Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Comment: 95 pages, 48 figure

Solidification and Gravity VII

International audienc

Modeling Dendritic Solidification using Lattice Boltzmann and Cellular Automaton Methods

This dissertation presents the development of numerical models based on lattice Boltzmann (LB) and cellular automaton (CA) methods for solving phase change and microstructural evolution problems. First, a new variation of the LB method is discussed for solving the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term is treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The results showed that the model can deal with phase change problems more accurately and efficiently than explicit LB models. Furthermore, a new numerical technique is introduced for simulating dendrite growth in three dimensions. The LB method is used to calculate the transport phenomena and the CA is employed to capture the solid/liquid interface. It is assumed that the dendritic growth is driven by the difference between the local actual and local equilibrium composition of the liquid in the interface. The evolution of a threedimensional (3D) dendrite is discussed. In addition, the effect of undercooling and degree of anisotropy on the kinetics of dendrite growth is studied. Moreover, effect of melt convection on dendritic solidification is investigated using 3D simulations. It is shown that convection can change the kinetics of growth by affecting the solute distribution around the dendrite. The growth features of twodimensional (2D) and 3D dendrites are compared. Furthermore, the change in growth kinetics and morphology of Al-Cu dendrites is studied by altering melt undercooling, alloy composition and inlet flow velocity. The local-type nature of LB and CA methods enables efficient scaling of the model in petaflops supercomputers, allowing the simulation of large domains in 3D. The model capabilities with large scale simulations of dendritic solidification are discussed and the parallel performance of the algorithm is assessed. Excellent strong scaling up to thousands of computing cores is obtained across the nodes of a computer cluster, along with near-perfect weak scaling. Considering the advantages offered by the presented model, it can be used as a new tool for simulating 3D dendritic solidification under convection

Use of cellular automata-based methods for understanding material-process-microstructure relations in alloy-based additive processes

Deposition of metals through additive manufacturing has garnered research interest as of late due to the large range of potential industry applications. In particular, direct metal deposition processes such as Laser Engineered Net Shaping (LENS) have the ability to construct near net shape parts, open cellular structures, compositionally graded parts, and parts with improved mechanical properties over those manufactured via traditional methods such as casting and forging. To utilize additive processes to their full potential, it is imperative that the relationships among process parameters, development of the molten pool, microstructure, and properties are understood. Our goal in applying computational modeling to this problem is to aid in our understanding of such relationships to guide future experiments towards sets of alloying additions and deposition conditions that produce preferred microstructures. Cellular Automata (CA) based modeling techniques provide a way to bridge the scales of the complex phenomena that occur during AM processes, reducing them to physics-based rules for the evolution of cell state variables; in particular, this makes these methods well-suited for large scale parallel computing problems and large ensembles of simulations. CA is applied at the scale of individual dendrites yielding quantitative agreement with analytical models for dendrite tip undercooling as a function of solidification velocity. For dendritic colonies, CA modeled microstructures yielded favorable quantitative and qualitative agreement with expected trends in primary arm spacing, side branching, solute segregation, and non-equilibrium growth phenomena such as solute trapping and banded growth morphology. CA is also applied at the scale of multiple grains to investigate the columnar to equiaxed transition in 2D and 3D with varied nucleation undercooling, alloying addition, and interfacial response function. The lattice Boltzmann (LB) method for fluid transport is combined with COMSOL Multiphysics simulations of melt pool dynamics and the dendrite-scale CA for coupled simulation of fluid flow, solute transport, and solidification, yielding good agreement on microsegregation and dendrite arm spacing with experimental results for LENS alloy deposition. A thermal lattice Boltzmann (TLB) model of the melt pool is also developed and combined with the grain-scale CA for parallel, concurrent multiscale simulation of fluid flow, heat transport, and grain growth for LENS-representative conditions, showcasing the model\u27s ability to predict microstructure trends with changes in process conditions or alloying additions. The ability of CA to accurately predict many aspects of and trends regarding alloy solidification in additive processes show a promising future for using similar codes to augment experimental results for new alloy development, while the parallelizability and computational efficiency of CA show its potential for use in Exascale computing application codes

Multiscale modelling of the influence of convection on dendrite formation and freckle initiation during vacuum arc remelting

Vacuum Arc Remelting (VAR) is employed to produce homogeneous ingots with a controlled, fine, microstructure. It is applied to reactive and segregation prone alloys where convection can influence microstructure and defect formation. In this study, a microscopic solidification model was extended to incorporate both forced and natural convection. The Navier-Stokes equations were solved for liquid and mushy zones using a modified projection method. The energy conservation and solute diffusion equations were solved via a combined stochastic nucleation approach along with a finite difference solution to simulate dendritic growth. This microscopic model was coupled to a 3D transient VAR model which was developed by using a multi-physics modelling software package, PHYSICA. The multiscale model enables simulations covering the range from dendrites (in microns) to the complete process (in meters). These numerical models were used to investigate: (i) the formation of dendritic microstructures under natural and forced convections; (ii) initiation of solute channels (freckles) in directional solidification in terms of interdendritic thermosolutal convection; and (iii) the macroscopic physical dynamics in VAR and their influence on freckle formation. 2D and 3D dendritic microstructure were simulated by taking into account both solutal and thermal diffusion for both constrained and unconstrained growth using the solidification model. For unconstrained equiaxed dendritic growth, forced convection was found to enhance dendritic growth in the upstream region while retarding downstream growth. In terms of dimensionality, dendritic growth in 3D is faster than 2D and convection promotes the coarsening of perpendicular arms and side branching in 3D. For constrained columnar dendritic growth, downward interdendritic convection is stopped by primary dendritic arms in 2D; this was not the case in 3D. Consequently, 3D simulations must be used when studying thermosolutal convection during solidification, since 2D simulations lead to inappropriate results. The microscopic model was also used to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation during directional solidification at a microstructural level for the first time. These simulations show that the local remelting due to high solute concentrations and continuous upward convection of segregated liquid result in the formation of sustained open solute channels. High initial Sn compositions, low casting speeds and low temperature gradients, all promote the initiation of these solute channels and hence freckles. to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation during directional solidification at a microstructural level for the first time. These simulations show that the local remelting due to high solute concentrations and continuous upward convection of segregated liquid result in the formation of sustained open solute channels. High initial Sn compositions, low casting speeds and low temperature gradients, all promote the initiation of these solute channels and hence freckles

Solidification of metal alloys in pulse electromagnetic fields

This research studies the evolution of solidification microstructures in applied external physical fields including in a pulse electric current plus a static magnetic field, and a pulse electromagnetic field. A novel electromagnetic pulse device and a solidification apparatus were designed, built and commissioned in this research. It can generate programmable electromagnetic pulses with tuneable amplitudes, durations and frequencies to suit different alloys and sample dimensions for research at university laboratory and at synchrotron X-ray beamlines.Systematic studies were made using the novel pulse electromagnetic field device, together with finite element modelling of the multiphysics of the pulse electromagnetic field and microstructural characterisation of the samples made using scanning electron microscopy, X-ray imaging and tomography.The research demonstrated that the Lorentz force and magnetic flux are the dominant parameters for achieving the grain refinement and enhancing the solute diffusion. At a discharging voltage from 120 V, a complete equaxied dendritic structure can be achieved for Al-15Cu alloy samples, the strong Lorentz force not only disrupts the growing direction of primary dendrites, it is also enough to disrupts the growing directions of primary intermetallic Al2Cu phases in Al-35Cu alloy, resulting a refined solidification microstructures. The applied electromagnetic field also has significant effect on refining the eutectic structures and promoting the solute diffusion in the eutectic laminar structure.The research has demonstrated that the pulse electromagnetic field is a promising green technology for metal manufacture industry