■ Abstract 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.

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Phase-Field Models for Microstructure Evolution

The phase-field method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-field modeling technique. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-field equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-field models, different model formulations are exploited, depending on which is most common or most illustrative.

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An introduction to phase-field modeling of microstructure evolution

Physical and chemical properties of bimetallic surfaces

In recent years, well-defined and nearly perfect single crystal surfaces of oxide perovskites have become increasingly important. A single terminated surface is a prerequisite for reproducible thin film growth and fundamental growth studies. In this work, atomic and lateral force microscopy have been used to display different terminations of SrTiO3. We observe hydroxylation of the topmost SrO layer after immersion of SrTiO3 in water, which is used to enhance the etch-selectivity of SrO relative to TiO2 in a buffered HF solution. We reproducibly obtain perfect and single terminated surfaces, irrespective of the initial state of polished surfaces and the pH value of the HF solution. This approach to the problem might be used for a variety of multi-component oxide single crystals. True two-dimensional reflection high-energy electron diffraction intensity oscillations are observed during homo epitaxial growth using pulsed laser deposition on these surfaces.

Quasi-ideal strontium titanate crystal surfaces through formation of stontium hydroxide

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism...

Collective and single particle diffusion on surfaces

A series of simulations has been performed on grain boundaries in Ni and Ni3Al with and without boron doping using embedded atom-style potentials. A new procedure of obtaining “reference” data for boron related properties from electronic band structure calculations has been employed. Good agreement with existing experimental structural and energetic determinations was obtained. Boron is found to segregate more strongly to grain boundaries than to free surfaces. Adding boron to grain boundaries in Ni and Ni3Al increases their cohesive strength and the work required to pull apart the boundary. This effect is much more dramatic for Ni-rich boundaries than for stoichiometric or Al-rich boundaries. In some Ni-rich cases, adding boron increases the cohesive strength of the boundary to such an extent that the boundaries become stronger than the bulk. Bulk Ni3Al samples that are Ni-rich produce Ni-rich grain boundaries. The best cohesive properties of Ni3Al grain boundaries are obtained when the boundary is Ni saturated and also with boron present. Boron and nickel are found to cosegregate to the grain boundaries.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S088429140000947X

Investigation of the effects of boron on Ni3Al grain boundaries by atomistic simulations

We use ab initio density-functional theory supplemented with the embedded-atom method to study the self-diffusion of small clusters on the (111) surface of eight fcc metals. A zigzag motion is found to be important in the dimer and tetramer diffusions. The dimer diffuses by a zigzag and concerted motion. The trimer diffuses by a concerted three-atom motion. The tetramer diffuses through a zigzag motion where only two atoms move simultaneously in each step. Thus, instead of increasing, the migration energy is lowered (or stays constant) for the tetramer as compared to that for the trimer. This novel break of the upwards trend in migration energy is predicted to be a general phenomenon.

Self-Diffusion of Small Clusters on fcc Metal (111) Surfaces

Theoretical studies of grain boundaries in Ni3Al with boron or sulfur

The effects of solute dragon grain growth kinetics were studied in two dimensional (2-D) computer simulations by using a diffuse-interface field model. It is shown that, in the low velocity / low driving force regime, the velocity of a grain boundary motion departs from a linear relation with driving force (curvature) with solute drag. The nonlinear relation of migration velocity and driving force comes from the dependence of grain boundary energy and width on the curvature. The growth exponent m of power growth law for a polycrystalline system is affected by the segregation of solutes to grain boundaries. With the solute drag, the growth exponent m can take any value between 2 and 3 depending on the ratio of lattice diffusion to grain boundary mobility. The grain size and topological distributions are unaffected by solute drag, which are the same as those in a pure system.

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S. P. Chen

Papers

Investigation of the effects of boron on Ni3Al grain boundaries by atomistic simulations

Self-Diffusion of Small Clusters on fcc Metal (111) Surfaces

Theoretical studies of grain boundaries in Ni3Al with boron or sulfur

Computer Simulation of Grain Growth Kinetics with Solute Drag

Theoretical studies of ultrathin film-induced faceting on W(111) surfaces