From lamellae to Archimedean tessellations, templated-eutectics never cease to surprise.

Our new concept of template-directed solidification of eutectics leads to the emergence of an unprecedented and unexpected set of morphologies that can be reconfigured via a simple tuning knob, the rate of solidification, using exactly the same template and eutectic material.
From lamellae to Archimedean tessellations, templated-eutectics never cease to surprise.

Cover image courtesy David Montiel Taboada, University of Michigan, Ann Arbor

The development of materials with unique and powerful 3D internal structures (microstructures) is a forefront topic of science and technology. Often, it is the microstructure of the material, and not the material itself that prevents a material from providing the needed function. We want the materials and products of the future to be smart and multifunctional, and one way to do this is by incorporating highly functioning microstructures into these materials. The innovative approach of structuring bulk materials via templating (utilizing a mold to pattern a material) has opened up the possibility of designing products with tailor made materials. However, prior to our work [Ref 1], this approach was usually limited to materials such as polymers and in many cases the structure of the final material was simply a replica or inversion of the templates.

Our specific advance was to bring the concept of templated self-assembly to materials found in the most high technology applications, e.g. metals and ceramics. While eutectics can be chosen from a variety of material chemistries (organics, salts, ceramics, metals, semiconductors, glasses), it is metals and ceramics where eutectics find their greatest application, for example as the basis of turbine blades. Our initial studies [Refs 2-4] discussed some of the challenges and opportunities in this new field of template-directed solidification of eutectics. These fundamental studies laid down the stones for the paper covered in this blog.  

In this paper, we use laser interference lithography and electrodeposition to fabricate the templates, and selected a AgCl-KCl molten salt eutectic (a good model system). The overall process is fairly simple (see schematic in Figure 1a). The crucial aspect of these templates is that their periodicity is commensurate with the lamellar spacing of the eutectic (see Figure 1b and 1c). Dr. Runyu Zhang, a co-author in this study, added that “Beyond the hexagonal lattice that we currently demonstrated in the work, holographic lithography allows the design and fabrication of numerous other templates. These lattices could lead to either symmetric or even symmetry broken patterns in eutectics”.

Figure 1: a. Experiment schematic for infilling, subsequent directional solidification of eutectic in pillar templates and characterization of the resultant microstructures. b. Plan view SEM image of a pillar template sample showing the hexagonal arrangement of pillars. g as defined in the inset, can be controlled by varying the conditions during the template fabrication steps of laser interference lithography and electrodeposition. c. SEM image of AgCl (bright) – KCl (dark) lamellar eutectic. λ as defined in the inset. The solidification direction is out of the image (z-axis), as indicated by the red dotted circle. All scale bars are 1 μm.

While solidifying the AgCl-KCl eutectic within the template, the otherwise expected lamellar microstructure of the eutectic undergoes a remarkable transition. Depending on the rate of solidification, we observe a range of spoke-like arrangements of the eutectic phases (see Figure 2). Since these spoke-like patterns resemble the different number of leaves in a clover, we designated our templated-eutectic patterns with the same nomenclature. So, the 3-spoke pattern is called trefoil, 4-spoke quatrefoil, 5-spoke cinquefoil, and the 6-spoke as hexafoil, based on the number of KCl (false-colored in blue) spokes per unit cell of the template.

Figure 2: A variety of microstructures observed in this template-eutectic system. False-colored SEM images of a. trefoil, b. quatrefoil, c. cinquefoil, and d. hexafoil patterns with 3, 4, 5, and 6 KCl spokes per unit cell of the template, respectively, obtained by varying the solidification conditions. The solidification direction is out of the image (z-axis), as indicated by the red dotted circle. The template pillars are displayed as black, while AgCl as yellow, and KCl as blue. All scale bars are 1 μm.

In the absence of a template, the constituent species in the molten eutectic diffuse perpendicular to the solidification direction near the solidification front, which in this eutectic leads to a lamellar pattern. However, in the template, this natural edgewise diffusion is disturbed by the pillars such that the diffusion fields are compelled to obey the geometry constrained by the template. To maintain the requirement of consistent diffusion path lengths within this modified diffusion field, the eutectic solidifies in spoke-like patterns while preserving the overall hexagonal symmetry imposed by the template (see Figure 3a). Through phase-field simulations (see Figure 3b-3g), we found that aligning the solidification direction parallel to the axis of the pillars lead to robust formation of hybrid morphologies that maintain consistent diffusion length but constrained by the symmetry of the template. Dr. Erik Hanson, a co-author of the study, says “The phase-field model has a lot of potential to predict new patterns and guide the design of experiments”. Prof. Katsuyo Thornton, who led the theoretical portion of the study, agrees: “We can now explore the large parameter space, not only of the material properties such as the volume fraction of each solid phases and processing conditions that changes the diffusion length, but also the template features with different symmetry, shapes, and volume fractions. It is not easy to conduct such exploration solely by experiment due to the sheer number of experiments that must be performed, so simulations provide the key guidance to what parameter sets would be promising”.

Figure 3a. Schematic showing the mechanism of diffusion that leads to the emergence of spoke-like patterns. b-d. images of the initial conditions of phase-field simulations performed using the given lamellar spacing, λe-g. show the corresponding steady-state patterns: trefoil, cinquefoil, and hexafoil. The solidification direction is out of the image (z-axis), as indicated by the red dotted circle. The template pillars are displayed as black, while AgCl as yellow, and KCl as blue. All scale bars are 1 μm.

The solidification conditions and the expected patterns match well between the experimental results and the phase-field simulations. As Prof. Paul Braun states, “By combining simulation and experiment, we expect to find new pillar structures that could be used to generate additional interesting microstructures”. These results are a useful starting point in establishing the design rules that guide the choice of the appropriate template-eutectic systems to obtain not just a specific morphology, but also realize families of complex patterns that can be achieved by simply tuning the solidification conditions and find potential use in fields of optics, interface engineering, microfluidics, heat transport, and energy management.

Ref [1] Ashish A. Kulkarni, Erik Hanson, Runyu Zhang, Katsuyo Thornton, Paul V. Braun, “Archimedean lattices emerge in template-directed eutectic solidification”, Nature, 2020.

Ref [2] J. Kim, L.K. Aagesen, J.H. Choi, J. Choi, H.S. Kim, J. Liu, C.R. Cho, J.G. Kang, A. Ramazani, K. Thornton, P.V. Braun, “Template-Directed Directionally Solidified 3D Mesostructured AgCl-KCl Eutectic Photonic Crystals”, Advanced Materials 27, 4551-4559, 2015.

Ref [3] Ashish A. Kulkarni, Julia Kohanek, Kaitlin I. Tyler, Erik Hanson, Dong-Uk Kim, Katsuyo Thornton, Paul V. Braun, “Template-Directed Solidification of Eutectic Optical Materials”, Advanced Optical Materials, 6, 1800071, 2018.

Ref [4] Ashish A. Kulkarni, Julia Kohanek, Erik Hanson, Katsuyo Thornton, Paul V. Braun, “Control of Lamellar Eutectic Orientation via Template-Directed Solidification”, Acta Materialia, 166, 715-722, 2019.

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