Phase field approach to heterogeneous crystal nucleation in alloys

We extend the phase field model of heterogeneous crystal nucleation developed recently [L. Gránásy, T. Pusztai, D. Saylor, and J. A. Warren, Phys. Rev. Lett. 98, 035703 (2007)] to binary alloys. Three approaches are considered to incorporate foreign walls of tunable wetting properties into phase field simulations: a continuum realization of the classical spherical cap model (called Model A herein), a non-classical approach (Model B) that leads to ordering of the liquid at the wall, and to the appearance of a surface spinodal, and a non-classical model (Model C) that allows for the appearance of local states at the wall that are accessible in the bulk phases only via thermal fluctuations. We illustrate the potential of the presented phase field methods for describing complex polycrystalline solidification morphologies including the shish-kebab structure, columnar to equiaxed transition, and front-particle interaction in binary alloys

Ginzburg-landau-type multiphase field model for competing fcc and bcc nucleation

The official published version of the Article can be accesed from the link below - Copyright @ 2011 APSWe address crystal nucleation and fcc-bcc phase selection in alloys using a multiphase field model that relies on Ginzburg-Landau free energies of the liquid-fcc, liquid-bcc, and fcc-bcc subsystems, and determine the properties of the nuclei as a function of composition, temperature, and structure. With a realistic choice for the free energy of the fcc-bcc interface, the model predicts well the fcc-bcc phase-selection boundary in the Fe-Ni system.This work has been supported by the Hungarian Academy of Sciences under contract OTKA-K-62588, and by the ESA under PECS Contract No. 98059. Work by JRM has been sponsored by the Materials Sciences and Engineering Division, Office of Basic Energy Sci- ences, U.S. Department of Energy

Advanced operator-splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [Phys. Rev. B 75, 064107 (2007)] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed

Diffusion-controlled anisotropic growth of stable and metastable crystal polymorphs in the phase-field crystal model

The official published version of the article can be accessed from the link below - Copyright @ 2009 APSWe use a simple density functional approach on a diffusional time scale, to address freezing to the body-centered cubic (bcc), hexagonal close-packed (hcp), and face-centered cubic (fcc) structures. We observe faceted equilibrium shapes and diffusion-controlled layerwise crystal growth consistent with two-dimensional nucleation. The predicted growth anisotropies are discussed in relation with results from experiment and atomistic simulations. We also demonstrate that varying the lattice constant of a simple cubic substrate, one can tune the epitaxially growing body-centered tetragonal structure between bcc and fcc, and observe a Mullins-Sekerka-Asaro-Tiller-Grinfeld-type instability.This work has been supported by the EU FP7 Collaborative Project ENSEMBLE under Grant Agreement NMP4-SL-2008-213669, the Hungarian Academy of Sciences under contract OTKA-K-62588, the Academy of Finland via its COMP CoE grant, and by Tekes via its MASIT33 project. A. J. acknowledges financial support from the Finnish Academy of Science and Letters. T. P. acknowledges support from the Bolyai Ja´nos Grant

Shear enhanced heterogeneous nucleation in some Mg- and Al- alloys

Intensive shearing was applied to alloy melts at temperatures above their liquidus by using a twinscrew mechanism. The sheared melt was then cast into a TP1 mould for microstructural examination. Alloy melts with or without shearing were also filtered using the Prefil technique developed by N-Tech Ltd in order to analyse oxides and other second phase particles. The experimental results showed a significant grain refinement through enhancement of heterogeneous nucleation. The intensive melt shearing converted oxide films and agglomerates into well dispersed fine particles with a narrow size distribution. It was confirmed that the fine oxide particles can act as potent sites for nucleation during the solidification of the sheared melt. This paper presents the experimental results and theoretical analysis of shear enhanced heterogeneous nucleation during solidification of Mg- and Al-alloys. A multi-step heterogeneous nucleation mechanism has been proposed and discussed

Nucleation and phase selection in undercooled melts: Magnetic alloys of industrial relevance (MAGNEPHAS)

Studies of phase selection and microstructure evolution in high-performance magnetic materials are an urgent need for optimization of production routes. Containerless solidification experiments by electromagnetic levitation and drop tube solidification were conducted in undercooled melts of Fe-Co, Fe-Ni soft magnetic, and Nd-Fe-B hard magnetic alloys. Melt undercooling under microgravity was achieved in the TEMPUS facility during parabolic flight campaigns. For Fe-Co and Fe-Ni alloys significant effects of microgravity on metastable phase formation were discovered. Microstructure modifications as well as metastable phase formation as function of undercooling and melt flow were elucidated in Nd-Fe-B. Modeling of solidification processes, fluid flow and heat transfer provide predictive tools for microstructure engineering from the melt. They were developed as a link between undercooling experiments under terrestrial and microgravity conditions and the production routes of magnetic materials

Advanced operator splitting based semi-implicit spectral method to solve the binary and single component phase-field crystal model

We present extensive testing in order to find the optimum balance among errors associated with time integration, spatial discretization, and splitting for a fully spectral semi implicit scheme of the phase field crystal model. The scheme solves numerically the equations of dissipative dynamics of the binary phase field crystal model proposed by Elder et al. [Elder et al, 2007]. The fully spectral semi implicit scheme uses the operator splitting method in order to decompose the complex equations in the phase field crystal model into sub-problems that can be solved more efficiently. Using the combination of non-trivial splitting with the spectral approach, the scheme leads to a set of algebraic equations of diagonal matrix form and thus easier to solve. Using this method developed by the BCAST research team we are able to show that it speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Comparing both the finite difference scheme used by Elder et al [Elder et al, 2007] to the spectral semi implicit scheme, we are also able to show that the finite differencing cannot compete with the spectral differencing in regards to accuracy. This is mainly due to numerical dissipation in finite differencing. In addition the results show that this method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs. We have applied the semi-implicit spectral scheme for binary alloys to explore polycrystalline dendritic solidification. The kinetics of transformation has been analysed in terms of Johnson-Mehl-Avrami-Kolmogorov formalism. We show that Avrami plots are not linear, and the respective Avrami-Kolmogorov exponents (PAK) vary with the transformed fraction (or time). Using the semi-implicit spectral scheme we have been able to provide extensive numerical testing of methods in solving the single component case. This has been demonstrated by using unconditional time stepping with comparable simulations using conditional time stepping. We show the accuracy of the solution for unconditional time stepping is not compromised and furthermore computational efficiency can be significantly increased with the introduction of this scheme. Finally we have investigated how the composition of the initial liquid phase influences the eutectic morphology evolving during solidification. This is the first study that addresses this question using the dynamical density functional theory.EThOS - Electronic Theses Online ServiceEPSRCGBUnited Kingdo

Crystal nucleation and growth of spherulites demonstrated by coral skeletons and phase-field simulations

Spherulites are radial distributions of acicular crystals, common in biogenic, geologic, and synthetic systems, yet exactly how spherulitic crystals nucleate and grow is still poorly understood. To investigate these processes in more detail, we chose scleractinian corals as a model system, because they are well known to form their skeletons from aragonite (CaCO3) spherulites, and because a comparative study of crystal structures across coral species has not been performed previously. We observed that all 12 diverse coral species analyzed here exhibit plumose spherulites in their skeletons, with well-defined centers of calcification (CoCs), and crystalline fibers radiating from them. In 7 of the 12 species, we observed a skeletal structural motif not observed previously: randomly oriented, equant crystals, which we termed “sprinkles”. In Acropora pharaonis, these sprinkles are localized at the CoCs, while in 6 other species, sprinkles are either layered at the growth front (GF) of the spherulites, or randomly distributed. At the nano- and micro-scale, coral skeletons fill space as much as single crystals of aragonite. Based on these observations, we tentatively propose a spherulite formation mechanism in which growth front nucleation (GFN) of randomly oriented sprinkles, competition for space, and coarsening produce spherulites, rather than the previously assumed slightly misoriented nucleations termed “non-crystallographic branching”. Phase-field simulations support this mechanism, and, using a minimal set of thermodynamic parameters, are able to reproduce all of the microstructural variation observed experimentally in all of the investigated coral skeletons. Beyond coral skeletons, other spherulitic systems, from aspirin to semicrystalline polymers and chocolate, may also form according to the mechanism for spherulite formation proposed here. Statement of Significance: Understanding the fundamental mechanisms of spherulite nucleation and growth has broad ranging applications in the fields of metallurgy, polymers, food science, and pharmaceutical production. Using the skeletons of reef-building corals as a model system for investigating these processes, we propose a new spherulite growth mechanism that can not only explain the micro-structural diversity observed in distantly related coral species, but may point to a universal growth mechanism in a wide range of biologically and technologically relevant spherulitic materials systems

Suppression of Phase Separation in LiFePO4 Nanoparticles During Battery Discharge

Using a novel electrochemical phase-field model, we question the common belief that LixFePO4 nanoparticles separate into Li-rich and Li-poor phases during battery discharge. For small currents, spinodal decomposition or nucleation leads to moving phase boundaries. Above a critical current density (in the Tafel regime), the spinodal disappears, and particles fill homogeneously, which may explain the superior rate capability and long cycle life of nano-LiFePO4 cathodes.Comment: 27 pages, 8 figure