for dislocation formation in epitaxial multilayer films26,27, and models for spherical interfaces,28 which is consistent with our measured spacing.

Figure 1. TEM images of A-C) Au@Ag nanocubes and D-F) Au@Cu nanocubes. High resolution images of B,C) coherent-interface in Au@Ag nanocubes, and E,F) Moiré


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fringes and misfit dislocations within Au@Cu nanocubes. Scale bar is 50 nm for A and D, 10 nm for B and E, and 2 nm for C and F.

Nanocubes are dropcast onto a silicon wafer for uniaxial compression inside an SEM using a diamond flat punch indenter. Nanocubes are strained to ~30% at a constant loading rate of 0.001 mN/s (strain rate of 0.01-0.03/s). Mechanical testing is performed under load-controlled conditions by using a voice-coil system to generate force and a capacitive sensor to measure displacement. The mechanical tester is oriented relative to the SEM pole piece such that the nanocube and the flat punch tip can be imaged simultaneously. A pre- and post-compression SEM image of the nanocube is examined together with the stress-strain curve (Figure S4). Post-compression SEM images showed a decrease in height and an increase in the cross-sectional area at the top of the nanocube, but not at the bottom, indicating that friction at the bottom surface prevents free expansion. Force-displacement curves are corrected for indentation of the nanocube into the substrate by using the elastic contact model for a square shaped punch into an elastic half-space.29 This correction accounts for < 1% of the measured strain. Tip and


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frame stiffness is more than 1000 times larger than nanocube stiffness and can be ignored. Figure 2A and B shows typical engineering stress-strain curves for Au@Ag and Au@Cu nanocubes under compression, respectively. 18 tests were performed on Au@Ag nanocubes and 17 tests on Au@Cu nanocubes. These stress-strain curves are characterized by linear elastic loading, yield and extended plasticity, and then unloading. Plastic flow is characterized by discrete slip events. Au@Ag nanocubes have a yield strength of 495 ± 150 MPa with no obvious strain hardening. Au@Cu nanocubes have a yield strength of 829 ± 268 MPa with pronounced strain hardening. Flow stress at large strain was characterized using the linear strain hardening rate, Θ = ∂σ / ∂ε. Au@Ag nanocubes exhibited a Θ of 0.87 ± 0.85 GPa whereas Au@Cu nanocubes exhibited a Θ of 3.9 ± 1.9 GPa. While we cannot measure cross-sectional area as a function of strain

in situ, we can estimate true stress-strain curves assuming Ag and Cu are incompressible. The representative curves are shown in Figure S5. For Au@Ag nanocubes, we observe little/no strain hardening and strain softening behavior while Au@Cu nanocubes still strain harden, albeit at a lower magnitude.


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Figure 2. Representative engineering stress-strain curves for A) Au@Ag and B) Au@Cu nanocubes in compression.

The elastic-plastic behavior of Au@Ag nanocubes is similar to that observed in single crystal fcc metal nanopillars.30,31 The strain hardening behavior of Au@Cu nanocubes, on the other hand, is surprising, because the strain hardening mechanisms in the bulk, e.g. dislocation entanglement,32 is unlikely to operate in the small volume of the nanocube. Furthermore, the difference in stacking fault energy (SFE) for Au, Ag, and Cu, 32.7, 17.3, and 47.5 mJ/m2, respectively, can be ignored given the small differences between Au/Ag and Au/Cu.33 Therefore, the strain hardening behavior is likely caused by the interaction between dislocations and the Au core. The size of plastic slip events also differs between the Au@Ag and Au@Cu nanocubes. The largest slip event in the Au@Ag


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nanocubes was approximately 0.21 while Au@Cu nanocubes had a narrower distribution of slip events with no slip events larger than 0.11. These results indicate that different mechanisms are responsible for the mechanical behavior of Au@Ag and Au@Cu nanocubes. In particular, the stress-strain behavior of the Au@Cu nanocubes differs from other micro and nano-sized metallic samples studied to date, which implies that the AuCu interface plays an important role. In order to observe the slip activities in the nanocubes in more detail, the nanocubes were dropcast on a copper TEM grid, compressed inside the SEM and then imaged in the TEM. Nanocubes were partially obscured by the TEM grid, but large regions of the core and shell could still be imaged. Figure 3A shows a representative post-compression TEM image of an Au@Ag nanocube. A slip offset is present at the surface of the nanocube, and slip bands extend from the corners and cross the Au core. The contrast and geometry of these features indicate that these are likely to be either stacking faults 𝑎

originating from Shockley partial dislocations with a 6〈211〉 Burgers vector or twinning due to multiple stacking faults on adjacent planes. The core-shell interface remains spherical


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(Figure 3B), which may be due to dislocations passing in front or behind the Au core rather than through it. There is no evidence that dislocation motion was impeded at the Au-Ag interface. Post-compression TEM images of Au@Cu nanocubes show a great deal of strain, and no shear bands (Figure 3C). Slip offsets emanate from the top two corners of the nanocube that are smaller in size than those observed in the Au@Ag nanocubes. After deformation, individual threading dislocations can no longer be identified and the core remains circular (Figure 3D). A previous study on Au@Pd core-shell nanocrystals showed that the mixing of miscible metals at the interface can relieve strain energy and reduce dislocation density.34 This could be occurring in the Au@Cu nanocubes as Au and Cu are miscible metals.


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Figure 3. TEM images of post-compression A,B) Au@Ag, and C,D) Au@Cu nanocubes. B and D are high magnification images of defects near the Au core. Scale bar is 25 nm in A and C and 10 nm in B and D.

To understand the atomic structure and deformation mechanisms of Au@Ag and Au@Cu nanocubes, molecular dynamics (MD) simulations are performed using the LAMMPS program.35 To reduce computational costs, the nanocubes in MD simulations have a dimension of 20 nm with a core diameter of 5 nm. The Au@Ag nanocube models are generated by first creating a fcc Ag cube, and then replacing the Ag atoms within a spherical region with Au atoms (i.e. the Au core has the same lattice constant as Ag). The


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structure is equilibrated by MD simulations at room temperature, resulting in a coherent Au/Ag interface with no misfit dislocations. The nanocube is then confined between two flat, frictionless, indenting potentials. MD simulations of compression tests are performed with the top indenter moving at a constant speed of 2 × 108 m/s and the bottom indenter fixed, corresponding to a strain rate of 107/s. Figure 4A-B show MD snapshots of the Au@Ag nanocube. Starting from a defect-free structure, stacking faults first nucleate from the nanocube surfaces at ~5% strain, and propagate across the nanocube (Movie S1). Upon relaxation after 20% strain, the Au@Ag nanocube contain several stacking faults 𝑎

that span the entire width (some of which intersect each other), as well as 6〈211〉 Shockley partial dislocations near corners and surfaces. These results agree with postcompression TEM images (Figure 3B). The MD predicted engineering stress-strain curve (Figure 4C) showed no strain hardening behavior, consistent with the experimental data. The true stress—strain curve of the MD simulation (Figure S5) shows slight strain softening. The higher yield strength predicted by MD (907 MPa) is likely caused by the much higher strain rate (due to the time scale limitation) of MD compared with


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experiments. Based on our MD simulations and experimental observations, we conclude that the Au@Ag nanocube deforms by surface nucleated partial dislocations, which moves across the nanocube unimpeded by the Au core.

Figure 4. MD simulation of Au@Ag nanocube. Snapshots A) before and B) after deformation to 20%. Green lines represent full dislocations and red planes represent stacking faults. C) Compressive engineering stress-strain curve.

The atomistic structures of the Au@Cu nanocube are generated using a similar approach as above, except that the initial lattice constant of the Au core region does not match that of the surrounding shell. To model a nanocube with fully relaxed misfit strain,


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a spherical region inside the Cu cube is replaced by a sphere of the same radius consisting of Au atoms having the intrinsic lattice constant of Au. After energy minimization, a network of misfit dislocations is formed at the spherical interface between Au and Cu (Figure S6). The misfit dislocation network contains dislocations with Burgers 𝑎

vectors of both 2〈110〉 and 𝑎〈100〉, consistent with experimental observations. By tuning the initial lattice parameter of the Au sphere (and hence the number of Au atoms) prior to energy minimization, we obtain nanocube structures with partially relaxed misfit strain, and containing threading dislocations in the Cu shell, similar to those observed in experiment (Figure S6). However, subsequent MD simulations of the deformation process using this structure showed no strain hardening (Figure S6), which is inconsistent with the mechanical behavior of the experimental Au@Cu nanocubes. In fact, the MD simulated Au@Cu nanocube showed similar behavior as the Au@Ag nanocubes, in which yielding occurs by the motion of surface-nucleated dislocations. To understand the discrepancy between the experimental and simulated Au@Cu nanocube compressions, we consider the role of the misfit and threading dislocations in


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the Au@Cu nanocubes. MD simulation shows that the misfit dislocation network is tightly bound to the Au/Cu interface, while the threading dislocations are mobile. The critical stress to activate the threading dislocations (and cause yielding) can be estimated by the Frank-Read-like expression 𝜏c = 𝜇𝑏/𝑙, where 𝜇 is shear modulus, 𝑏 is the magnitude of the Burgers vector, and 𝑙 is the length of the threading dislocation. Setting 𝐷cube and 𝑑core equal to the diameters of the nanocube and the core, respectively, the threading dislocation length can be estimated as 𝑙 ≈ (𝐷cube ― 𝑑core)/2. Using the size of the nanocubes in our experiments, we find a critical stress of 𝜏c ≈ 610 MPa, which is consistent with the experimentally observed yield stress. This indicates that in the experiments, the threading dislocations can move and cause yielding before dislocations nucleate from the surface. On the other hand, using the smaller size of the nanocubes in the MD model, the Frank-Read expression would give a much higher critical stress of 𝜏c ≈ 2570 MPa. Dislocation nucleation at the surface of the nanocube may occur before this 𝜏c is reached, which leads to the same deformation mechanism as for the Au@Ag nanocubes. This suggests that the discrepancy between the MD simulations and experiments is due to the much smaller size of the nanocube in the MD model.


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To confirm this hypothesis and to elucidate the mechanism for strain hardening, discrete dislocation dynamics (DDD) simulations of a Au@Cu nanocube compression were performed using the ParaDiS program (See Methods for simulation details).36 The simulated Au@Cu nanocube was identical in size as the experimental nanocube (85 nm cube size and 25 nm core diameter). The initial interfacial misfit dislocation network of the DDD simulated Au@Cu nanocube was extracted from a MD model of a Au@Cu nanocube with a 25 nm core diameter (Figure S7).37 The DDD nanocube also contained three threading dislocations on different slip planes in the Cu shell, to emulate the experimental defect structure (Figure 5A). The DDD compressive stress-strain curve is shown in Figure 5C. The yield stress is 754 MPa, which is consistent with the experimental value, and validates the estimate from the Frank-Read-based expression. However, different hardening behaviors result from the use of a penetrable and impenetrable Au core model with the same misfit dislocation network. For the case where the Au core is impenetrable, the dislocation velocity in the core region is set to 0 m/s. If the threading dislocations are allowed to penetrate the Au core, an elastic-perfect-plastic behavior is observed with no strain hardening (Figure 5C), which is inconsistent with the


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experimental observations. On the other hand, if the Au core is impenetrable to the threading dislocations, a strain hardening rate of Θ = 16.1 GPa is observed (see Movie S2). The Au core is also observed to be impenetrable in MD simulation, in which dislocations wrap around the Au core instead of cutting through it (see Movie S3).

Figure 5. DDD simulation of Au@Cu nanocubes. Snapshots A) before and B) after deformation to 3.6% for an impenetrable Au core. C) Compressive stress-strain curves for an impenetrable and a penetrable core.

In DDD simulations with the impenetrable core model, the threading dislocations are predicted to wrap around the Au core, in a single-arm version of the classical Orowan


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looping mechanism. Note that in the case of both the penetrable and the impenetrable core, the threading dislocations interact with the stress fields of the misfit dislocations. Given the difference between the experimentally observed (Θ = 3.9 GPa) and simulated strain hardening rate (Θ = 16.1 GPa), it is possible that additional mechanisms are active in the experimental nanocubes which are not captured in simulation. For instance, dislocation loops could bypass the precipitate through cross-slip after a critical number of loops are formed.38–40 Dislocation nucleation at free surfaces could occur once a critical stress is reached, which may lead to a lower strain hardening rate compared to the DDD simulations. In summary, compression tests were performed on Au@Ag and Au@Cu nanocubes using in-situ SEM mechanical testing, and the deformation mechanisms are analyzed using TEM observations, and MD and DDD simulations. We find that the Au@Ag nanocubes are initially dislocation free and the Au-Ag interface does not significantly alter the strength and deformation of the nanocubes. Plastic deformation in the Au@Ag nanocubes occurs through the nucleation of dislocations at surfaces. Strain hardening does not occur because dislocation motion within the nanocube is not impeded by other dislocations or the Au-Ag interface. In contrast, Au@Cu nanocubes contain both a misfit dislocation network and threading dislocations before compression, and exhibit pronounced strain hardening. Based on theoretical analysis and simulations, we conclude


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that the Au@Cu nanocubes yield by the motion of threading dislocations, and the strain hardening behavior is caused by the inability of the dislocations to penetrate the core, leading to an asymmetric Orowan loop-like mechanism. The mechanisms for dislocation-precipitate interactions presented here contribute to the design of strong and damage tolerant alloys and nanocomposites. The strength and deformation at single nano-precipitates in metallic nanocubes can be considered in the context of arrays of nano-precipitates in bulk alloys. For instance, the stochastic nature of dislocation activity at single nano-precipitates can provide information about the nonuniform rate of dislocation transmission within an array of nano-precipitates. Changes in the strength of an individual nano-precipitate with increasing strain can indicate the distribution of strengths within an ensemble of nano-precipitates during deformation. In addition, the mechanical behavior of the bimetallic core-shell nanocubes can be used to predict the properties of other nanostructures with complex microstructures, such as lithographed metals used in MEMS devices. The stability of misfit and threading dislocations is critical to the optical, electronic, and catalytic properties of metallic and semiconductor core-shell nanostructures (e.g. quantum dots, nanocrystals and


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nanowires), and must be understood in order to optimize the performance of these materials.

Supporting Information. The following files are available free of charge. -

Detailed methods with additional figures detailing experimental conditions as well as set up of MD/DDD simulations. (PDF)

-

Movie of MD simulation of Au@Ag nanocube compression (MPG)

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Movie of DDD simulation of Au@Cu nanocube compression (MPG)

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Movie of MD simulation of Au@Cu nanocube showing impenetrability of core (MPG)

AUTHOR INFORMATION

Corresponding Author *X. Wendy Gu 452 Escondido Mall, Room 227, Stanford University, Stanford, CA 94305


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[email protected] 510-295-8597

Author Contributions All authors helped to design the experiments. MTK synthesized nanoparticles, performed in situ SEM experiments, and acquired TEM images. YW performed MD simulations. NB performed DDD simulations. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Acknowledgement

XWG acknowledges financial support from Stanford start-up funds. MTK is supported by the National Defense and Science Engineering Graduate Fellowship. This work is partly supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412 (YF, NB and WC). Part of NB’s work was performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07NA27344. Part of this work was performed at the


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Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-1542152 with the assistance of Dr. Ann Marshall and Dr. Richard Chin.

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Strengthening Mechanism of a Single Precipitate in a Metallic Nanocube

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