Marco Berghoff

Calibration of a multi-phase field model with quantitative angle measurement

Over the last years, the phase-field method has been established to model capillarity-induced microstructural evolution in various material systems. Several phase-field models were introduced and different studies proved that the microstructure evolution is crucially affected by the triple junction (TJ’s) mobilities as well as the evolution of the dihedral angles. In order to understand basic mechanisms in multi-phase systems, we are interested in the time evolution of TJ’s, especially in the contact angles in these regions. Since the considered multi-phase systems consist of a high number of grains, it is not feasible to measure the angles at all TJ’s by hand. In this work, we present a method enabling the localization of TJ’s and the measurement of dihedral contact angles in the diffuse interface inherent in the phase-field model. Based on this contact angle measurement method, we show how to calibrate the phase-field model in order to satisfy Young’s law for different contact angles.

Description of hard-sphere crystals and crystal-fluid interfaces: A comparison between density functional approaches and a phase-field crystal model

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

Massively parallel phase-field simulations for ternary eutectic directional solidification

Microstructures forming during ternary eutectic directional solidification processes have significant influence on the macroscopic mechanical properties of metal alloys. For a realistic simulation, we use the well established thermodynamically consistent phase-field method and improve it with a new grand potential formulation to couple the concentration evolution. This extension is very compute intensive due to a temperature dependent diffusive concentration. We significantly extend previous simulations that have used simpler phase-field models or were performed on smaller domain sizes. The new method has been implemented within the massively parallel HPC framework waLBerla that is designed to exploit current supercomputers efficiently. We apply various optimization techniques, including buffering techniques, explicit SIMD kernel vectorization, and communication hiding. Simulations utilizing up to 262,144 cores have been run on three different supercomputing architectures and weak scalability results are shown. Additionally, a hierarchical, mesh-based data reduction strategy is developed to keep the I/O problem manageable at scale.

Phase-Field Simulations at the Atomic Scale in Comparison to Molecular Dynamics

Early solidification is investigated using two different simulation techniques: the molecular dynamics (MD) and the phase-field (PF) methods. While the first describes the evolution of a system on the basis of motion equations of particles, the second grounds on the evolution of continuous local order parameter field. The aim of this study is to probe the ability of the mesoscopic phase-field method to make predictions of growth velocity at the nanoscopic length scale. For this purpose the isothermal growth of a spherical crystalline cluster embedded in a melt is considered. The system in study is Ni modeled with the embedded atom method (EAM). The bulk and interfacial properties required in the PF method are obtained from MD simulations. Also the initial configuration obtained from MD data is used in the PF as input. Results for the evolution of the cluster volume at high and moderate undercooling are presented.

Application of Large-Scale Phase-Field Simulations in the Context of High-Performance Computing

In material science, simulations became a common tool for the understanding of the underlying behaviour of different classes of materials. Due to the growing complexity of problems at hand, the simulation domains, and therefore the computational effort is steadily increasing. We presents various application of the phase-field method; ranging from the solidification of ternary eutectics and pure ice systems to the interaction of multiple liquid phases on fibers. All these topics have in common, that they need a large number of cores to investigate the decisive physical effects in adequate time. We show an overview of the results for this wide range of applications and the scaling behaviour of the used software frameworks.

Compound Droplets on Fibers

Droplets on fibers have been extensively studied in the recent years. Although the equilibrium shapes of simple droplets on fibers are well established, the situation becomes more complex for compound fluidic systems. Through experimental and numerical investigations, we show herein that compound droplets can be formed on fibers and that they adopt specific geometries. We focus on the various contact lines formed at the meeting of the different phases and we study their equilibrium state. It appears that, depending on the surface tensions, the triple contact lines can remain separate or merge together and form quadruple lines. The nature of the contact lines influences the behavior of the compound droplets on fibers. Indeed, both experimental and numerical results show that, during the detachment process, depending on whether the contact lines are triple or quadruple, the characteristic length is the inner droplet radius or the fiber radius.

Efficient techniques for bridging from atomic to mesoscopic scale in phase-field simulations

We show simulation techniques that enable to computationally bridge from the atomistic up to the mesoscopic scale. To evaluate the efficiency, we use a phase-field method to simulate symmetric thermal dendrites and start the computation at an early stage of solidification related to nucleation. The early structures are taken from the molecular dynamics method. The proposed techniques allow to simulate three dimensional dendrites from the state of nuclei ≈ 50 A up to a size proportional to μ m where ternary side-arms start to grow.

Skalenübergreifende Modellierung und Optimierung vom atomistischen kristallinen Phasenfeldmodell bis zur mesoskopischen Phasenfeldmethode

Erweiterung der kristallinen Phasenfeldmethode fur mehrkomponentige Mischungen, wie ternare dendritische und lamellare eutektische Erstarrungen. Vergleich vom Keimwachstum mit Molekulardynamiksimulationen und Phasenfeldmethode. Parameter und initiale Datenstrukturen werden verwendet, um ausgehend von einem kleinen Atomcluster, einen Dendriten mit ternaren Seitenarmen zu simulieren. Optimierungstechniken zur Reduzierung des Rechenaufwandes werden entwickelt.