Arthur F. Voter

Efficient Annealing of Radiation Damage Near Grain Boundaries via Interstitial Emission

Preventing Radiation Damage Inside a nuclear reactor, long-term exposure to radiation causes structural damage and limits the lifetimes of the reactor components. Bai et al. (p. 1631; see the Perspective by Ackland) now show, using three simulation methods able to cover a wide range of time and length scales, that grain boundaries in copper can act as sinks for radiation-induced defects. The boundaries are able to store up defects, in the form of interstitials, which subsequently annihilate with vacancies in the bulk. This recombination mechanism has a lower energy barrier than the bulk equivalent, and so provides a lower-cost route for the copper to self-heal. Simulations show that grain boundaries store and annihilate radiation-induced defects in copper. Although grain boundaries can serve as effective sinks for radiation-induced defects such as interstitials and vacancies, the atomistic mechanisms leading to this enhanced tolerance are still not well understood. With the use of three atomistic simulation methods, we investigated defect–grain boundary interaction mechanisms in copper from picosecond to microsecond time scales. We found that grain boundaries have a surprising “loading-unloading” effect. Upon irradiation, interstitials are loaded into the boundary, which then acts as a source, emitting interstitials to annihilate vacancies in the bulk. This unexpected recombination mechanism has a much lower energy barrier than conventional vacancy diffusion and is efficient for annihilating immobile vacancies in the nearby bulk, resulting in self-healing of the radiation-induced damage.

Temperature-accelerated dynamics for simulation of infrequent events

We present a method for accelerating dynamic simulations of activated processes in solids. By raising the temperature, but allowing only those events that should occur at the original temperature, the time scale of a simulation is extended by orders of magnitude compared to ordinary molecular dynamics, while preserving the correct dynamics at the original temperature. The main assumption behind the method is harmonic transition state theory. Importantly, the method does not require any prior knowledge about the transition mechanisms. As an example, the method is applied to a study of surface diffusion, where concerted processes play a key role. In the example, times of hours are achieved at a temperature of 150 K.

A method for accelerating the molecular dynamics simulation of infrequent events

For infrequent-event systems, transition state theory (TST) is a powerful approach for overcoming the time scale limitations of the molecular dynamics (MD) simulation method, provided one knows the locations of the potential-energy basins (states) and the TST dividing surfaces (or the saddle points) between them. Often, however, the states to which the system will evolve are not known in advance. We present a new, TST-based method for extending the MD time scale that does not require advanced knowledge of the states of the system or the transition states that separate them. The potential is augmented by a bias potential, designed to raise the energy in regions other than at the dividing surfaces. State to state evolution on the biased potential occurs in the proper sequence, but at an accelerated rate with a nonlinear time scale. Time is no longer an independent variable, but becomes a statistically estimated property that converges to the exact result at long times. The long-time dynamical behavior is ex...

Accurate Interatomic Potentials for Ni, Al and Ni3Al

To obtain meaningful results from atomistic simulations of materials, the interatomic potentials must be capable of reproducing the thermodynamic properties of the system of interest. Pairwise potentials have known deficiencies that make them unsuitable for quantitative investigations of defective regions such as crack tips and free surfaces. Daw and Baskes [Phys. Rev. B 29, 6443 (1984)] have shown that including a local “volume” term for each atom gives the necessary many-body character without the severe computational dependence of explicit n-body potential terms. Using a similar approach, we have fit an interatomic potential to the Ni 3 Al alloy system. This potential can treat diatomic Ni 2 , diatomic Al 2 , fcc Ni, fcc Al and L1 2 Ni 3 Al on an equal footing. Details of the fitting procedure are presented, along with the calculation of some properties not included in the fit.

EAM STUDY OF SURFACE SELF-DIFFUSION OF SINGLE ADATOMS OF FCC METALS NI, CU, AL, AG, AU, PD AND PT

Abstract Self-diffusion of single adatoms on the (100), (110), (111), (311), and (331) surfaces of fcc metals is investigated with the embedded atom method (EAM). The general trend of activation energies for these surfaces is consistent with experimental observations. The calculated activation energies for Ni are in excellent agreement with experimental data, but those for Al and Pt differ from experimental values by up to a factor of 3. The estimated pre-exponential factors are in the range of 10 −4 −10 −2 cm 2 s , in good agreement with experiment.

Introduction to the Kinetic Monte Carlo Method

Monte Carlo refers to a broad class of algorithms that solve problems through the use of random numbers. They first emerged in the late 1940’s and 1950’s as electronic computers came into use [1], and the name means just what it sounds like, whimsically referring to the random nature of the gambling at Monte Carlo, Monaco. The most famous of the Monte Carlo methods is the Metropolis algorithm [2], invented just over 50 years ago at Los Alamos National Laboratory. Metropolis Monte Carlo (which is not the subject of this chapter) offers an elegant and powerful way to generate a sampling of geometries appropriate for a desired physical ensemble, such as a thermal ensemble. This is accomplished through surprisingly simple rules, involving almost nothing more than moving one atom at a time by a small random displacement. The Metropolis algorithm and the numerous methods built on it are at the heart of many, if not most, of the simulations studies of equilibrium properties of physical systems. In the 1960’s researchers began to develop a different kind of Monte Carlo algorithm for evolving systems dynamically from state to state. The earliest application of this approach for an atomistic system may have been Beeler’s 1966 simulation of radiation damage annealing [3]. Over the next 20 years, there were developments and applications in this area (e.g., see [3, 4, 5, 6, 7]), as well as in surface adsorption, diffusion and growth (e.g., see [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]), in statistical physics (e.g., see [18, 19, 20]), and likely other areas, too. In the 1990’s the terminology for this approach settled in as kinetic Monte Carlo, though the early papers typically don’t use this term [21]. The popularity and range of applications of kinetic Monte Carlo (KMC) has continued to grow and KMC is now a common tool for studying materials subject to irradiation, the topic of this book. The purpose of this chapter is to provide an introduction to this KMC method, by taking the reader through the basic concepts underpinning KMC and how it is typically implemented, assuming no prior knowledge of these kinds of simulations. An appealing property of KMC is that it can, in principle, give the exact dynamical evolution of a system. Although this ideal is virtually never achieved, and usually not even attempted, the KMC method is presented here from this point of view because it makes a good framework for

Dynamical corrections to transition state theory for multistate systems: Surface self‐diffusion in the rare‐event regime

We derive an expression for the classical rate constant between any two states of a multistate system. The rate is given as the transition state theory rate of escape from the originating state, multiplied by a dynamical correction factor in the form of a time‐correlation function which is evaluated using molecular dynamics techniques. This method is desiged to treat cases in which reactive state‐change events are so infrequent (e.g., at low temperature) that direct molecular dynamics calculations are unfeasible. In this regime where dynamical recrossings occur much more quickly than the average time between reactive state changes, the concept of a rate between two nonadjacent states becomes meaningful. We apply the method to the surface diffusion of Rh on Rh(100) at the temperatures employed in field ion microscope experiments.

Transition state theory description of surface self-diffusion: Comparison with classical trajectory results

We have computed the surface self‐diffusion constants on four different crystal faces [fcc(111), fcc(100), bcc(110), and bcc(211)] using classical transition state theory methods. These results can be compared directly with previous classical‐trajectory results which used the same Lennard‐Jones 6‐12 potential and template model; the agreement is good, though dynamical effects are evident for the fcc(111) and bcc(110) surfaces. Implications are discussed for low‐temperature diffusion studies, which are inaccessible to direct molecular dynamics, and the use of ab initio potentials rather than approximate pairwise potentials.

Highly optimized empirical potential model of silicon

We fit an empirical potential for silicon using the modified embedded atom (MEAM) functional form, which contains a nonlinear function of a sum of pairwise and three-body terms. The three-body term is similar to the Stillinger-Weber form. We parametrized our model using five cubic splines, each with 10 fitting parameters, and fitted the parameters to a large database using the force-matching method. Our model provides a reasonable description of energetics for all atomic coordinations, Z, from the dimer (Z = 1) to fcc and hcp (Z = 12). It accurately reproduces phonons and elastic constants, as well as point defect energetics. It also provides a good description of reconstruction energetics for both the 30° and 90° partial dislocations. Unlike previous models, our model accurately predicts formation energies and geometries of interstitial complexes - small clusters, interstitial-chain and planar {311} defects.

Synchronization of trajectories in canonical molecular-dynamics simulations: Observation, explanation, and exploitation

For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system.