Influence of Zinc Anisotropy on Solidification Microstructures: Experimental Results and Phase-Field Simulations

Due to a distortion of its hexagonal unit cell along the c-axis compared to hexagonal-close-packed metals (c/a = 1.856 instead of 1.633), zinc is characterised by a large anisotropy of its solid-liquid interfacial energy. While previous studies have focused on the use of zinc alloys for galvanic coating of steel sheets, there has been relatively few investigations of the effect of this anisotropy on the formation of dendritic microstructure in Zn-Al bulk specimens. The aim of this thesis is thus to understand the effect of the large solid-liquid interfacial energy anisotropy on the growth morphologies of Zn-Al alloys. This investigation is of great scientific interest as zinc dendrites grow along directions with an edgy tip. Given the importance of the solid-liquid interfacial energy on the solidification microstructure, in situ observations of liquid alloy droplets in a solid matrix under near-equilibrium conditions were performed and reported here for the first time. The setup used has been found relatively accurate (with a 10% error) for measurements of large anisotropies. However, due to the limited resolution of the X-ray tomography beamline, low anisotropy measurements have fairly large errors. In order to study dendrite morphologies in Zn-4wt.%Al-0.17wt.%Pb, specimens were prepared in two ways: (i) Bridgman growth in a fixed temperature gradient and constant speed of 0.067 mm/s and (ii) directional solidification from a water-cooled steel chill, with a solidification velocity on the order of 0.3 mm/s. The samples were then studied by optical microscopy, SEM and EBSD as well as by X-ray tomography. Detailed phase-field simulations were used to understand the dendrite morphologies that formed in these experiments. Both experimental observations and phase-field simulations confirmed that, at low velocity, Zn dendrites grow preferentially along with short secondary arms along . The growth morphology of dendrites is very peculiar, with the presence of doublets/triplets of primary trunks in a transverse section: it can be accounted for by the very large solid-liquid interfacial energy anisotropy of zinc (and thus the presence of forbidden orientations). As c-axis secondary arms grow, their lateral surface start to have a normal which is no longer allowed by the equilibrium shape. Therefore, they start bending along the closest growth direction, i.e., and eventually form new primary trunks. However, under faster solidification conditions, the microstructure displays a mix of grains with two different principal growth directions, namely and . The gradual transition of Zn dendrites from to with increasing solidification speed is suspected to be due to the fact that the dendrite tips along these two directions do not exhibit the same shape and radii of curvature. Because of the large solid-liquid interfacial energy anisotropy, dendrites must have a sharp tip (i.e., a slope discontinuity) perpendicular to the basal plane and a smooth radius of curvature in the basal plane, the angle of the edge being almost constant. On the other hand, dendrites have two equal radii of curvature. Thus, when the growth rate is increased, dendrites have only one adaptable radius, whereas dendrites have two. At some velocity, it becomes easier for dendrites to reject solute compared to dendrites.

Texture Formation in Hot-Dip Galvanized Coatings

Aurèle Mariaux

Continuous hot-dip galvanization is a process during which steel sheets are coated with a layer of Zn-Al alloy to protect them against corrosion. As the name indicates, this is achieved by dipping the preheated sheet into a bath of molten alloy. The sheet is then withdrawn and cooled down in air. The solidification microstructure of such coatings is made of large zinc grains (spangles), which preferentially have their hexagonal ‹0001› axis perpendicular to the sheet plane (basal texture). The mechanisms leading to this preferred orientation were investigated in this study, with a particular focus on nucleation and dendritic growth. An experiment was designed to reproduce the solidification stage of hot-dip galvanization on a laboratory scale. Industrial coatings were remelted in an infrared image furnace and solidified under controlled cooling conditions. Thanks to the wide range of possible cooling rates, the influence of this parameter on the size and orientation of the zinc grains could be investigated. The thermal plateau induced by the solidification of the thin coating could be detected, even for fairly thick steel sheets. However, the signal was better for larger coating/steel thickness ratio. A minimum coating thickness and Al content are needed if Fe-Zn intermetallic outbursts are to be avoided during remelting. Additionally, skin-pass, as well as any deformation of the coated sheets, must be avoided prior to these laboratory experiments. A coupled cellular automaton — finite volume model was concurrently developed to simulate solidification. It was then used to obtain the nucleation parameters of the spangles by inverse modeling based on the remelting experiments. The model accounts for the effects of zinc crystal symmetry and of the confined coating geometry on nucleation and growth phenomena. In particular, the preferred orientation of the grains is included in the nucleation site distribution. Its basal part is still an estimate, but it could be refined from new experimental measurements with the infrared remelting device. On a more fundamental side, a mathematical formulation of the anisotropic solid-liquid interfacial energy of Zn-Al alloys was derived from the equilibrium shape of liquid droplets in a solid matrix. This property changes by more than 40% between the c axis and the basal plane. This very large variation has important effects on the solidification mechanisms. The interfacial energy, as well as the wetting conditions for an anisotropic grain, were then implemented in a phase field model, which was used to simulate the growth of zinc dendrites in coatings. It revealed that the growth directions and velocities are strongly influenced by the film thickness and by anisotropic wetting effects. The possibility that the preferred zinc orientation could be induced by the textured steel substrate was investigated by comparing the orientation of zinc grains with that of the ferrite grains underneath. It was observed that spangles with a random orientation distribution are independent of the substrate. Unfortunately, the observed specimen did not exhibit a basal coating texture and thus, the existence of a relation between basal grains and ferrite texture could not be investigated. The anisotropy formulation was also used to extend the classical theory of heterogeneous nucleation to anisotropic metals. These computations showed that a basal orientation of the nuclei is strongly favored from an energy point of view. Such developments can explain the occurrence of basal grains around holes that form during infrared remelting, so-called rose structures. Preferential basal nucleation and the wetting influence on dendrite growth are also responsible for the morphology transition observed in Galfan, a Zn-Al coating of eutectic composition: when appropriate cooling conditions are applied, a shiny layer of basal grains forms at the top surface before the onset of eutectic solidification. Finally, these mechanisms could also explain the preferential basal orientation of regular hot-dip galvanized coatings. However, the conditions on a galvanizing line do not meet the criteria that are requested to activate them in Galfan. Additionally, the texture of hot-dip coatings is reported to depend on the surface preparation of the sheet, although the anisotropic nucleation theory does not consider the steel substrate. Further investigations on these contradictions are needed before these mechanisms can be used to explain the preferred orientation in regular galvanized coatings.

EPFL2010

Interfacial Energy Anisotropy and Growth Morphologies in Aluminium-Zinc Alloys

Jonathan Friedli

This thesis presents an investigation aimed at the understanding of the effect of interfacial energy anisotropy on growth morphologies in Al-Zn alloys. Most low alloyed metals form dendritic structures that grow along directions that correspond to low index crystal axes, e.g., 〈100〉 directions in fcc aluminum. However, recent findings [Gon06, Gon08] have shown that an increase in the zinc content of Al-Zn continuously changes the dendrite growth direction from 〈100〉 to 〈110〉 in the (100) plane. At intermediate compositions, 〈320〉 dendrites and textured seaweeds were even observed. The reason for this dendrite orientation transition (DOT) is that this system exhibits a large solubility of the element zinc, which forms hexagonal crystals, in the primary fcc aluminum phase, thus modifying its weak solid-liquid interfacial energy anisotropy γsl. Due to the complexity of the phenomenology, there is still no satisfactory theory that predicts all the observed microstructures. The goal of this work was to measure the anisotropy of γsl, to gain further insight in the dendrite growth morphologies and mechanisms in Al-Zn via X-ray tomography and investigate the relationship between dendrite growth directions and the anisotropy of γsl via phase-field modeling. The values of the anisotropy in Al-82 wt.% Zn, obtained by equilibrium shape measurement, suggests a DOT in a regime with very low anisotropy, favoring the formation of seaweed structures. The enhanced experimental procedures and observation methods allowed an unprecedented characterization of such complex morphologies. Observations showed that seaweeds are far from random structures. They grow in a (100) symmetry plane by an alternating growth direction mechanism and are therefore less hierarchically ordered than common dendrites. Phase-field simulations of equiaxed growth of a dilute alloy showed that the DOT is not a continuous transition of growth directions, but rather a competition between the 〈100〉 and the 〈110〉 character of dentrites. However, crystallographic orientation measurements showed that the macroscopic texture evolves as evidenced by Gonzales and Rappaz. This showed that the preferred growth direction is not the same as the final texture of a sample, which is uncommon. Simulations of directional growth showed that seaweeds, which do not appear in equiaxed growth, are in fact produced by the interplay of low or degenerate crystalline anisotropy and the misorientation of the crystal with respect to the thermal gradient.

EPFL2011

Structure and dynamics of actin network at the leading edge of migrating cells

Sébastien Schaub

Crawling motion is characteristic of most animal cells and is principally based on actin-myosin II cytoskeletal system. The major components and reactions contributing to motility have been identified, but the overall picture of how these molecular events are orchestrated to result in the motion of the cell is still missing. We used a combination of experimental imaging, image analysis, and numerical modeling to analyze at a quantitative level how the elements of the actin-myosin machinery are coordinated in several important aspects of the crawling motion: the assembly of the characteristic pattern of actin network in the leading lamellipodium, the interaction between retrograde flow of the actin network and substrate adhesions, and the coordination of motion and assembly of actin and myosin II polymers over the entire cell during steady-state migration. First, we used enhanced phase contrast microscopy correlated with fluorescence and electron microscopy to investigate the supra-filament organization of actin in the lamellipodium of motile fish epidermal keratocytes. We showed a close correspondence between individual filament orientations and optical criss-cross network pattern by quantifying the orientational distribution of features in electron microscopy and optical microscopy images. We tested the hypothesis that the criss-cross pattern observed by optical microscopy results from variation of actin density, which is due to stochastic events of branching and capping of filaments. Based on this hypothesis, we produced simulated images of lamellipodium similar to experimental images. These simulations provided quantitative tools to estimate structural and dynamical parameters of the actin network in lamellipodia, notably the filament length, the actin concentration, the curvature of filaments and capping rate. Protrusion at the edge of the cell is coupled to the substrate adhesion, but at the same time is associated with the retrograde flow of the actin network away from the edge. We observed that focal adhesions were mostly localized at the boundary between the fast retrograde flow zone (the lamellipodium) and the slower flow zone (the lamellum). We analyzed simultaneously the actin flow and the formation of focal adhesion. Based on these results, we proposed a multi-stage model for the advance of the leading edge of migrating cell: advance of the lamellipodium is followed by the formation of the nascent adhesion complexes, which results in the reduction of the flow rate, advance of the lamellum, and then protrusion of the lamellipodium from a new base. We finally focused on the dynamics of the acto-myosin system in entire migrating cell. For this purpose, we developed a tracking program which allowed quantifying motion, contraction and assembly of cytoskeletal components. We measured the dynamics of actin, myosin II and their relative motion in migrating fish keratocytes. These results supported the dynamic network contraction model suggesting that the actin network deformed by myosin II drives the translocation of cell body. Focusing on the different aspects of the crawling motion, and balancing experimental and theoretical approaches, we obtained original results, which contributed to a better understanding of the dynamics of the lamellipodium and crawling motion in general.

EPFL2006