Towards an atomistic understanding of apatite–collagen biomaterials: linking molecular simulation studies of complex-, crystal- and composite-formation to experimental findings

The investigation of the atomistic mechanisms of crystal nucleation constitutes a major challenge to both experiment and theory. Understanding the underlying principles of composite materials formation represents an even harder task. For the investigation of the mechanisms of crystal nucleation a profound knowledge of the ion–solvent and the ion–ion interactions in solution is required. Studying biocomposites like fluorapatite–collagen materials, we must furthermore account for the biomolecules and their effect on the growth process. Molecular simulation approaches directly offer atomistic resolution and hence appear particularly suited for detailed mechanistic analyses. However, the computational effort is typically immense and for a long time the investigation of crystal nucleation from atomistic simulations was considered as impossible. We therefore developed special simulation strategies, which allowed to considerably extent the limitations of computational studies in this field. In combination with advanced experimental investigations this provided new insights into the nucleation of biomimetic apatite–gelatin composites and the mechanisms of hierarchical growth at the micro- and mesoscopic scale. Along this line, molecular simulation studies reflect a powerful tool to achieve a profound understanding of the complex growth processes of apatite/collagen composites. Apart from reviewing related work we outline future directions and discuss the perspectives of simulation studies for the investigation of biomineralization processes in general.     

Integrating in situ TEM experiments and atomistic simulations for defect mechanics

With recent advances in computational modeling and in situ transmission electron microscopy (TEM) technologies, there have been increased efforts to apply these approaches to understand defect-based mechanisms dictating deformation mechanics. In situ TEM experiments and atomistic simulations each have their own unique limitations, including observable length and time scales and accessibility of information, motivating approaches that combine the two approaches. In this paper, we review recent studies that combine atomistic simulations and in situ TEM experiments to understand defect mechanisms associated with deformation of metals and alloys. In addition, we discuss ongoing developments in characterization and simulation capabilities that are expected to significantly advance the field of defect mechanics and allow greater integration between atomistic simulations and in situ TEM experiments.     

Multiscale Modeling of Deformation in Polycrystalline Thin Metal Films on Substrates

The time‐dependent irreversible deformation of a thin metal film constrained by a substrate is investigated by a mesoscopic discrete dislocation simulation scheme incorporating information from atomistic studies of dislocation nucleation mechanisms. The simulations take into account dislocation climb along the grain boundaries in the film as well as dislocation glide along slip planes inclined and parallel to the film/substrate interface. The calculated flow stress and other features are compared with relevant experimental observations. The work is focused on deformation of a polycrystalline film without a cap layer, for which diffusive processes play an important role. The dislocation‐based simulations reveal information on the prevailing deformation mechanisms under different conditions and for different film thicknesses. Despite of the limitations of the two‐dimensional dislocation model, the simulations exhibit a film thickness dependent transition between creep dominated and dislocation glide dominated deformation, which is in good agreement with experimental observations.     

Atomistic Simulation of Phase Transformation and Fracture in Ordered Intermetallics

A review of computer simulations carried out at our Center for Materials Simulation applied to stud-ying the different atomistic processes of fracture and displacive (martensitic) transformations is pres-ented.Since these processes can happen extremely rapidly and involve only a small number of atomsinitially,they are ideally suited for molecular dynamics type simulations which can currently onlyspan times of the order of one nanosecond and involve at most a million atoms.A method is alsopresented for simulating much larger samples for much longer times through the use of theMonte-Carlo technique combined with a Ginzburg-Landau free energy functional,where the rele-vant material parameters are determined from molecular dynamics runs on the same alloy system.Asummary of studies on fracture simulations in the ordered intermetallics NiAI and RuAl is given,aswell as a discussion of the observation and analysis of the heterogeneous nucleation of themartensitic transformation in NiAI which shows localized soft mode phenomena.It is concluded thatcomputer simulations,whether of the atomistic molecular dynamics type or of the larger scaleMonte-Carlo variety,are rapidly becoming of greater and greater use in understanding the propertiesof solids under a wide rancle of temperature and stress conditions.     

Multiscale coupling using a finite element framework at finite temperature

This paper presents the formulation and application of a multiscale methodology that couples three domains using a finite element framework. The proposed method efficiently models atomistic systems by decomposing the system into continuum, bridging, and atomistic domains. The atomistic and bridging domains are solved using a combined finite element–molecular mechanics simulation where the system is discretized into atom/nodal centric elements based on the atomic scale finite element method. Coupling between the atomistic domain and continuum domain is performed through the bridging cells, which contain locally formulated atoms whose displacements are mapped to the nodes of the bridging cell elements. The method implements a temperature‐dependent potential for finite temperature simulations. Validation and demonstration of the methodology are provided through three case studies: displacement in a one‐dimensional chain, stress around nanoscale voids, and fracture. From these studies differences between multiscale and fully atomistic simulations were very small with the simulation time of the proposed methodology being approximately a tenth of the time of the fully atomistic model. Copyright © 2012 John Wiley & Sons, Ltd.     

Atomic mechanisms of grain boundary diffusion: Low versus high temperatures

We analyze recent results of atomistic computer simulations of grain boundary (GB) diffusion in metals. At temperatures well below the bulk melting point T_m GB diffusion occurs by random walk of individual vacancies and self-interstitials. Both defects are equal participants in the diffusion process and can move by a large variety of diffusion mechanisms, many of which are collective transitions. GB diffusion coefficients can be computed by kinetic Monte Carlo simulations. At high temperatures, the presence of large concentrations of point defects is likely to alter the diffusion mechanisms. Molecular dynamics simulations of GB structure and diffusion in copper reveal a continuous GB premelting in close vicinity of T_m. However, diffusion in high-energy GBs becomes almost independent of the GB structure (“universal”) at temperatures well below T_m. This behavior can be tentatively explained in terms of heterophase fluctuations from the solid to the liquid phase. The exact diffusion mechanisms in the presence of heterophase fluctuations are yet to be established.     

Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments

Nanoindentation has become ubiquitous for the measurement of mechanical properties at ever-decreasing scales of interest, including some studies that have explored the atomic-level origins of plasticity in perfect crystals. With substantial guidance from atomistic simulations, the onset of plasticity during nanoindentation is now widely believed to be associated with homogeneous dislocation nucleation. However, to date there has been no compelling quantitative experimental support for the atomic-scale mechanisms predicted by atomistic simulations. Our purpose here is to significantly advance the quantitative potential of nanoindentation experiments for the study of dislocation nucleation. This is accomplished through the development and application of high-temperature nanoindentation testing, and the introduction of statistical methods to quantitatively evaluate data. The combined use of these techniques suggests an unexpected picture of incipient plasticity that involves heterogeneous nucleation sites, and which has not been anticipated by atomistic simulations.     

Revealing the Cluster‐Cloud and Its Role in Nanocrystallization

Elucidating the early stages of crystallization from supersaturated solutions is of critical importance, but remains a great challenge. An in situ liquid cell transmission electron microscopy study reveals an intermediate state of condensed atomic clusters during Pd and Au crystallizations, which is named a “cluster‐cloud.” It is found that nucleation is initiated by the collapse of a cluster‐cloud, first forming a nanoparticle. The subsequent particle maturation proceeds via multiple out‐and‐in relaxations of the cluster‐cloud to improve crystallinity: from a poorly crystallized phase, the particle evolves into a well‐defined single‐crystal phase. Both experimental investigations and atomistic simulations suggest that the cluster‐cloud‐mediated nanocrystallization involves an order–disorder phase separation and reconstruction, which is energetically favored compared to local rearrangements within the particle. This finding grants new insights into nanocrystallization mechanisms, and provides useful information for the improvement of synthesis pathways of nanocrystals.     

Multiple time scale method for atomistic simulations

A novel multiple time scale approach is proposed which combines dynamic and static atomistic methods in one numerical simulation. The method is especially effective for modeling processes that consist of two distinct phases: the slow phase when atomic equilibrium positions barely change and the fast phase associated with a rapid change of the system’s configuration. In this case, the slow phase can be effectively modeled using static energy minimization while molecular dynamics (MD) can be applied when specific dynamic effects have to be captured. Compared to direct MD simulations, the new method allows for computational cost savings, and eventually simulation timescale extension, since the major part of the simulation can be modeled as static, without the need to follow vibrations of individual atoms and comply with the critical time step requirement of molecular dynamics. As a result, this approach may allow for modeling loading velocities and strain rates that are more realistic than those currently attainable through direct MD simulations. The fundamental issues in developing this method include the correlation between the MD time scale and quasi-static step-like procedure as well as finding effective criteria for switching between the static and dynamic regimes. The method was inspired by and is applied to simulations of atomic-scale stick-slip friction. Possible applications of the new method to other nano-mechanical problems are also discussed.     

Uniaxial deformation of face-centered-cubic(Ni)-ordered B2(NiAl) bicrystals: atomistic mechanisms near a Kurdjumov–Sachs interface

Creating tailored interfaces between soft and hard materials is a promising route to simultaneously enhance ductility and strength of multicomponent materials. Here, we study deformation mechanisms in a model bicrystal, with a Kurdjumov–Sachs (KS) interface, between face-centered-cubic Ni and ordered-B2 NiAl slabs using molecular dynamics simulations. The bicrystals were uniaxially deformed by strain rates of \(10^7\) and \(10^9\,\hbox {s}^{-1}\) by holding temperatures constant at 300, 500, 700, and 900 K for each strain rate. Our simulations reveal atomistic processes that create sessile and glissile dislocations, and their reactions during high-strain rate deformation. At \(10^9\,\hbox {s}^{-1}\) strain rates, dislocation processes enhance ductility and cause large-scale atomic rearrangements in the KS interfacial region. This subsequently causes nucleation, growth, and coalescence of nano-voids into cracks inside the harder B2-ordered phase bordering the interface. Our results suggest that interfaces between “soft”–“hard” materials likely withstand high-strain rates better.     

Microscopic origin of the fast crystallization ability of Ge-Sb-Te phase-change memory materials

Ge-Sb-Te materials are used in optical DVDs and non-volatile electronic memories (phase-change random-access memory). In both, data storage is effected by fast, reversible phase changes between crystalline and amorphous states. Despite much experimental and theoretical effort to understand the phase-change mechanism, the detailed atomistic changes involved are still unknown. Here, we describe for the first time how the entire write/erase cycle for the Ge(2)Sb(2)Te(5) composition can be reproduced using ab initio molecular-dynamics simulations. Deep insight is gained into the phase-change process; very high densities of connected square rings, characteristic of the metastable rocksalt structure, form during melt cooling and are also quenched into the amorphous phase. Their presence strongly facilitates the homogeneous crystal nucleation of Ge(2)Sb(2)Te(5). As this simulation procedure is general, the microscopic insight provided on crystal nucleation should open up new ways to develop superior phase-change memory materials, for example, faster nucleation, different compositions, doping levels and so on.     

Interatomic potential to predict the glass-forming ability of Ni–Nb–Mo ternary alloys

With the recently proposed formulation, an interatomic n-body potential was first constructed for the Ni–Nb–Mo metal system, and then applied to atomistic simulations to investigate the glass formation of the Ni–Nb–Mo ternary alloys. The simulations not only clarify the atomistic process of the metallic glass formation but also predict for the ternary system of a quantitative composition region within which metallic glass formation is energetically favored. In addition, the energy difference between crystalline solid solution and disordered phase i.e., the driving force for a supersaturated solid solution to amorphize could be considered as an indicator of the glass-forming ability (GFA) for a specific alloy. The GFAs of a series of Ni–Nb–Mo alloys were derived from the simulations, leading to pinpoint the Ni₅₅Nb₃₀Mo₁₅ alloy with superior GFA in this ternary metal system. The Ni₅₅Nb₃₀Mo₁₅ alloy can be considered as the optimized ternary metallic glass for thermal stability and manufacturability.     

Dislocation modelling at atomistic and mesoscopic scales

Several basic dislocation mechanisms have recently been examined in detail by atomistic simulations. In parallel, mesoscale approaches of dislocation behaviour are being developed for the study of single crystal plasticity. Linking atomistic and mesoscopic simulations is emerging as a new challenge for materials modelling.     

Void coalescence processes quantified through atomistic and multiscale simulation

Simulation of ductile fracture at the atomic scale reveals many aspects of the fracture process including specific mechanisms associated with void nucleation and growth as a precursor to fracture and the plastic deformation of the material surrounding the voids and cracks. Recently we have studied void coalescence in ductile metals using large-scale atomistic and continuum simulations. Here we review that work and present some related investigations. The atomistic simulations involve three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. No pronounced shear flow is found in the coalescence process. We also discuss a technique for optimizing the calculation of fine-scale information on the fly for use in a coarse-scale simulation, and discuss the specific case of a fine-scale model that calculates void growth explicitly feeding into a coarse-scale mechanics model to study damage localization. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Nanoscale void nucleation and growth and crack tip stress evolution ahead of a growing crack in a single crystal

A constrained three-dimensional atomistic model of a cracked aluminum single crystal has been employed to investigate the growth behavior of a nanoscale crack in a single crystal using molecular dynamics simulations with the EAM potential. This study is focused on the stress field around the crack tip and its evolution during fast crack growth. Simulation results of the observed nanoscale fracture behavior are presented in terms of atomistic stresses. Major findings from the simulation results are the following: (a) crack growth is in the form of void nucleation, growth and coalescence ahead of the crack tip, thus resembling that of ductile fracture at the continuum scale; (b) void nucleation occurs at a certain distance ahead of the current crack tip or the forward edge of the leading void ahead of the crack tip; (c) just before void nucleation the mean atomic stress (or equivalently its ratio to the von Mises effective stress, which is called the stress constraint or triaxiality) has a high concentration at the site of void nucleation; and (d) the stress field ahead of the current crack tip or the forward edge of the leading void is more or less self-similar (so that the forward edge of the leading void can be viewed as the effective crack tip).     

Atomistic modeling of plastic deformation in B2-FeAl/Al nanolayered composites

In this work, the deformation response of the B2-FeAl/Al intermetallic composites, as a model material system for nanolayered composites comprised of intermetallic interfaces, has been explored. We use atomistic simulations to study the deformation mechanisms and the interface misfit dislocation structure of B2-FeAl/Al nanolayered composites. It is shown that two sets of dislocations are contained in the interface misfit dislocation network and are correlated with the initial dislocation nucleation from the interfaces. The effects of layer thickness on the uniaxial deformation response of the B2-FeAl/Al multilayers are investigated. We observed that under compressive loading the smaller proportion of the FeAl layers leads to the lower overall flow stress. Under tensile loading, the void formation mechanism is investigated, suggesting the interface structure and the dislocation activities in the FeAl layers playing a significant role to trigger the strain localization which leads to void nucleation commencing at the interface. It is also found that the deformation behavior in the “weak” Fe/Cu interface behaves substantially different than that of the “strong” FeAl/Al interface. The atomistic modeling study of the nanolayered composites here underpinned the mechanical response of “strong” intermetallic interface material systems. There is no void nucleation during the entire plastic deformations in the Fe/Cu simulations, which is attributed to much higher dislocation density, more slip systems activated, and relative uniformly distributed dislocation traces in the Fe phase of the Fe/Cu multilayers.

     

Computer simulations for the design of microstructural developments in ceramics

This paper is to study the computer simulation of microstructural developments in ceramics mainly by Monte Carlo (MC) model and partly by molecular dynamics (MD). Plural mechanisms of mass transfer were introduced in the MC simulation of sintering and grain growth in ceramics at micron-size particle. The MC simulations were performed at the array of two-dimensional triangular lattices and were developed to sintering and grain growth in the complex systems involving a liquid phase and the second solid phase. The MD simulation was applied to the sintering of nano-size particles of ionic ceramics and showed the characteristic features in sintering process at atomic levels. The MC and MD simulations for sintering process are useful for microstructural design for ceramics.     

Design and analysis of sandwiched fullerene-graphene composites using molecular dynamics simulations

Computational design of a novel carbon based hybrid material that is composed of fullerene units covalently sandwiched between parallel graphene sheets is presented. In this regard, atomistic models for the proposed novel material structure are generated via a systematic approach by employing different fullerene types (i.e. C₁₈₀, C₃₂₀, C₅₄₀ and C₇₂₀) as sandwich cores. Then, thermodynamic stability of the atomistic structures is checked by monitoring free energy profiles and junctional bond configurations which are obtained through classical molecular dynamics (MD) simulations. Thermodynamic feasibility of all atomistic specimens with different fullerene types is suggested by the energy profiles, because total configuration energies for all systems are minimized and remained stable over a long period of time. Furthermore, mechanical behavior of the nano-sandwiched material system is investigated by performing compression tests via MD simulations and basic deformation mechanisms underlying the compressive response are determined. By detailed examination, it is shown that proposed nano-sandwiched material can be identified as quasi-foam material due to comparable energy absorbing characteristics. Furthermore, regarding the effect of fullerene size on the compressive response, it is found that for a given stress level, specimens with larger fullerenes exhibit higher energy absorbing capacity.