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Several previous studies demonstrated that defect-free faceted nanocrystals of face-centered cubic metals (such as Au, Ni, and Pd) exhibit extraordinarily high mechanical strength approaching the theoretical strength of the respective metals. In the present work, we have studied the compressive strength of Pt nanoparticles fabricated by the solid-state dewetting method optimized for producing nanoparticles with a variety of shapes and sizes. The particles exhibit a well-pronounced size effect on strength, with the smallest particles achieving the highest compressive strength of 9.5 GPa corresponding to the lower limit of the theoretical strength of Pt. However, the average strength of the Pt particles normalized by the respective shear modulus is significantly lower than that of Au and Ni nanoparticles fabricated by a similar dewetting method. We have also established a correlation between the particles strength and shape described by the ratio of the particle top facet and projected diameters. Smaller values of this ratio correlate with higher compressive strength. Based on the experimental data obtained, we formulate a power law describing the combined effect of the particle size and shape on its strength. Our results are in qualitative agreement with previous computational studies demonstrating that the theoretical strength of Pt normalized by its shear modulus is significantly lower than that of other face-centered cubic metals.

The classic paradigm of physical metallurgy is that the addition of alloying elements to metals increases their strength. It is less known if the solution-hardening can occur in nano-scale objects, and it is totally unknown how alloying can impact the strength of defect-free faceted nanoparticles. Purely metallic defect-free nanoparticles exhibit an ultra-high strength approaching the theoretical limit. Tested in compression, they deform elastically until the nucleation of the first dislocation, after which they collapse into a pancake shape. Here, we show by experiments and atomistic simulations that the alloying of Ni nanoparticles with Co reduces their ultimate strength. This counter-intuitive solution-softening effect is explained by solute-induced local spatial variations of the resolved shear stress, causing premature dislocation nucleation. The subsequent particle deformation requires more work, making it tougher. The emerging compromise between strength and toughness makes alloy nanoparticles promising candidates for applications., This work explores the impact of alloying on mechanical properties of nanoparticles in Ni-Co binary system. Combined experiment and atomistic simulation show surprising solution-softening effect in nanoparticles that contradicts the traditional solution-hardening effect in bulk alloys.

Deformation-induced grain-growth in nanocrystalline materials is a widely-reported phenomenon that has been attributed to grain boundary (GB) processes. In this paper, we report on the opposite phenomenon, wherein a stable nanocrystalline (NC) Cu-Ta alloy undergoes a further refinement of the nano-grains during severe plastic deformation (SPD). SPD up to 250% results in a significant grain-size reduction despite the 350°C increase in temperature caused by the deformation process. Experiments and atomistic-simulations show that this unexpected grain-refinement is a direct result of well-dispersed Ta-nanoclusters throughout grain centers and along GBs acting as kinetic-pinning agents and suppressing GB processes that occur during recrystallization.

Nanocrystalline (NC) materials possess excellent room temperature properties, such as high strength, wear resistance, and toughness as compared to their coarse-grained counterparts. However, due to the excess free energy, NC microstructures are unstable at higher temperatures. Significant grain growth is observed already at moderately low temperatures, limiting the broader applicability of NC materials. Here, we present a design approach that leads to a significant improvement in the high temperature tensile creep resistance (up to 0.64 of the melting temperature) of a NC Cu-Ta alloy. The design approach involves alloying of pure elements to create a distribution of nanometer sized solute clusters within the grains and along the grain boundaries. We demonstrate that the addition of Ta nanoclusters inhibits the migration of grain boundaries at high temperatures and reduces the dislocation motion. This leads to a highly unusual tensile creep behavior, including the absence of any appreciable steady-state creep deformation normally observed in almost all materials. This design strategy can be readily scaled-up for bulk manufacturing of creep-resistant NC parts and transferred to other multicomponent systems such as Ni-based alloys.

Interaction of vacancies with grain boundaries (GBs) is involved in many processes occurring in materials, including radiation damage healing, diffusional creep, and solid-state sintering. We analyze a model describing a set of processes occurring at a GB in the presence of a non-equilibrium, non-homogeneous vacancy concentration. Such processes include vacancy diffusion toward, away from, and across the GB, vacancy generation and absorption at the GB, and GB migration. Numerical calculations within this model reveal that the coupling among the different processes gives rise to interesting phenomena, such as vacancy-driven GB motion and accelerated vacancy generation/absorption due to GB motion. The key combinations of the model parameters that control the kinetic regimes of the vacancy-GB interactions are identified via a linear stability analysis. Possible applications and extensions of the model are discussed.e's comments, Comment: 35 pages, 9 figures. Minor revisions per referee's comments. Published in Acta Materialia. Supplementary file containing additional figures is available from first author (mcfadden@nist.gov)

The potential benefits of nanocrystalline (NC) alloys for use in various structural applications stem from their enhanced mechanical strengths. However, deformation-induced grain growth in NC materials reduces the strength and is a widely reported phenomenon occurring even at low-temperatures. Controlling such behavior is critical for the maturation of bulk nanocrystalline metals in various advanced engineering applications. Here, we disclose the mechanism by which grain boundary sliding and rotation are suppressed when a NC material is truly thermo-mechanically stabilized against grain growth. Unlike in any other known nanocrystalline metals, the absence of sliding and rotation during loading, at extreme temperatures, is related to short-circuit solute diffusion along the grain boundaries causing the formation of solute clusters and thus a significant change of the grain boundary structures. The departure of this unusual behavior from the well-established norm leads to a strong enhancement of many mutually exclusive properties, such as thermo-mechanical strength, creep resistance, and exceptionally high electrical/thermal conductivity. This work demonstrates that Cu-based nanocrystalline alloys can be used in applications where conventional Cu-based polycrystalline materials are not viable.

Large-scale atomistic computer simulations of materials heavily rely on interatomic potentials predicting the energy and Newtonian forces on atoms. Traditional interatomic potentials are based on physical intuition but contain few adjustable parameters and are usually not accurate. The emerging machine-learning (ML) potentials achieve highly accurate interpolation within a large DFT database but, being purely mathematical constructions, suffer from poor transferability to unknown structures. We propose a new approach that can drastically improve the transferability of ML potentials by informing them of the physical nature of interatomic bonding. This is achieved by combining a rather general physics-based model (analytical bond-order potential) with a neural-network regression. This approach, called the physically informed neural network (PINN) potential, is demonstrated by developing a general-purpose PINN potential for Al. We suggest that the development of physics-based ML potentials is the most effective way forward in the field of atomistic simulations., Traditional machine learning potentials suffer from poor transferability to unknown structures. Here the authors present an approach to improve the transferability of machine-learning potentials by including information on the physical nature of interatomic bonding.

Previously published data, not ours, on the coarsening of solid \ensuremath{\beta}-Sn particles in a liquid Pb-Sn matrix of near-eutectic composition are reanalyzed within the framework of the trans-interface-diffusion-controlled (TIDC) theory of coarsening. The data were obtained under conditions of microgravity from specimens heat-treated at 458 K and containing four equilibrium volume fractions ${f}_{e}$ equaling 0.10, 0.15, 0.20, and 0.30. We show that the rate constants $k({f}_{e})$ in the traditional coarsening equation ${\ensuremath{\langle}r\ensuremath{\rangle}}^{3}\ensuremath{\approx}k({f}_{e})t$ for the kinetics of growth of the average particle radius $\ensuremath{\langle}r\ensuremath{\rangle}$ are nearly independent of ${f}_{e}$, in disagreement with numerous theories wherein coarsening is controlled by diffusion in the host matrix phase. Atom transport in TIDC coarsening is instead controlled by slow diffusion through the diffuse interface, of width \ensuremath{\delta}, separating the dispersed particles from the matrix; the kinetics of this process is independent of ${f}_{e}$. Atomistic simulations were performed to estimate the properties of the solid-liquid (S-L) interface at 458 K, 2 K above the Pb-Sn eutectic temperature. The S-L interfaces normal to (001) and (010) of tetragonal \ensuremath{\beta}-Sn were examined and found to have nearly identical properties, including interface widths of \ensuremath{\sim}1.7 nm. In conjunction with the diffusivities in solid \ensuremath{\beta}-Sn and liquid hypereutectic Pb-Sn at 458 K, we estimate that TIDC coarsening should prevail for solid Sn particles \ensuremath{\sim}1700 \ensuremath{\mu}m in radius, far exceeding the maximum radius of \ensuremath{\sim}100 \ensuremath{\mu}m measured experimentally. The TIDC theory also predicts that the kinetics of growth obeys the equation ${\ensuremath{\langle}r\ensuremath{\rangle}}^{n}\ensuremath{\propto}t$. The temporal exponent $n$ was evaluated to be \ensuremath{\sim}2.5, as ascertained by analyzing data on the particle size distributions (PSDs; histograms) for the alloys with ${f}_{e}=0.15$, 0.20, and 0.30. The histograms were converted to experimental cumulative distribution functions (ECDFs) and analyzed using the Kolmogorov-Smirnov (K-S) test applied to the theoretical CDFs predicted by the TIDC theory. We report the first successful application of the K-S test to experimental PSDs concomitant with particle coarsening. From every aspect of the experimental data amenable to analysis, we conclude that the coarsening behavior of solid Sn particles in liquid hypereutectic Pb-Sn alloys is fully consistent with the predictions of the TIDC theory of coarsening.

The classic paradigm of physical metallurgy is that the addition of alloying elements to metals increases their strength. It is less known if the solution-hardening can occur in nano-scale objects, and it is totally unknown how alloying can impact the strength of defect-free faceted nanoparticles. Purely metallic defect-free nanoparticles exhibit an ultra-high strength approaching the theoretical limit. Tested in compression, they deform elastically until the nucleation of the first dislocation, after which they collapse into a pancake shape. Here, we show by experiments and atomistic simulations that the alloying of Ni nanoparticles with Co reduces their ultimate strength. This counter-intuitive solution-softening effect is explained by solute-induced local spatial variations of the resolved shear stress, causing premature dislocation nucleation. At the same time, the subsequent deformation of the particle requires more work, making it tougher. The emerging compromise between strength and toughness can make alloy nanoparticles promising candidates for applications.

Large-scale atomistic simulations of materials heavily rely on interatomic potentials, which predict the system energy and atomic forces. One of the recent developments in the field is constructing interatomic potentials by machine-learning (ML) methods. ML potentials predict the energy and forces by numerical interpolation using a large reference database generated by quantum-mechanical calculations. While high accuracy of interpolation can be achieved, extrapolation to unknown atomic environments is unpredictable. The recently proposed physically-informed neural network (PINN) model significantly improves the transferability by combining a neural network regression with a physics-based bond-order interatomic potential. Here, we demonstrate that general-purpose PINN potentials can be developed for body-centered cubic (BCC) metals. The proposed PINN potential for tantalum reproduces the reference energies within 2.8 meV/atom. It accurately predicts a broad spectrum of physical properties of Ta, including (but not limited to) lattice dynamics, thermal expansion, energies of point and extended defects, the dislocation core structure and the Peierls barrier, the melting temperature, the structure of liquid Ta, and the liquid surface tension. The potential enables large-scale simulations of physical and mechanical behavior of Ta with nearly first-principles accuracy while being orders of magnitude faster. This approach can be readily extended to other BCC metals.

Large-scale atomistic computer simulations of materials rely on interatomic potentials providing computationally efficient predictions of energy and Newtonian forces. Traditional potentials have served in this capacity for over three decades. Recently, a new class of potentials has emerged, which is based on a radically different philosophy. The new potentials are constructed using machine-learning (ML) methods and a massive reference database generated by quantum-mechanical calculations. While the traditional potentials are derived from physical insights into the nature of chemical bonding, the ML potentials utilize a high-dimensional mathematical regression to interpolate between the reference energies. We review the current status of the interatomic potential field, comparing the strengths and weaknesses of the traditional and ML potentials. A third class of potentials is introduced, in which an ML model is coupled with a physics-based potential to improve the transferability to unknown atomic environments. The discussion is focused on potentials intended for materials science applications. Possible future directions in this field are outlined.

Interatomic potentials constitute the key component of large-scale atomistic simulations of materials. The recently proposed physically-informed neural network (PINN) method combines a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential applicable to both metals and nonmetals. In this paper, we present a modified version of the PINN method that accelerates the potential training process and further improves the transferability of PINN potentials to unknown atomic environments. As an application, a modified PINN potential for Al has been developed by training on a large database of electronic structure calculations. The potential reproduces the reference first-principles energies within 2.6 meV per atom and accurately predicts a wide spectrum of physical properties of Al. Such properties include, but are not limited to, lattice dynamics, thermal expansion, energies of point and extended defects, the melting temperature, the structure and dynamic properties of liquid Al, the surface tensions of the liquid surface and the solid-liquid interface, and the nucleation and growth of a grain boundary crack. Computational efficiency of PINN potentials is also discussed.

We show that molecular dynamics (MD) simulations are capable of reproducing the drag of solute segregation atmospheres by moving grain boundaries (GBs). Although lattice diffusion is frozen out on the MD timescale, the accelerated GB diffusion provides enough atomic mobility to allow the segregated atoms to follow the moving GB. This finding opens the possibility of studying the solute drag effect with atomic precision using the MD approach. We demonstrate that a moving GB activates diffusion and alters the short-range order in the lattice regions swept during its motion. It is also shown that a moving GB drags an atmosphere of non-equilibrium vacancies, which accelerate diffusion in surrounding lattice regions.

Nanocrystalline Cu-Ta alloys are emerging as a new class of structural materials preserving the nano-scale grain size up to the melting point of Cu. This extraordinary structural stability is caused by the strong pinning of grain boundaries (GBs) by Ta nano-clusters precipitating from the unstable solid solution after mechanical alloying. Many aspects of the Ta stabilization effect remain elusive and call for further experimental and simulation work. In previous atomistic computer simulations of stress-driven GB migration [JOM 68, 1596 (2016)], the GB–cluster interactions in Cu-Ta alloys have been studied for several different compositions and GB velocities. The results have pointed to the Zener pinning as the main mechanism responsible for the grain stabilization. This paper extends the previous work to the motion of individual GBs driven by capillary forces whose magnitude is similar to that in real nanocrystalline materials. Both the impingement of a moving GB on a set of Ta clusters and the GB unpinning from the clusters are studied as a function of temperature and alloy composition. The results demonstrate a quantitative agreement with the Zener pinning model and confirm the “unzip” mechanism of unpinning found in the previous work. In the random Cu-Ta solid solution, short-circuit Ta diffusion along stationary and moving GBs leads to the nucleation and growth of new GB clusters, which eventually stop the GB motion.

Direct experimental observations reveal that grain boundaries in aluminium oxide migrate by a chain of structural phase transformations within the boundary core.

Molecular dynamics (MD) simulations are applied to study solute drag by curvature-driven grain boundaries (GBs) in Cu–Ag solid solution. Although lattice diffusion is frozen on the MD timescale, the GB significantly accelerates the solute diffusion and alters the state of short-range order in lattice regions swept by its motion. The accelerated diffusion produces a nonuniform redistribution of the solute atoms in the form of GB clusters enhancing the solute drag by the Zener pinning mechanism. This finding points to an important role of lateral GB diffusion in the solute drag effect. A 1.5 at.%Ag alloying reduces the GB free energy by 10–20% while reducing the GB mobility coefficients by more than an order of magnitude. Given the greater impact of alloying on the GB mobility than on the capillary driving force, kinetic stabilization of nanomaterials against grain growth is likely to be more effective than thermodynamic stabilization aiming to reduce the GB free energy.

Nanocrystalline materials possess excellent room temperature properties, such as high strength, wear resistance, and toughness as compared to their coarse-grained counterparts. However, due to excess free energy, nanocrystalline microstructures are unstable at higher temperatures. Significant grain growth is observed already at moderately low temperatures, limiting their broader applicability. Here, we present a design approach that leads to a significant improvement in the high temperature tensile creep resistance (up to 0.64 of the melting temperature Tm) of a nanocrystalline Cu-Ta alloy. The design approach involves alloying of pure elements for engineering nanometer sized solute clusters within the solvent grains as well as along the grain boundaries. Using a chemically optimized nanocrystalline Cu-3at.%Ta alloy as a model material system, we demonstrate that the addition of Ta nanoclusters inhibits the migration of the planar defects at higher temperatures and reduces the dislocation motion, leading to extraordinary high temperature properties. For instance, the NC Cu-3Ta alloy tested under tensile creep conditions up to the temperature of 873 K (0.64Tm) displays highly unusual behavior, including the absence of any appreciable steady-state creep deformation which is normally observed in almost all materials. This approach can be readily scaled-up for bulk manufacturing of creep resistant nanocrystalline parts. Moreover, this design strategy can be transferred to other multicomponent systems such as Ni-based alloys for making nanocrystalline materials with tailored properties.

Mg grain boundary (GB) segregation and GB diffusion can impact the processing and properties of Al-Mg alloys. Yet, Mg GB diffusion in Al has not been measured experimentally or predicted by simulations. We apply atomistic computer simulations to predict the amount and the free energy of Mg GB segregation, and the impact of segregation on GB diffusion of both alloy components. At low temperatures, Mg atoms segregated to a tilt GB form clusters with highly anisotropic shapes. Mg diffuses in Al GBs slower than Al itself, and both components diffuse slowly in comparison with Al GB self-diffusion. Thus, Mg segregation significantly reduces the rate of mass transport along GBs in Al-Mg alloys. The reduced atomic mobility can be responsible for the improved stability of the microstructure at elevated temperatures.

While it is known that alloy components can segregate to grain boundaries (GBs), and that the atomic mobility in GBs greatly exceeds the atomic mobility in the lattice, little is known about the effect of GB segregation on GB diffusion. Atomistic computer simulations offer a means of gaining insights into the segregation-diffusion relationship by computing the GB diffusion coefficients of the alloy components as a function of their segregated amounts. In such simulations, thermodynamically equilibrium GB segregation is prepared by a semi-grand canonical Monte Carlo method, followed by calculation of the diffusion coefficients of all alloy components by molecular dynamics. As a demonstration, the proposed methodology is applied to a GB is the Cu-Ag system. The GB diffusivities obtained exhibit non-trivial composition dependencies that can be explained by site blocking, site competition, and the onset of GB disordering due to the premelting effect.

We perform a systematic study of thermal resistance and conductance of tilt grain boundaries (GBs) in Si using classical molecular dynamics. The GBs studied are naturally divided into three groups according to the structural units forming the GB core. We find that, within each group, the GB thermal conductivity strongly correlates with the excess GB energy. All three groups predict nearly the same GB conductivity extrapolated to the high-energy limit. This limiting value is close to the thermal conductivity of amorphous Si, suggesting similar heat transport mechanisms. While the lattice thermal conductivity decreases with temperature, the GB conductivity slightly increases. However, at high temperatures it turns over and starts decreasing if the GB structure undergoes a premelting transformation. Analysis of vibrational spectra of GBs resolved along different directions sheds light on the mechanisms of their thermal resistance. The existence of alternating tensile and compressive atomic environments in the GB core gives rise to localized vibrational modes, frequency gaps creating acoustic mismatch with lattice phonons, and anharmonic vibrations of loosely bound atoms residing in open atomic environments.

A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain boundary and the solute drag force, and permits a broad exploration of the parameter space and different dynamic regimes. The grain boundary phases continue to exist in the moving grain boundary and show a dynamic hysteresis loop, a dynamic critical line, and other features that are similar to those for equilibrium phases. Grain boundary motion strongly affects the relative stability of the phases and can even stabilize phases that are absolutely unstable under equilibrium conditions. Grain boundary phase transformations are accompanied by drastic changes in the boundary mobility. The results are analyzed in the context of non-equilibrium thermodynamics. Unresolved problems and future work are discussed.

Tetradymite-structured chalcogenides such as bismuth telluride (Bi2Te3) are of significant interest for thermoelectric energy conversion and as topological insulators. Dislocations play a critical role during synthesis and processing of such materials and can strongly affect their functional properties. The dislocations between quintuple layers present special interest since their core structure is controlled by the van der Waals interactions between the layers. In this work, using atomic-resolution electron microscopy, we resolve the basal dislocation core structure in Bi2Te3, quantifying the disregistry of the atomic planes across the core. We show that, despite the existence of a stable stacking fault in the basal plane gamma surface, the dislocation core spreading is mainly due to the weak bonding between the layers, which leads to a small energy penalty for layer sliding parallel to the van der Waals gap. Calculations within a semidiscrete variational Peierls-Nabarro model informed by first-principles calculations support our experimental findings., The atomic level core structure of dislocations in non-metallic materials such as chalcogenides remains elusive. Here, the authors combine atomic-resolution electron microscopy and simulations to image a dislocation core in bismuth telluride and show it spreads because of weak bonding between atomic layers.

Under intense heating and/or deformation, pure nanocrystalline (NC) metals exhibit significant grain coarsening, thus preventing the study of length scale effects on their physical response under such conditions. Hence, in this study, we use in-situ TEM heating experiments, atomistic modeling along with elevated temperature compression tests on a thermally stabilized nanostructured Cu–10 at.% Ta alloy to assess the microstructural manifestations caused by changes in temperature. Results reveal the thermal stability attained in NC Cu-10 at.% Ta diverges from those observed for conventional coarse-grained metals and other NC metals. Macroscopically, the microstructure, such as Cu grain and Ta based cluster size resists evolving with temperature. However, local structural changes at the interface between the Ta based clusters and the Cu matrix have a profound effect on thermo-mechanical properties. The lattice misfit between the Ta clusters and the matrix tends to decrease at high temperatures, promoting better coherency. In other words, the misfit strain was found to decrease monotonically from 12.9% to 4.0% with increase in temperature, leading to a significant change in flow stress, despite which (strength) remains greater than all known NC metals. Overall, the evolution of such fine structures is critical for developing NC alloys with exceptional thermo-mechanical properties. Keywords: In situ TEM, Nanocrystalline, Atomistic, Misfit strain

We review the recent progress in theoretical understanding and atomistic computer simulations of phase transformations in materials interfaces, focusing on grain boundaries (GBs) in metallic systems. Recently developed simulation approaches enable the search and structural characterization of GB phases in single-component metals and binary alloys, calculation of thermodynamic properties of individual GB phases, and modeling of the effect of the GB phase transformations on GB kinetics. Atomistic simulations demonstrate that the GB transformations can be induced by varying the temperature, loading the GB with point defects, or varying the amount of solute segregation. The atomic-level understanding obtained from such simulations can provide input for further development of thermodynamics theories and continuous models of interface phase transformations while simultaneously serving as a testing ground for validation of theories and models. They can also help interpret and guide experimental work in this field.

Solute atoms can segregate to elastically deformed lattice regions around a dislocation and form an equilibrium distribution called the Cottrell atmosphere. We compare two approaches to describe Cottrell atmospheres. In the Eshelby theory, the solid solution is represented by a composite material obtained by insertion of misfitting elastic spheres (solute atoms) into an elastic matrix (solvent). The theory proposed by Larche and Cahn (LC) treats the solution as an elastic continuum and describes elasto-chemical equilibrium using the concept of open-system elastic coefficients. The two theories are based on significantly different concepts and diverge in some of their predictions, particularly regarding the existence of screening of dislocation stress fields by atmospheres. To evaluate predictive capabilities of the two theories, we perform atomistic computer simulations of Al segregation on a dislocation in Ni. The results confirm the existence of hydrostatic stress screening in good agreement with the LC theory. The composition field is also in much better agreement with the LC prediction than with the Eshelby theory. However, the simulations confirm the logarithmic divergence of the total amount of solute segregation as expected from the Eshelby theory, whereas the LC theory predicts the total segregation to be zero. Several other aspects of the two theories are analyzed. Possible non-linear extensions of the LC theory are outlined.

Immiscible Cu-Ta alloys produced by mechanical alloying are currently the subject of intensive research due to their mechanical strength combined with extraordinary structural stability at high temperatures. Previous experimental and simulation studies suggested that grain boundaries (GBs) in Cu-Ta alloys are stabilized by Ta nano-clusters coherent with the Cu matrix. To better understand the stabilization effect of Ta, we performed atomistic computer simulations of GB–cluster interactions in Cu-Ta alloys with various compositions and GB velocities. The study focuses on a single plane GB driven by an applied shear stress due to the shear-coupling effect. The results of the simulations are in close quantitative agreement with the Zener model of GB pinning. This agreement and the large magnitude of the unpinning stress confirm that the structural stability of these alloys is due to the drastically decreased GB mobility rather than a reduction in GB energy. For comparison, we simulated GB motion in a random solid solution. While the latter also reduces the GB mobility, the effect is not as strong as in the presence of Ta clusters. GB motion in the random solution itself induces precipitation of Ta clusters due to short-circuit diffusion of Ta in GBs, suggesting a possible mechanism of cluster formation inside the grains.

This paper presents an overview of recent computer simulations of grain boundary (GB)diffusion focusing on atomistic understanding of diffusion mechanisms. At low temperatures when GBstructure is ordered, diffusion is mediated by point defects inducing collective jumps of several atomsforming a chain. At high temperatures when GB structure becomes highly disordered, the diffusionprocess can be analyzed by statistical methods developed earlier for supercooled liquids and glasses.Previous atomistic simulations reported in the literature as well as the new simulations presented in thispaper reveal a close similarity between diffusion mechanisms in GBs and in supercooled liquids. GBdiffusion at high temperatures is dominated by collective displacements of atomic groups (clusters),many of which have one-dimensional geometries similar to strings. The recent progress in this fieldmotivates future extensions of atomistic simulations to diffusion in alloy GBs, particularly in glassformingsystems.

Material objects with micrometer or nanometer dimensions can exhibit much higher strength than macroscopic objects, but this strength rarely approaches the maximum theoretical strength of the material. Here, we demonstrate that faceted single-crystalline nickel (Ni) nanoparticles exhibit an ultrahigh compressive strength (up to 34 GPa) unprecedented for metallic materials. This strength matches the available estimates of Ni theoretical strength. Three factors are responsible for this record-high strength: the large Ni shear modulus, the smooth edges and corners of the nanoparticles, and the thin oxide layer on the particle surface. This finding is supported by molecular dynamics simulations that closely mimic the experimental conditions, which show that the mechanical failure of the strongest particles is triggered by homogeneous nucleation of dislocation loops inside the particle. The nucleation of a stable loop is preceded by multiple nucleation attempts accompanied by unusually large local atomic displacements caused by thermal fluctuations., While metallic nanosized objects are stronger than their macroscopic counterparts, they rarely reach the metal’s maximum theoretical strength. Here, the authors produce faceted nickel nanoparticles and show that their strength under compression matches the theoretically predicted strength in the literature.

Atomistic computer simulations are capable of providing insights into physical mechanisms responsible for the extraordinary structural stability and strength of immiscible Cu–Ta alloys. To enable reliable simulations of these alloys, we have developed an angular-dependent potential (ADP) for the Cu–Ta system by fitting to a large database of first-principles and experimental data. This, in turn, required the development of a new ADP potential for elemental Ta, which accurately reproduces a wide range of properties of Ta and is transferable to severely deformed states and diverse atomic environments. The new Cu–Ta potential is applied for studying the kinetics of grain growth in nano-crystalline Cu–Ta alloys with different chemical compositions. Ta atoms form nanometer-scale clusters preferentially located at grain boundaries (GBs) and triple junctions. These clusters pin some of the GBs in place and cause a drastic decrease in grain growth by the Zener pinning mechanism. The results of the simulations are well consistent with experimental observations and suggest possible mechanisms of the stabilization effect of Ta.

The immiscible Cu-Ta system has garnered recent interest due to observations of high strength and thermal stability attributed to the formation of Ta-enriched particles. This work investigated a metastable Cu-1 at.% Ta solid solution produced via mechanical alloying followed by subsequent consolidation into a bulk specimen using equal channel angular extrusion at 973 K (700°C). Microstructural characterization revealed a decreased number density of Ta clusters, but with an equivalent particle size compared to a previously studied Cu-10 at.% Ta alloy. Molecular dynamic stimulations were performed to understand the thermal evolution of the Ta clusters. The cluster size distributions generated from the simulations were in good agreement with the experimental microstructure.

The concept of utilizing ferromagnetic shape memory alloys as embedded sensory particles in aluminum alloys for damage detection is discussed. When embedded in a material, a shape memory particle can undergo an acoustically detectable solid-state phase transformation when the local strain reaches a critical value. The emitted acoustic signal can be used for real-time damage detection. To study the transition behavior of the sensory particle inside a metal matrix under load, a simulation approach based on a coupled atomistic-continuum model is used. The simulation results indicate a strong dependence of the particle’s pseudoelastic response on its crystallographic orientation with respect to the loading direction. These results serve as a basis for understanding the efficacy and variability in the sensory particle transformation to detect damage processes.

The formation of a metastable Cu–Ta solid solution in a mechanically alloyed Cu–10 at.%Ta alloy and its subsequent decomposition during annealing was investigated by atom probe tomography. During annealing, the as-milled Cu-rich alloy undergoes phase separation; Ta atoms diffuse out of the Cu lattice to form Ta clusters and particles along grain boundaries and within the Cu grains. The role of the Ta clusters and the nature of the solid solution as a potential strengthening mechanism for these alloys are discussed.

We report on molecular dynamics (MD) simulations of a tricrystal composed of a cylindrical grain embedded at the center of a plane grain boundary (GB). The embedded grain shrinks by capillary forces and eventually vanishes. This process is often accompanied by rotation of the embedded grain in either a clockwise or counter-clockwise direction. Using the geometric theory of coupling between GB motion and grain translations, we propose a model capable of predicting the direction of the grain rotation depending on the crystallographic parameters of the three grains. Full agreement has been found between the model predictions and the MD simulation results for both spontaneous grain shrinkage and in the presence of applied shear stresses. The consequences of these results for grain rotation in polycrystalline materials and possible extensions of the model to multiple grains are discussed.

Nanocrystalline Cu–Ta alloys belong to an emerging class of immiscible materials with potential for high-temperature applications. Differential scanning calorimetry (DSC), Vickers microhardness, transmission and scanning electron microscopy (TEM/SEM), and atomistic simulations have been applied to study the structural evolution in high-energy cryogenically alloyed nanocrystalline Cu–10 at.%Ta. The thermally induced coarsening of the as-milled microstructure was investigated and it was found that the onset of grain growth occurs at temperatures higher than that for pure nanocrystalline Cu. The total heat release associated with grain growth was 0.553 kJ/mol. Interestingly, nanocrystalline Cu–10 at.%Ta maintains a mean grain size (GS) of 167 nm after annealing at 97% of its melting point. The increased microstructural stability is attributed to a combination of thermodynamic and kinetic stabilization effects which, in turn, appear to be controlled by segregation and diffusion of Ta solute atoms along grain boundaries (GBs). The as-milled nanocrystalline Cu–10 at.%Ta exhibits Vickers microhardness values near 5 GPa surpassing the microhardness of conventional pure nanocrystalline Cu by ∼2.5 GPa.

An optimized interatomic potential has been constructed for silicon using a modified Tersoff model. The potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature and other properties. The proposed potential is compared with three other potentials from the literature. The potentials demonstrate reasonable agreement with first-principles binding energies of small Si clusters as well as single-layer and bilayer silicenes. The four potentials are used to evaluate the thermal stability of free-standing silicenes in the form of nano-ribbons, nano-flakes and nano-tubes. While single-layer silicene is mechanically stable at zero Kelvin, it is predicted to become unstable and collapse at room temperature. By contrast, the bilayer silicene demonstrates a larger bending rigidity and remains stable at and even above room temperature. The results suggest that bilayer silicene might exist in a free-standing form at ambient conditions., Comment: Submitted for publication in the Physical Review B

We derive analytical solutions for the autocorrelation and cross-correlation functions of the kinetic, potential, and total energy of a Langevin oscillator. These functions are presented in both the time and frequency domains and validated by independent numerical simulations. The results are applied to address the long-standing issue of temperature fluctuations in canonical systems.

Molecular dynamics simulations of a quasi-harmonic solid are conducted to elucidate the meaning of temperature fluctuations in canonical systems and validate a well-known but frequently contested equation predicting the mean square of such fluctuations. The simulations implement two virtual and one physical (natural) thermostat and examine the kinetic, potential and total energy correlation functions in the time and frequency domains. The results clearly demonstrate the existence of quasi-equilibrium states in which the system can be characterized by a well-defined temperature that follows the mentioned fluctuation equation. The emergence of such states is due to the wide separation of timescales between thermal relaxation by phonon scattering and slow energy exchanges with the thermostat. The quasi-equilibrium states exist between these two timescales when the system behaves as virtually isolated and equilibrium., Comment: Accepted for publication in the Physical Review B

Many grain boundaries (GBs) in crystalline materials develop highly disordered, liquidlike structures at high temperatures. In alloys, this premelting effect can be fueled by solute segregation and can occur at lower temperatures than in single-component systems. A premelted GB can be modeled by a thin liquid layer located between two solid-liquid interfaces interacting by a disjoining potential. We propose a single analytical form of the disjoining potential describing repulsive, attractive, and intermediate interactions. The potential predicts a variety of premelting scenarios, including thin-to-thick phase transitions. The potential is verified by atomistic computer simulations of premelting in three different GBs in Cu-Ag alloys employing a Monte Carlo technique with an embedded atom potential. The disjoining potential has been extracted from the simulations by analyzing GB width fluctuations. The simulations confirm all shapes of the disjoining potential predicted by the analytical model. One of the GBs was found to switch back and forth between two (thin and thick) states, confirming the existence of thin-to-thick phase transformations in this system. The proposed disjoining potential also predicts the possibility of a cascade of thin-to-thick transitions caused by compositional oscillations (patterning) near solid-liquid interfaces.

Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling effect has been well confirmed for symmetrical tilt GBs, little is known about the coupling ability of asymmetrical boundaries. In this work we apply a combination of molecular dynamics and phase field crystal simulations to investigate stress-driven motion of asymmetrical GBs between cubic crystals over the entire range of inclination angles. Our main findings are that the coupling effect exists for most of the asymmetrical GBs and that the coupling factor exhibits a non-trivial dependence on both the misorientation and inclination angles. This dependence is characterized by a discontinuous change of sign of the coupling factor, which reflects a transition between two different coupling modes over a narrow range of angles. Importantly, the magnitude of the coupling factor becomes large or divergent within this transition region, thereby giving rise to a sliding-like behavior. Our results are interpreted in terms of a diagram presenting the domains of existence of the two coupling modes and the transition region between them in the plane of misorientation and inclination angles. The simulations reveal some of the dislocation mechanisms responsible for the motion of asymmetrical tilt GBs. The results of this study compare favorably with existing experimental measurements and provide a theoretical ground for the design of future experiments.

We report on molecular dynamics simulations of an isolated cylindrical grain in copper shrinking under capillary forces. At low temperatures, the coupling between grain boundary (GB) migration and grain translation induces rotation of the grain towards higher or lower misorientation angles, depending on the initial misorientation. The dynamics of the GB motion and grain rotation are studied as functions of the initial misorientation angle and temperature. The effects of imposed constraints blocking the grain rotation or exerting a cyclic torque are examined. The simulation results verify several predictions of the model proposed by Cahn and Taylor [Acta Mater 52, 4887 (2004)]. They also indicate that the GB motion is never perfectly coupled but instead involves at least some amount of sliding. This, in turn, requires continual changes (annihilation or nucleation) in the GB dislocation content. Dislocation mechanisms that can be responsible for the motion of curved GBs and dislocation annihilation in them are proposed.

Nanocrystalline Cu–Ta alloys belong to an emerging class of immiscible high-strength materials with a significant potential for high-temperature applications. Using molecular dynamics simulations with an angular-dependent interatomic potential, we study the effect of Ta on the resistance to grain growth and mechanical strength of nanocrystalline Cu–6.5 at.% Ta alloys. Ta segregation at grain boundaries greatly increases structural stability and strength in comparison with pure copper and alloys with a uniform distribution of the same amount of Ta. At high temperatures, the segregated Ta atoms agglomerate and form a set of nanoclusters located at grain boundaries. These nanoclusters are capable of pinning grain boundaries and effectively preventing grain growth. It is suggested that the nanoclusters are precursors to the formation of larger Ta particles found in Cu–Ta alloys experimentally.

A new interatomic potential has been developed for the Ni-Cr system in the angular-dependent potential (ADP) format by fitting the potential parameters to a set of experimental and first-principles data. The ADP potential reproduces a wide range of properties of both elements as well as binary alloys with reasonable accuracy, including thermal and mechanical properties, defects, melting points of Ni and Cr, and the Ni-Cr phase diagram. The potential can be used for atomistic simulations of solidification, mechanical behavior and microstructure of the Ni-based and Cr-based phases as well as two-phase alloys.

A model of hydride formation and dissolution has been proposed for a single spherical particle and for a collection of such particles with a given size distribution. The phase transformation strain gives rise to an elastic barrier to the transformation, which scales with the volume of the particle and produces a hysteresis effect known experimentally. Experimentally observed finite slopes of hydrogen pressure vs. chemical composition plots (instead of expected plateaus) are explained by the model for both the hydrogenization and dehydrogenization processes. These finite slopes and the amount of the pressure hysteresis depend on elastic properties of the hydride and metal phases, the transformation strain, and on the particle-size distribution in the powder.