Metastable systems pose significant problems in both analysis and simulation. We discuss here the evolution of microstructure in a shape-memory alloy where energetic contributions from disparate scales play determining roles. This is a challenge for modelling since the finest length scales cannot be ‘seen’ at macroscopic level. We then provide a mechanism for kinetics that gives a different notion metastability.

We consider some examples of triple junction equilibration in the presence of grain boundary energy anisotropy. It is shown that the presence of one or two cusp-trapped grain boundaries can reduce the restrictions upon the dihedral angles formed with the remaining (isotropic) boundaries This allows for a reduction in the average grain boundary curvature, and thus in the driving force for grain boundary migration.

A lattice statics Green's function method is described for modeling an edge dislocation in a crystal lattice. The edge dislocation is created by introducing a half plane of vacancies as in Volterra's construction. The defect space is decomposed into a part that has translation symmetry and a localized end space. The Dyson's equation for the defect Green's function is solved by using a defect space Fourier transform method for the translational part and matrix partitioning for the localized part. Preliminary results for a simple cubic model are presented.

A theoretical analysis is presented of the electromigration-induced dynamics of transgranular voids in metallic thin films. The analysis is based on self-consistent dynamical simulations of current-driven void surface propagation coupled with the distribution of the electric field in the metallic film. The simulation predictions highlight the rich nonlinear dynamics of current-driven evolution of voids that become faceted due to the strongly anisotropic nature of surface diffusion. The numerical results are analyzed based on approximate analytical solutions to faceted void migration and a linearized theory for the morphological stability of planar void facets.

Localized instabilities formation on the free surface of solids has been studied when sources of non-homogeneous stress such as dislocations or precipitates are present in the bulk. This formalism of localized perturbations has been used to describe the butterfly transformation of cubic precipitates in superalloys and the contraction of rectangular specimens under stress.

The interaction of a dilute suspension of spherical particles with a moving solidifying front is investigated analytically. The front emerges during the unidirectional solidification of a dilute binary alloy. A linear stability analysis of the planar interface reveals that the presence of the particles has a destabilizing effect, i.e. the critical value of the control parameter, taken here to be the concentration faraway from the interface, for the onset of the Mullins-Sekerka instability is lowered due to the particles' presence.

Numerical methods for time stepping the Cahn-Hilliard equation are given and discussed. The methods are unconditionally gradient stable, and are uniquely solvable for all time steps. The schemes require the solution of ill-conditioned linear equations, and numerical methods to accurately solve these equations are also discussed.

There discussed some possibilities basic concept of the nonlinear system theory and methods of modeling the microstructure of solids. It is demonstrated, that the substance distribution on the surface and in the volume of some materials possesses a determined chaotic character.

The production and morphology of hetero-structures presents problems at a variety of length-scales. A common problem is the production and accommodation of stresses in the film due to mis-match. We shall first discuss examples of atomistic nucleation and growth at interfaces and the use of atomistic simulations to obtain parameters for rate-theory models of cluster and film growth. We shall then consider the effect of stress on growing films. In strained-layer semi-conductor systems, for example, the growth of small islands gives rise to stress distributions which differ strongly from those in continuous layers. Interesting strain effects are also observed in ceramics. We will discuss the relationship between stress and the growth and morphology of films, where effective medium models may be used to derive effective bulk properties for films with imperfections such as porosity and cracks.

We have studied phase separation and subsequent coarsening of the microstructure in a two-dimensional square lattice using a stochastic Monte Carlo model and a deterministic mean field model. The differences and similarities between these approaches are discussed. We have found that a realistic diffusion mechanism through a vacancy motion in Monte Carlo simulations is cruicial in producing different coarsening mechanisms over a range of temperatures. This cannot be captured by the mean field model, in which the transformation is governed by the minimization of a free energy functional.

An extension of the classical Cahn-Hilliard equation, including elastic interactions is presented. This generalized diffusion equation allows real time simulation of phase-transformations, such as GP-zone formation in a near-commercial ΔICu alloy. No a priori assumptions about kinetics, diffusion fields, as well as precipitate shape are necessary. Shape of precipitates and kinetic of simulated GP-zone formation are in qualitatively good agreement with experiments of Sato and Takahashi, and the concurrenltly derived interfacial energies are reasonable.

Two algorithms for a numerical solution of the Cahn-Hilliard equation are presented. While the simple finite difference scheme does not converge, a slightly more complicated Fourier spectral method behaves reasonable as tested for a synthetic chemical potential.

The Potts Monte Carlo model was used to simulate microstructural evolution and characterize grain size distribution during the final stages of sintering. Simultaneous grain growth, pore migration and pore shrinkage were simulated in a system with an initial porosity of 10% with varying ratios of grain boundary mobility to pore shrinkage rates. This investigation shows that the presence of pores changes the grain size distribution and the topological characteristics due to pinning of grains by pores. As pores shrink away, their pinning effect decreases. Once pore shrinkage is complete, normal grain growth is achieved.

A grain growth model based on the results of Monte-Carlo simulations is proposed for silicon nitride. The model was derived from the Potts model; in addition, principal characteristics of silicon nitride such as presence of liquid phase and anisotropy of grain growth were introduced. Employing this model, microstructure development of silicon nitride was investigated.

Under certain simulation conditions, several grains grew in preference to other grains, and consequently, a self-reinforced microstructure was produced similar to that of actual silicon nitride. In particular, liquid phase fraction was found to be dominant factor affecting microstructure development.

Portland cement-based materials are usually composites, where the matrix consists of portland cement paste. Cement paste is a material formed from the hydration reaction of portland cement, usually a calcium silicate material, with water. The microstructure of cement paste changes drastically over a time period of about one week, with slower changes occurring over subsequent weeks to months. The effect of this hydration process on the changing microstructure can be represented using computer simulation techniques applied to three dimensional digital image-based models. Percolation theory can be used to understand the evolving microstructure in terms of the three percolation thresholds that are of importance in the cement paste microstructure: the set point, capillary porosity percolation, and the percolation of the C-S-H phase.

The evolution of dendritic morphology is simulated for a binary alloy using a two-dimensional cellular automaton growth algorithm. Solute diffusion is modeled with an alternate-direction implicit finite difference technique. Interface curvature and kinetic anisotropy are implemented through configurational terms which are incorporated into the growth potential used by the automaton. The weighting of the anisotropy term is explored and shown to be essential for overcoming grid-induced anisotropy, permitting more realistic development of dendritic morphologies. Dendritic structures are generated for both uniform and directional cooling conditions.

A 3D model has been developed to simulate both primary static recrystallization and recovery of cold worked aluminium alloys. The model is based on a modified cellular automaton approach and incorporates the influence of crystallographic texture and microstructure in respect to both mechanisms mentioned above. The model takes into account oriented nucleation using an approach developed by Nes for aluminium alloys. The subsequent growth of the nuclei depends on the local stored energy of the deformed matrix (i.e. the driving pressure) and the misorientation between a growing nucleus and its surrounding matrix (i.e. the grain boundary mobility). This approach allows to model preferred growth of grains that exhibit maximum growth rate orientation relationship, e.g. for aluminium alloys a 40° <111> relationship with the surrounding matrix. The model simulates kinetics, microstructure and texture development during heat treatment, discrete in time and space.

This paper describes our recent progress in developing a finite element method for simulating interface motion. Attention is focused on two mass transport mechanisms: interface migration and surface diffusion. A classical theory states that, for interface migration, the local normal velocity of an interface is proportional to the free energy reduction associated with a unit volume of atoms detach from one side of the interface and attach to the other side. We express this theory into a weak statement, in which the normal velocity and any arbitrary virtual motion of the interface relate to the free energy change associated with the virtual motion. An example with two degrees of freedom shows how the weak statement works. For a general case, we divide the interface into many elements, and use the positions of the nodes as the generalized coordinates. The variations of the free energy associated with the variations of the nodal positions define the generalized forces. The weak statement connects the velocity components at all the nodes to the generalized forces. A symmetric, positive-definite matrix appears, which we call the viscosity matrix. A set of nonlinear ordinary differential equations evolve the nodal positions. We then treat combined surface diffusion and evaporation-condensation in a similar method with generalized coordinates including both nodal positions and mass fluxes. Three numerical examples are included. The first example shows the capability of the method in dealing with anisotropic surface energy. The second example is pore-grain boundary separation in the final stage of ceramic sintering. The third example relates to the process of mass reflow in VLSI fabrication.

This paper presents a three-dimensional simulation for the surface evolution of a strained film on a thick substrate. The simulation shows that an initially random morphology will first transform into a profile dominated by two-dimensional ridges, and then into a three-dimensional island surface. The simulation also demonstrates that the ridge-island transition is a kinetic process which can be delayed by changing the initial morphology.

The grain coalescence phenomenon in the growth of heteroepitaxial diamond film on (001) silicon substrate by microwave plasma chemical vapor deposition was examined by using high-resolution electron microscopy. It was shown that this phenomenon evidently occurs between two diamond grains with a small-angle tilt. The coalescence was completed after some more growth steps following the meeting of such two grains, indicating the difficulty for the lattice matching in grain boundary. By performing simulation of a step-by-step growth of two diamond grains on a (001) silicon substrate with molecular orbital PM3 method, it was shown that the bonding regeneration between the two grains is essential for the coalescence and the coalescence is only possible when the orientation difference between the grains is sufficiently small so as to allow efficient overlap of electron cloud in the grain boundary. This study indicates that single crystal diamond growth may be possible by the current CVD growth techniques via further reduction of the surface roughness to gain a heteroepitaxy with very small grain tilting.

The origin of mis-oriented diamond grains frequently observed in heteroepitaxial diamond films on (001) silicon surfaces was studied. By statistically analyzing the in-plane rotation angles of diamond grains in scanning electron microscopy observations, it was found that the distribution of the grain orientation is not random and two satellite distribution peaks at about 20° and 30° accompany the main distribution peak at zero degree referenced to the <110> direction of substrate. The interface structure corresponding to the main distribution peak at zero degree of oriented diamond growth has been proposed in our previous studies. In this study, our molecular orbital PM3 simulation of a step-by-step diamond nucleation further reveals two other metastable diamond/silicon interfacial structures. The orientations of the corresponding diamond grains are parallel to the (001) silicon surface but with in-plane rotations of 20° and 30° respectively with respect to the <110> direction. We relate these two mis-oriented growths to the two satellite peaks of grain orientation distribution. Based on this study, the possibility in experiment to reduce the formation of mis-oriented configurations and to obtain a perfectly oriented diamond growth is discussed.