Nature | Vol 577 | 16 January 2020 | 355Article
Archimedean lattices emerge in template-
directed eutectic solidification
Ashish A. Kulkarni1,2,3, Erik Hanson^4 , Runyu Zhang1,2,3, Katsuyo Thornton^4 & Paul V. Braun1,2,3,5*Template-directed assembly has been shown to yield a broad diversity of highly
ordered mesostructures^1 ,^2 , which in a few cases exhibit symmetries not present in the
native material^3 –^5. However, this technique has not yet been applied to eutectic
materials, which underpin many modern technologies ranging from high-
performance turbine blades to solder alloys. Here we use directional solidification of a
simple AgCl-KCl lamellar eutectic material within a pillar template to show that
interactions of the material with the template lead to the emergence of a set of
microstructures that are distinct from the eutectic’s native lamellar structure and the
template’s hexagonal lattice structure. By modifying the solidification rate of this
material–template system, trefoil, quatrefoil, cinquefoil and hexafoil mesostructures
with submicrometre-size features are realized. Phase-field simulations suggest that
these mesostructures appear owing to constraints imposed on diffusion by the
hexagonally arrayed pillar template. We note that the trefoil and hexafoil patterns
resemble Archimedean honeycomb and square–hexagonal–dodecagonal lattices^6 ,
respectively. We also find that by using monolayer colloidal crystals as templates, a
variety of eutectic mesostructures including trefoil and hexafoil are observed, the
former resembling the Archimedean kagome lattice. Potential emerging applications
for the structures provided by templated eutectics include non-reciprocal
metasurfaces^7 , magnetic spin-ice systems^8 ,^9 , and micro- and nano-lattices with
enhanced mechanical properties^10 ,^11.Eutectic materials have been considered for use as optical metamateri-
als^12 ,^13 and plasmonic structures^14 , and for mechanical^15 and energy-har-
vesting^16 applications. During solidification, the constituent species in
the molten eutectic diffuse perpendicular to the solidification direction
near the solidification front. The kinetics of this mass transport in the
liquid just ahead of the solidification front drives arrangement of the
solid phases in patterns with generally consistent length scales that are
roughly inversely proportional to the square root of the solidification
velocity^17. Decades of research on solidification of binary and ternary
eutectic systems indicate that only a limited set of regular mesostruc-
tures emerge, even over a broad range of processing conditions^17 –^21. By
engineering the heat removal, for example, the microstructure could
be modified from straight to curved lamellae^21 ,^22 , or from lamellar to
rod-like^23 ; however, the resulting microstructures are still quite similar
to those found in the native eutectic. As we describe here, this limita-
tion can be overcome by introducing a template phase into which the
eutectic melt is solidified. Although the introduction of a template has
been demonstrated to drive the self-assembly of organic molecules^24
into highly ordered patterns^1 ,^2 ,^25 ,^26 and new symmetries^3 –^5 ,^27 –^29 , such an
approach has not been applied to any eutectic system. As we previously
reviewed^30 , only now is the promise of the effects of a template on a
solidifying eutectic for forming new and complex eutectic mesostruc-
tures beginning to be exploited^31 ,^32.
Here, starting with the well-studied AgCl-KCl eutectic^31 –^33 (see Meth-
ods for details), we examine how a template affects what would other-
wise be a regular lamellar microstructure (see the scanning electron
microscopy (SEM) image in Fig. 1a). The templates used in this work
consist of a hexagonal lattice of Ni pillars that are 4–6 μm tall and 500–
620 nm in diameter (see Fig. 1b and Methods for details), with edge gaps,
g (defined in the inset of Fig. 1b), of 160–290 nm. Pillar diameters and g
were selected to be comparable to the accessible range of the average
lamellar spacing, λ (defined in the inset of Fig. 1a), in the AgCl-KCl lamel-
lar eutectic. Outside the template, a lamellar structure emerges with
a λ that depends on the solidification rate (see Extended Data Fig. 1a),
as expected. However, inside the pillar template, there is a remarkable
transition, and a broad array of solidification-rate-dependent complex
mesostructures appear. When λ is commensurate with the edge gaps
in the template, the pillars modify the phase separation of the eutectic
such that spoke-like patterns in AgCl and KCl are realized instead of the
regular lamellar structure. We designate the resultant structures as
trefoil (see Fig. 1c), quatrefoil (see Fig. 1e), cinquefoil (see Fig. 1f) and
hexafoil (see Fig. 1g), based on the number of KCl spokes per unit cell
of the template (see schematic in Extended Data Fig. 2). Remarkably,
the trefoil pattern resembles the Archimedean honeycomb lattice
(see schematic in Fig. 1d) of roughly hexagonally shaped AgCl and KCl
domains. In contrast, the hexafoil pattern resembles the Archimedeanhttps://doi.org/10.1038/s41586-019-1893-9
Received: 1 April 2019
Accepted: 11 October 2019
Published online: 15 January 2020
(^1) Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA. (^2) Materials Research Laboratory, University of Illinois at Urbana-Champaign,
Champaign, IL, USA.^3 Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Champaign, IL, USA.^4 Department of Materials Science and
Engineering, University of Michigan, Ann Arbor, MI, USA.^5 Department of Chemistry, University of Illinois at Urbana-Champaign, Champaign, IL, USA. *e-mail: [email protected]