Ternary eutectic dendrites: Pattern formation and scaling properties

Phase-Field Modeling of Biomineralization in Mollusks and Corals: Microstructure vs Formation Mechanism

While biological crystallization processes have been studied on the microscale extensively, there is a general lack of models addressing the mesoscale aspects of such phenomena. In this work, we investigate whether the phase-field theory developed in materials' science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route, via ion-by-ion addition from a fluid state, and a nonclassical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with an appropriate choice of the model parameters, microstructures similar to those found in biomineralized systems can be obtained along both routes, though the time-scale of the nonclassical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math and simulated by phase-field theory.

NiTi-Nb micro-trusses fabricated via extrusion-based 3D-printing of powders and transient-liquid-phase sintering

We present a novel additive manufacturing method for NiTi-Nb micro-trusses combining (i) extrusion-based 3D-printing of liquid inks containing NiTi and Nb powders, solvents, and a polymer binder into micro-trusses with 0/90° ABAB layers of parallel, ∼600 µm struts spaced 1 mm apart and (ii) subsequent heat-treatment to remove the binder and solvents, and then bond the NiTi powders using liquid phase sintering via the formation of a transient NiTi-Nb eutectic phase. We investigate the effects of Nb concentration (0, 1.5, 3.1, 6.7 at.% Nb) on the porosity, microstructure, and phase transformations of the printed NiTi-Nb micro-trusses. Micro-trusses with the highest Nb content exhibit long channels (from 3D-printing) and struts with smaller interconnected porosity (from partial sintering), resulting in overall porosities of ∼75% and low compressive stiffnesses of 1-1.6 GPa, similar to those of trabecular bone and in agreement with analytical and finite element modeling predictions. Diffusion of Nb into the NiTi particles from the bond regions results in a Ni-rich composition as the Nb replaces Ti atoms, leading to decreased martensite/austenite transformation temperatures. Adult human mesenchymal stem cells seeded on these micro-trusses showed excellent viability, proliferation, and extracellular matrix deposition over 14 days in culture.

STATEMENT OF SIGNIFICANCE

Near-equiatomic NiTi micro-trusses are attractive for biomedical applications such as stents, actuators, and bone implants because of their combination of biocompatibility, low compressive stiffness, high surface area, and shape-memory or superelasticity. Extrusion-based 3D-printing of NiTi powder-based inks into micro-trusses is feasible, but the subsequent sintering of the powders into dense struts is unachievable due to low diffusivity, large particle size, and low packing density of the NiTi powders. We present a solution, whereby Nb powders are added to the NiTi inks, thus forming during sintering a eutectic NiTi-Nb liquid phase which bonds the solid NiTi powders and improves densification of the struts. This study investigates the microstructure, porosity, phase transformation behavior, compressive stiffness, and cytocompatibility of these printed NiTi-Nb micro-trusses.

Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and CBr_{4}-C_{2}Cl_{6} eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed "numerical experiments", the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

The Solidification of Multicomponent Alloys

Various topics taken from the author's research portfolio that involve multicomponent alloy solidification are reviewed. Topics include: ternary eutectic solidification and Scheil-Gulliver paths in ternary systems. A case study of the solidification of commercial 2219 aluminum alloy is described. Also described are modifications of the Scheil-Gulliver analysis to treat dendrite tip kinetics and solid diffusion for multicomponent alloys.