Atomistic long-term simulation of heat and mass transport

Abstract

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

Finite-temperature non-equilibrium quasi-continuum analysis of nanovoid growth in copper at low and high strain rates

“…Following Kulkarni et al (2008) and Venturini et al (2014), we specifically consider systems consisting of N identical particles, e.g., atoms or molecules. An extension to systems comprised of particles of different species may be found in Venturini et al (2014).…”

“…An extension to systems comprised of particles of different species may be found in Venturini et al (2014). We assume that the statistics of the system obeys Jaynes' principle of maximum entropy (Jaynes, 1957a,b) (see also Zubarev, 1974;Callen, 1985).…”

“…In this study, we overcome these difficulties by means of the finite-temperature quasicontinuum method (HotQC) of Kulkarni et al (Kulkarni et al, 2008;Ariza et al, 2012;Ponga et al, 2012;Venturini et al, 2014). The aim of HotQC is to account for thermal effects, including atomic-level heat conduction, without the need for tracking every thermal vibration of the atoms.…”

“…However, they can be effectively approximated by means of variational meanfield theory and the resulting variational framework provides a convenient basis for the formulation of computationally tractable models, with or without spatial coase-graining. The fidelity of HotQC has been carefully assessed by Kulkarni et al (2008) and Venturini et al (2014) by direct comparison with experimental observation, including equilibrium properties of metallic alloys including lattice parameter, linear thermal expansion coefficient, elastic moduli and surface segregation concentration. Venturini et al (2014) have additionally assessed the fidelity of empirical kinetic relations by means of two test cases: Heat conduction in silicon nanowires and hydrogen storage in palladium.…”

“…The fidelity of HotQC has been carefully assessed by Kulkarni et al (2008) and Venturini et al (2014) by direct comparison with experimental observation, including equilibrium properties of metallic alloys including lattice parameter, linear thermal expansion coefficient, elastic moduli and surface segregation concentration. Venturini et al (2014) have additionally assessed the fidelity of empirical kinetic relations by means of two test cases: Heat conduction in silicon nanowires and hydrogen storage in palladium. In all cases, the ability of HotQC to properly account for equilibrium properties, structure-dependent transport properties and the longterm behavior of atomic systems over exceedingly long times is remarkable.…”