Papers by Author: Markus Rettenmayr

Abstract: A model for simulating mushy zone resolidification in a temperature gradient is presented. For describing macroscopic mass transport in the liquid phase in the mushy zone, an extended diffusion equation is solved numerically using the Finite Difference Method. Temperature dependent local equilibria at each position in the mushy zone are calculated using the thermodynamic software package ChemApp. The resolidification model treats multicomponent alloying systems and accounts for multiphase equilibria. Simulation results for peritectic Cu-40wt%Al and eutectic Al-5wt%Si-1wt%Mg alloys are compared with microstructures from temperature gradient annealing experiments. It is shown that the model is well suited to predict mushy zone resolidification in multicomponent and multiphase alloys. The predicted evolution of the liquid fraction is qualitatively in full agreement with the observed microstructures, including local remelting at the peritectic temperature prior to resolidification, an effect that was first predicted by the model and confirmed by the experiments.

Abstract: An experimental approach employing temperature and concentration gradients is presented that is suitable for determining impurity diffusion coefficients in a single experimental cycle. The Al-Cu system is used to illustrate the feasibility of the method. In a single phase α-Al solid solution, concentration gradients are generated by exposing a cylindrical sample to steep temperature gradients and by annealing until the initially formed mushy zone is re-solidified. The annealing is performed such that a symmetric, ramp shaped profile in the form of a roof is generated. The sample is then again exposed to a temperature gradient at somewhat lower temperatures for an extended time period. The symmetric profile then becomes asymmetric due to the varying diffusion coefficient along the sample. Information on the pre-exponential factor D₀ and the activation energy for diffusion Q_D is retrieved from the asymmetry of the resulting concentration profile. The asymmetry becomes increasingly pronounced with longer diffusion times, yielding an increasing accuracy of the diffusion coefficients. The experimental approach is generally applicable to alloy systems with finite solubility.

Abstract: Melting of a single-phase polycrystalline material is known to start by the formation of liquid films at the surface and at grain boundaries. The internal liquid films are not necessarily quiescent, but can migrate to avoid/reduce supersaturation in the solid phase. The migration is discussed in the literature to be governed by coherency strains of the solid/liquid interface, by concentration gradients in the liquid or by concentration gradients in the solid phase. A phase transformation model for diffusional phase transformations considering interface thermodynamics (possible deviations from local deviations) has been put up to describe the migration of the solid/liquid (trailing) and the liquid/solid (leading) interfaces of the liquid film. New experimental results on melting in a temperature gradient in combination with simulation calculations reveal that concentration fluctuations in the liquid phase trigger the liquid film migration and determine the migration direction, until after a short time in the order of microseconds the process is governed by diffusion in the solid phase.

Abstract: Melting and solidification are both phase transformations involving a liquid and a solid phase. In a simplifying procedure melting could be treated as the inverse process of solidification. However, there are substantial differences in the thermodynamics and kinetics of melting and solidification. The elaboration of a model for melting of binary alloys has lead to the possibility to also describe solidification processes more consistently. Input parameters in the model are the Gibbs Free Energy curves and the diffusion coefficients in the liquid and solid phase, respectively. Assumptions about the thermodynamic state of the interface like local equilibrium are not necessary, recently developed interface thermodynamics is coupled with the kinetic equations. Simulations results for steady-state melting and solidification are compared. The treatment of both solidification and melting yields some insight in the proper¬ties of the liquid/solid interface and its role during the phase transformation.

Abstract: Solidification and melting are phase transitions from the liquid to solid state or vice versa and are thus often assumed to be similar processes with only opposite direction. However, they can be fundamentally different, i.e. asymmetric, in aspects of both thermodynamics and kinetics. It is known that superheat in the solid is difficult to obtain, unlike supercooling in the liquid. This is often attributed to the fact that nucleation in the liquid can occur (homogeneously or heterogeneously) in the bulk, in the solid it will occur at outer or inner surfaces of the crystal. A further asymmetry is evident as the growing phase is a phase with fast diffusion kinetics in the case of melting, with slow diffusion kinetics in the case of solidification. Two types of experiments (solutal melting and melting/resolidification in a temperature gradient) are presented that allow an evaluation and quantification of the consequences of these asymmetries.