Advances of and by phase-field modelling in condensed-matter physics

Emmerich, Heike

doi:10.1080/00018730701822522

Cited by 210 publications

(148 citation statements)

References 243 publications

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“…Fourth-order spatial terms arise naturally in phase-field models with conserved order parameters [22,21,40]. Our model is also analogous to that describing the flow of thin fluid films sliding down an inclined plane.…”

Section: Related Models In Fluid Mechanicsmentioning

confidence: 85%

“…The model predicts a saturation overshoot at the tips of the fingers, a feature that is believed to be essential for the instability of the infiltration front [70,42,30,71,31]. The mathemat-ical structure of the model is analogous to that describing the flow of thin films and driven contact lines [50,77,49,18,86,52,27,26,75,44,53], and to phase-field models of epitaxial growth of surfaces, binary transitions and solidification [21,22,19,40].…”

Section: Introductionmentioning

confidence: 97%

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Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Cueto‐Felgueroso

Juanes

2009

Journal of Computational Physics

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This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.

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Section: Related Models In Fluid Mechanicsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 97%

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Cueto‐Felgueroso

Juanes

2009

Journal of Computational Physics

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“…The main advantage of this model is that it is not necessary to explicitly track the position of a sharp interface in complex microstructural patterns. The phase-field model has been applied to a variety of solidification processes, [18][19][20][21][22] and its capability of affording a qualitative understanding of phenomena has generally been acknowledged. Despite this success, however, a long-standing issue regarding the quantitative aspect of the phase-field model remained unresolved until recently.…”

Section: Advances In Quantitative Computation Of Solidification Micromentioning

confidence: 99%

“…The phasefield model has emerged as a powerful tool for describing the microstructural evolution processes. [18][19][20][21][22][23] This is a diffuse interface approach, in which the interface is not sharp but diffuse, exhibiting non-zero thickness. The main advantage of this model is that it is not necessary to explicitly track the position of a sharp interface in complex microstructural patterns.…”

Section: Advances In Quantitative Computation Of Solidification Micromentioning

confidence: 99%

“…In 1993, Kobayashi succeeded in reproducing a complicated dendrite structure using the phase-field model. 17 Since then, phase-field simulation [18][19][20][21][22][23] has become a major tool for the simulation of solidification. The main advantage of the phase-field model is that it is not necessary to explicitly track the position of a sharp interface in complex microstructural patterns.…”

Section: Introductionmentioning

confidence: 99%

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Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages

Shibuta

Ohno

Takaki

2015

JOM

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Thanks to the recent progress in high-performance computational environments, the range of applications of computational metallurgy is expanding rapidly. In this paper, cutting-edge simulations of solidification from atomic to microstructural levels performed on a graphics processing unit (GPU) architecture are introduced with a brief introduction to advances in computational studies on solidification. In particular, million-atom molecular dynamics simulations captured the spontaneous evolution of anisotropy in a solid nucleus in an undercooled melt and homogeneous nucleation without any inducing factor, which is followed by grain growth. At the microstructural level, the quantitative phase-field model has been gaining importance as a powerful tool for predicting solidification microstructures. In this paper, the convergence behavior of simulation results obtained with this model is discussed, in detail. Such convergence ensures the reliability of results of phase-field simulations. Using the quantitative phase-field model, the competitive growth of dendrite assemblages during the directional solidification of a binary alloy bicrystal at the millimeter scale is examined by performing two-and threedimensional large-scale simulations by multi-GPU computation on the supercomputer, TSUBAME2.5. This cutting-edge approach using a GPU supercomputer is opening a new phase in computational metallurgy.

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Simulating Microstructural Evolution using the Phase Field Method

Wang

Chen

Zhou

2012

Characterization of Materials

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The key to predict material properties is the state of microstructure. Because microstructural evolution is a typical nonlinear, nonlocal, and multiparticle dynamic problem, computer simulations play an ever increasingly important role in predicting key microstructural features and their time evolution during various processes such as phase transformations, domain coarsening, and plastic deformation. A plethora of computational methods and algorithms have been developed in recent years to complement theoretical and experimental studies to explore the high dimensional material‐ and processing‐parameter space, which would not only lower the cost but also increase the efficiency of optimizing existing materials and developing new ones. In this article, a brief account of the basic features of each method, including the conventional front‐tracking methods and techniques without front‐tracking (such as Continuum/Microscopic/Coarse‐Grained Phase Field Method; Mesoscopic/Atomistic Monte Carlo; Cellular Automata; Discrete Lattice Model; Phase Field Crystal Model; Diffusive Molecular Dynamics; Microscopic Master Equations; Inhomogeneous Path Probability Method; and Molecular Dynamics) will be presented first, followed by detailed descriptions of the fundamentals of various phase‐field methods at different length scales and their model formulations. The applications of the phase field methods will be demonstrated by examples of coherent precipitation, grain growth, ferroelectric domain structure formation, dislocation core structures, and dislocation‐precipitate interactions. Existing challenges and future trends of the phase‐field methods are discussed at the end of the article.

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Advances of and by phase-field modelling in condensed-matter physics

Cited by 210 publications

References 243 publications

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages

Simulating Microstructural Evolution using the Phase Field Method

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