Tomas Diaz de la Rubia

A multiscale model of plasticity

Abstract A framework for investigating size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale is presented. The model is based on fundamental physical laws that govern dislocation motion and their interaction with various defects and interfaces. Particularly, the multi-scale framework merges two scales, the nano-microscale where plasticity is determined by explicit three-dimensional dislocation dynamics analysis providing the material length-scale, and the continuum scale where energy transport is based on basic continuum mechanics laws. The result is a hybrid elasto-viscoplastic simulation model coupling discrete dislocation dynamics with finite element analyses. With this hybrid approach, one can address complex size-dependent problems including, dislocation boundaries, dislocations in heterogeneous structures, dislocation interaction with interfaces and associated shape changes and lattice rotations, as well as deformation in nano-structured materials, localized deformation and shear bands.

Molecular dynamics computer simulations of displacement cascades in metals

Abstract MD simulations of displacement cascades have become important in the study of atomic-scale processes in radiation damage. Here, we review recent advances and discuss results on a variety of processes in pure metals and alloys. The MD procedures, and the many-body interatomic potentials on which most recent simulations are based, are described, and then the general features of cascades in metals are reviewed. The ways in which the cascade state during the thermal-spike phase can be investigated are presented, and it is found that a liquid-like core is generated for cascade energies above 1 to 2 keV. This is shown to have important consequences for atomic mixing, disordering in ordered alloys, and vacancy clustering. Frenkel-pair production efficiency in the primary damage state at the end of the cascade process is found to be well below the NRT theoretical value in all the metals and alloys modelled to date. Clustering of interstitials is a persistent feature of cascade simulations for all pure metals. The mechanisms underlying these results are discussed, and it is observed that the simulations are in generally good agreement with what has been found by experiment.

An atomistic simulator for thin film deposition in three dimensions

We describe an atomistic simulator for thin film deposition in three dimensions (ADEPT). The simulator is designed to bridge the atomic and mesoscopic length scales by using efficient algorithms, including an option to speed up surface diffusion using events with multiple diffusion hops. Sputtered particles are inserted and assigned ballistic trajectories with angular distributions appropriate for magnetron sputtering. Atoms on the surface of the film execute surface diffusion hops with rates that depend on the local configuration, and are consistent with microscopic reversibility. The potential energies are chosen to match information obtained from a database of first principles and molecular dynamics (MD) calculations. Efficient computation is accomplished by selecting atoms with probabilities that are proportional to their hop rates. A first implementation of grain boundary effects is accomplished by including an orientation variable with each occupied site. Energies and mobilities are assigned to atom...

Dislocation multi-junctions and strain hardening

At the microscopic scale, the strength of a crystal derives from the motion, multiplication and interaction of distinctive line defects called dislocations. First proposed theoretically in 1934 (refs 1–3) to explain low magnitudes of crystal strength observed experimentally, the existence of dislocations was confirmed two decades later. Much of the research in dislocation physics has since focused on dislocation interactions and their role in strain hardening, a common phenomenon in which continued deformation increases a crystals strength. The existing theory relates strain hardening to pair-wise dislocation reactions in which two intersecting dislocations form junctions that tie the dislocations together. Here we report that interactions among three dislocations result in the formation of unusual elements of dislocation network topology, termed ‘multi-junctions’. We first predict the existence of multi-junctions using dislocation dynamics and atomistic simulations and then confirm their existence by transmission electron microscopy experiments in single-crystal molybdenum. In large-scale dislocation dynamics simulations, multi-junctions present very strong, nearly indestructible, obstacles to dislocation motion and furnish new sources for dislocation multiplication, thereby playing an essential role in the evolution of dislocation microstructure and strength of deforming crystals. Simulation analyses conclude that multi-junctions are responsible for the strong orientation dependence of strain hardening in body-centred cubic crystals.

3D dislocation dynamics : Stress-strain behavior and hardening mechanisms in fcc and bcc metals

A dislocation dynamics (DD) model for plastic deformation, connecting the macroscopic mechanical properties to basic physical laws governing dislocation mobility and related interaction mechanisms, has been under development. In this model there is a set of critical reactions that determine the overall results of the simulations, such as the stress-strain curve. These reactions are, annihilation, formation of jogs, junctions, and dipoles, and cross-slip. In this paper we discuss these reactions and the manner in which they influence the simulated stress- strain behavior in fcc and bcc metals. In particular, we examine the formation (zipping) and strength of dipoles and junctions, and effect of jogs, using the dislocation dynamics model. We show that the strengths (unzipping) of these reactions for various configurations can be determined by direct evaluation of the elastic interactions. Next, we investigate the phenomenon of hardening in metals subjected to cascade damage dislocations. The microstructure investigated consists of small dislocation loops decorating the mobile dislocations. Preliminary results reveal that these loops act as hardening agents, trapping the dislocations and resulting in increased hardening.

Lattice Monte Carlo models of thin film deposition

Monte Carlo models of crystal growth have contributed to the theoretical understanding of thin film deposition, and are now becoming available as tools to assist in device fabrication. Because they combine efficient computation and atomic-level detail, these models can be applied to a large number of crystallization phenomena. They have played a central role in the understanding of the surface roughening transition and its effect on crystal growth kinetics. In addition, columnar growth, vacancy and impurity trapping, and other growth phenomena that are closely related to atomic-level structure have been investigated by these simulations. In this chapter we review some of these applications and discuss MC modeling of sputter deposition based on materials parameters derived from first principles and molecular dynamics methods. We discuss models of deposition which include the atomic scale, but can also simulate film structure evolution on time scales of the order of hours. By the use of advanced computers and algorithms, we can now simulate systems large enough to exhibit clustered, columnar, and polycrystalline film structures. The event distribution is determined from molecular dynamics simulations, which can give diffusion rates, defect production, sputtering yields, and other information needed to match real materials. We discuss simulations of deposition into small vias and trenches, and their extension to the length scale of real devices through scaling relations.

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.

A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics

We present a framework coupling continuum elasto-viscoplasticity with three-dimensional discrete dislocation dynamics. In this approach, the elastic response is governed by the classical Hooke s law and the viscoplastic behavior is determined by the motion of curved dislocations in a three-dimensional space. The resulting hybrid continuum-discrete framework is formulated into a standard finite element model where the dislocation-induced stress is homogenized over each element with a similar treatment for the dislocation-induced plastic strain, The model can be used to investigate a wide range of small scale plasticity phenomena, including microshear bands, adiabatic shear bands, stability and formation of dislocation cells, thin films and multiplayer structures. Here we present results pertaining to the formation of deformation bands and surface distortions under dynamic loading conditions and show the capability of the model in analyzing complicated deformation-induced patterns.

Ab initio energetics of boron-interstitial clusters in crystalline Si

We have performed an extensive first-principles study of the energetics of boron clustering in silicon in the presence of excess self-interstitial atoms (SIAs). We consider complexes with up to four B atoms and two SIAs. We have conducted an extensive search for the ground-state configurations and charge states of these clusters. We find the cluster containing three B atoms and one SIA(B3I) to be remarkably stable, while all our clusters with more than 80% boron content are unstable. Hence, we propose B3I to be a stable nucleus that can grow to larger clusters. The energetics presented here can be used as input to large-scale predictive models for B diffusion and activation during ion implantation and thermal annealing.

First-principles calculation of intrinsic defect formation volumes in silicon

We present an extensive first-principles study of the pressure dependence of the formation enthalpies of all the know vacancy and self-interstitial configurations in silicon, in each charge state from -2 through +2. The neutral vacancy is found to have a formation volume that varies markedly with pressure, leading to a remarkably large negative value (-0.68 atomic volumes) for the zero-pressure formation volume of a Frenkel pair (V + I). The interaction of volume and charge was examined, leading to pressure--Fermi level stability diagrams of the defects. Finally, we quantify the anisotropic nature of the lattice relaxation around the neutral defects.