Showing papers by "David J. Srolovitz published in 2005"

Oxygen Diffusion in Yttria-Stabilized Zirconia: A New Simulation Model

Abstract: We present a multiscale modeling approach to study oxygen diffusion in cubic yttria-stabilized zirconia. In this approach, we employ density functional theory methods to calculate activation energies for oxygen migration in different cation environments. These are used in a kinetic Monte Carlo framework to calculate long-time oxygen diffusivities. Simulation results show that the oxygen diffusivity attains a maximum value at around 0.1 mole fraction yttria. This variation in the oxygen diffusivity with yttria mole fraction and the calculated values for the diffusivity agree well with experiment. The competing effects of increased oxygen vacancy concentration and increasing activation energy and correlation effects for oxygen diffusion with increasing yttria mole fraction are responsible for the observed dopant content dependence of the oxygen diffusivity. We provide a detailed analysis of cation-dopant-induced correlation effects in support of the above explanation.

Effect of Fe Segregation on the Migration of a Non-Symmetric Σ5 Tilt Grain Boundary in Al

Abstract: We present an analysis, based upon atomistic simulation data, of the effect of Fe impurities on grain boundary migration in Al. The first step is the development of a new interatomic potential for Fe in Al. This potential provides an accurate description of Al–Fe liquid diffraction data and the bulk diffusivity of Fe in Al. We use this potential to determine the physical parameters in the Cahn–Lucke–Stuwe (CLS) model for the effect of impurities on grain boundary mobility. These include the heat of segregation of Fe to grain boundaries in Al and the diffusivity of Fe in Al. Using the simulation-parameterized CLS model, we predict the grain boundary mobility in Al in the presence of Fe as a function of temperature and Fe concentration. The order of magnitude and the trends in the mobility from the simulations are in agreement with existing experimental results.

Systematic prediction of kinetically limited crystal growth morphologies.

Abstract: We develop a new, combined experimental and theoretical approach to make reliable predictions for the limiting case of surface reaction kinetics controlled growth. We solve the inverse problem of determining the growth velocity from observations of the evolution of the morphology of GaN islands grown by metalorganic chemical vapor deposition and make use of crystal symmetry and established theorems. We are able to predict the growth for both convex and concave surfaces, with faceted and curved features. We also give a general guideline for deducing growth velocities from experimental observations.

Thermodynamics and kinetics in materials science : a short course

Abstract: 1 Basic laws of thermodynamics 2 Phase equilibria I 3 Thermodynamic theory of solutions 4 Phase equilibria II 5 Thermodyanmics of chemical reactions 6 Interfacial phenomena 7 Thermodynamics of stressed systems 8 Kinetics of homogeneous chemical reactions 9 Thermodynamics of irreversible processes 10 Diffusion 11 Kinetics of heterogeneous processes 12 Introduction to statistical thermodynamics of gases 13 Introduction to statistical thermodynamics of condensed matter Example problem solutions Appendices

Shear ordering in thin films of spherical block copolymer.

Abstract: We have investigated shear-induced alignment of a bilayer of spherical diblock copolymer micelles within thin films using molecular dynamics simulations at two different levels of coarse-graining. At the microscopic level, the copolymers are modeled as bead and spring chains with specific interaction potentials which produce strongly segregated spherical micelles. The simulations qualitatively reveal that long-range shear-induced ordering of hexagonally arranged micelles arises because of the tendency of micelles to pursue trajectories of minimum frictional resistance against micelles in the opposing layer. This influences their alignment in the direction of shear without them breaking apart and reforming within the time scale of the simulations. As observed in experiments, the ordering is shown to be very sensitive to the film thickness and shearing rates. To access larger lengths and longer time scales, we further coarse-grain our system to a mesoscopic level where an individual micelle is represented by a spherical particle, which interacts with other micelles through an effective potential obtained from the microscopic simulations. This approach enables us to follow the time evolution of global order from locally ordered domains. An exponentially fast growth of the orientational correlation length of the hexagonal pattern at early times, followed by a crossover to linear growth, is found in the presence of shear, in contrast to the much slower power-law scalings observed in experiments without shear.

Grain boundary self-diffusion in Ni: Effect of boundary inclination

Abstract: We examined the influence of the boundary plane on grain-boundary diffusion in Ni through a series of molecular dynamics simulations. A series of 〈010〉 Σ5 tilt boundaries, including several high symmetry and low symmetry boundary planes, were considered. The self-diffusion coefficient is a strong function of boundary inclination at low temperature but is almost independent of inclination at high temperature. At all temperatures, the self-diffusion coefficients are low when at least one of the two grains has a normal with low Miller indices. The grain boundary self-diffusion coefficient is an Arrhenius function of temperature. The logarithm of the pre-exponential factor in the Arrhenius expression was shown to be nearly proportional to the activation energy for diffusion. The activation energy for self-diffusion in a (103) symmetric tilt boundary is much higher than in boundaries with other inclinations. We discuss the origin of the boundary plane density–diffusion coefficient correlation.

Stochastic simulation of dislocation glide in tantalum and Ta-based alloys

Abstract: We employ a kinetic Monte Carlo algorithm to simulate the motion of a1/2〈111〉-oriented screw dislocation on a {011}-slip plane in body centered cubic Ta and Ta-based alloys. The dislocation moves by the kink model: double kink nucleation, kink migration and kink–kink annihilation. Rates of these unit processes are parameterized based upon existing first principles data. Both short-range (solute–dislocation core) and long-range (elastic misfit) interactions between the dislocation and solute are considered in the simulations. Simulations are performed to determine dislocation velocity as a function of stress, temperature, solute concentration, solute misfit and solute–core interaction strength. The dislocation velocity is shown to be controlled by the rate of nucleation of double kinks and the dependence of the double kink nucleation rate on stress and temperature are consistent with existing analytical predictions. In alloys, dislocation velocity depends on both the short- and long-range solute dislocation interactions as well as on the solute concentration. The short-range solute–core interactions are shown to dominate the effects of alloying on dislocation mobility. The present simulation method provides the critical link between atomistic calculations of fundamental dislocation and solute properties and large scale dislocation dynamics that typically employ empirical equations of motion.

Point defect dynamics in bcc metals

Abstract: We present an analysis of the time evolution of self-interstitial atom and vacancy (point defect) populations in pure bcc metals under constant irradiation flux conditions. Mean-field rate equations are developed in parallel to a kinetic Monte Carlo (kMC) model. When only considering the elementary processes of defect production, defect migration, recombination and absorption at sinks, the kMC model and rate equations are shown to be equivalent and the time evolution of the point defect populations is analyzed using simple scaling arguments. We show that the typically large mismatch of the rates of interstitial and vacancy migration in bcc metals can lead to a vacancy population that grows as the square root of time. The vacancy cluster size distribution under both irreversible and reversible attachment can be described by a simple exponential function. We also consider the effect of highly mobile interstitial clusters and apply the model with parameters appropriate for vanadium and $\ensuremath{\alpha}$-iron.

Effects of Lanthanide Dopants on Oxygen Diffusion in Yttria‐Stabilized Zirconia

Abstract: The effects of lanthanide co-dopants on oxygen diffusion in yttria-stabilized zirconia (YSZ) are studied using a combined first principles density functional theory (DFT)/kinetic Monte Carlo (kMC) modeling approach. DFT methods are used to calculate barrier energies for oxygen migration in different local cation environments, which are then input into kMC simulations to obtain long-time oxygen diffusivities and activation energies. Simulation results show a substantial increase in the maximum value of the oxygen diffusivity upon co-doping and in the dopant content at which this value is obtained for Lu-co-doped YSZ; while relatively little change is seen for Gd-co-doped YSZ. Examination of the DFT barrier energies reveals a linear scaling of barrier heights with the size of cations at the diffusion transition state. Using this strong correlation, oxygen diffusivity is examined in YSZ co-doped with several lanthanide elements. The oxygen diffusivity decreases with dopant atomic number (and decreasing dopant ion size) for co-dopants smaller than Y, and changes relatively little when Y is replaced by co-dopants larger than it. These results are broadly consistent with experiment, and are explained in terms of cation-dopant and vacancy concentration-dependent correlation effects, with the aid of a simple analytical model.

Pyramidal structural defects in erbium silicide thin films

Abstract: A new pyramidal structural defect, 5 to 8 micron wide, has been discovered in thin films of epitaxial erbium disilicide formed by annealing thin Er films on Si(001) substrates at temperatures of 500 to 800C. Since these defects form even upon annealing in vacuum of TiN-capped films their formation is not due to oxidation. The pyramidal defects are absent when the erbium disilicide forms on amorphous substrates, which suggests that epitaxial strains play an important role in their formation. We propose that these defects form as a result of the separation of the silicide film from the substrate and its buckling in order to relieve the compressive, biaxial epitaxial stresses. Silicon can then diffuse through the silicide or along the interface to fully or partially fill the void between the buckled erbium disilicide film and the substrate.

Kinetic Monte Carlo method for dislocation migration in the presence of solute

Abstract: We present a kinetic Monte Carlo method for simulating dislocation motion in alloys within the framework of the kink model. The model considers the glide of a dislocation in a static, three-dimensional solute atom atmosphere. It includes both a description of the short-range interaction between a dislocation core and the solute and long-range solute-dislocation interactions arising from the interplay of the solute misfit and the dislocation stress field. Double-kink nucleation rates are calculated using a first-passage-time analysis that accounts for the subcritical annihilation of embryonic double kinks as well as the presence of solutes. We explicitly consider the case of the motion of a -oriented screw dislocation on a {l_brace}011{r_brace}-slip plane in body-centered-cubic Mo-based alloys. Simulations yield dislocation velocity as a function of stress, temperature, and solute concentration. The dislocation velocity results are shown to be consistent with existing experimental data and, in some cases, analytical models. Application of this model depends upon the validity of the kink model and the availability of fundamental properties (i.e., single-kink energy, Peierls stress, secondary Peierls barrier to kink migration, single-kink mobility, solute-kink interaction energies, solute misfit), which can be obtained from first-principles calculations and/or molecular-dynamics simulations.

Phase-field model for grain boundary grooving in multi-component thin films

Abstract: Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the evolution of the phases, composition, microstructure and morphology of such thin films. The phase-field model is quite general, describing compounds and solid solution alloys with sufficient freedom to choose solubilities, grain boundary and interface energies, and heats of segregation to all interfaces. We present analytical results which describe the interface profiles, with and without segregation, and confirm them using numerical simulations. We demonstrate that the present model accurately reproduces the theoretical grain boundary groove angles both at and far from equilibrium. As an example, we apply the phase-field model to the special case of a Ni(Pt)Si (Ni/Pt silicide) thin film on an initially flat silicon substrate.

Level Set Dislocation Dynamics Method

Abstract: Although dislocation theory had its origins in the early years of the last century and has been an active area of investigation ever since (see [1, 2, 3]), our ability to describe the evolution of dislocation microstructures has been limited by the inherent complexity and anisotropy of the problem. This complexity has several contributing features. The interactions between dislocations are extraordinarily long-ranged and depend on the relative positions of all dislocation segments and the orientation of their Burgers vectors and line orientation. Dislocation mobility depends on the orientations of the Burgers vector and line direction with respect to the crystal structure. A description of the dislocation structure within a solid is further complicated by such topological events as annihilation, multiplication and reaction. As a result, analytical descriptions of dislocation structure have been limited to a small number of the simplest geometrical configurations. More recently, several dislocation dynamics simulation methods have been developed that account for complex dislocation geometries and/or the motion of multiple, interacting dislocations.