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Now showing items 1 - 16 of 29235

  • Phase field benchmark problems targeting fluid flow and electrochemistry

    Jokisaari, A. M.   Wu, W.   Voorhees, P. W.   Guyer, J. E.   Warren, J. A.   Heinonen, O. G.  

    In this work, we continue our development of phase field model benchmark problems with the addition of a third set, complimenting our previously developed problems for diffusion, precipitation, dendritic growth and linear elasticity. These benchmark problems are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from the phase field community. The first problem in this third set targets Stokes flow, with a particular emphasis on flow around an obstruction placed asymmetrically in the domain. While Stokes flow is not traditionally in the canon of phase field problems, it is a class of problems gaining importance in areas such as filtration and water purification. The second problem deals with coupled Cahn-Hilliard diffusion and electrostatic forces, which is an important area in energy storage and battery sciences. We present our own solutions and discuss sources of numerical errors for the Stokes problem as well as simple checks to avoid fundamental issues in the coupled diffusion-electrostatics problem. The latter problem contains some subtleties that we expand on in an Appendix.
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  • Benchmark problems for numerical implementations of phase field models

    Jokisaari, A. M.   Voorhees, P. W.   Guyer, J. E.   Warren, J.   Heinonen, O. G.  

    We present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative. (C) 2016 Elsevier B.V. All rights reserved.
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  • Direct Observation of "Pac-Man" Coarsening

    Yu, X. X.   Gulec, A.   Yoon, A.   Zuo, J. M.   Voorhees, P. W.   Marks, L. D.  

    We report direct observation of a "Pac-Man" like coarsening mechanism of a self-supporting thin film of nickel oxide. The ultrathin film has an intrinsic morphological instability due to surface stress leading to the development of local thicker regions at step edges. Density functional theory calculations and continuum modeling of the elastic instability support the model for the process.
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  • Coarsening of complex microstructures following spinodal decomposition

    Park, C. -L.   Gibbs, J. W.   Voorhees, P. W.   Thornton, K.  

    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. (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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  • Phase field benchmark problems for dendritic growth and linear elasticity

    Jokisaari, A. M.   Voorhees, P. W.   Guyer, J. E.   Warren, J. A.   Heinonen, O. G.  

    We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidification and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of (1) dendritic growth simulations performed with different time integrators and (2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. These numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.
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  • Thin film phase transformation kinetics: From theory to experiment

    Moghadam, M. M.   Voorhees, P. W.  

    The Level-set method simulation is used to address the effect of finite size on kinetics of thin film phase transformations. The results are first interpreted using the classic Johnson-Mehl-Avrami-Kolmogorov (JMAK) description of a nucleation and growth phase transformation that yields the average Avrami exponent and rate constant as a function of film thickness. The analysis reveals that the JMAK framework can yield a spurious thickness dependent activation energy for the transformation. To overcome this problem, we propose an analysis that allows all the kinetic parameters, including the nucleation rate and interface growth velocity in films to be determined from experiment. (C) 2016 Elsevier Ltd. All rights reserved.
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  • Ostwald ripening of faceted Si particles in an Al-Si-Cu melt

    Shahani, A. J.   Xiao, X.   Skinner, K.   Peters, M.   Voorhees, P. W.  

    The microstructural evolution of an Al-Si-Cu alloy during Ostwald ripening is imaged via synchrotron based, four-dimensional (i.e., space and time resolved) X-ray tomography. Samples of composition Al-32 wt%Si-15 wt%Cu were annealed isothermally at 650 degrees C, in the two-phase solid-liquid regime, while tomographic projections were collected in situ over the course of five hours. Advances in experimental methods and computational approaches enable us to characterize the local interfacial curvatures and velocities during ripening. The sequence of three-dimensional reconstructions and interfacial shape distributions shows highly faceted Si particles in a copper-enriched liquid, that become increasingly isotropic or rounded over time. In addition, we find that the coarsening rate constant is approximately the same in the binary and ternary systems. By coupling these experimental measurements with CAL-PHAD modeling and ab initio molecular dynamics simulation, we assess the influence of Cu on the coarsening process. Finally, we find the unusual "pinning" of microstructure at the junction between rough and smooth interfaces and suggest a mechanism for this behavior. (C) 2016 Elsevier B.V. All rights reserved.
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  • A phase-field study of the aluminizing of nickel

    Philippe, T.   Erdeniz, D.   Dunand, D. C.   Voorhees, P. W.  

    A quantitative phase-field approach for multiphase systems that is based upon CALPHAD free energies is used to model the aluminization of nickel wires, wherein vapour-phase alloying is used to deposit Al on the surface of the Ni wire and then the wire is annealed so that to remove all Al gradients and achieve a homogenous Ni-Al alloy. Both processes are modelled and numerical results are compared with experiments. It is found that the kinetics of both processes is controlled by bulk diffusion. During aluminization at 1273K, formation and growth of intermetallics, Ni2Al3 NiAl and Ni3Al, are strongly dependent on the Al content in the vapour phase. Ni2Al3 growth is very fast compared with NiAl and Ni3Al. It is also found that an intermediate Al content in the vapour phase is preferable for aluminization, since the Ni2Al3 coating thickness is difficult to control. Ni2Al3 is found to disappear in a few minutes during homogenization at 1373K. Thereafter, the NiAl phase, in which the composition is highly non-uniform after aluminization, continues growing until the supersaturation in this phase vanishes. Then, NiAl coating disappears concomitantly with the growth of Ni3Al, which disappears thereafter. Finally, the Al concentration profile in Ni(Al) homogenizes.
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  • Level-set simulation of anisotropic phase transformations via faceted growth

    Moghadam, M. M.   Voorhees, P. W.  

    Level-set method is used to simulate phase transformations with anisotropic kinetics where the transforming interface is faceted. The method overcomes previous limitation of this simulation methodology in tracking dynamic evolution of a large number of growing grains. The method is then used to simulate multi-grain phase transformations where the facets are three low-index ([1 0 0], [1 1 1], [1 1 0]) planes that yield morphologies including cube, octahedron and rhombic dodecahedron. The microstructure evolves under site-saturated nucleation and constant nucleation rate. The cube morphology undergoes fastest transformation followed by octahedron, rhombic dodecahedron and sphere. It is also shown that the Johnson-Mehl-Avrami-Kolmorgorov theory can be used to describe the kinetics of the faceted phase transformation. The resulting microstructure shows non-convex grain shapes with highly corrugated surfaces. The structures are also characterized using the average grain length along certain low index crystallographic directions, the coherent length. This measurement shows that for a cubic morphology, there is a significant difference in the coherent length for low index directions, while there is no meaningful difference in the coherent length for kinetic Wulff shapes of other anisotropies examined. (C) 2017 Published by Elsevier B.V.
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  • Modeling interface-controlled phase transformation kinetics in thin films

    Pang, E. L.   Vo, N. Q.   Philippe, T.   Voorhees, P. W.  

    The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is widely used to describe phase transformation kinetics. This description, however, is not valid in finite size domains, in particular, thin films. A new computational model incorporating the level-set method is employed to study phase evolution in thin film systems. For both homogeneous (bulk) and heterogeneous (surface) nucleation, nucleation density and film thickness were systematically adjusted to study finite-thickness effects on the Avrami exponent during the transformation process. Only site-saturated nucleation with isotropic interface-kinetics controlled growth is considered in this paper. We show that the observed Avrami exponent is not constant throughout the phase transformation process in thin films with a value that is not consistent with the dimensionality of the transformation. Finite-thickness effects are shown to result in reduced time-dependent Avrami exponents when bulk nucleation is present, but not necessarily when surface nucleation is present. (C) 2015 AIP Publishing LLC.
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  • Measurement of Interfacial Evolution in Three Dimensions

    Rowenhorst, D. J.   Voorhees, P. W.  

    The experimental measurement of the evolution of interfaces in three dimensions is reviewed, concentrating on the evolution of polycrystalline and solid-liquid systems, including growth and coarsening in dendritic systems and evolution during liquid-phase sintering. Both ex situ destructive techniques and in situ nondestructive techniques are considered. The importance of making three-dimensional measurements that can be quantified and unambiguously compared with theory is discussed, showing that these measurements provide a direct validation of theory and critical initial conditions for simulations.
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  • Pinch-off of rods by bulk diffusion RID B-6700-2009 RID B-7373-2009

    Aagesen, L. K.   Johnson, A. E.   Fife, J. L.   Voorhees, P. W.   Miksis, M. J.   Poulsen, S. O.   Lauridsen, E. M.   Marone, F.   Stampanoni, M.  

    The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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  • The dynamics of coarsening in highly anisotropic systems:Si particles in Al-Si liquids

    Shahani, A. J.   Gulsoy, E. B.   Roussochatzakis, V. J.   Gibbs, J. W.   Fife, J. L.   Voorhees, P. W.  

    The 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. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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  • Spatial correlations in symmetric and asymmetric bicontinuous structures RID B-6700-2009

    Genau, A. L.   Voorhees, P. W.  

    Spatial correlations of interfacial curvature are compared for symmetric and asymmetric two-phase mixtures produced following spinodal decomposition as given by a numerical solution to the Cahn-Hilliard equation in three dimensions. By calculating radial distribution functions of the density of interfacial area as a function of the mean interfacial curvature of these bicontinuous microstructures, it is found that long-range diffusive interactions, in combination with the morphology of the system, yield a variety of correlations and anticorrelations over a range of length scales. The asymmetric mixtures show some similarities to the symmetric mixtures, as well as other unique features. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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  • The topology and morphology of bicontinuous interfaces during coarsening RID B-6700-2009

    Kwon, Y.   Thornton, K.   Voorhees, P. W.  

    We investigate the late-stage coarsening of three-dimensional two-phase mixtures via conserved dynamics over a range of volume fractions. We find that the phases remain bicontinuous at volume fractions as low as 36%. The morphologies of these bicontinuous structures depend on the volume fraction, and they differ from the corresponding structure of a symmetric mixture coarsening via nonconserved dynamics. However, these structures have nearly the same scaled genus of approximately 0.13, possibly indicating a universality in the topology of bicontinous structures undergoing self-similar coarsening. Copyright (C) EPLA, 2009
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  • Convection in a mushy zone forced by sidewall heat losses RID B-7344-2009 RID B-6700-2009

    Roper, S. M.   Davis, S. H.   Voorhees, P. W.  

    We calculate the convective state due to weak sidewall heat losses in a mushy zone during the steady directional solidification of a binary alloy. The configuration consists of a warm liquid region and a cold solid region separated by a mixed phase region, the mushy zone, which is modeled as a reactive porous matrix. The structure of the convection that arises from horizontal temperature gradients, induced by the heat losses at the sidewalls, is characterized by a set of nondimensional parameters that describe the effects of latent heat, composition, permeability, and thermal and solutal buoyancy. We observe a wide range of behaviors and show that, as the critical Rayleigh number for convection in a horizontally uniform mush is reached, we begin to see the precursors of chimneys near the cooled boundaries. The strength of the cooling plays an important role in determining the strength and degree of localization of the convection near the boundary. We find, in common with other authors, that upflow, in this case caused by lighter fluid being released at the cooled sidewalls, leads to regions of dissolution, which are precursors to chimney formation. Although a treatment of the stability of the steady convective states presented is not considered, we identify the effects of the different physical parameters on the steady states.
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