Atomistic Continuum Research Articles

Ultrafast laser ablation of gold in liquids: Effect of laser pulse overlap-induced surface porosity on size distribution of formed nanoparticles

Pulsed Laser Ablation in Liquids (PLAL) manifested itself as a powerful tool for the synthesis of nanoparticles (NPs) from a variety of materials of high demand in biomedicine. The mechanisms and regimes of nanostructures formation, however, still require clarification in order to better control the final NPs characteristics. Here, we present a numerical study of femtosecond laser-ablative production of metal (gold) NPs in water ambient using an advanced atomistic continuum approach, combining the Molecular Dynamics (MD) and Two Temperature Model into the frames of a single MD-TTM computational method. The model describes non-equilibrium laser-induced phase transitions at atomic level and accounts for the effect of free carriers in continuum. With the MD-TTM model we investigated the effect of slight porosity arising due to a partial overlap of laser craters during the scanning of laser beam over the target surface under a high repetition rate of laser pulses. For that purpose, we perform a simulation of 270 fs laser pulse interaction with solid and porous gold targets at the incident fluence of 2.5 J/cm2. The obtained results revealed the manifestation of different regimes of ablation and different yield of the obtained NPs. The simulation results are compared with the corresponding experimental data. We found that depending on the scanning speed the ablation can follow thermal and spallation mechanisms of the material ejection, which are responsible for the appearance of fine and course populations of NPs correspondingly. In the case of clean target’s surface ablation, when at high scanning speed of 3840 mm/s each pulse hits a fresh area, the material ejection is governed by both mechanisms, which leads to the appearance of bimodal population of NPs. Alternatively, a moderate scanning speed of 840 mm/s results in a partial overlap of the sequential laser spots on the surface and generated slight porosity removes the accumulation of laser-induced stresses. The spallation mechanism of the material ejection is therefore suppressed, which results in generation of a monomodal fine population of NPs with a 20 times larger yield. The obtained data are of importance to predict and control size characteristics of laser-synthesized nanomaterials.

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. The gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.

A multiscale framework for atomistic–continuum transition in nano-powder compaction process using a cap plasticity model

In this paper, a computational atomistic-continuum multiscale framework is presented for the simulation of the nano-powder compaction process using a cone-cap plasticity model. The atomistic representative volume element (RVE) comprises of nano-powder particles that is used to perform the molecular dynamics analysis in order to capture the mechanical behavior of nano-powder material. The periodic boundary condition is applied over the atomistic RVE to satisfy the inter-scale kinematic compatibility, and the stress tensor is derived according to the inter-scale energetic consistency principals from the nanoscale at each material point of the powder component. A multiscale framework is performed using the constitutive law of the coarse-scale domain enhanced by the molecular dynamics results of the fine-scale domain. The coarse-scale constitutive law is conformed to the cone-cap plasticity model as a robust and capable constitutive relation in modeling the powder compaction process, in which the cap plasticity parameters are determined using the data derived from the molecular dynamics simulations. The mechanical response of nano-powder particles within the RVE is obtained from the confining pressure test and true-triaxial test, where a sensitivity analysis is accomplished on the computed parameters of the cone-cap plasticity model. The enhanced cap plasticity model is then employed to simulate various industrial nano-powder components that illustrates the performance and efficiency of the proposed multiscale computational homogenization method.

Static analysis and vibration characteristics of some noncarbon nanotubes through atomistic continuum coupled modelling

Static analysis and vibration characteristics of some noncarbon nanotubes through atomistic continuum coupled modelling

Investigating shock wave propagation, evolution, and anisotropy using a moving window concurrent atomistic–continuum framework

Despite their success in microscale modeling of materials, atomistic methods are still limited by short time scales, small domain sizes, and high strain rates. Multiscale formulations can capture the continuum-level response of solids over longer runtimes, but using such schemes to model highly dynamic, nonlinear phenomena is very challenging and an active area of research. In this work, we develop novel techniques within the concurrent atomistic–continuum (CAC) multiscale framework to simulate shock wave propagation through a two-dimensional, single-crystal lattice. The technique is described in detail, and two moving window methods are incorporated to track the shock front through the domain and thus prevent spurious wave reflections at the atomistic–continuum interfaces. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of two materials. We then use the moving window techniques to perform parametric studies which analyze the shock front’s structure. Finally, we compare the efficiency of our model to molecular dynamics simulations. This work showcases the framework’s capability for simulating dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and alloys.

Transmitting multiple high-frequency phonons across length scales using the concurrent atomistic–continuum method

Coupled atomistic–continuum methods can describe large domains and model dynamic material behavior for a much lower computational cost than traditional atomistic techniques. However, these multiscale frameworks suffer from wave reflections at the atomistic–continuum interfaces due to the numerical discrepancy between the fine-scaled and coarse-scaled models. Such reflections are non-physical and may lead to unfavorable outcomes such as artificial heating in the atomistic region. In this work, we develop a technique to allow the full spectrum of phonons to be incorporated into the coarse-scaled regions of a periodic concurrent atomistic–continuum (CAC) framework. This scheme tracks phonons generated at various time steps and thus allows multiple high-frequency wave packets to travel between the atomistic and continuum regions. Simulations performed with this method demonstrate the ability of the technique to preserve the coherency of waves with a range of wavevectors as they propagate through the domain. This work has applications for systems with defined boundary conditions and may be extended to more complex problems involving waves randomly nucleated from an impact within a multiscale framework.

Microstructure models of cement: their importance, utility, and current limitations

Microstructure models seek to explain or predict various material properties in terms of the structure or chemical composition at scales of several hundred nanometres to several hundred micrometres. Such models therefore bridge the scaling gap between atomistic models and continuum methods, and consequently can help establish and validate scaling relations across those scales. Microstructure models have been applied to cementitious materials for at least four decades to help understand setting, strength development, rheological properties, mechanical behavior, and transport properties. This letter describes the current state of cement microstructure modelling in several areas that are important for engineering. It is not meant to be an exhaustive review, instead highlighting the kinds of models that can now be applied to different aspects of cement binder behaviour. Special attention is paid to challenges or limitations of each kind of model. This is done to promote the judicious use and interpretation of models and especially to indicate where future research could make inroads on problems that are currently inaccessible to microstructure models.

A parallel algorithm for the concurrent atomistic-continuum methodology

In this work we present a parallel algorithm for the Concurrent Atomistic Continuum (CAC) formulation that can be integrated into existing molecular dynamics codes. The CAC methodology is briefly introduced and its parallel implementation in LAMMPS is detailed and then demonstrated through benchmarks that compare CAC simulation results with corresponding all-MD (molecular dynamics) results. The parallel efficiency of the algorithm is demonstrated when simulating systems represented by both atoms and finite elements. The verification benchmarks include dynamic crack propagation and branching in a Si single crystal, wave propagation and scattering in a Si phononic crystal, and phonon transport through the phase interface in a PbTe/PbSe heteroepitaxial system. In each of these benchmarks the CAC algorithm is shown to be in good agreement with MD-only models. This parallel CAC algorithm thus offers one of the first scalable multiscale material simulation methodologies that relies solely on atomic-interaction models.

An atomistic–continuum multiscale analysis for heterogeneous nanomaterials and its application in nanoporous gold foams

In this paper, an atomistic–continuum homogenization multiscale method is developed to study the nonlinear behavior of heterogeneous nanomaterials. The atomistic representative volume element (RVE) with vacancy and/or void defects are analyzed by employing the fully atomistic method, in which the nucleation, migration, and elimination of dislocation, as well as the dislocation-vacancy interaction, are captured. The coarse-scale material domain is modeled within the framework of the nonlinear finite element method, and the impression of nanoscale material defects is investigated by upscaling the stress tensor and tangent modulus from the atomistic RVE based on the Hill-Mandel principle. The principle of inter-scale kinematic compatibility is implemented using the periodic boundary condition. The mechanical behavior of atomistic RVE under various deformation modes is elucidated through stress – strain and dislocation density – strain curves. Due to the random nature of defects on the atomistic scale, a statistical procedure is exerted to numerically investigate the effect of influential parameters on the RVE mechanical behavior. Finally, the impression of vacancy and/or nanoscale void defects on the multiscale simulation of coarse-scale materials is illustrated in several numerical examples. The obtained results of the multiscale analysis is also verified with experimental data. Moreover, the compaction behavior of nanoporous gold foam is studied through the proposed multiscale method that highlights a good agreement with the fully atomistic analysis.

Moving window techniques to model shock wave propagation using the concurrent atomistic–continuum method

Atomistic methods have successfully modeled different aspects of shock wave propagation in materials over the past several decades, but they suffer from limitations which restrict the total runtime and system size. Multiscale methods have been able to increase the length and time scales that can be modeled but employing such schemes to simulate wave propagation and evolution through engineering-scale domains is an active area of research. In this work, we develop two distinct moving window approaches within a Concurrent Atomistic–Continuum (CAC) framework to model shock wave propagation through a one-dimensional monatomic chain. In the first method, the entire CAC system travels with the shock in a conveyor fashion and maintains the shock front in the middle of the overall domain. In the second method, the atomistic region follows the shock by the simultaneous coarsening and refinement of the continuum regions. The CAC and moving window frameworks are verified through dispersion relation studies and phonon wave packet tests. We achieve good agreement between the simulated shock velocities and the values obtained from theory with the conveyor technique, while the coarsen-refine technique allows us to follow the propagating wave front through a large-scale domain. This work showcases the ability of the CAC method to accurately simulate propagating shocks and also demonstrates how a moving window technique can be used in a multiscale framework to study highly nonlinear, transient phenomena.

Crystal Plasticity Phase-Field Model with Crack Tip Enhancement Through a Concurrent Atomistic-Continuum Model

This paper develops a method for physics-based augmentation of the Helmholtz free energy density functionals, used in coupled crystal plasticity phase-field finite element (CP-PF FE) models of fracture in crystalline metallic materials. Specifically, the defect and crack surface energy components are enhanced with terms that mechanistically account for the presence of atomic-scale, crack-tip nucleated dislocations. The additional terms in the free energy representation are motivated and calibrated by energy equivalence between a concurrent atomistic–continuum scale model and the CP-PF FE model. The atomistic domain of the concurrent model incorporates a time-accelerated, molecular dynamics (MD) LAMMPS code, while the continuum domain is modeled by a dislocation-density crystal plasticity FE model. The concurrent model transfers and transforms discrete dislocations in the atomistic domain to dislocation densities in the crystal plasticity domain. Dislocation densities are transported in the continuum domain by solving the advection equation using a particle-based reproducing kernel particle method with collocation. A new form of the defect energy density is proposed by considering the effect of crack-tip nucleated dislocations. Parameters in the augmented defect and surface energies are evaluated by comparing with the concurrent model results. A comparison of crack propagation with and without contributions from the nucleated dislocations demonstrates a significant effect of nucleated dislocations on the evolution of the crack.

A Multiscale Investigation on the Thermal Transport in Polydimethylsiloxane Nanocomposites: Graphene vs. Borophene.

Graphene and borophene are highly attractive two-dimensional materials with outstanding physical properties. In this study we employed combined atomistic continuum multi-scale modeling to explore the effective thermal conductivity of polymer nanocomposites made of polydimethylsiloxane (PDMS) polymer as the matrix and graphene and borophene as nanofillers. PDMS is a versatile polymer due to its chemical inertia, flexibility and a wide range of properties that can be tuned during synthesis. We first conducted classical Molecular Dynamics (MD) simulations to calculate the thermal conductance at the interfaces between graphene and PDMS and between borophene and PDMS. Acquired results confirm that the interfacial thermal conductance between nanosheets and polymer increases from the single-layer to multilayered nanosheets and finally converges, in the case of graphene, to about 30 MWm−2 K−1 and, for borophene, up to 33 MWm−2 K−1. The data provided by the atomistic simulations were then used in the Finite Element Method (FEM) simulations to evaluate the effective thermal conductivity of polymer nanocomposites at the continuum level. We explored the effects of nanofiller type, volume content, geometry aspect ratio and thickness on the nanocomposite effective thermal conductivity. As a very interesting finding, we found that borophene nanosheets, despite having almost two orders of magnitude lower thermal conductivity than graphene, can yield very close enhancement in the effective thermal conductivity in comparison with graphene, particularly for low volume content and small aspect ratios and thicknesses. We conclude that, for the polymer-based nanocomposites, significant improvement in the thermal conductivity can be reached by improving the bonding between the fillers and polymer, or in other words, by enhancing the thermal conductance at the interface. By taking into account the high electrical conductivity of borophene, our results suggest borophene nanosheets as promising nanofillers to simultaneously enhance the polymers’ thermal and electrical conductivity.

A concurrent atomistic-crystal plasticity multiscale model for crack propagation in crystalline metallic materials

This paper develops a coupled concurrent atomistic–continuum multiscale model for analyzing crack propagation and associated mechanisms in crystalline metallic materials. This modeling framework can be used to develop effective continuum-scale constitutive models for crack evolution in deforming domains characterized by crystal plasticity. The atomistic region is modeled by the molecular dynamics (MD) code LAMMPS, while the continuum region is modeled by a dislocation density crystal plasticity FE model. A novel method is developed to transfer discrete dislocations in the atomistic domains to dislocation densities in the continuum domain. Propagation of dislocation densities in the continuum domain is modeled by the advection equation of a conserved quantity using the reproducing kernel particle method (RKPM) in conjunction with the collocation method. Validation studies are conducted by comparing results of the concurrent model with those by MD for nickel single crystal specimen with an embedded crack. An analytical model of the crack tip nucleated dislocation density evolution is developed for inclusion in crystal plasticity models. The effect of applied strain-rate and temperature on the parameters of this model are studied.

Energetics of graphene origami and their “spatial resolution”

The extreme thinness of graphene combined with its tensile strength made it a material appealing for discussing and even making complex cut-kirigami or folded-only origami. In the case of origami, its stability is mainly defined by the positive energy of the single- or double-fold curvature deformation counterbalanced by the energy reduction due to favorable van der Waals contacts. These opposite sign contributions also have notably different scaling with the size L of the construction, the contacts contributing in proportion to area ~ L2, single folds as ~ L, and highly strained double-fold corners as only ~ L0 = const. Computational analysis with realistic atomistic-elastic representation of graphene allows one to quantify these energy contributions and to establish the length scale, where a single fold is favored (7 nm 21 nm), defining the size of the smallest possible complex origami designs as L ≫ 21 nm. The flexibility and foldability of graphene are some of its attractive properties inspiring the designs of origami structures with potential use in flexible electronics and electromechanical nanodevices. The aesthetics, precision, and ease of folding and stability, however, have limitations at the nanoscale. Here, by means of large-scale atomistic calculations and continuum models, it is quantified how the dimensions determine the relative robustness of the elementary folds of graphene (a single fold and a double-folded graphene forming a single order-four vertex), thereby mapping the spatial resolution limits and providing important guidance for graphene nano-origami realizations.

Elastic Properties and Nonlinear Elasticity of the Noncarbon Hexagonal Lattice Nanomaterials Based on the Multiscale Modeling

Abstract This study presents the elastic properties and nonlinear elasticity of the two-dimensional noncarbon nanomaterials of hexagonal lattice structures having molecular structure XY. Four nitride-based and two phosphide-based two-dimensional nanomaterials, having graphene-like hexagonal lattice structure, are considered in the present study. The four empirical parameters associated with the attractive and repulsive terms of the Tersoff–Brenner potential are calibrated for noncarbon nanomaterials and tested for elastic properties, nonlinear constitutive behavior, bending modulus, bending and torsional energy. The mathematical identities for the tangent constitutive matrix in terms of the interatomic potential function are derived through an atomistic–continuum coupled multiscale framework of the extended version of Cauchy–Born rule. The results obtained using newly calibrated empirical parameters for cohesive energy, bond length, elastic properties, and bending rigidity are compared with those reported in the literature through experimental investigations and quantum mechanical calculations. The continuum approximation is attained through the finite element method. Multiscale evaluations for elastic properties and nonlinear stretching of the nanosheets under in-plane loads are also compared with those obtained from atomistic simulations.

Modeling the damage evolution and recompression behavior during laser shock loading of aluminum microstructures at the mesoscales

Damage evolution in metals during laser-shock loading (spallation) is a complex phenomenon accompanied by extremely high temperatures, pressures, and strain rates that affect the void nucleation/growth mechanisms. The current modeling efforts at the atomic scales to investigate the evolution of microstructure undergoing the spall failure at the atomic scales are limited to a hybrid atomistic–continuum method that combines the two-temperature model (TTM) with the molecular dynamics (MD) simulations. This manuscript demonstrates this capability by investigating the mechanisms of nucleation/evolution of voids for a nanocrystalline Al system experiencing an ultrafast laser pulse. This capability, however, is unable to model the laser shock response of experimental systems (with grain sizes greater than 100 nm and thicknesses in the microns) as well as the post-spall behavior (damage growth or recompression behavior). This work combines the TTM with the quasi-coarse-grained dynamics (QCGD) method to extend MD-TTM simulations to the mesoscales. The hybrid QCGD-TTM approach retains the laser energy absorption, heat generation/transfer, and microstructure evolution (melting, defects, and damage) behavior predicted by MD-TTM simulations. The QCGD-TTM simulations allow the investigation of the wave propagation behavior, the evolution of microstructure (defects and damage), temperature, and pressure at the time and length scales of laser-shock experiments. The QCGD-TTM simulations reported here investigate the nucleation and post-spall damage evolution behavior during spall failure of sc-Al and 0.5 µm grain-sized pc-Al films with a thickness of up to 2 µm. The QCGD-TTM-predicted damage evolution behavior captures the post-spall behavior observed experimentally and retains the atomistic characteristics of void nucleation and void collapse.

Si/Ge (111) Semicoherent Interfaces: Responses to an In‐Plane Shear and Interactions with Lattice Dislocations

Concurrent atomistic–continuum simulations are employed to study Si/Ge (111) semicoherent interfaces in terms of their responses to an in‐plane shear and interactions with lattice dislocations. Three types of Si/Ge interfaces, differing in interfacial structures and energy, are considered. Type I interface coincides with the shuffle‐set slip plane and contains a hexagonal network of edge dislocations. Type II and Type III interfaces both coincide with the glide‐set slip plane, yet they contain, respectively, a triangular and a hexagonal network of Shockley partial dislocations. The simulations show that among the three types of interfaces, 1) Type I interface is the least stable subject to an in‐plane shear and 2) Type III interface impedes the gliding of lattice dislocations the most significantly.

A concurrent multiscale study of dynamic fracture

Dynamic fracture is a complex multiscale physical phenomenon. The process occurs in multiple time and length scales. Macroscopic behaviors such as crack instability and brittle/ductile transition are consequences and combinations of a series of microscopic events such as dynamic dislocation motions and formation of nano voids. On the other hand, the atomistic bond breaking and the motion of dislocation are strongly affected by continuum stress field as well. Thus, delineating the underlining multiscale process is demanding to understand the fundamental physics. In this work, we employed previously proposed concurrent multiscale method between multiscale micromorphic molecular dynamics (MMMD) and peridynamics to simulate dynamic fracture. To achieve widely adaptive message translation, especially for heterogeneous messages, the coupling utilizes the recently developed MMMD which has an intrinsic multiscale structure to serve as the translator for the messages from different scales. The main innovations of this work are: (1) The proposed MMMD/Peridynamics coupling is a non-local to non-local multiscale method; (2) The coarse-scale peridynamic model is built based on an atomistic-informed Cauchy–Born material model that has minimum empiricism, and (3) The multiscale method has the consistent dynamic fracture criterion at all scales. We investigate the crack nucleation, branching and propagation under different loading rates, putting the emphasis on brittle/ductile transition and crack propagation through the atomistic–continuum interface. Quantitative results of nucleation, bifurcation and the crack speed under different loading rates are presented and discussed in the paper.

Comparative modeling of the disregistry and Peierls stress for dissociated edge and screw dislocations in Al

Many elementary deformation processes in metals involve the motion of dislocations. The planes of glide and specific processes dislocations prefer depend heavily on their atomic core structures. Atomistic simulations are desirable for dislocation modeling but their application to even sub-micron scale problems is in general computationally costly. Accordingly, continuum-based approaches, such as the phase-field microelasticity, phase-field dislocation dynamics (PFDD), generalized Peierls–Nabarro (GPN) models, and the concurrent atomistic–continuum (CAC) method, have attracted increasing attention in the field of dislocation modeling because they well represent both short-range cores interactions and long-range stress fields of dislocations. To better understand their similarities and differences, it is useful to compare these methods in the context of benchmark simulations and predictions. In this paper, we apply the CAC method and different PFDD variants – one of them is equivalent to a GPN model – to simulate an extended (i.e., dissociated) dislocation in Al with initially pure edge or pure screw character in terms of the disregistry. CAC and discrete forms of PFDD are also employed to calculate the Peierls stress. By conducting comprehensive convergence studies, we quantify the dependence of these measures on time/grid resolution and simulation cell size. Several important but often overlooked differences between PFDD/GPN variants are clarified. Our work sheds light on the advantages and limitations of each method, as well as the path towards enabling them to effectively model complex dislocation processes at larger length scales.

A comprehensive review on the modeling of smart piezoelectric nanostructures

In this paper, a comprehensive review of nanostructures that exhibit piezoelectric behavior on all mechanical, buckling, vibrational, thermal and electrical properties is presented. It is firstly explained vast application of materials with their piezoelectric property and also introduction of other properties. Initially, more application of material which have piezoelectric property is introduced. Zinc oxide (ZnO), boron nitride (BN) and gallium nitride (GaN) respectively, are more application of piezoelectric materials. The nonlocal elasticity theory and piezoelectric constitutive relations are demonstrated to evaluate problems and analyses. Three different approaches consisting of atomistic modeling, continuum modeling and nano-scale continuum modeling in the investigation atomistic simulation of piezoelectric nanostructures are explained. Focusing on piezoelectric behavior, investigation of analyses is performed on fields of surface and small scale effects, buckling, vibration and wave propagation. Different investigations are available in literature focusing on the synthesis, applications and mechanical behaviors of piezoelectric nanostructures. In the study of vibration behavior, researches are studied on fields of linear and nonlinear, longitudinal and transverse, free and forced vibrations. This paper is intended to provide an introduction of the development of the piezoelectric nanostructures. The key issue is a very good understanding of mechanical and electrical behaviors and characteristics of piezoelectric structures to employ in electromechanical systems.