Phase field analysis of eutectic breakdown.

In this paper an isotropic multi-phase-field model is extended to include the effects of anisotropy and the spontaneous nucleation of an absent phase. This model is derived and compared against a published single phase model. Results from this model are compared against results from other multi-phase models, additionally this model is used to examine the break down of a regular two dimensional eutectic into a single phase dendritic front

Phase-field simulations of solidification in binary and ternary systems using a finite element method

We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling non-isothermal solidification in multicomponent multiphase systems. In this approach, a set of governing equations for the phase-field variables, for the concentrations of the alloy components and for the temperature has to be solved numerically, ensuring local entropy production and the conservation of mass and inner energy. To efficiently perform numerical simulations, we developed a numerical scheme to solve the governing equations using a finite element method on an adaptive non-uniform mesh with highest resolution in the regions of the phase boundaries. Simulation results of the solidification in ternary Ni$_{60}$Cu$_{40-x}$Cr$_{x}$ alloys are presented investigating the influence of the alloy composition on the growth morphology and on the growth velocity. A morphology diagram is obtained that shows a transition from a dendritic to a globular structure with increasing Cr concentrations. Furthermore, we comment on 2D and 3D simulations of binary eutectic phase transformations. Regular oscillatory growth structures are observed combined with a topological change of the matrix phase in 3D. An outlook for the application of our methods to describe AlCu eutectics is given.Comment: 5 pages, 3 figures, To appear in the proceedings of 14th "International Conference on Crystal Growth", ICCG-14, 9-13 August 2004 Grenoble Franc

Description of hard sphere crystals and crystal-fluid interfaces: a critical 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.Comment: 21 page

Three-dimensional phase-field study of crack-seal microstructures - insights from innovative post-processing techniques

Numerical simulations of vein evolution contribute to a better understanding of processes involved in their formation and possess the potential to provide invaluable insights into the rock deformation history and fluid flow pathways. The primary aim of the present article is to investigate the influence of a “realistic” boundary condition, i.e. an algorithmically generated “fractal” surface, on the vein evolution in 3-D using a thermodynamically consistent approach, while explaining the benefits of accounting for an extra dimensionality. The 3-D simulation results are supplemented by innovative numerical post-processing and advanced visualization techniques. The new methodologies to measure the tracking efficiency demonstrate the importance of accounting the temporal evolution; no such information is usually accessible in field studies and notoriously difficult to obtain from laboratory experiments as well. The grain growth statistics obtained by numerically post-processing the 3-D computational microstructures explain the pinning mechanism which leads to arrest of grain boundaries/multi-junctions by crack peaks, thereby, enhancing the tracking behavior

Phase Field Modeling of Fracture and Stress Induced Phase Transitions

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting from a sharp interface formulation we derive the elastic equations and the dissipative interface kinetics. We develop a phase field model to simulate these processes numerically; in the sharp interface limit, it reproduces the desired equations of motion and boundary conditions. We perform large scale simulations of fracture processes to eliminate finite-size effects and compare the results to a recently developed sharp interface method. Details of the numerical simulations are explained, and the generalization to multiphase simulations is presented

Rotating Directional Solidification of Ternary Eutectic Microstructures in Bi-In-Sn: A Phase-Field Study

For the first time, the experimental processing condition of a rotating directional solidification is simulated in this work, by means of a grand-potential-based phase-field model. To simulate the rotating directional solidification, a new simulation setup with a rotating temperature field is introduced. The newly developed configuration can be beneficent for a more precise study of the ongoing adjustment mechanisms during temperature gradient controlled solidification processes. Ad hoc, the solidification of the ternary eutectic system Bi-In-Sn with three distinct solid phases α,β,δ is studied in this paper. For this system, accurate in situ observations of both directional and rotating directional solidification experiments exist, which makes the system favorable for the investigation. The two-dimensional simulation studies are performed for both solidification processes, considering the reported 2D patterns in the steady state growth of the bulk samples. The desired αβαδ phase ordering repeat unit is obtained within both simulation types. By considering anisotropy of the interfacial energies, experimentally reported tilted lamellae with respect to normal vectors of the solidification front, as well as predominant role of αβ anisotropy in tilting phenomenon, are observed. The results are validated by using the Jackson–Hunt analysis and by comparing with the existing experimental data. The convincing agreements indicate the applicability of the introduced method