HotQC simulation of nanovoid growth under tension in copper

Ariza, Manuel R. Gómez; Romero, Ignacio; Ponga, Mauricio; Ortiz, Michael

doi:10.1007/978-94-007-4626-8_8

Cited by 12 publications

(24 citation statements)

References 43 publications

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“…In this manner, meanfield models become controlled approximation schemes resulting in convergent sequences of approximations. Likewise, the variational structure of the theory provides a basis for variational time discretization cf., e. g., Ortiz and Stainier (1999); Yang et al (2006)) and for spatial coarsegraining, e. g., by recourse to the quasi-continuum method (Tadmor et al, 1996;Knap and Ortiz, 2001;Kulkarni et al, 2008;Ariza et al, 2012). These and other extensions suggest worthwhile avenues for further work.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

Atomistic long-term simulation of heat and mass transport

Venturini

Wang

Romero

et al. 2014

Journal of the Mechanics and Physics of Solids

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114

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We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomiclevel properties while simultaneously entailing time scales much longer than * Corresponding author E-mail address: ortiz@caltech.edu (M. Ortiz). September 27, 2014 those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable. Preprint submitted to Journal of the Mechanics and Physics of Solids

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Section: Summary and Concluding Remarksmentioning

confidence: 99%

Atomistic long-term simulation of heat and mass transport

Venturini

Wang

Romero

et al. 2014

Journal of the Mechanics and Physics of Solids

Self Cite

114

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“…This subset is dense, i.e., it contains every atom close to the defect but gradually coarsen away from it. We track the positions of these atoms and infer the position of other (non-representative atoms) from the position of the representative atoms by introducing linear finite elements shape functions based on a mesh T a with nodes P a as in the atomistic quasi-continuum formulations [15,19,20,40,41,42,43]. Note that this mesh is Lagrangian.…”

Section: Coarse Grained Representation Of Atomsmentioning

confidence: 99%

Large scale ab-initio simulations of dislocations

Ponga

Bhattacharya

Ortiz

2020

Journal of Computational Physics

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We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale ab-intio simulations. The approach is based on MacroDFT, a coarse-grained density functional theory method that accurately computes the electronic structure but with sub-linear scaling resulting in a tremendous reduction in cost. Due to its implementation in real-space, MacroDFT has the ability to harness petascale resources to study materials and alloys through accurate ab-initio calculations. Thus, the proposed methodology can be used to investigate dislocation cores and other defects where long range elastic defects play an important role, such as in dislocation cores, grain boundaries and near precipitates in crystalline materials. We demonstrate the method by computing the relaxed dislocation cores in prismatic dislocation loops and dislocation segments in magnesium (Mg). We also study the interaction energy with a line of Aluminum (Al) solutes. Our simulations elucidate the essential coupling between the quantum mechanical aspects of the dislocation core and the long range elastic fields that they generate. In particular, our quantum mechanical simulations are able to describe the logarithmic divergence of the energy in the far field as is known from classical elastic theory. In order to reach such scaling, the number of atoms in the simulation cell has to be exceedingly large, and cannot be achieved with the state-of-the-art density functional theory implementations.

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“…We are interested in adopting some of the methodology of HotQC [11,12,13,14] to facilitate implementation. In short, the HotQC method uses the maximum-entropy principle to obtain the least biased probability distribution function in terms of the information-theoretical notion of entropy [20], from which we obtain the grand canonical free-energy, Eq.…”

Section: Analogy With Mass Transport Modelmentioning

confidence: 99%

A unified framework for heat and mass transport at the atomic scale

Ponga¹,

Sun²

2018

Modelling Simul. Mater. Sci. Eng.

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We present a unified framework to simulate heat and mass transport in systems of particles. The proposed framework is based on kinematic mean field theory and uses a phenomenological master equation to compute effective transport rates between particles without the need to evaluate operators. We exploit this advantage and apply the model to simulate transport phenomena at the nanoscale. We demonstrate that, when calibrated to experimentally-measured transport coefficients, the model can accurately predict transient and steady state temperature and concentration profiles even in scenarios where the length of the device is comparable to the mean free path of the carriers. Through several example applications, we demonstrate the validity of our model for all classes of materials, including ones that, until now, would have been outside the domain of computational feasibility.Keywords: Nanoscale heat transport, Thermo-mechanical coupling, Mass diffusion in Solids, Finite temperature, Kinematic mean field theory.Nanoscale heat conduction is a subject of great interest due to its applications to the next-generation of nano-and micro-electronic devices, where the heat flux generated can be exceedingly large in comparison with that seen in the current generation of electronics [1,2]. Thus, it is of utmost importance to understand how heat is carried at these small scales. However, modeling and simulation of heat transport at the nanoscale is a complicated undertaking; the classical Fourier equation is no longer valid and common atomistic simulation techniques -such as molecular dynamics (MD) -are not able to model all classes of materials accurately. This is due to the fact that when the lengths of these devices become comparable to the mean free-path, the classical Fourier equation (FE) is no longer valid for predicting their behavior due to the fact that the heat carriers can scatter upon interaction with interfaces and defects, resulting in a lower conductivity than bulk materials [1,2,3]. As such, nanoscale thermal properties are intimately coupled to the distribution and * Corresponding author

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HotQC simulation of nanovoid growth under tension in copper

Cited by 12 publications

References 43 publications

Atomistic long-term simulation of heat and mass transport

Atomistic long-term simulation of heat and mass transport

Large scale ab-initio simulations of dislocations

A unified framework for heat and mass transport at the atomic scale

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