Session W25: Focus Session: Modeling of Rare Events: Methods and Applications I

Pathways to forming glass

Upon supercooling at a finite rate, many liquids transform to glass. It is a non-equilibrium transition that depends upon both the material and the cooling protocols. We have used methods of transition path sampling to study this phenomenon in models of glass forming liquids. For the models considered, we establish the order of the transition and the nature of excitations that distinguish a melt from a glass.   

The kinetic activation-relaxation technique: an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search

While kinetic Monte Carlo algorithm has been proposed almost 40 years ago, its application in materials science has been mostly limited to lattice-based motion due to the difficulties associated with identifying new events and building usable catalogs when atoms moved into off-lattice position. Here, I present the kinetic activation-relaxation technique (kinetic ART) is an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search [1]. It combines ART nouveau [2], a very efficient unbiased open-ended activated method for finding transition states, with a topological classification [3] that allows a discrete cataloguing of local environments in complex systems, including disordered materials. In kinetic ART, local topologies are first identified for all atoms in a system. ART nouveau event searches are then launched for new topologies, building an extensive catalog of barriers and events. Next, all low energy events are fully reconstructed and relaxed, allowing to take complete account of elastic effects in the system's kinetics. Using standard kinetic Monte Carlo, the clock is brought forward and an event is then selected and applied before a new search for topologies is launched. In addition to presenting the various elements of the algorithm, I will discuss three recent applications to ion-bombarded silicon, defect diffusion in Fe and structural relaxation in amorphous silicon.\\[4pt] This work was done in collaboration with Laurent Karim B\'{e}land, Peter Brommer, Fedwa El-Mellouhi, Jean-Fran\c{c}ois Joly and Laurent Lewis.\\[4pt] [1] F. El-Mellouhi, N. Mousseau and L.J. Lewis, Phys. Rev. B. \textbf{78}, 153202 (2008); L.K. B\'{e}land \emph{et al.}, Phys. Rev. E \textbf{84}, 046704 (2011).\newline [2] G.T. Barkema and N. Mousseau, Phys. Rev. Lett. \textbf{77}, 4358 (1996); E. Machado-Charry \emph{et al.}, J. Chem Phys. 135, 034102, (2011).\newline [3] B.D. McKay, Congressus Numerantium \textbf{30}, 45 (1981).   

An improved Activation-Relaxation Technique method for finding transition pathways

The Activation-Relaxation Technique nouveau (ARTn) is an eigenvector following method for systematic search of saddle points and transition pathways on a given potential energy surface. We propose a variation of this method aiming at improving the efficiency of the local convergence close to the saddle point. The efficiency of the method is demonstrated in the case of point defects in body centered cubic iron. We also prove the convergence and robustness of a simplified version of this new algorithm. Joint work with E. Cances, M.-C. Marinica, K. Minoukadeh and F. Willaime.   

Entropic stabilization of nanoscale voids in materials under tension

While preexisting defects are known to act as nucleation sites for plastic deformation in strained materials, the kinetics of the early stages of plastic yield are still poorly understood. We use a wide range of atomistic simulation techniques (molecular dynamics, accelerated molecular dynamics, umbrella sampling, etc) to investigate the kinetics of plastic yield around small nanoscale voids in copper under uniaxial tensile strain. We demonstrate that, at finite temperatures, these voids are stabilized by strong entropic effects and show that their lifetime is significant even when the static mechanical instability limit is exceeded. This stabilization phenomenon dramatically affects the yield kinetics: the lifetime of the voids is seen to increase with increasing temperature, in contrast with the usual thermally-activated behavior. Even accounting for thermal activation, very small voids prove to be extremely inefficient nucleation sites for plasticity.   

Estimate Exponential Large Mean Exit Time for Diffusion Process

We propose an efficient numerical method to estimate the mean exit time of a high dimensional diffusion process associated with an Ito SDE with a gradient drift and small $\epsilon$ diffusion coefficient, starting from a stable equilibrium of the drift. It is well-known that the mean exit time is exponential large in $\epsilon$ and thus the direct simulation of the SDE requires long time integration. Our method only requires the simulation time $O(1 / \epsilon)$ and is based on the Ornstein-Uhlenbeck diffusion in each dimension.   

K-ART study of defect evolution on experimental time scales in bcc iron and Cu--Zr interfaces

Defects in metals are challenging to study in linear simulation schemes like molecular dynamics (MD), as diffusive activation barriers are typically high compared to $k_BT$, and most ressources are devoted to integrating out thermal vibration. Simultaneously, low-energy non-diffusive rearrangements (so-called basins) are serious obstacles for methods that use state-to-state trajectories like kinetic Monte Carlo (KMC). We combined the kinetic Activation-Relaxation technique (k-ART, [1]), an off-lattice, self-learning KMC method which correctly reproduces long-range interactions, with an autonomous basin identification scheme that averages over all in-basin transitions. This allows us to study defect evolution on much longer time scales than MD. In this talk, we present results on the vacancy cluster formation in bcc iron and interface diffusion in the Cu--Zr system.\\[4pt] [1] B\'{e}land, Brommer, \emph{et al.}, \emph{Phys.\ Rev.\ E}, {\bf 84}, 046704 (2011).   

Accelerated Molecular Dynamics of GaAs(001) Homoepitaxy: Effects of Long-Range Disorder

GaAs homoepitaxy and heteroepitaxy are both fundamentally and technologically significant. From a fundamental perspective, recent experimental work has shown that the GaAs(001) $\beta $2(2x4) substrate can transform and play an active role in diffusion and the morphologies that form during thin-film growth. Structural transformations lead to a substrate with local (2x4) domains that exhibit long-range disorder characteristic of c(2x8). At experimentally relevant temperatures, these transformations are mediated by rare events that occur over time scales ranging from ns to ms, which makes it difficult to probe the kinetics with conventional rare-event techniques. We develop an accelerated molecular dynamics (MD) protocol to deal with this challenge and we apply it to describe the temperature-dependent long-range structure of the surface. Our results are in agreement with experiment. Adatom diffusion occurs over longer time scales than those associated with transformations of the surface. Our accelerated MD studies indicate that adatom diffusion on this surface occurs via different mechanisms than those suggested by previous theoretical studies based on first-principles density-functional theory.   

Ultimate self-learning metabasin escape algorithm for supercooled liquids and glasses

A generic history-penalized metabasin escape algorithm is presented in this work without any predetermined parameters. The configuration space location and volume of imposed penalty functions are determined in self-learning processes as the complete 3N-dimensional potential energy surface is sampled. The computational efficiency is demonstrated using the binary Lennard-Jones liquid supercooled to the glass transition temperature, which shows an exponential enhancement over previous algorithm implementations.   

Modeling Correlation and Defect Effects on Mixed Polaronic and Ionic Transport in Rare-Earth Phosphates

Rare-earth phosphates are promising candidates for intermediate-temperature proton-conducting fuel cell membranes, with Sr-doped CePO$_{4}$ showing particularly high conductivity in oxidizing conditions. Since this high conductivity is likely due to hole-polarons rather than protons, the defect chemistry of incorporating charge carriers (protons versus holes versus oxygen vacancies) is currently being investigated with experiments and calculations. In this work, the dominant charge carrier and its transport in CePO$_{4}$ is calculated with density functional theory and compared to conductivity and photon beam experiments. In particular, we present ab-intio calculations on the thermodynamics of the dopants and defects and proton and hole-polaron mobilities. For the case of hole-polaron mobilities, the strength of the coupling with the lattice and the electronic coupling between sites will be investigated.