A Phase‐Field Model for Crystallization into Multiple Grain Structures

Assadi, H.

doi:10.1002/3527603506.ch3

Cited by 8 publications

(6 citation statements)

References 17 publications

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“…Moreover, due to the probabilistic nature of the method, not only curvaturedriven grain coarsening, but also stochastic coarsening, can be modelled. The latter is especially relevant for coarsening of grains in the nanometre range [109].…”

Section: Phase-field Simulations Of Inoculationmentioning

confidence: 99%

Phase-field modelling for metals and colloids and nucleation therein—an overview

Emmerich¹

2009

J. Phys.: Condens. Matter

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Phase-field modelling, as it is understood today, is still a young discipline in condensed matter physics, which established itself for that class of systems in condensed matter physics, which can be characterized by domains of different phases separated by a distinct interface. Driven out of equilibrium, their dynamics results in the evolution of those interfaces, during which those might develop into well-defined structures with characteristic length scales at the nano-, micro- or mesoscale. Since the material properties of such systems are, to a large extent, determined by those small-scale structures, acquiring a precise understanding of the mechanisms that drive the interfacial dynamics is a great challenge for scientists in this field. Phase-field modelling is an approach that allows us to tackle this challenge simulation-based. This overview summarizes briefly the essentials of the conceptual background of the phase-field method, as well as recent issues the phase-field community is focusing on, as far as they are related to nucleation. To that end a brief introduction to the basic understanding underlying the diffuse interface description, which is the conceptual backbone of phase-field modelling, is given at the beginning, followed by a detailed picture of its achievements so far in applications to nucleation phenomena in metals and colloids. Within the most relevant fields of condensed matter physics, approached by phase-field modelling until now, applications to metallic systems are a traditional domain of phase-field modelling and nucleation phenomena therein have been addressed by several groups. This paper provides an overview of these. Advances in the field of colloidal systems, on the other hand, are only more recent and are addressed here in the context of contributions to soft matter physics in general.

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Section: Phase-field Simulations Of Inoculationmentioning

confidence: 99%

Phase-field modelling for metals and colloids and nucleation therein—an overview

Emmerich¹

2009

J. Phys.: Condens. Matter

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“…The differential equations for φ and C can be derived from the free‐energy functional (Emmerich, 2003a; Assadi, 2004; Hubert & Emmerich, 2005): …”

Section: Phase‐field Model and Simulation Resultsmentioning

confidence: 99%

“…Here ε and ν are constant values, G is an operator depending on the local symmetries of the crystal, and g ( φ , C ) is the local energy density, represented by a fourth‐order polynomial function (for details, see Assadi, 2004).…”

Section: Phase‐field Model and Simulation Resultsmentioning

confidence: 99%

“…a liquid). This was simplified by Assadi (2004) and folded into the phase‐field parameter – which is a reasonable approximation, as the solid–liquid differences measured by φ also represent how ‘ordered’ a region is. However, this simplification turned out to be insufficient for examining the growth of crystals at triple point boundaries and resulted in errors stemming from the layout of the calculation grid.…”

Section: Phase‐field Model and Simulation Resultsmentioning

confidence: 99%

“…Langer, 1986;Chen & Khachaturyan, 1991;Wang et al, 1993;Kobayashi et al, 2000;Emmerich, 2009). In particular, it proved to be a very powerful approach for studying front evolution problems -as in growing veins -under multiphysical influences (Emmerich, 2003b;Emmerich & Siquieri, 2006), often accompanied by the formation of several distinct phases (Emmerich & Siquieri, 2006; or grains of multiple orientations (Assadi, 2004;Hubert & Emmerich, 2005) and interactions of different governing mechanisms over several time and length scales (Emmerich et al, 2004;Eck & Emmerich, 2006).…”

Section: Transport Of Solute With Convective Contributionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling the evolution of vein microstructure with phase‐field techniques – a first look

Hubert¹,

Emmerich²,

Urai

2009

Journal Metamorphic Geology

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Vein microstructures in the Earth's crust contain a wealth of information on the physical conditions of crystal growth, but correct interpretation requires an improved understanding of the processes involved. In this paper the processes involved in the formation of veins are briefly reviewed, and the possibilities of modelling these processes using the phase-field method are discussed. This technique, which is established in the computational materials science community to investigate crystallization processes, is shown to be a powerful tool to describe processes during vein formation and other geological processes involving crystal growth.

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Phase-Field Modeling of Eutectic Growth in a Ti-Fe System with Multiple Nuclei and Misorientations

Ebrahimi

Rezende

Emmerich

2012

Metall Mater Trans A

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A Phase‐Field Model for Crystallization into Multiple Grain Structures

Cited by 8 publications

References 17 publications

Phase-field modelling for metals and colloids and nucleation therein—an overview

Phase-field modelling for metals and colloids and nucleation therein—an overview

Modelling the evolution of vein microstructure with phase‐field techniques – a first look

Phase-Field Modeling of Eutectic Growth in a Ti-Fe System with Multiple Nuclei and Misorientations

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