Annual Review of Materials Research - Volume 32, 2002

Methods of density functional theory in statistical mechanics have been applied extensively over the past 15 years to problems in the equilibrium and dynamic properties of materials. They allow the incorporation of microscopic atomic and molecular forces at a much lower computational cost than direct simulation. This review discusses recent advances in the calculation of density functionals for materials, with particular emphasis on fluids at walls and in porous media, on crystal nucleation and growth from the melt, and on complex fluids and biomolecules. The extension of equilibrium density functional methods to approximate theories of phase transition dynamics is emphasized.

The paper is about cellular automaton models in materials science. It gives an introduction to the fundamentals of cellular automata and reviews applications, particularly for those that predict recrystallization phenomena. Cellular automata for recrystallization are typically discrete in time, physical space, and orientation space and often use quantities such as dislocation density and crystal orientation as state variables. Cellular automata can be defined on a regular or nonregular two- or three-dimensional lattice considering the first, second, and third neighbor shell for the calculation of the local driving forces. The kinetic transformation rules are usually formulated to map a linearized symmetric rate equation for sharp grain boundary segment motion. While deterministic cellular automata directly perform cell switches by sweeping the corresponding set of neighbor cells in accord with the underlying rate equation, probabilistic cellular automata calculate the switching probability of each lattice point and make the actual decision about a switching event by evaluating the local switching probability using a Monte Carlo step. Switches are in a cellular automaton algorithm generally performed as a function of the previous state of a lattice point and the state of the neighboring lattice points. The transformation rules can be scaled in terms of time and space using, for instance, the ratio of the local and the maximum possible grain boundary mobility, the local crystallographic texture, the ratio of the local and the maximum-occurring driving forces, or appropriate scaling measures derived from a real initial specimen. The cell state update in a cellular automaton is made in synchrony for all cells. The review deals, in particular, with the prediction of the kinetics, microstructure, and texture of recrystallization. Couplings between cellular automata and crystal plasticity finite element models are also discussed.

We review progress made in quantitatively ascertaining the various statistical correlation functions that are fundamental to determining the material properties of specific classes of disordered materials. Topics covered include the definitions of the correlation functions, a unified theoretical means of representing and computing the different statistical descriptors, structural characterization from two-dimensional and three-dimensional images of materials, scalar order metrics and particle packings, and reconstruction techniques.

The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.

A fracture mechanics framework has been developed for predicting crack initiation and growth in full-scale components and structures from test specimen data. Much knowledge has also been gained about the mechanisms by which fracture occurs in a variety of materials. However, the development of quantitative connections between models of the physical processes of fracture and macroscale measures of fracture resistance is still at an early stage. A key difficulty is that fracture spans several length scales from the atomistic to the macroscopic scale. In this paper, some analyses are reviewed that use micromechanical modeling to predict fracture toughness from the physics of separation and plastic flow processes. Attention is confined to fracture by cleavage in metal crystals, under both monotonic and cyclic loading conditions. The role of models at the dislocation size scale in bridging the gap between atomistic and continuum descriptions is highlighted.

An overview of the phase-field method for modeling solidification is presented, together with several example results. Using a phase-field variable and a corresponding governing equation to describe the state (solid or liquid) in a material as a function of position and time, the diffusion equations for heat and solute can be solved without tracking the liquid-solid interface. The interfacial regions between liquid and solid involve smooth but highly localized variations of the phase-field variable. The method has been applied to a wide variety of problems including dendritic growth in pure materials; dendritic, eutectic, and peritectic growth in alloys; and solute trapping during rapid solidification.

Various methods for calculating the free energies of fluids, solids, and discrete spin systems are reviewed with particular emphasis on applications relevant in materials science. First, traditional methodologies based on harmonic approximations and thermodynamic integration are examined to highlight the workings of these very useful and robust techniques. Several newer and more specialized strategies are then discussed to provide a snapshot of current practices. Our aim here is to compare and contrast several related techniques and to provide an assessment of their relative strengths.

Computation is one of the centerpieces of both the physical and biological sciences. A key thrust in computational science is the explicit mechanistic simulation of the spatiotemporal evolution of materials ranging from macromolecules to intermetallic alloys. However, our ability to simulate such systems is in the end always limited in both the spatial extent of the systems that are considered, as well as the duration of the time that can be simulated. As a result, a variety of efforts have been put forth that aim to finesse these challenges in both space and time through new techniques in which constraint is exploited to reduce the overall computational burden. The aim of this review is to describe in general terms some of the key ideas that have been set forth in both the materials and biological setting and to speculate on future developments along these lines. We begin by developing general ideas on the exploitation of constraint as a systematic tool for degree of freedom thinning. These ideas are then applied to case studies ranging from the plastic deformation of solids to the interactions of proteins and DNA.

Lattice statics (0 K) and Monte Carlo (Metropolis algorithm) simulation are utilized to determine equilibrium and metastable structures of 21 [110] symmetric tilt boundaries between 0° and 180° at 800 K, employing a Ni embedded-atom method potential; attention is paid to the effects of the macroscopic and microscopic degrees of freedom (DOFs) on grain boundary (GB) structure. Segregation of Pd is studied at all GB structures at 800 K, employing Monte Carlo and overlapping distributions Monte Carlo simulation, which yield the Gibbsian interfacial excess of Pd (ΓPd) as a function of tilt angle for both stable and metastable structures, thereby demonstrating that ΓPd is an anisotropic function of a GB's five macroscopic DOFs. In addition, atom-probe experiments on GBs on an Fe-3 at.% Si alloy, whose five macroscopic DOFs are measured by transmission electron microscopy, directly yield ΓSi and thereby demonstrate experimentally that this quantity is an anisotropic function of these DOFs.

Vacancies and self-interstitial defects in silicon are here investigated by means of semi-empirical quantum molecular dynamics simulations performed within the tight-binding model. We extensively discuss the process of formation and migration of native point defects and investigate their interaction and clustering phenomena. The formation of larger stable structures is further studied by combining tight-binding and Monte Carlo simulations.

Tight-binding simulation results provide a global picture for defect-induced microstructure evolution in bulk silicon. These results are consistent with state-of-the-art experimental data and elucidate many relevant atomic-scale mechanisms.

The kinetic Monte Carlo method is a powerful tool for exploring the evolution and properties of a wide range of problems and systems. Kinetic Monte Carlo is ideally suited for modeling the process of chemical vapor deposition, which involves the adsorption, desorption, evolution, and incorporation of vapor species at the surface of a growing film. Deposition occurs on a time scale that is generally not accessible to fully atomistic approaches such as molecular dynamics, whereas an atomically resolved Monte Carlo method parameterized by accurate chemical kinetic data is capable of exploring deposition over long times (min) on large surfaces (mm²). There are many kinetic Monte Carlo approaches that can simulate chemical vapor deposition, ranging from coarse-grained model systems with hypothetical input parameters to physically realistic atomic simulations with accurate chemical kinetic input. This article introduces the kinetic Monte Carlo technique, reviews some of the major approaches, details the construction and implementation of the method, and provides an example of its application to a technologically relevant deposition system.

Obtaining a good atomistic description of diffusion dynamics in materials has been a daunting task owing to the time-scale limitations of the molecular dynamics method. We discuss promising new methods, derived from transition state theory, for accelerating molecular dynamics simulations of these infrequent-event processes. These methods, hyperdynamics, parallel replica dynamics, temperature-accelerated dynamics, and on-the-fly kinetic Monte Carlo, can reach simulation times several orders of magnitude longer than direct molecular dynamics while retaining full atomistic detail. Most applications so far have involved surface diffusion and growth, but it is clear that these methods can address a wide range of materials problems.

We review the recent progress in our understanding of the mechanical and electrical properties of carbon nanotubes, emphasizing the theoretical aspects. Nanotubes are the strongest materials known, but the ultimate limits of their strength have yet to be reached experimentally. Modeling of nanotube-reinforced composites indicates that the addition of small numbers of nanotubes may lead to a dramatic increase in the modulus, with only minimal crosslinking. Deformations in nanotube structures lead to novel structural transformations, some of which have clear electrical signatures that can be utilized in nanoscale sensors and devices. Chemical reactivity of nanotube walls is facilitated by strain, which can be used in processing and functionalization. Scanning tunneling microscopy and spectroscopy have provided a wealth of information about the structure and electronic properties of nanotubes, especially when coupled with appropriate theoretical models. Nanotubes are exceptional ballistic conductors, which can be used in a variety of nanodevices that can operate at room temperature. The quantum transport through nanotube structures is reviewed at some depth, and the critical roles played by band structure, one-dimensional confinement, and coupling to nanoscale contacts are emphasized. Because disorder or point defect–induced scattering is effectively averaged over the circumference of the nanotube, electrons can propagate ballistically over hundreds of nanometers. However, severe deformations or highly resistive contacts isolate nanotube segments and lead to the formation of quantum dots, which exhibit Coulomb blockade effects, even at room temperature. Metal-nanotube and nanotube-nanotube contacts range from highly transmissive to very resistive, depending on the symmetry of two structures, the charge transfer, and the detailed rehybridization of the wave functions. The progress in terms of nanotube applications has been extraordinarily rapid, as evidenced by the development of several nanotube-based prototypical devices, including memory and logic circuits, chemical sensors, electron emitters and electromechanical actuators.

Atomistic aspects of dynamic fracture in a variety of brittle crystalline, amorphous, nanophase, and nanocomposite materials are reviewed. Molecular dynamics (MD) simulations, ranging from a million to 1.5 billion atoms, are performed on massively parallel computers using highly efficient multiresolution algorithms. These simulations shed new light on (a) branching, deflection, and arrest of cracks; (b) growth of nanoscale pores ahead of the crack and how pores coalesce with the crack to cause fracture; and (c) the influence of these mechanisms on the morphology of fracture surfaces. Recent advances in novel multiscale simulation schemes combining quantum mechanical, molecular dynamics, and finite-element approaches and the use of these hybrid approaches in the study of crack propagation are also discussed.

Polymers offer a wide spectrum of possibilities for materials applications, in part because of the chemical complexity and variability of the constituent molecules, and in part because they can be blended together with other organic as well as inorganic components. The majority of applications of polymeric materials is based on their excellent mechanical properties, which arise from the long-chain nature of the constituents. Microscopically, this means that polymeric materials are able to respond to external forces in a broad frequency range, i.e., with a broad range of relaxation processes. Computer simulation methods are ideally suited to help to understand these processes and the structural properties that lead to them and to further our ability to predict materials properties and behavior. However, the broad range of timescales and underlying structure prohibits any one single simulation method from capturing all of these processes.

This manuscript provides an overview of some of the more popular computational models and methods used today in the field of molecular and mesoscale simulation of polymeric materials, ranging from molecular models and methods that treat electronic degrees of freedom to mesoscopic field theoretic methods.

Computational mechanics comprises all types of computer modeling of the mechanical behavior of materials. In this contribution we concentrate on new developments in modeling based on the finite element method (FEM), especially deformation analyses based on numerical homogenization techniques (self-consistent embedding procedure, matricity model), simulations of real microstructural cut-outs, damage analyses of artificial and real microstructures, and multiscale modeling aspects. The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material, with the mechanical behavior to be determined iteratively in a self-consistent manner. Stress-strain curves have been calculated for a number of metal matrix composites with the embedded cell method and verified with literature data of a particle reinforced Ag/58vol.%Ni composite and for a transversely loaded uniaxially fiber reinforced Al/46vol.%B composite. Good agreement has been obtained between experiment and calculation, and the embedded cell model is thus found to well represent metal matrix composites with randomly arranged inclusions. Systematic studies of the mechanical behavior of fiber- and particle-reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strengthening levels for regular inclusion arrangements from conventional unit cell models. It is found that with increasing inclusion volume fractions pronounced differences in composite strengthening exist between all models. Finally, closed-form expressions are derived to predict composite strengthening for regular fiber arrangements and for realistic random fiber or particle arrangements as a function of matrix hardening and particle volume fraction. The impact of the results on effectively designing technically relevant metal matrix composites reinforced by randomly arranged strong inclusions is emphasized. Atomistic modeling such as Monte Carlo (MC) simulations and molecular dynamics (MD) methods, dislocation theoretical modeling, and continuum mechanical methods are applied in order to provide insight into the mechanical behavior of materials. Simulations are presented graphically in a systematic manner for different material systems and are compared with experimental results. Finally, it will be shown that the results can be used to predict the future behavior of materials presently in service and even to design new materials.