Phase-field modeling of the dendrite orientation transition in Al-Zn alloys

With a few exceptions, phase-field simulations of dendritic growth in cubic materials have been modeled using simple expressions for the interfacial energy anisotropy and with strong anisotropy. However, recent experimental results show that the Dendrite Orientation Transition (DOT) observed in Al-Zn alloys by Gonzales and Rappaz [Met. Mat. Trans. A37 (2006) 2797] occurs at weak anisotropy, and modeling these results requires at least two anisotropy parameters. In the present work, we solve the corresponding phase-field model on an adaptive grid, after measuring and compensating for the grid anisotropy. A systematic scan of equiaxed growth simulations was performed in the range of the anisotropy parameter space where the transition is expected. We find separate domains of existence of < 100 > and < 110 > dendrites, similar to those previously reported by Haxhimali et al. [Nat. Mat. 5 (2006) 660] for pure materials. In the so-called hyperbranched regime, lying between the < 100 > and < 110 > regions, we observe a competition between < 100 > and < 110 > growth directions, but no seaweed structures. Directional solidification simulations showed the stabilizing effect of the thermal gradient on the twofold splitting of < 110 > dendrites, and the importance of the choice of anisotropy parameters. We also found a strong dependence between the orientation of the crystal axes with respect to the thermal gradient and the actual growth direction. Finally, 3-dimensional seaweed microstructures were modeled for the first time, demonstrating that this pattern is a result of not only the values of anisotropy parameters, but also a consequence of directional solidification.

Dendritic Growth Morphologies in Al-Zn Alloys-Part II: Phase-Field Computations

Jonathan Dantzig, Paolo Di Napoli, Jonathan Friedli, Michel Rappaz

In Part I of this article, the role of the Zn content in the development of solidification microstructures in Al-Zn alloys was investigated experimentally using X-ray tomographic microscopy. The transition region between dendrites found at low Zn content and dendrites found at high Zn content was characterized by textured seaweed-type structures. This Dendrite Orientation Transition (DOT) was explained by the effect of the Zn content on the weak anisotropy of the solid-liquid interfacial energy of Al. In order to further support this interpretation and to elucidate the growth mechanisms of the complex structures that form in the DOT region, a detailed phase-field study exploring anisotropy parameters' space is presented in this paper. For equiaxed growth, our results essentially recapitulate those of Haxhimali et al.[1] in simulations for pure materials. We find distinct regions of the parameter space associated with and dendrites, separated by a region where hyperbranched dendrites are observed. In simulations of directional solidification, we find similar behavior at the extrema, but in this case, the anisotropy parameters corresponding to the hyperbranched region produce textured seaweeds. As noted in the experimental work reported in Part I, these structures are actually dendrites that prefer to grow misaligned with respect to the thermal gradient direction. We also show that in this region, the dendrites grow with a blunted tip that oscillates and splits, resulting in an oriented trunk that continuously emits side branches in other directions. We conclude by making a correlation between the alloy composition and surface energy anisotropy parameters.

Springer Verlag2013

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

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

Alexandre Durussel

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.