Computational Thermodynamics and Kinetics: Microstructure Evolution I
Sponsored by: TMS: Chemistry and Physics of Materials Committee, TMS: Computational Materials Science and Engineering Committee
Program Organizers: Niaz Abdolrahim, University of Rochester; Stephen Foiles, Sandia National Laboratories; James Morris, Oak Ridge National Laboratory; Raymundo Arroyave, Texas A & M University
Monday 8:30 AM
February 27, 2017
Location: San Diego Convention Ctr
Session Chair: David Montiel, University of Michigan; William Andrews, University of Michigan
8:30 AM Invited
Predicting the Evolution of He Precipitate Networks in Metals Using Phase-field Models: Dina Yuryev1; Michael Demkowicz2; 1Massachusetts Institute of Technology; 2Texas A&M University
Helium (He) implanted into metal composites precipitates into complex, interconnected networks of bubbles and voids. We model the growth, coalescence, and stability of these networks using the phase field method. Our approach accounts for preferential wetting and dewetting of precipitates from heterophase interfaces with location-dependent energies. We demonstrate our approach for interfaces with linear chains of wettable patches and find that different wetting energies and patch spacings give rise to different He precipitate morphologies. Applications of our simulations to the design of He damage-resistant composites will be discussed.
3-D Phase-field Modeling of Electromigration-induced Damage in Polycrystalline Thin Films : Grain-boundary Slit Propagation and Hillock Formation: Arnab Mukherjee1; Kumar Ankit2; Britta Nestler2; 1Karlsruhe University of Applied Sciences; 2Karlsruhe Institute of Technology
Electromigration-induced damage in polycrystalline interconnects manifest as slit or hillock (depending on the direction of electric field), propagating along a grain boundary (GB) that intersects an external surface. A phase-field model which accounts for electron wind force and curvature-induced fluxes along the surface and GBs is developed. Using the phase-field method, we validate the numerically simulated slit-tip kinetics and width with the previous sharp interface calculations. The validated model is then extended to investigate slit propagation at grain multi-junctions. A detailed parametric study on polycrystalline thin films sheds light on the dynamics of intricate interplay between coarsening and GB slit propagation wherein multi-junctions are observed to be more susceptible to damage. Furthermore, incipient hillocks ensue GB migration which ultimately results in coarsening in polycrystalline films.
Capillary-Mediated Interfacial Perturbation Fields: Their Exposure via Phase Field Equilibration: Martin Glicksman1; Kumar Ankit2; 1Florida Institute of Technology; 2Karlsruhe Institute of Technology (KIT), Campus South
Sharp interface theory shows that curved interfaces, with or without energy anisotropy, develop capillary-mediated ‘bias’ fields, which are responsible for stimulating subsequent pattern development at mesoscopic scales. Analytically scalar bias fields are (minus) the surface divergence of the tangential interfacial heat fluxes, driven by gradients in the chemical potential. Bias fields modulate the interface speed, stimulating pattern formation. Symmetrical grain boundary grooves with various dihedral angles at their triple points were equilibrated via grand-canonical phase-field simulations in a constant applied thermal gradient. A weak residual cooling field was uncovered when the gradient field was subtracted from the equilibrated interface potential. This persistent cooling found on a stationary grain boundary groove, while surprising, agrees closely with the cubic ‘bias’ field derived for the grain boundary groove shape using sharp interface theory. This simulation provides strong quantitative support for the existence of autogenous perturbation fields on evolving interfaces.
Comparison of the Phase-field Models to Predict the Recrystallization Kinetics: Julia Kundin1; 1University Bayreuth
For the prediction of the grain growth and recrystallization exist two, roughly classified, continuous methods. One method is the multi-phase-field models. The second method is the phase-field model of Kobayashi, Warren and Carter (KWC) with two or three order parameters that make the model more efficient and more promising for the description of polycrystals. The present work proposes an extension to the KWC model to incorporate the recrystallization process by means of an order parameter for recrystallized grains. The results of the simulation of the recrystallization process obtained by the extended KWC model are compared to existing results in the literature obtained by the original KWC model and to experimental data. The procedure of the parameter estimation for a simple isotropic case is suggested. The ability of the model to describe the grain boundaries with low misorientation and to incorporate the boundary diffusion with the impurity segregation is discussed.
10:00 AM Break
10:20 AM Invited
Grain Boundary Segregation in Binary Alloys: A Diffuse Interface Model: Fadi Abdeljawad1; Stephen Foiles1; Brad Boyce1; Khalid Hattar1; Blythe Clark1; 1Sandia National Laboratories
Segregation of elemental species/impurities to grain boundaries (GBs) strongly influences a wide range of materials processes. In nanocrystalline (NC) alloys, GB segregation has been proposed as a route to thermally stabilize the grain structure of such systems. Herein, based on a diffuse interface model that accounts for both bulk and GB thermodynamics, solute-GB interactions, and GB migration, we present quantitative analysis of GB segregation and its impact on grain growth dynamics. First, analytical treatments are presented, which establish regimes where the reduction in GB energy can be large. Then we turn our attention to immiscible NC alloys, where the interplay between GB segregation and bulk precipitation determines the extent of solute partitioning between the grains and GBs, affecting the overall thermal stability of these systems. Finally, we highlight several features and limitations of the modeling framework and discuss further extensions aimed at incorporating microstructural anisotropy into the segregation behavior.
Strong Interfacial Energy Anisotropy in the PRISMS-PF Phase Field Model Code: William Andrews1; Stephen DeWitt1; Shiva Rudraraju1; Larry Aagesen2; Katsuyo Thornton1; 1University of Michigan; 2Idaho National Lab
Interfacial energy anisotropy is frequently observed in materials. When the anisotropy is sufficiently large, flat facets and sharp corners (edges) form in the equilibrium shape of a second-phase particle, and interfaces with unstable orientations undergo thermal faceting, the decomposition of thermodynamically unstable orientations into stable ones. We have developed and verified a phase field model with bulk diffusion and strong interfacial anisotropy that can generate nearly flat facets and that results in the expected corner (edge) and thermal-faceting behavior, while retaining well-posedness via the incorporation of a higher-order regularization term. This model has been implemented in the phase field (PF) code developed within the Center for PRedictive Integrated Structural Materials Science (PRISMS), which is an open source phase field code that employs the deal.II finite element library. The effect of the regularization on simulated equilibrium shapes, as well as the features and performance of the PRISMS-PF implementation, will be discussed.
First-principles/Phase-field Modeling of Equilibrium θ^' Precipitation in Al-Cu Alloys: Kyoungdoc Kim1; M. P. Gururajan2; C. Wolverton1; P. W. Voorhees1; 1Northwestern University; 2Indian Institute of Technology Bombay
The growth of equilibrium Al2Cu (θ^') morphology in Al-Cu alloys is examined using a phase field method with the parameters supplied by first-principles methods. The phase field method allows for an interfacial energy that is highly anisotropic: there are missing orientations and corners on the Wulff shape. This yields a plate-shaped equilibrium θ^' precipitate. Also, we consider the effects of a mismatch in elastic-moduli (elastic inhomogeneity) of Al and θ^', as well as tetragonal misfit strain anisotropy. The results show that the aspect ratio of a precipitate with the anisotropy of interfacial and strain energy as given by the first-principles methods is significantly smaller than the equilibrium aspect ratio observed in the experiment. Specifically, the computed equilibrium aspect ratio of the particle morphology is almost ten-times smaller than the aspect ratio observed in experiment. We conclude that the experimental equilibrium morphology is strongly influenced by the kinetics of particle growth.
Conversion of an Internal Freedom to Configurational Freedom by Cluster Variation Method: Tetsuo Mohri1; 1Tohoku University
An entropy of an alloy generally reflects the configurational freedom of an atomic arrangement. Cluster Variation Method (CVM) has been recognized as a reliable theoretical tool to calculate configurational entropy of a given alloy system. Recent development of Continuous Displacement CVM (CDCVM) expands the calculation by indluding local atomic displacements. In the CDCVM, atoms displaced in the different positions are regarded as different atomic species and the freedom of atomic displacements are converted to the configurational freedom of multicomponent alloys. Such a conversion of internal freedom of an alloy can be extended to magnetic freedom and collective atomic displacement leading to phase transiton. In this talk, we summarize the progress of Continuous Displacement Cluster Variation Method and discuss its extension to phase transition kinetics.
Nonlinear Elastic Effects in Phase Field Crystal and Amplitude Equations:Comparison to Ab Initio Simulations of bcc Metals and Graphene: Claas Hüter1; Martin Friak2; Marc Weikamp1; Jörg Neugebauer3; Nigel Goldenfeld4; Bob Svendsen5; Robert Spatschek1; 1Forschungszentrum Jülich; 2Institute of Physics of Materials, Academy of Sciences of the Czech Republic; 3MPIE; 4University of Illinois at Urbana-Champaign; 5RWTH Aachen University
We advance the description of nonlinear elastic deformations in terms of the phase field crystal model and corresponding amplitude equation formulations. We identify the sources of geometric and constitutional nonlinearity. The former is expressed through a finite strain tensor based on the inverse right Cauchy-Green deformation tensor. It correctly catches the strain dependence of the stiffness for anisotropic and isotropic behavior, while the elastic energy can be expressed equivalently through the left deformation tensor only in isotropic one- and two-dimensional situations. In the isotropic low-temperature regime, the nonlinear elastic effects are related to the Birch-Murnaghan equation of state. The bcc amplitude equations yield a bulk modulus derivative K'= 4. If the strain dependence of the density wave amplitudes is taken into account, this reflects elastic weakening. For general anisotropic deformations, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.