Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations.

Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ([Formula: see text]), He atoms ([Formula: see text]), and temperature (T). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of [Formula: see text] vacancies and [Formula: see text] helium atoms, the [Formula: see text] ratio that causes the event, the resulting increase in [Formula: see text], and the associated shift of the bubble depth are formulated as a function of [Formula: see text] and T. In the bursting model, a bubble must simultaneously reach a certain depth and [Formula: see text] ratio in order to burst. The burst depth and [Formula: see text] are also modeled as a function of [Formula: see text] and T. The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.

Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten.

We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2⟨111⟩ shear loops, followed by gliding and growth of these loops and reactions to form ⟨100⟩ dislocations. Furthermore, dislocation gliding on the ⟨111⟩{211} twin systems nucleates 1/6⟨111⟩ twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.

Effect of helium flux on near-surface helium accumulation in plasma-exposed tungsten.

We report results of object kinetic Monte Carlo (OKMC) simulations to understand the effect of helium flux on the near-surface helium accumulation in plasma-facing tungsten, which is initially pristine, defect-free, and has a (100) surface orientation. These OKMC simulations are performed at 933 K for fluxes ranging from 1022to 4 × 1025He/m2 s with 100 eV helium atoms impinging on a (100) surface up to a maximum fluence of 4 × 1019He/m2. In the near-surface region, helium clusters interact elastically with the free surface. The interaction is attractive and results in the drift of mobile helium clusters towards the surface as well as increased trap mutation rates. The associated kinetics and energetics of the above-mentioned processes obtained from molecular dynamics simulations are also considered. The OKMC simulations indicate that in pristine tungsten, as the flux decreases, the retention of implanted helium decreases, and its depth distribution shifts to deeper below the surface. Furthermore, the fraction of retained helium diffusing into the bulk increases as well, so much so that for the flux of 1022He/m2 s, almost all of the retained helium diffused into the bulk with minimal/negligible near-surface helium accumulation. At a given flux, with increasing fluence, the fraction of retained helium initially decreases and then starts to increase after reaching a minimum. The occurrence of the retention minimum shifts to higher fluences as the flux decreases. Although the near-surface helium accumulation spreads deeper into the material with decreasing flux and increasing fluence, the spread appears to saturate at depths between 80 and 100 nm. We present a detailed analysis of the influence of helium flux on the size and depth distribution of total helium and helium bubbles.

Elastic Properties of Plasma-Exposed Tungsten Predicted by Molecular-Dynamics Simulations.

We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma-facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in the development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth significantly affects both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-property database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.

Theoretical Model of Helium Bubble Growth and Density in Plasma-Facing Metals.

We present a theoretically-motivated model of helium bubble density as a function of volume for high-pressure helium bubbles in plasma-facing tungsten. The model is a good match to the empirical correlation we published previously [Hammond et al., Acta Mater. 144, 561-578 (2018)] for small bubbles, but the current model uses no adjustable parameters. The model is likely applicable to significantly larger bubbles than the ones examined here, and its assumptions can be extended trivially to other metals and gases. We expect the model to be broadly applicable and useful in coarse-grained models of gas transport in metals.

Formation and Mechanical Behavior of Nanocomposite Superstructures from Interlayer Bonding in Twisted Bilayer Graphene.

We report a comprehensive study on the design of two-dimensional graphene-diamond nanocomposite superstructures formed through interlayer covalent bonding of twisted bilayer graphene with commensurate bilayers. The interlayer bonding is induced by patterned hydrogenation that leads to the formation of superlattices of two-dimensional nanodiamond domains embedded between the two graphene layers. We generalize a rigorous algorithm for the formation of all possible classes of these superstructures: the structural parameters employed to design such carbon nanocomposites include the commensurate bilayer's twist angle, the stacking type of the nanodomains where the interlayer bonds are formed, the interlayer bond pattern, and the interlayer C-C bond density that is proportional to the concentration of sp3-hybridized interlayer-bonded C atoms. We also analyze systematically the mechanical behavior of these nanocomposite superstructures on the basis of molecular-dynamics simulations of uniaxial tensile straining tests according to a reliable interatomic bond-order potential. We identify a range of structural parameters over which the fracture of these superstructures is ductile, mediated by void formation, growth, and coalescence, contrary to the typical brittle fracture of graphene. We introduce a ductility metric as an order parameter for the brittle-to-ductile transition, demonstrate its direct dependence on the fraction of sp3-hybridized interlayer-bonded C atoms, and show that increasing the fraction of interlayer-bonded C atoms beyond a critical level in certain classes of these superstructures induces their ductile mechanical response.

Multiscale Shear-Lag Analysis of Stiffness Enhancement in Polymer-Graphene Nanocomposites.

Graphene and other two-dimensional (2D) materials are of emerging interest as functional fillers in polymer-matrix composites. In this study, we present a multiscale atomistic-to-continuum approach for modeling interfacial stress transfer in graphene-high-density polyethylene (HDPE) nanocomposites. Via detailed characterization of atomic-level stress profiles in submicron graphene fillers, we develop a modified shear-lag model for short fillers. A key feature of our approach lies in the correct accounting of stress concentration at the ends of fillers that exhibits a power-law dependence on filler ("flaw") size, determined explicitly from atomistic simulations, without any ad hoc modeling assumptions. In addition to two parameters that quantify the end stress concentration, only one additional shear-lag parameter is required to quantify the atomic-level stress profiles in graphene fillers. This three-parameter model is found to be reliable for fillers with dimensions as small as ∼10 nm. Our model predicts accurately the elastic response of aligned graphene-HDPE composites and provides appropriate upper bounds for the elastic moduli of nanocomposites with more realistic randomly distributed and oriented fillers. This study provides a systematic approach for developing hierarchical multiscale models of 2D material-based nanocomposites and is of particular relevance for short fillers, which are, currently, typical of solution-processed 2D materials.

A Comparison of the Elastic Properties of Graphene- and Fullerene-Reinforced Polymer Composites: The Role of Filler Morphology and Size.

Nanoscale carbon-based fillers are known to significantly alter the mechanical and electrical properties of polymers even at relatively low loadings. We report results from extensive molecular-dynamics simulations of mechanical testing of model polymer (high-density polyethylene) nanocomposites reinforced by nanocarbon fillers consisting of graphene flakes and fullerenes. By systematically varying filler concentration, morphology, and size, we identify clear trends in composite stiffness with reinforcement. To within statistical error, spherical fullerenes provide a nearly size-independent level of reinforcement. In contrast, two-dimensional graphene flakes induce a strongly size-dependent response: we find that flakes with radii in the 2-4 nm range provide appreciable enhancement in stiffness, which scales linearly with flake radius. Thus, with flakes approaching typical experimental sizes (~0.1-1 µm), we expect graphene fillers to provide substantial reinforcement, which also is much greater than what could be achieved with fullerene fillers. We identify the atomic-scale features responsible for this size- and morphology-dependent response, notably, ordering and densification of polymer chains at the filler-matrix interface, thereby providing insights into avenues for further control and enhancement of the mechanical properties of polymer nanocomposites.

Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses.

Binary polymer nanoparticle glasses provide opportunities to realize the facile assembly of disparate components, with control over nanoscale and mesoscale domains, for the development of functional materials. This work demonstrates that tunable electrical percolation can be achieved through semiconducting/insulating polymer nanoparticle glasses by varying the relative percentages of equal-sized nanoparticle constituents of the binary assembly. Using time-of-flight charge carrier mobility measurements and conducting atomic force microscopy, we show that these systems exhibit power law scaling percolation behavior with percolation thresholds of ∼24-30%. We develop a simple resistor network model, which can reproduce the experimental data, and can be used to predict percolation trends in binary polymer nanoparticle glasses. Finally, we analyze the cluster statistics of simulated binary nanoparticle glasses, and characterize them according to their predominant local motifs as (p(i), p(1-i))-connected networks that can be used as a supramolecular toolbox for rational material design based on polymer nanoparticles.

Helium segregation on surfaces of plasma-exposed tungsten.

We report a hierarchical multi-scale modeling study of implanted helium segregation on surfaces of tungsten, considered as a plasma facing component in nuclear fusion reactors. We employ a hierarchy of atomic-scale simulations based on a reliable interatomic interaction potential, including molecular-statics simulations to understand the origin of helium surface segregation, targeted molecular-dynamics (MD) simulations of near-surface cluster reactions, and large-scale MD simulations of implanted helium evolution in plasma-exposed tungsten. We find that small, mobile He n (1⩽ n ⩽ 7) clusters in the near-surface region are attracted to the surface due to an elastic interaction force that provides the thermodynamic driving force for surface segregation. This elastic interaction force induces drift fluxes of these mobile He n clusters, which increase substantially as the migrating clusters approach the surface, facilitating helium segregation on the surface. Moreover, the clusters' drift toward the surface enables cluster reactions, most importantly trap mutation, in the near-surface region at rates much higher than in the bulk material. These near-surface cluster dynamics have significant effects on the surface morphology, near-surface defect structures, and the amount of helium retained in the material upon plasma exposure. We integrate the findings of such atomic-scale simulations into a properly parameterized and validated spatially dependent, continuum-scale reaction-diffusion cluster dynamics model, capable of predicting implanted helium evolution, surface segregation, and its near-surface effects in tungsten. This cluster-dynamics model sets the stage for development of fully atomistically informed coarse-grained models for computationally efficient simulation predictions of helium surface segregation, as well as helium retention and surface morphological evolution, toward optimal design of plasma facing components.

Equilibrium Shape of Colloidal Crystals.

Assembling colloidal particles into highly ordered configurations, such as photonic crystals, has significant potential for enabling a broad range of new technologies. Facilitating the nucleation of colloidal crystals and developing successful crystal growth strategies require a fundamental understanding of the equilibrium structure and morphology of small colloidal assemblies. Here, we report the results of a novel computational approach to determine the equilibrium shape of assemblies of colloidal particles that interact via an experimentally validated pair potential. While the well-known Wulff construction can accurately capture the equilibrium shape of large colloidal assemblies, containing O(10(4)) or more particles, determining the equilibrium shape of small colloidal assemblies of O(10) particles requires a generalized Wulff construction technique which we have developed for a proper description of equilibrium structure and morphology of small crystals. We identify and characterize fully several "magic" clusters which are significantly more stable than other similarly sized clusters.

Phase behavior of the 38-atom Lennard-Jones cluster.

We have developed a coarse-grained description of the phase behavior of the isolated 38-atom Lennard-Jones cluster (LJ38). The model captures both the solid-solid polymorphic transitions at low temperatures and the complex cluster breakup and melting transitions at higher temperatures. For this coarse model development, we employ the manifold learning technique of diffusion mapping. The outcome of the diffusion mapping analysis over a broad temperature range indicates that two order parameters are sufficient to describe the cluster's phase behavior; we have chosen two such appropriate order parameters that are metrics of condensation and overall crystallinity. In this well-justified coarse-variable space, we calculate the cluster's free energy landscape (FEL) as a function of temperature, employing Monte Carlo umbrella sampling. These FELs are used to quantify the phase behavior and onsets of phase transitions of the LJ38 cluster.

Colloidal cluster crystallization dynamics.

The crystallization dynamics of a colloidal cluster is modeled using a low-dimensional Smoluchowski equation. Diffusion mapping shows that two order parameters are required to describe the dynamics. Using order parameters as metrics for condensation and crystallinity, free energy, and diffusivity landscapes are extracted from brownian dynamics simulations using bayesian inference. Free energy landscapes are validated against Monte Carlo simulations, and mean first-passage times are validated against dynamic simulations. The resulting model enables a low-dimensional description of colloidal crystallization dynamics.

Equilibrium compositional distribution in freestanding ternary semiconductor quantum dots: the case of In(x)Ga(1-x)As.

We report the findings of a systematic computational study that addresses the effects of surface segregation on the atomic distribution at equilibrium of constituent group-III atoms in freestanding ternary semiconductor In(x)Ga(1-x)As nanocrystals. Our analysis is based on density functional theory calculations in conjunction with Monte Carlo simulations of the freestanding nanocrystals using a DFT-re-parameterized valence force field description of interatomic interactions. We have determined the equilibrium concentration profiles as a function of nanocrystal size (d), composition (x), and temperature (T). The ranges of d, x, and T are explored and demonstrate surface segregation and phase separation that leads to different extents of alloying in the nanocrystal core and in the near-surface regions. We find that formation of core/shell-like quantum dots characterized by an In-deficient core and an In-rich shell with a diffuse interface is favored at equilibrium. The analysis elucidates the relationship between the constituent species distribution in the nanocrystal and the parameters that can be tuned experimentally to design synthesis routes for tailoring the properties of ternary quantum dots.

A Smoluchowski model of crystallization dynamics of small colloidal clusters.

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

Fokker-Planck analysis of separation dependent potentials and diffusion coefficients in simulated microscopy experiments.

Total internal reflection microscopy (TIRM) and video microscopy (VM) are methods for nonintrusively measuring weak colloidal interactions important to many existing and emerging applications. Existing analyses of TIRM measured single particle trajectories can be used to extract particle-surface potentials and average particle diffusion coefficients. Here we develop a Fokker-Planck (FP) formalism to simultaneously extract both particle-surface interaction potentials and position dependent diffusion coefficients. The FP analysis offers several advantages including capabilities to measure separation dependent hydrodynamic interactions and nonequilibrium states that are not possible with existing analyses. The FP analysis is implemented to analyze Brownian dynamic simulations of single particle TIRM and VM experiments in several configurations. Relative effects of spatial and temporal sampling on the correct interpretation of both conservative and dissipative forces are explored and show a broad range of applicability for accessible experimental systems. Our results demonstrate the ability to extract both static and dynamic information from microscopy measurements of isolated particles near surfaces, which provides a foundation for further investigation of particle ensembles and nonequilibrium systems.

Kinetic Monte Carlo simulations of surface growth during plasma deposition of silicon thin films.

Based on an atomically detailed surface growth model, we have performed kinetic Monte Carlo (KMC) simulations to determine the surface chemical composition of plasma deposited hydrogenated amorphous silicon (a-Si:H) thin films as a function of substrate temperature. Our surface growth kinetic model consists of a combination of various surface rate processes, including silyl (SiH(3)) radical chemisorption onto surface dangling bonds or insertion into Si-Si surface bonds, SiH(3) physisorption, SiH(3) surface diffusion, abstraction of surface H by SiH(3) radicals, surface hydride dissociation reactions, as well as desorption of SiH(3), SiH(4), and Si(2)H(6) species into the gas phase. Transition rates for the adsorption, surface reaction and diffusion, and desorption processes accounted for in the KMC simulations are based on first-principles density-functional-theory computations of the corresponding optimal pathways on the H-terminated Si(001)-(2x1) surface. Results are reported for two types of KMC simulations. The first employs a fully ab initio database of activation energy barriers for the surface rate processes involved and is appropriate for modeling the early stages of growth. The second uses approximate rates for all the relevant processes to account properly for the effects on the activation energetics of interactions between species adsorbed at neighboring surface sites and is appropriate to model later stages of growth toward a steady state of the surface composition. The KMC predictions for the temperature dependence of the surface concentration of SiH(x(s)) (x = 1,2,3) species, the surface hydrogen content, and the surface dangling-bond coverage are compared to experimental measurements on a-Si:H films deposited under operating conditions for which the SiH(3) radical is the dominant deposition precursor. The predictions of both KMC simulation types are consistent with the reported experimental data, which are based on in situ attenuated total reflection Fourier transformed infrared spectroscopy.

Coarse molecular-dynamics analysis of an order-to-disorder transformation of a krypton monolayer on graphite.

The thermally induced order-to-disorder transition of a monolayer of krypton (Kr) atoms adsorbed on a graphite surface is studied based on a coarse molecular-dynamics (CMD) approach for the bracketing and location of the transition onset. A planar order parameter is identified as a coarse variable, psi, that can describe the macroscopic state of the system. Implementation of the CMD method enables the construction of the underlying effective free-energy landscapes from which the transition temperature, T(t), is predicted. The CMD prediction of T(t) is validated by comparison with predictions based on conventional molecular-dynamics (MD) techniques. The conventional MD computations include the temperature dependence of the planar order parameter, the specific heat, the Kr-Kr pair correlation function, the mean square displacement and corresponding diffusion coefficient, as well as the equilibrium probability distribution function of Kr-atom coordinates. Our findings suggest that the thermally induced order-to-disorder transition at the conditions examined in this study appears to be continuous. The CMD implementation provides substantial computational gains over conventional MD.

Current-induced stabilization of surface morphology in stressed solids.

We examine the surface morphological evolution of a conducting crystalline solid under the simultaneous action of an electric field and mechanical stress based on a fully nonlinear model and combining linear stability theory with self-consistent dynamical simulations. We demonstrate that electric current, through surface electromigration, can stabilize the surface morphology of the stressed solid against cracklike surface instabilities. The results also have more general implications for the morphological response of solid surfaces under the simultaneous action of multiple external forces.

Mechanisms and energetics of hydride dissociation reactions on surfaces of plasma-deposited silicon thin films.

We report results from a detailed analysis of the fundamental silicon hydride dissociation processes on silicon surfaces and discuss their implications for the surface chemical composition of plasma-deposited hydrogenated amorphous silicon (a-Si:H) thin films. The analysis is based on a synergistic combination of first-principles density functional theory (DFT) calculations of hydride dissociation on the hydrogen-terminated Si(001)-(2x1) surface and molecular-dynamics (MD) simulations of adsorbed SiH(3) radical precursor dissociation on surfaces of MD-grown a-Si:H films. Our DFT calculations reveal that, in the presence of fivefold coordinated surface Si atoms, surface trihydride species dissociate sequentially to form surface dihydrides and surface monohydrides via thermally activated pathways with reaction barriers of 0.40-0.55 eV. The presence of dangling bonds (DBs) results in lowering the activation barrier for hydride dissociation to 0.15-0.20 eV, but such DB-mediated reactions are infrequent. Our MD simulations on a-Si:H film growth surfaces indicate that surface hydride dissociation reactions are predominantly mediated by fivefold coordinated surface Si atoms, with resulting activation barriers of 0.35-0.50 eV. The results are consistent with experimental measurements of a-Si:H film surface composition using in situ attenuated total reflection Fourier transform infrared spectroscopy, which indicate that the a-Si:H surface is predominantly covered with the higher hydrides at low temperatures, while the surface monohydride, SiH((s)), becomes increasingly more dominant as the temperature is increased.