Thermal-field effects on interface dynamics and microstructure selection during alloy directional solidification

Abstract

We carry out three-dimensional phase-field simulations to model unique experimental observations of cellular and dendritic solidification structures formed under diffusive growth conditions in the DSI (Directional Solidification Insert) of the DECLIC (DEvice for the study of Critical LIquids and Crystallization) aboard the International Space Station. We had previously shown experimentally that complex thermal conditions affect the stationary position of the solid-liquid interface, as well as its dynamics of relaxation towards this stationary position over a finite time after the onset of sample pulling. Here, we discuss the effects of thermal diffusion within the adiabatic zone of the directional solidification setup and of latent heat release at the solid-liquid interface by means of quantitative phase-field simulations. Simulations and experiments characterize the entire evolution of the primary spacing of cellular/dendritic array structures from the onset of morphological instability to the establishment of the final steady-state spacing, including the transient coarsening regime associated with a sharp increase of spacing. Accounting for these thermal effects leads to a major improvement in the agreement between simulations and microgravity measurements for both the time of occurrence of morphological instability after the start of the experiment and the subsequent spacing evolution, which are not accurately predicted using the standard frozen temperature approximation.

Effect of sub-boundaries on primary spacing dynamics during 3D directional solidification conducted on DECLIC-DSI

“…Local direct measurements of cell spacing associated to splittings lead to a value of stability limit max  280 µm. This value is close to the predicted maximum limit 308 µm by PF simulation [44]. Lastly, the spreading of the stretching within each SG also contributes to limit tip-splittings.…”

“…By using the method in Refs. [41,44], we construct a regular hexagonal array as shown in Fig. 7a, which we use as an initial condition.…”

“…However, the comparison with 3D phase-field simulations evidenced some differences in primary spacings that are partly explained by the specificities of the thermal field in the 3D geometries [43,44]. Especially, a new modeling approach was developed that couples the 3D phase-field model to a timedependent calculation of the thermal diffusion in the adiabatic zone [44], thus accounting for latent heat release and finite heat transport [43]. The comparison with the classical approach, using frozen temperature approximation, evidenced major improvements in the agreement between the new approach of simulation and microgravity experiments for inception of morphological instability and stationary values of spacings.…”

“…This led us for example to redetermine the solute partition coefficient of the succinonitrile-camphor alloy, focusing on the alloy concentration range used in DECLIC-DSI [42]. However, the comparison with 3D phase-field simulations evidenced some differences in primary spacings that are partly explained by the specificities of the thermal field in the 3D geometries [43,44]. Especially, a new modeling approach was developed that couples the 3D phase-field model to a timedependent calculation of the thermal diffusion in the adiabatic zone [44], thus accounting for latent heat release and finite heat transport [43].…”

“…However, simulations still tend to underestimate the stationary spacing (see Fig. 8c of [44]). This important study on the influence of the thermal field points out that 3D experiments introduce additional unavoidable deviations from ideal models of solidification, which are negligible or controllable in thin samples, and which affect the microstructure characteristics and dynamics.…”