Christopher Race

Ab initio and atomistic study of generalized stacking fault energies in Mg and Mg-Y alloys

Magnesium-yttrium alloys show significantly improved room temperature ductility when compared with pure Mg. We study this interesting phenomenon theoretically at the atomic scale employing quantum-mechanical (so-called ab initio) and atomistic modeling methods. Specifically, we have calculated generalized stacking fault energies for five slip systems in both elemental magnesium (Mg) and Mg-Y alloys using (i) density functional theory and (ii) a set of embedded-atom-method (EAM) potentials. These calculations predict that the addition of yttrium results in a reduction in the unstable stacking fault energy of basal slip systems. Specifically in the case of an I2 stacking fault, the predicted reduction of the stacking fault energy due to Y atoms was verified by experimental measurements. Wefind a similar reduction for the stable stacking fault energy of the {11¯

The treatment of electronic excitations in atomistic models of radiation damage in metals

Atomistic simulations are a primary means of understanding the damage done to metallic materials by high energy particulate radiation. In many situations the electrons in a target material are known to exert a strong influence on the rate and type of damage. The dynamic exchange of energy between electrons and ions can act to damp the ionic motion, to inhibit the production of defects or to quench in damage, depending on the situation. Finding ways to incorporate these electronic effects into atomistic simulations of radiation damage is a topic of current major interest, driven by materials science challenges in diverse areas such as energy production and device manufacture. In this review, we discuss the range of approaches that have been used to tackle these challenges. We compare augmented classical models of various kinds and consider recent work applying semi-classical techniques to allow the explicit incorporation of quantum mechanical electrons within atomistic simulations of radiation damage. We also outline the body of theoretical work on stopping power and electron-phonon coupling used to inform efforts to incorporate electronic effects in atomistic simulations and to evaluate their performance.

How good is damped molecular dynamics as a method to simulate radiation damage in metals

Classical molecular dynamics (MD) is a frequently used technique in the study of radiation damage cascades because it provides information on very small time and length scales inaccessible to experiment. In a radiation damage process, energy transfer from ions to electrons may be important, yet there is continued uncertainty over how to accurately incorporate such effects in MD. We introduce a new technique based on the quantum mechanical Ehrenfest approximation to evaluate different methods of accounting for electronic losses. Our results suggest that a damping force proportional to velocity is sufficient to model energy transfer from ions to electrons in most low energy cascades. We also find, however, that a larger rate of energy transfer is seen when the ionic kinetic energy is confined to a focused sequence of collisions. A viscous damping coefficient dependent on the local atomic environment is shown to be an excellent model for electronic energy losses in low energy cascades in metals.

Electronic damping of atomic dynamics in irradiation damage of metals

We investigate the transfer of energy from a harmonically oscillating atom in a metal to the electronic subsystem, using a direct simulation method based on time-dependent tight-binding (TDTB). We present our results in terms of a viscous damping coefficient β to enable direct comparison with previous MD and Langevin dynamics simulations, over an ionic energy range relevant for radiation damage. Analysis of our results using time-dependent perturbation theory shows that the rate of energy transfer to the electrons is independent of the frequency of the driven atom at high electronic temperatures, but at low temperature may vary by an order of magnitude. Our simulations show β also to be dependent on the electronic temperature, the position of the atom within the unit cell and even the direction of oscillation. We conclude that a TDTB simulation can give the electronic damping for an infinite metal over a limited simulation time window dependent on system size, and show how to monitor errors in dynamic simulations due to finite-size effects.

Electronic excitations and their effect on the interionic forces in simulations of radiation damage in metals

Using time-dependent tight-binding simulations of radiation damage cascades in a model metal we directly investigate the nature of the excitations of a system of quantum mechanical electrons in response to the motion of a set of classical ions. We furthermore investigate the effect of these excitations on the attractive electronic forces between the ions. We find that the electronic excitations are well described by a Fermi-Dirac distribution at some elevated temperature, even in the absence of the direct electron-electron interactions that would be required in order to thermalize a non-equilibrium distribution. We explain this result in terms of the spectrum of characteristic frequencies of the ionic motion. Decomposing the electronic force into four well-defined components within the basis of instantaneous electronic eigenstates, we find that the effect of accumulated excitations in weakening the interionic bonds is mostly (95%) accounted for by a thermal model for the electronic excitations. This result justifies the use of the simplifying assumption of a thermalized electron system in simulations of radiation damage with an electronic temperature dependence and in the development of temperature-dependent classical potentials.

Resonant charging and stopping power of slow channelling atoms in a crystalline metal

Fast moving ions travel great distances along channels between low-index crystallographic planes, slowing through collisions with electrons, until finally they hit a host atom initiating a cascade of atomic displacements. Statistical penetration ranges of incident particles are reliably used in ion-implantation technologies, but a full, necessarily quantum-mechanical, description of the stopping of slow, heavy ions is challenging and the results of experimental investigations are not fully understood. Using a self-consistent model of the electronic structure of a metal, and explicit treatment of atomic structure, we find by direct simulation a resonant accumulation of charge on a channelling ion analogous to the Okorokov effect but originating in electronic excitation between delocalized and localized valence states on the channelling ion and its transient host neighbours, stimulated by the time-periodic potential experienced by the channelling ion. The charge resonance reduces the electronic stopping power on the channelling ion. These are surprising and interesting new chemical aspects of channelling, which cannot be predicted within the standard framework of ions travelling through homogeneous electron gases or by considering either ion or target in isolation.

An improved model of interatomic forces for large simulations of metals containing excited electrons

We derive a form for the non-conservative damping forces on metal ions due to their interactions with electrons, and present the result in the second-moment tight-binding approximation suitable for direct and efficient inclusion in a large-scale molecular dynamics simulation. We demonstrate that this form accurately captures the direction, velocity, temperature and local atomic environment dependence of the non-adiabatic force in quantum mechanical simulations in which electronic stopping is accurately calculated. No previous empirical damping force is able to reproduce this rich behaviour.

Quantifying uncertainty in molecular dynamics simulations of grain boundary migration

Molecular dynamics simulations of simple bicrystal systems have been much used as a tool to explore how the migration of grain boundaries varies with their structure and with experimental conditions. In order to permit the exploration of a large parameter space, many studies are forced to rely on a small number of simulations (often a single simulation) for each configuration. The motion of a grain boundary is inherently statistical and any variability in the measured grain boundary velocity should be taken into account in subsequent analysis of trends in grain boundary mobility. Here we present the results of large numbers of simulations of equivalent boundaries, which show that this variability can be large, particularly when small systems are simulated. We show how a bootstrap resampling approach can be used to characterise the statistical uncertainty in boundary velocity using the information present in a single simulation. We show that the approach is robust across a variety of system sizes, temperatures and driving force strengths and types, and provides a good order-of-magnitude measure of the population standard deviation across multiple equivalent simulations.

Quantum–classical simulations of the electronic stopping force and charge on slow heavy channelling ions in metals

By simulating the passage of heavy ions along open channels in a model crystalline metal using semi-classical Ehrenfest dynamics we directly investigate the nature of non-adiabatic electronic effects. Our time-dependent tight-binding approach incorporates both an explicit quantum mechanical electronic system and an explicit representation of a set of classical ions. The coupled evolution of the ions and electrons allows us to explore phenomena that lie beyond the approximations made in classical molecular dynamics simulations and in theories of electronic stopping. We report a velocity-dependent charge-localization phenomenon not predicted by previous theoretical treatments of channelling. This charge localization can be attributed to the excitation of electrons into defect states highly localized on the channelling ion. These modes of excitation only become active when the frequency at which the channelling ion moves from interstitial point to equivalent interstitial point matches the frequency corresponding to excitations from the Fermi level into the localized states. Examining the stopping force exerted on the channelling ion by the electronic system, we find broad agreement with theories of slow ion stopping (a stopping force proportional to velocity) for a low velocity channelling ion (up to about 0.5 nm fs(-1) from our calculations), and a reduction in stopping power attributable to the charge localization effect at higher velocities. By exploiting the simplicity of our electronic structure model we are able to illuminate the physics behind the excitation processes that we observe and present an intuitive picture of electronic stopping from a real-space, chemical perspective.

The Treatment of Electronic Excitations in Atomistic Simulations of Radiation Damage—A Brief Review

The material of this chapter closely follows the contents of a review article [1] written by the present author and submitted for publication in the Institute of Physics journal Reports on Progress in Physics.