Invariant and univariant eutectic solidification in ternary alloys

While solidification structures with a large variety of morphologies and scales continue to be promising candidates for advanced applications in addition to the conventional ones, solidification science has been focused on understanding and building the bridges between theory and application, aiming to describe the solidification process at all length scales and enabling enhanced control over the final microstructure and resulting material properties. The knowledge of solidification built over the decades has been mostly based on simple cases like single phase formation one or two component or coupled growth in peritectic or eutectic alloys, whereas the understanding on much more complex multiphase solidification is very limited. As a result of this, multiphase structure formation, which has been mostly approached as extensions of the simpler cases mentioned above, has many open questions regarding dynamics of the process. Ternary alloys serve as a good example for the onset of understanding of multiphase solidification, where different kinds of reactions could take place along a solidification path. With additional degree of freedom, most of these reaction have different characteristic than their simpler counterparts, and many important aspects which can be disregarded for simpler cases come into play. The main goal of the present study is to understand and quantify the microstructural evolution during directional solidification of ternary Al-Cu-Ag system by focusing on different aspect of formation dynamics. Among many different possibilities with respect to phase and morphology, we focus ternary invariant eutectic, univariant coupled eutectic growth, and finally binary eutectic growth. The first challenge taken is quantification and parameterization of ternary invariant structures. Secondly, we focused on univariant two-phase coupled growth and examined the effect of convection, finally we study the texture selection in binary eutectic as an initiation of understanding this process in ternary and higher order eutectics. During our experimental studies, we have also come across two more subtopics which are important for comprehensive understanding of microstructural evolution. These are the quantification of the effect of solid state reaction causing deviation from the true solidifications in ternary invariant eutectic Al-Cu-Ag and the other one is effect of pre-holding period which alters the front and in results changing the initial stages of solidification which are carried until the end of the process

Modeling of reaction-diffusion transport into a core-shell geometry

Fickian diffusion into a core-shell geometry is modeled. The interior core mimics pancreatic Langerhan islets and the exterior shell acts as inert protection. The consumption of oxygen diffusing into the cells is approximated using Michaelis-Menten kinetics. The problem is transformed to dimensionless units and solved numerically. Two regimes are identified, one that is diffusion limited and the other consumption limited. A regression is fit that describes the concentration at the center of the cells as a function of the relevant physical parameters. It is determined that, in a cell culture environment, the cells will remain viable as long as the islet has a radius of around $142 \mu m$ or less and the encapsulating shell has a radius of less than approximately $283 \mu m$. When the islet is on the order of $100 \mu m$ it is possible for the cells to remain viable in environments with as little as $4.6\times10^{-2} mol/m^{-3}$ $O_2$. These results indicate such an encapsulation scheme may be used to prepare artificial pancreas to treat diabetes

Invariant and univariant eutectic solidification in ternary alloys

While solidification structures with a large variety of morphologies and scales continue to be promising candidates for advanced applications in addition to the conventional ones, solidification science has been focused on understanding and building the bridges between theory and application, aiming to describe the solidification process at all length scales and enabling enhanced control over the final microstructure and resulting material properties. The knowledge of solidification built over the decades has been mostly based on simple cases like single phase formation one or two component or coupled growth in peritectic or eutectic alloys, whereas the understanding on much more complex multiphase solidification is very limited. As a result of this, multiphase structure formation, which has been mostly approached as extensions of the simpler cases mentioned above, has many open questions regarding dynamics of the process. Ternary alloys serve as a good example for the onset of understanding of multiphase solidification, where different kinds of reactions could take place along a solidification path. With additional degree of freedom, most of these reaction have different characteristic than their simpler counterparts, and many important aspects which can be disregarded for simpler cases come into play. The main goal of the present study is to understand and quantify the microstructural evolution during directional solidification of ternary Al-Cu-Ag system by focusing on different aspect of formation dynamics. Among many different possibilities with respect to phase and morphology, we focus ternary invariant eutectic, univariant coupled eutectic growth, and finally binary eutectic growth. The first challenge taken is quantification and parameterization of ternary invariant structures. Secondly, we focused on univariant two-phase coupled growth and examined the effect of convection, finally we study the texture selection in binary eutectic as an initiation of understanding this process in ternary and higher order eutectics. During our experimental studies, we have also come across two more subtopics which are important for comprehensive understanding of microstructural evolution. These are the quantification of the effect of solid state reaction causing deviation from the true solidifications in ternary invariant eutectic Al-Cu-Ag and the other one is effect of pre-holding period which alters the front and in results changing the initial stages of solidification which are carried until the end of the process.</p

Crystal orientation relationships in ternary eutectic Al-Al2Cu-Ag2Al

The microstructure of ternary eutectic Al-Al2Cu-Ag2Al arranges in several patterns of three solid phases during directional solidification. One key question for understanding the behavior of this system is if and how the patterns depend on crystal orientation relationships (ORs) between the solid phases. In order to study the correlation between the ORs and the evolving patterns for different process conditions, electron backscatter diffraction (EBSD) is performed on samples of directionally solidified ternary eutectic Al-Al2Cu-Ag2Al which have been processed with different solidification velocities and temperature gradients. The results show that characteristic ORs occur, influencing the type of the evolving pattern, the alignment of the phases and the degree of order. For one specific OR the pattern was observed to change in response to an imposed increase in the growth velocity even though the OR was retained. Based on the obtained EBSD results, an explanation for the observed behavior is proposed. For the other ORs, specific microstructures were observed for each of them. The outcomes demonstrate that knowledge about crystal ORs is essential to improve the understanding of the pattern formation in complex eutectic alloys

Modeling of reaction-diffusion transport into a core-shell geometry

Fickian diffusion into a core-shell geometry is modeled. The interior core mimics pancreatic Langerhan islets and the exterior shell acts as inert protection. The consumption of oxygen diffusing into the cells is approximated using Michaelis-Menten kinetics. The problem is transformed to dimensionless units and solved numerically. Two regimes are identified, one that is diffusion limited and the other consumption limited. A regression is fit that describes the concentration at the center of the cells as a function of the relevant physical parameters. It is determined that, in a cell culture environment, the cells will remain viable as long as the islet has a radius of around 142μm or less and the encapsulating shell has a radius of less than approximately 283μm. When the islet is on the order of 100μm it is possible for the cells to remain viable in environments with as little as 4.6×10−2mol/m−3 O2. These results indicate such an encapsulation scheme may be used to prepare artificial pancreas to treat diabetes.This is a pre-print of the article King, Clarence C., Amelia Ann Brown, Irmak Sargin, Kaitlin M. Bratlie, and Scott P. Beckman. "Modeling of reaction-diffusion transport into a core-shell geometry." arXiv preprint arXiv:1808.06766v1 (2018). Posted with permission.</p

Influence of growth velocity variations on the pattern formation during the directional solidification of ternary eutectic Al-Ag-Cu

In order to control the evolving microstructure in complex eutectics and other multi-phase systems, it is important to understand the adjustment mechanisms and the parameters that determine pattern evolution. Here, a combined experimental and simulation approach is taken to investigate the response of a three-phase eutectic system to changes in solidification velocity. Using Al-Ag-Cu as a model system, large scale three-dimensional phase-field simulations are compared to directionally solidified samples containing both, velocity increases and decreases. The experimental results are obtained by synchrotron tomography for detailed consideration of the microstructure directly before and after a targeted velocity change and by traditional SEM analysis of sample cross sections to capture effects over longer length scales. In addition to qualitative analysis of the images, the microstructures are statistically assessed using phase fractions, shape factor and nearest neighbor statistics. Both, simulation and experiment show an immediate change in phase fraction as a result of a change in growth velocity. Adjustment of the microstructural pattern occurs more slowly over a relatively long length scale, due to splitting, merging and overgrowing events. Novel quantification techniques emphasize that ternary eutectic phase arrangements are complex and continuously evolving structures which, even under ideal conditions, do not reach steady state growth as quickly as previously believed