Elastic constants and statistical ensembles in molecular dynamics

Solids that are also liquids: elastic tensors of superionic materials

Superionics are fascinating materials displaying both solid- and liquid-like characteristics: as solids, they respond elastically to shear stress; as liquids, they display fast-ion diffusion at normal conditions. In addition to such scientific interest, superionics are technologically relevant for energy, electronics, and sensing applications. Characterizing and understanding their elastic properties is, e.g., urgently needed to address their feasibility as solid-state electrolytes in all-solid-state batteries. However, static approaches to elasticity assume well-defined reference positions around which atoms vibrate, in contrast with the quasi-liquid motion of the mobile ions in fast ionic conductors. Here, we derive the elastic tensors of superionics from ensemble fluctuations in the isobaric-isothermal ensemble, exploiting extensive Car-Parrinello simulations. We apply this approach to paradigmatic Li-ion conductors, and complement with a block analysis to compute statistical errors. Static approaches sampled over the trajectories often overestimate the response, highlighting the importance of a dynamical treatment in determining elastic tensors in superionics.

Isothermal and adiabatic elastic constants from virial fluctuations

We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential energies of atomic groups that make up the total potential energy. It is shown that in the thermodynamic limit, the Born term, which depends on the second derivatives of potential energy, can be expressed exactly in terms of equilibrium averages that involve two types of atomic-group virials. As a result, the new form of the Born term involves only first derivatives of either atomic-group or total potential energies. The derived elastic constant expressions involving the two forms of the Born terms are tested and compared using molecular-dynamics simulations of crystalline argon and silicon. For both materials, the elastic constants obtained using the two forms of the Born term are in good agreement. In particular, the new form of the Born term converges to the same value as the original Born term but at a slower rate. The results for silicon also agree well with the results from the previous molecular-dynamics studies.

Rigorous expressions for thermodynamic properties in the NpH ensemble

Molecular expressions for thermodynamic properties of fluids and derivatives of the entropy up to third order in the isoenthalpic-isobaric ensemble are derived by using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032]. They are expressed in a systematic way by phase-space functions, which represent derivatives of the phase-space volume with respect to enthalpy and pressure. The expressions for thermodynamic properties contain only ensemble averages of combinations of the kinetic energy and volume of the system. Thus, the calculation of thermodynamic properties in the isoenthalpic-isobaric ensemble does not require volume derivatives of the potential energy. This is particularly advantageous in Monte Carlo simulations when the interactions between molecules are described by very accurate ab initio pair and nonadditive three-body potentials. The derived expressions are validated by Monte Carlo simulations for the simple Lennard-Jones model fluid as a test case.

Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review

Energetic molecular crystals are widely applied for military and civilian purposes, and molecular forcefields (FF) are indispensable for treating the microscopic issues therein. This article reviews the three types of molecular FFs that are applied widely for describing energetic crystals-classic FFs, consistent FFs, and reactive FFs (ReaxFF). The basic principle of each type of FF is briefed and compared, with the application introduced, predicting polymorph, morphology, thermodynamics, vibration spectra, thermal property, mechanics, and reactivity. Finally, the advantages and disadvantages of these FFs are summarized, and some directions of future development are suggested.

Structural transition in two-dimensional Hertzian spheres in the presence of random pinning

Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional system with the Hertz potential for α=5/2. It has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of first order, and finally, there is a continuous BKT-type transition from tetratic to the square crystal.

Calculation of elastic constants of embedded-atom-model potentials in the NVT ensemble

A method for the calculation of elastic constants in the NVT ensamble using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential is studied in detail. It is shown that, in such NVT MD simulations, the evaluation of elastic constants is robust and accurate because it gives the elastic tensor in a single simulation which converges using a small number of time steps and particles. These results highlight the applicability of this method in (i) the calculation of local elastic constants of nonhomogeneous crystalline materials and (ii) the calibration of interatomic potentials, as a fast and accurate alternative to the common method of explicit deformation, which requires a set of consistent simulations at different conditions. The method is demonstrated for the calculation of the elastic constants of copper in the temperature range of 0-1000 K, and results agree with the target values used for the potential calibration. The various contributions to the values of the elastic constants, namely, the Born, stress fluctuation, and ideal gas terms, are studied as a function of temperature.

Behavior of viscoelastic models with thermal fluctuations

Fluctuating viscoelasticity for conformation-tensor-based models is studied at equilibrium, in simple-shear deformation, and in uniaxial extension. The models studied are the upper-convected Maxwell model, the FENE-P model with finite chain-extensibility, and the Giesekus model with anisotropic drag. Using numerical simulations, the models are compared in detail both with each other and with analytical predictions for the Maxwell model. At equilibrium, the models differ only marginally, both in terms of static and dynamic characteristics. When deformed, the average mechanical response of the Maxwell model is unaffected by the strength of thermal fluctuations, while the mechanical response of the FENE-P and Giesekus models show a slight decrease the stronger the fluctuations in simple shear, whereas the decrease in uniaxial extension is marginal. For all models, the standard deviation of the mechanical response increases with increasing strength of fluctuations, and the magnitude of the standard deviation relative to the average for given fluctuation strength generally decreases the stronger the deformation, this effect being stronger for uniaxial extension than for simple-shear deformation.

Conformational Insight on WT- and Mutated-EGFR Receptor Activation and Inhibition by Epigallocatechin-3-Gallate: Over a Rational Basis for the Design of Selective Non-Small-Cell Lung Anticancer Agents

Non-small cell lung cancer (NSCLC) represents a difficult condition to treat, due to epidermal growth factor receptor (EGFR) kinase domain mutations, which lead to ligand-independent phosphorylation. Deletion of five amino acids (ELREA) in exon 19 and mutational change from leucine to arginine at position 858 (L858R) are responsible for tyrosine kinase domain aberrant activation. These two common types of EGFR-mutated forms are clinically associated with high response with Tyrosine Kinase Inhibitors (TKI); however, the secondary T790M mutation within the Tyrosine Kinase Domain (TKD) determines a resistance to these EGFR-TKIs. Using molecular dynamic simulation (MD), the present study investigated the architectural changes of wild-type and mutants EGFR's kinase domains in order to detect any conformational differences that could be associated with a constitutively activated state and thus to evaluate the differences between the wild-type and its mutated forms. In addition, in order to evaluate to which extent the EGFR mutations affect its inhibition, Epigallocatechin 3-Gallate (EGCG) and Erlotinib (Erl), known EGFR-TKI, were included in our study. Their binding modes with the EGFR-TK domain were elucidated and the binding differences between EGFR wild-type and the mutated forms were evidenced. The aminoacids mutations directly influence the binding affinity of these two inhibitors, resulting in a different efficacy of Erl and EGCG inhibition. In particular, for the T790M/L858R EGFR, the binding modes of studied inhibitors were compromised by aminoacidic substitution confirming the experimental findings. These results may be useful for novel drug design strategies targeting the dimerization domain of the EGFR mutated forms, thus preventing receptor activation.

Theory of applying shear strains from boundary walls: Linear response in glasses

We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linear-response expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expressed in terms of the inter-particle correlations, as has been shown in the previous literature. Our stress relaxation function includes the effect of the boundary walls and can be used for inhomogeneous flow response. We show the presence of long-ranged, long-lived correlations among the fluctuations of the forces from the walls and the displacements of all the particles in the cell. We confirm these theoretical results numerically in a two-dimensional model glass. As an application, we describe emission and propagation of transverse sounds after boundary wall motions using these time-correlation functions. We also find resonant sound amplification when the frequency of an oscillatory shear approaches that of the first transverse sound mode.

Mechanical Properties in Metal-Organic Frameworks: Emerging Opportunities and Challenges for Device Functionality and Technological Applications

Some of the most remarkable recent developments in metal-organic framework (MOF) performance properties can only be rationalized by the mechanical properties endowed by their hybrid inorganic-organic nanoporous structures. While these characteristics create intriguing application prospects, the same attributes also present challenges that will need to be overcome to enable the integration of MOFs with technologies where these promising traits can be exploited. In this review, emerging opportunities and challenges are identified for MOF-enabled device functionality and technological applications that arise from their fascinating mechanical properties. This is discussed not only in the context of their more well-studied gas storage and separation applications, but also for instances where MOFs serve as components of functional nanodevices. Recent advances in understanding MOF mechanical structure-property relationships due to attributes such as defects and interpenetration are highlighted, and open questions related to state-of-the-art computational approaches for quantifying their mechanical properties are critically discussed.

Assessment of the mechanical properties of monolayer graphene using the energy and strain-fluctuation methods

Molecular statics and dynamics simulations were performed to investigate the mechanical properties of a monolayer graphene sheet using an efficient energy method and strain-fluctuation method. Using the energy method, we observed that the mechanical properties of an infinite graphene sheet are isotropic, whereas for a finite sheet, they are anisotropic. This work is the first to report the temperature-dependent elastic constants of graphene between 100 and 1000 K using the strain-fluctuation method. We found that the out-of-plane thermal excursions in a graphene membrane lead to strong anharmonic behavior, which allows large deviations from isotropic elasticity. The computed Young's modulus and Poisson's ratio of a sheet with an infinite spatial extent are 0.939 TPa and 0.223, respectively. We also found that graphene sheets with both finite and infinite spatial extent satisfy the Born elastic stability conditions. We extracted the variation in bending modulus with the system size at zero kelvin (0.83 eV) using a formula derived from the Foppl-von Karman approach. When the temperature increases, the Young's modulus of the sample decreases, which effectively reduces the longitudinal and shear wave velocities.

On flexible force fields for metal-organic frameworks: Recent developments and future prospects

Classical force field simulations can be used to study structural, diffusion, and adsorption properties of metal-organic frameworks (MOFs). To account for the dynamic behavior of the material, parameterization schemes have been developed to derive force constants and the associated reference values by fitting on ab initio energies, vibrational frequencies, and elastic constants. Here, we review recent developments in flexible force field models for MOFs. Existing flexible force field models are generally able to reproduce the majority of experimentally observed structural and dynamic properties of MOFs. The lack of efficient sampling schemes for capturing stimuli-driven phase transitions, however, currently limits the full predictive potential of existing flexible force fields from being realized. This article is categorized under: Structure and Mechanism > Computational Materials ScienceMolecular and Statistical Mechanics > Molecular Mechanics.

Stress-stress fluctuation formula for elastic constants in the NPT ensemble

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the NPT ensemble based on known expressions in the NVT ensemble. We validate the formula in the NPT ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the NVT ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the formula, we apply it to determine the elastic constants of a simulated lipid bilayer.

Atomic and global mechanical properties of systems described by the Stillinger-Weber potential

Analytical expressions for the stress and elasticity tensors of materials, in which the interactions are described by the Stillinger-Weber potential, are derived in the context of the stress fluctuation formalism. The derived formulas can be used both in Monte Carlo and molecular dynamics simulations. As an example of possible applications, they are employed to calculate the influence of the temperature and system size on the mechanical properties of crystalline cubic boron nitride. The system has been studied by molecular dynamics simulations. The computed mechanical properties are in good agreement with available experimental data and first principle calculations. In the studied crystalline cubic boron nitride system, the employed formalism is of higher accuracy than the 'small-strain' non-equilibrium method. The dominant contributions to the elastic constants stem from the Born and stress fluctuation terms. An increase in the system size reduces the statistical uncertainties in the computation of the mechanical properties. A rise of the temperature leads to a slight increase in the observed uncertainties. The derived expressions for the stress and elasticity tensors are further decomposed into sums of atomic level stress and atomic level elasticity tensors. The developed factorization enables us (i) to quantify the contribution of the various chemical groups, in the case under consideration of the different atoms, to the observed mechanical properties and (ii) to determine the elastic constants with reduced computational uncertainties. The reason is that the exact values of some terms of the proposed factorization can be determined theoretically beforehand. Thus, they can be substituted in the derived formulas leading to an enhanced convergence.

Elastic properties of gold supracrystals: Effects of nanocrystal size, ligand length, and nanocrystallinity

Atomistic molecular dynamics simulations are performed to study the elastic properties of alkylthiol-functionalized gold supracrystals. The predicted Young's and shear moduli are around 1 GPa and 100 MPa, respectively. We show that, with increasing NC size, the Young's modulus decreases while the shear modulus essentially remains invariant; with increasing ligand length, the Young's modulus increases but the shear modulus decreases. Moreover, significant increase in the Young's modulus is seen when the polycrystalline NCs are replaced by single-crystal ones of the same size. All these are in reasonable agreement with available experiments. We attribute the mechanisms to the interaction between capping ligands as well as its variations caused by the change in ligand length and NC geometry. The results may deepen our understanding of elastic properties of the supracrystals and their influential factors.

Dynamical heterogeneities and defects in two-dimensional soft colloidal crystals

In this paper we study a two-dimensional system of charged colloidal particles using Brownian dynamics simulations. We determine the phase diagram and investigate the dynamics of this system in the density regime where hexatic and solid phases are stable. We find that the dynamics in these phases is heterogeneous by means of the spontaneous formation and diffusion of highly mobile defects. We identify two key mechanisms associated with the areas of high mobility. The first mechanism involves the highly cooperative motion of a closed loop of particles which shift coherently along the loop until each particle has replaced the position of its predecessor in the chain. The second mechanism involves the spontaneous creation of vacancy-interstitial pairs which diffuse within the hexatic and solid phases. We further explore quantitatively the properties of the open-ended and closed rearrangement strings and find that in the crystal phase the string-size distribution can be approximately matched with a simple, random walk description of vacancies and interstitials on a lattice.

Deviatoric stress-driven fusion of nanoparticle superlattices

We model the mechanical response of alkanethiol-passivated gold nanoparticle superlattice (supercrystal) at ambient and elevated pressures using large-scale molecular dynamics simulation. Because of the important roles of soft organic ligands in mechanical response, the supercrystals exhibit entropic viscoelasticity during compression at ambient pressure. Applying a hydrostatic pressure of several hundred megapascals on the superlattice, combined with a critical deviatoric stress of the same order along the [110] direction of the face-centered-cubic supercrystal, can drive the room-temperature sintering ("fusion") of gold nanoparticles into ordered gold nanowire arrays. We discuss the molecular-level mechanism of such phenomena and map out a nonequilibrium stress-driven processing diagram, which reveals a region in stress space where fusion of nanoparticles can occur, instead of other competing plasticity or phase transformation processes in the supercrystal. We further demonstrate that, for silver-gold (Ag-Au) binary nanoparticle superlattices in sodium chloride-type superstructure, stress-driven fusion along the [100] direction leads to the ordered formation of Ag-Au multijunction nanowire arrays.

Melting and superheating in solids with volume shrinkage at melting: a molecular dynamics study of silicon

The thermodynamics of homogeneous melting in superheated crystalline solids with volume shrinkage at melting is investigated using extensive molecular dynamics simulation in conjunction with a classical nucleation theory. A liquid-solid co-existing model is established to overcome the difficult in observing liquid phase formation in a superheated Si crystal. We found that melting is governed by two major factors, the volume change induced strain energy and the curvature of the interface between the liquid and the solid phases. The driving force for melting in superheating regime is lowered by the additional strain energy that restricts homogeneous nucleation of a liquid phase till temperature rises above the normal melting point, thus causing superheating. However, due to the abnormal behavior in the compressibility of the silicon liquid in the superheating regime, the degree of superheating in terms of the liquid nucleation gap becomes significantly reduced. More potential complications caused by the change of the atomic bonding in Si at melting are discussed.

Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

The truncation of a pair potential at a distance rc is well known to imply, in general, an impulsive correction to the pressure and other moments of the first derivatives of the potential. That, depending on rc, the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G(T) around the glass transition temperature Tg.

Molecular dynamics method to locally resolve Poisson's ratio: Mechanical description of the solid-soft-matter interphase

A method based on "small-deformation mechanical response" has been developed to locally resolve the Poisson's ratio via molecular dynamics simulations. The approach can be used for simple and composite materials to characterize systems with two or more continuous phases in the framework of periodic boundary conditions. The proposed technique represents a simple method to obtain a local mechanical description of complex systems. A polystyrene bulk, a silica bulk, and a polystyrene-silica heterogeneous composite material have been characterized under imposed strain. The results show the effects of local material inhomogeneities which are present in the glassy material and in the composite system. The Poisson's ratio spatial profiles for silica, the polystyrene bulk, and in the interphase region between the soft polymer bulk and the hard surface have also been calculated. The obtained local mechanical description can be employed in micromechanical models developed to predict the overall mechanical properties of multicomponent materials.

Thermodynamic and Elastic Properties of Polyethylene at Elevated Temperatures

Over the years molecular modeling techniques, such as Molecular Mechanics, Monte Carlo and Molecular Dynamics have been applied to study the equilibrium thermodynamic and mechanical properties of materials. The accuracy of the predictions made by these techniques strongly depend on the force fields employed to represent the interactions in the studied system. Recently developed force field parameters for crystalline polyethylene are shown to reproduce the mechanical properties of polyethylene accurately through molecular mechanics. Here, we will present the statistical fluctuation formulae for the elevated temperature equilibrium thermodynamic and elastic properties in terms of microscopic variables such as energy, enthalpy, pressure, volume, microscopic strain or stress tensors and present preliminary results of our calculations.

Deformation Behavior of FCC Crystalline Metallic Nanowires Under High Strain Rates

We used molecular dynamics (MD) methods to study the deformation behavior of metallic alloy crystal nanowires of pure Cu, NiCu alloy and NiAu alloy, under high rates of uniaxial tensile strain, ranging from 5* 108/s to 5* 10/s. These nanowires are just about 2 nm thick and hence cannot sustain dislocations, instead we find that deformation proceeds through twinning and coherent slipping mechanisms. NiAu has a 13% size mismatch whereas NiCu only 2.5%. As a result the critical strain rate at which the “nanowire crystals” flow like a “liquid” is 100 times smaller for NiAu. We also calculated the elastic constants at each strain state for all strain rates to identify the relation between mechanical “shear” instability and deformation process.

The elastic stability, bifurcation and ideal strength of gold under hydrostatic stress: an ab initio calculation

In this paper, we employ an ab initio density functional theory calculation to investigate the elastic stability of face-centered cubic Au under hydrostatic deformation. We identify the elastic stiffness constant B(ijkl) as the coefficient in the stress-strain relation for an arbitrary deformed state, and use it to test the stability condition. We show that this criterion bears the same physics as that proposed earlier by Frenkel and Orowan and agrees with the Born-Hill criterion. The results from those two approaches agree well with each other. We show that the stability limit, or instability, of the perfect Au crystal under hydrostatic expansion is not associated with the bulk stiffness modulus as predicted in the previous work; rather it is caused by a shear instability associated with the vanishing rhombohedral shear stiffness modulus. The deviation of the deformation mode from the primary hydrostatic loading path signals a bifurcation or symmetry breaking in the ideal crystal. The corresponding ideal hydrostatic strength for Au is 19.2 GPa at the Lagrangian expansion strain of ∼0.06. In the case of compression, Au remains stable over the entire pressure range in our calculation.

Expressions for the stress and elasticity tensors for angle-dependent potentials

The stress and elasticity tensors for interatomic potentials that depend explicitly on bond bending and dihedral angles are derived by taking strain derivatives of the free energy. The resulting expressions can be used in Monte Carlo and molecular dynamics simulations in the canonical and microcanonical ensembles. These expressions are particularly useful at low temperatures where it is difficult to obtain results using the fluctuation formula of Parrinello and Rahman [J. Chem. Phys. 76, 2662 (1982)]. Local elastic constants within heterogeneous and composite materials can also be calculated as a function of temperature using this method. As an example, the stress and elasticity tensors are derived for the second-generation reactive empirical bond-order potential. This potential energy function was used because it has been used extensively in computer simulations of hydrocarbon materials, including carbon nanotubes, and because it is one of the few potential energy functions that can model chemical reactions. To validate the accuracy of the derived expressions, the elastic constants for diamond and graphite and the Young's Modulus of a (10,10) single-wall carbon nanotube are all calculated at T = 0 K using this potential and compared with previously published data and results obtained using other potentials.

Elastic constants of diamond from molecular dynamics simulations

The elastic constants of diamond between 100 and 1100 K have been calculated for the first time using molecular dynamics and the second-generation, reactive empirical bond-order potential (REBO). This version of the REBO potential was used because it was redesigned to be able to model the elastic properties of diamond and graphite at 0 K while maintaining its original capabilities. The independent elastic constants of diamond, C(11), C(12), and C(44), and the bulk modulus were all calculated as a function of temperature, and the results from the three different methods are in excellent agreement. By extrapolating the elastic constant data to 0 K, it is clear that the values obtained here agree with the previously calculated 0 K elastic constants. Because the second-generation REBO potential was fit to obtain better solid-state force constants for diamond and graphite, the agreement with the 0 K elastic constants is not surprising. In addition, the functional form of the second-generation REBO potential is able to qualitatively model the functional dependence of the elastic constants and bulk modulus of diamond at non-zero temperatures. In contrast, reactive potentials based on other functional forms do not reproduce the correct temperature dependence of the elastic constants. The second-generation REBO potential also correctly predicts that diamond has a negative Cauchy pressure in the temperature range examined.

Differences between solid superheating and liquid supercooling

The thermodynamic and kinetic behaviors for solid superheating and liquid supercooling were critically examined and compared via molecular-dynamics simulations. It is shown that the large elastic energy associated with internal melting and solid-liquid interface disorder play important roles in superheating. The growth rate is anisotropic for supercooling, but isotropic for superheating. Supercooling can be well described by the classical nucleation theory, whereas superheating shows many exceptions. The underlying mechanisms for these differences are discussed.

Application of the Wolf damped Coulomb method to simulations of SiC

A multibody interatomic potential is developed for bulk SiC using a modification of the Wolf et al. summation technique [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)] for the electrostatic interaction. The technique is modified to account for the short-range nonpoint charge effect. The nonelectrostatic interaction is modeled by a simple Morse-stretch term. This potential is then applied to beta-SiC to calculate various bulk properties using molecular dynamics simulations. The simulated x-ray diffraction pattern, radial distribution functions, lattice constant, elastic constants, and defect energy agree well with experimental data.

Mechanical heterogeneities in model polymer glasses at small length scales

Molecular simulations of a model, deeply quenched polymeric glass show that the elastic moduli become strongly inhomogeneous at length scales comprising several tens of monomers; these calculations reveal a broad distribution of local moduli, with regions of negative moduli coexisting within a matrix of positive moduli. It is shown that local moduli have the same physical meaning as that traditionally ascribed to moduli obtained from direct measurements of local constitutive behaviors of macroscopic samples.

Improved simulation method for the calculation of the elastic constants of crystalline and amorphous systems using strain fluctuations

In this paper, a method is proposed for calculating the elastic constants of arbitrarily soft or stiff systems using strain fluctuations. For stiff materials, for example, strain fluctuations may be enhanced by appropriate choice of elastic constants for the bath. Example calculations of the isothermal elastic constants of the nearest-neighbor Lennard-Jones fcc crystal demonstrate improved convergence properties over standard techniques. Elastic constants for a model amorphous polymer system are also presented.

Atomistic mechanisms governing elastic limit and incipient plasticity in crystals

Nanometre-scale contact experiments and simulations demonstrate the potential to probe incipient plasticity--the onset of permanent deformation--in crystals. Such studies also point to the need for an understanding of the mechanisms governing defect nucleation in a broad range of fields and applications. Here we present a fundamental framework for describing incipient plasticity that combines results of atomistic and finite-element modelling, theoretical concepts of structural stability at finite strain, and experimental analysis. We quantify two key features of the nucleation and subsequent evolution of defects. A position-sensitive criterion based on elastic stability determines the location and character of homogeneously nucleated defects. We validate this stability criterion at both the atomistic and the continuum levels. We then propose a detailed interpretation of the experimentally observed sequence of displacement bursts to elucidate the role of secondary defect sources operating locally at stress levels considerably smaller than the ideal strength required for homogeneous nucleation. These findings provide a self-consistent explanation of the discontinuous elastic plastic response in nanoindentation measurements, and a guide to fundamental studies across many disciplines that seek to quantify and predict the initiation and early stages of plasticity.

Geometric approach to the pressure tensor and the elastic constants

Expressions are obtained for the pressure tensor in the canonical and the microcanonical ensemble for both isolated and periodic systems, using the same geometric approach to thermodynamic derivatives as has been used previously to define the configurational temperature. The inherent freedom of the method leads to a straightforward proof of the equivalence of atomic and molecular pressures, for short molecules and for molecules exceeding the dimensions of a periodic simulation box. The effect of holonomic constraints on the pressure is discussed. Expressions for the elastic constants are derived in the same manner.

Melting mechanisms at the limit of superheating

The atomic-scale details during melting of a surface-free Lennard-Jones crystal were monitored using molecular dynamics simulations. Melting occurs when the superheated crystal spontaneously generates a sufficiently large number of spatially correlated destabilized particles that simultaneously satisfy the Lindemann and Born instability criteria. The accumulation and coalescence of these internal local lattice instabilities constitute the primary mechanism for homogeneous melt nucleation inside the crystal, in lieu of surface nucleation for equilibrium melting. The vibrational and elastic lattice instability criteria as well as the homogeneous nucleation theory all coincide in determining the superheating limit.

Mechanism for negative poisson ratios over the alpha- beta transition of cristobalite, SiO2: A molecular-dynamics study

The adiabatic elastic constants ( C(ij)) of cristobalite have been evaluated successfully over the temperature range of 300-1800 K using the molecular-dynamics method with a fluctuation formula. Cristobalite shows a negative Poisson ratio over this temperature range. However, the mechanisms differ between the alpha and beta phases. In the cubic beta phase, C44 exhibits a value extremely close to C11 rather than C12, in contrast to the Cauchy relation. This predicts a remarkable property that the longitudinal and transverse velocities coincide for the acoustic waves propagating along the [100] direction.

Correct microcanonical ensemble in molecular dynamics

The statistical-mechanics ensemble corresponding to equilibrium molecular dynamics simulations is different than the usual microcanonical EVN ensemble. Historically molecular dynamics has been associated with the EVNM ensemble, where M is the constant total linear momentum of the system. We show that the correct ensemble associated with molecular dynamics is the EVNMG ensemble where G is the constant of the motion associated with Galilean boosts. The ensemble associated with molecular dynamics simulations has, apparently, not been previously recognized. An earlier problem with the pressure in the new ensemble disappears.