Phase Field Methods

Karma, Alain

doi:10.1016/b0-08-043152-6/01219-5

Cited by 37 publications

(26 citation statements)

References 55 publications

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“…The commonly accepted microscopic solvability theory of steadystate dendrite growth [9][10][11][12] , which builds on the earlier diffusive transport theory of Ivantsov 13 , has led to the understanding that crystalline anisotropy is a crucial parameter that uniquely determines the growth rate and tip radius of dendrites, which is the basic scaling length for the entire dendritic network. Predictions of this theory have been largely validated by phase-field simulations of dendritic evolution over the past few years for both small [14][15][16][17][18][19] and large 20 growth rate. Moreover, molecular dynamics (MD) simulation methods [21][22][23][24][25][26][27][28][29][30] as well as experimental techniques 31,32 have recently been developed to accurately compute anisotropic interfacial properties that control dendritic evolution.…”

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confidence: 99%

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Orientation selection in dendritic evolution

et al. 2006

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D endritic alloy microstructures are formed during a wide range of solidification processes from casting to welding. These microstructures result from a morphological instability of the solid-liquid interface that produces dendrites, which are highly hierarchical branched patterns with primary-, secondary-and higher-order branches. As alloy impurities segregate in the interdendritic liquid during solidification, the spatially inhomogeneous distribution of impurities in the completely solidified alloy is a direct footprint of the dendritic network that formed and coarsened during the solidification process. It also determines the formation and distribution of secondary phases, and thus has a profound influence on the properties of a wide range of technologically important structural materials, from light-weight aluminium alloys used in the automotive industry to nickel-based superalloys used for turbine blades. The study of dendritic growth 1,2 has also been of long-standing fundamental interest because of the ubiquity of branched structures exhibited by diverse interfacial pattern formation systems [3][4][5] .Major theoretical and computational advances over the past two decades have improved our fundamental understanding of dendrite growth, as well as new capabilities to simulate and predict dendritic microstructures on experimentally relevant length and timescales 6 and to elucidate new pattern formation mechanisms 7,8 that enlarge the scope of our understanding of these structures. The commonly accepted microscopic solvability theory of steadystate dendrite growth 9-12 , which builds on the earlier diffusive transport theory of Ivantsov 13 , has led to the understanding that crystalline anisotropy is a crucial parameter that uniquely determines the growth rate and tip radius of dendrites, which is the basic scaling length for the entire dendritic network. Predictions of this theory have been largely validated by phase-field simulations of dendritic evolution over the past few years for both small [14][15][16][17][18][19] and large 20 growth rate. Moreover, molecular dynamics (MD) simulation methods [21][22][23][24][25][26][27][28][29][30] as well as experimental techniques 31,32 have recently been developed to accurately compute anisotropic interfacial properties that control dendritic evolution.Despite this progress, dendrite growth theory remains limited to predicting the steady-state characteristics of dendrites growing along simple crystallographic directions, such as the 100 directions that correspond to the main crystal axes for materials with cubic symmetry, or the six directions in the basal plane of

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confidence: 99%

“…We used a well-established methodology [14][15][16][17][18] to carry out quantitative simulations at low undercooling, which was previously used to study 100 dendrites with a single anisotropy parameter ε 1 > 0 and ε 2 = 0. The present simulations only differ by the incorporation of two anisotropy parameters with γ defined by equation (1).…”

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Orientation selection in dendritic evolution

et al. 2006

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“…Therefore, equilibrium can be found by minimizing the contributions from ψ and c independently. The solution to δG/δψ = 0 is [13] …”

Section: Analytical Resultsmentioning

confidence: 99%

“…The functional derivatives of the free energy with respect to ψ and c i are If there is no segregation, all Y i are zero and we recover (12) and (13). The equilibrium on sublattice i, given by δG/δc i = 0, is independent of the other sublattices.…”

Section: Resultsmentioning

confidence: 99%

Phase-field model for grain boundary grooving in multi-component thin films

Bouville¹,

Hu²,

Chen³

et al. 2006

Modelling Simul. Mater. Sci. Eng.

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Abstract. Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the evolution of the phases, composition, microstructure and morphology of such thin films. The phase-field model is quite general, describing compounds and solid solution alloys with sufficient freedom to choose solubilities, grain boundary and interface energies, and heats of segregation to all interfaces. We present analytical results which describe the interface profiles, with and without segregation, and confirm them using numerical simulations. We demonstrate that the present model accurately reproduces the theoretical grain boundary groove angles both at and far from equilibrium. As an example, we apply the phase-field model to the special case of a Ni(Pt)Si (Ni/Pt silicide) thin film on an initially flat silicon substrate.

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“…[85][86][87][88][89] In the field of solidification and casting, this model has attracted much attention, since quite impressive outcomes of the dendrite structure were demonstrated by Kobayashi,90,91) Wheeler et al 92) and Warren and Boettinger. 93) The development of the alloy solidification model by Kim et al 94) and the multiphase-field model by Steinbach et al 95) represent important works in phase-field modeling.…”

Section: Phase-field Modeling (Microscopic-scale)mentioning

confidence: 99%

Methodological Progress for Computer Simulation of Solidification and Casting

Nakajima

Zhang²,

Oikawa

et al. 2010

ISIJ Int.

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The dramatic progress made over the last 10 to 15 years in the field of "computer simulation of solidification and casting" is greatly due to the supports by academic as well as industrial research. The driving force behind this undertaking was the promise of predictive capabilities that will allow process and material developments. Here, the recent works on modeling were summarized, for the macrosegregation in the macroscale simulation, and the Cellular Automaton, the solidification path combined with the microsegregation, the phase-field model in the meso-scale and micro-scale simulation.

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Phase Field Methods

Cited by 37 publications

References 55 publications

Orientation selection in dendritic evolution

Orientation selection in dendritic evolution

Phase-field model for grain boundary grooving in multi-component thin films

Methodological Progress for Computer Simulation of Solidification and Casting

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