Thermodynamics and interdiffusion at interfaces with potential jumps, part II
Mechanical Properties of Metallic Materials and their Microstructural Origins
Final Report Abstract
The capabilities of the interface dissipation model from the first project period have been intensively characterized and a relationship between two of the input parameters has been established for the case of high interface Péclet numbers. This will in the future reduce the effort that is necessary for both fitting simulation results to experimental data and comparing it with other models. An extensive comparison between the interface dissipation model and the HR-model showed a clear qualitative difference in the thermo-kinetic results of both models, which is yet to be resolved in order to develop a universal numerical model describing the transition from diffusion controlled dendritic growth to heat flux controlled solidification with non-equilibrium partitioning of solute. Moreover, it has been elaborated in which respect the interface dissipation model needs further amendment to precisely describe experimental results, whereas the sharp interface model reproduces the experimental data to a satisfying degree in its present state. An important step towards the goal of phase-field simulations within the transition region from solutally to thermally controlled growth has been accomplished with the implementation of the stagnant film boundary condition. Significant advance concerning the sharp interface model has been accomplished: the in-house sharp interface model was extended for anisotropic growth of dendrites of binary alloys under nonisothermal conditions. With this it was possible to quantitatively reproduce that dendritic growth modes are in the case of small growth velocities controlled by solutal diffusion, at moderate velocities controlled by both the diffusion and thermal field, and for high growth rates controlled by the thermal field only. Considering a finite diffusion speed in the bulk liquid resulted in the emergence of partitionless growth modes beyond a critical undercooling. Furthermore, considering forced convective flow in the model further improved the reproduction of experimental results and known discrepancies between experimental data and previous models were resolved. On the basis of a scaling analysis, criteria for the influence of convective flow were established. These results are of general relevance and can be applied to other types of flow. Additionally, a phase-field model describing rapid solidification of an ordered binary alloy from an undercooled liquid was developed. For rapidly growing crystals, both analogies and qualitative differences to known non-equilibrium effects were found. Furthermore, good qualitative agreement between the predictions of the new model and both the theory of kinetic phase transitions and experimental data was achieved. During the course of the project it was found that under certain circumstances the simulated system did not always converge towards a steady state. Instead, the simulations in some cases predicted continuous decelerating behavior. While this phenomenon was known and criteria for simplified systems were already available in the literature, such criteria were now derived for general binary alloy systems: if the relation between the interfacial concentration at the solid side of the interface cs and the interface velocity is negative, δcs ⁄ v < 0, the steady state is dynamically stable; if it is positive, δcs ⁄ v > 0, the steady state is dynamically unstable and the aforementioned decelerating behavior can be expected. The collaboration project with 6 publication published in the first and 7 in the second funding period is considered to have been very productive. Many contributions to current questions in simulation of solidification with the influence of non-equilibrium effects have been worked out. As for the central goal of the project to develop a universal model from diffusion controlled dendritic growth to temperature controlled solidification with non-equilibrium partitioning of solute, a major step has been achieved by comparing the theoretical approaches and clearly defining open issues.
Publications
- Modeling the flow in diffuse interface methods of solidification, Physical Review E 92 (2015) 023303
A. Subhedar, I. Steinbach, and F. Varnik
(See online at https://doi.org/10.1103/PhysRevE.92.023303) - Disorder trapping by rapidly moving phase interface in an undercooled liquid, EJP Web of Conferences 151 (2017) 05001-1-10
P. K. Galenko, D. Danilov, I. G. Nizovtseva, K. Reuther, and M. Rettenmayr
(See online at https://doi.org/10.1051/epjconf/20171510) - Effect of convective flow on stable dendrite growth in rapid solidification of a binary alloy, J. Crystal Growth 457 (2017) 349-355
P. K. Galenko, D.A. Danilov, K. Reuther, D.V. Alexandrov, M. Rettenmayr, D.M. Herlach
(See online at https://doi.org/10.1016/j.jcrysgro.2016.07.042) - Effect of convective transport on dendritic crystal growth from pure and alloy melts, Applied Physics Letters 111 (2017) 031602-1-5
P. K. Galenko, K. Reuther, O.V. Kazak, D.V. Alexandrov, and M. Rettenmayr
(See online at https://doi.org/10.1063/1.4985340) - “Effect of microstructure during dendritic solidification on melt flow: A Phase-field – lattice-Boltzmann study” Proceedings of the 6th Decennial International Conference on Solidification Processing, (2017)
M. Tegeler, A. Monas, O. Shchyglo, I. Steinbach, F. Varnik
- Kinetic transition in the order–disorder transformation at a solid/liquid interface, Philosophical Transactions A 376 (2018) 20170207-1-12
P. K. Galenko, I.G. Nizovtseva, K. Reuther, and M. Rettenmayr
(See online at https://doi.org/10.1098/rsta.2017.0207) - Dynamic instability of the steady state of a planar front during non-equilibrium solidication of binary alloys, Journal of Crystal Growth 506 (2019) 55-60
K. Reuther, M. Rettenmayr
(See online at https://doi.org/10.1016/j.jcrysgro.2018.10.008) - Solute trapping in non-equilibrium solidification: A comparative model study, Materialia 6 (2019) 100256
K. Reuther, S. Hubig, I. Steinbach, M. Rettenmayr
(See online at https://doi.org/10.1016/j.mtla.2019.100256)
