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.

/pdf/an-introduction-to-phase-field-modeling-of-microstructure-2cm9coegv9.pdf

An introduction to phase-field modeling of microstructure evolution

Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

http://li.mit.edu/Archive/Papers/10/Wang10.pdf

Phase field modeling of defects and deformation

This paper reviews findings on the anisotropy of the grain boundary energies. After introducing the basic concepts, there is a discussion of fundamental models used to understand and predict grain boundary energy anisotropy. Experimental methods for measuring the grain boundary energy anisotropy, all of which involve application of the Herring equation, are then briefly described. The next section reviews and compares the results of measurements and model calculations with the goal of identifying generally applicable characteristics. This is followed by a brief discussion of the role of grain boundary energies in nucleating discontinuous transitions in grain boundary structure and chemistry, known as complexion transitions. The review ends with some questions to be addressed by future research and a summary of what is known about grain boundary energy anisotropy.

/pdf/grain-boundary-energy-anisotropy-a-review-2lxthzw517.pdf

Grain boundary energy anisotropy: a review

Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

/pdf/sparse-data-structure-and-algorithm-for-the-phase-field-21d4ld6wz1.pdf

Sparse data structure and algorithm for the phase field method

http://mimp.materials.cmu.edu/rohrer/papers/2009_12.pdf

Misorientation texture development during grain growth. Part I: Simulation and experiment

https://lagrit.lanl.gov/pdfs/2005_scripta_materialia_gruber_george_kuprat_rohrer_rollett.pdf

Effect of anisotropic grain boundary properties on grain boundary plane distributions during grain growth

Misorientation texture development during grain growth. Part II: Theory

A model is described for the development of anisotropic grain boundary character distributions from initially random distributions. The model is based on biased topological changes in the grain boundary network that eliminate and create boundaries during grain growth. The grain boundary energy influences the rates of these topological changes by altering the relative areas of the interfaces. The model predicts grain boundary character distributions that are inversely related to the grain boundary energy and are consistent with experimental observations.

/pdf/a-model-for-the-origin-of-anisotropic-grain-boundary-3788snnqdo.pdf

Jason Gruber

Papers

Sparse data structure and algorithm for the phase field method

Misorientation texture development during grain growth. Part I: Simulation and experiment

Effect of anisotropic grain boundary properties on grain boundary plane distributions during grain growth

Misorientation texture development during grain growth. Part II: Theory

A Model for the Origin of Anisotropic Grain Boundary Character Distributions in Polycrystalline Materials