The dynamics of interfaces during coarsening in solid–liquid systems

Fife, Julie L.; Gibbs, John W.; Gulsoy, Emine Begum; Park, C.-L.; Thornton, Katsuyo; Voorhees, Peter W.

doi:10.1016/j.actamat.2014.01.024

Cited by 34 publications

(44 citation statements)

References 27 publications

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“…In fact, the correlation between v and H has also been observed in experimental microstructures that are free from the simplifying assumptions made in this paper. For example, a similar correlation between v and H was found in the solid-liquid dendritic mixtures of Al-Cu alloy in which the diffusion of solute in the solid phase is negligible compared to that of the liquid phase [42]. It should be noted that the cubic term in the polynomial dependence of the average interfacial velocity, v H , on the mean curvature we observe is in direct contrast to the linear dependence of the interfacial velocity, v, on the mean curvature in nonconserved (Allen-Cahn) dynamics [35].…”

Section: Overall Morphologies and Interfacial Dynamicssupporting

confidence: 61%

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Coarsening of complex microstructures following spinodal decomposition

et al. 2017

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Coarsening plays a pivotal role in materials engineering, but our understanding of the dynamics of coarsening in morphologically complex systems is still limited. In this paper, we examine the correlations between the interfacial velocity and interfacial morphologies, and then predict the evolution of mean curvature based on the correlations. Three simulated structures with varying volume fractions, two bicontinuous and one nonbicontinuous, are generated using the Cahn-Hilliard equation. We find general correlations between interfacial velocity and mean curvature, as well as between interfacial velocity and the surface Laplacian of the mean curvature. Furthermore, we find that the probability of finding a patch of interface with a given normal velocity and the same local principal curvatures is described well by a Gaussian distribution, independent of the principal curvature values and the volume fractions of the structures. We also find that average interfacial velocity is described by a polynomial of the mean curvature and the net curvature. Based on this finding, we develop a semi-analytical approach to predicting the rate of change of the mean curvature, which determines the morphological evolution of complex microstructures.

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Section: Overall Morphologies and Interfacial Dynamicssupporting

confidence: 61%

“…( ) / 2 , which measures the overall "bend" of the interface and reduces to 1/ R in spherical geometry [42]. The static nonlocal property we examine is the surface Laplacian of the mean curvature, D S H , which describes the local variation of H (but not mass transfer in this bulk-diffusion-limited process).…”

Section: Calculation Of Interfacial Quantitiesmentioning

confidence: 99%

Coarsening of complex microstructures following spinodal decomposition

et al. 2017

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“…From differential geometry, j 1 and j 2 are the eigenvalues of the 2 Â 2 curvature matrix, H [51]. Once the interfacial curvatures are obtained, an ISD can be plotted, which provides the probability of locating an interfacial patch for a given range of principal curvatures [23,25,52]. Then, the ISDs at different time-steps can be used to track, quantitatively, the morphological 1 The annealing temperature for metallography was 10°C higher than that for in situ tomography.…”

Section: Interface Shape Distributionmentioning

confidence: 99%

“…In order to assess the morphological and topological complexity of Al-Si alloy, and to analyze its evolution in time, we require a four-dimensional (i.e., 3D space plus time) analysis. X-ray tomography (XRT) is a nondestructive characterization method, where it is possible to follow the evolution of the 3D microstructure as a function of time [24,25]. In particular, X-ray phase contrast tomography (PCT), where the phase is retrieved in the near-field regime, enables the study of systems consisting of elements with similar atomic numbers, such as in an Al-Si alloy [26,27].…”

Section: Introductionmentioning

confidence: 99%

The dynamics of coarsening in highly anisotropic systems: Si particles in Al–Si liquids

et al. 2015

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a b s t r a c tThe coarsening process of an Al-29.9wt%Si alloy is studied using four-dimensional phase contrast X-ray tomography. This alloy is composed of highly anisotropic, primary Si particles in an eutectic matrix. We analyze the morphology of the primary Si particles during coarsening by determining the interface normal distribution and the interface shape distribution. The inverse surface area per unit volume increases with the cube root of time despite the lack of microstructural self-similarity and highly anisotropic particle morphology. More specifically, over the time frame of the experiments, the Si particles evolve from mostly faceted domains to a more isotropic structure that is not given by the Wulff shape of the crystal. These trends can be rationalized by the presence of twin defects that intersect particle edges and that may provide the kink sites necessary for interfacial propagation, thus leading to a more isotropic structure. While in many cases the interfacial velocity of Si solid-liquid interfaces is highly anisotropic, the presence of many defects leads to a highly mobile interface and diffusion-limited coarsening.

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“…Note that Eqn (12) is not exact. It was however used recently also by Fife and others (2014) to study local growth velocities of Al-Cu microstructures in liquid-solid systems. The coefficients in Eqn (13) are chosen to be consistent with physical parameters in the latter work.…”

Section: Curvature Dominated Growth: Diffusion Limited Casementioning

confidence: 99%

Analysis of local ice crystal growth in snow

Krol¹,

Löwe²

2016

J. Glaciol.

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ABSTRACT. The structural evolution of snow under metamorphism is one of the key challenges in snow modeling. The main driving forces for metamorphism are curvature differences and temperature gradients, inducing water vapor transport and corresponding crystal growth, which is detectable by the motion of the ice/air interface. To provide quantitative means for a microscopic validation of metamorphism models, a VTK-based image analysis method is developed to track the ice/air interface in time-lapse μCT experiments to measure local interface velocities under both, isothermal and temperature gradient conditions. Using estimates of local temperatures from microstructure-based finite element simulations, a quantitative comparison of measured interface velocities with theoretical expressions is facilitated. For isothermal metamorphism, the data are compared with a kinetics and a diffusion limited growth law. In both cases the data are largely scattered but consistently show a mean curvature dependency of the interface velocity. For temperature gradient metamorphism, we confirm that the main contribution stems from the temperature gradient induced vapor flux, accompanied by effects of mean curvature as a secondary process. The scatter and uncertainties are discussed in view of the present theoretical understanding, the experimental setup and complications such as mechanical deformations.

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The dynamics of interfaces during coarsening in solid–liquid systems

Cited by 34 publications

References 27 publications

Coarsening of complex microstructures following spinodal decomposition

Coarsening of complex microstructures following spinodal decomposition

The dynamics of coarsening in highly anisotropic systems: Si particles in Al–Si liquids

Analysis of local ice crystal growth in snow

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