Scope:

The workshop aims to provide new perspectives on mathematical modeling of microstructural evolution. Novel theoretical and experimental methods will be presented, particularly concerning the growth of dendrites under a variety of boundary conditions.

Organizers:

1. Dr. Liubov Toropova (Ural Mathematical Center, Ural Federal University, Russia)
2. Prof. Dr. Dr. h.c. Markus Rettenmayr (Friedrich-Schiller-Universität Jena, Germany)

Presentations:

1. Boundary integral method for modeling solid/liquid interface – Dr. Ekaterina Titova (Ural Mathematical Center, Ural Federal University, Russia)

Convection has a significant influence on heat and mass transfer processes and, consequently, on the growth rate and shape of the propagating solid/liquid interface. The boundary integral method is used to find temperature and solute concentration distributions in the vicinity of crystals with given surface shape (including interfacial temperature and concentration). In addition, stability analysis of the boundary integral equation allows to select stable modes of dendritic growth. This leads to the condition of microscopic solvability, which allows to obtain a selection criterion for determining the parameters of the growing dendrite tip. The boundary integral method allows to numerically determine the shape of the solid/liquid interface, with or without the presence of convection.

2. Rapid diffusional solid state phase transformations - from massive transformation to solid state dendrites – Dr. Stephanie Lippmann (Friedrich-Schiller-Universität Jena, Germany)

Kinetics, internal stresses and interface control potentially lead to differences between solid/solid and solid/liquid phase transformations. In most cases, diffusion plays an important role in both solidification and solid state phase transformations, and similar microstructural features are observed. A special type of solid state transformation is the concentration invariant massive transformation that, in a given material, only occurs in a narrow range of experimental conditions. Close to these conditions, solid state dendrites can form and propagate with surprisingly high Interface velocities. In the presentation, examples of plane massive transformation fronts, instabilities and solid state dendrites are shown for Ti and Cu alloys.

Venue and time: Friedrich Schiller University. July 14, 2021 at 18.30 (EKB). The seminar is held in online format.

The photo shows the structure of the Al-Zn-Cu alloy