Nature - USA (2020-01-16)

Nature | Vol 577 | 16 January 2020 | 357

kagome lattice (see schematic overlaid on Fig. 4c), approximating AgCl
and KCl as triangles and silica colloids as hexagons. These results sug-
gest that such patterns can be obtained not only from pillar templates,
but also from other two-dimensionally arranged obstacles. Owing to
the planar geometry of the sample, the solidification front appears to
remain parallel to the substrate throughout the template (see Extended
Data Fig. 9c, d).
The realization of complex mesostructures from solidification
of a simple system consisting of a lamellar eutectic in a hexagonally
arranged template indicates that the complex thermal and diffusion
landscapes imposed by a template on a solidifying eutectic can lead

to intricate and rather unexpected patterns. Given the classes of pat-

terns observed, we suggest it would be interesting to consider whether

templates could modify the structure of metal-dielectric eutectics (for

example, Ge-Al and Cu-Cu 3 P) to form non-reciprocal metasurfaces^7 ,

Co-based eutectics to form magnetic spin-ice systems^8 ,^9 , and mechani-

cally robust eutectics such as NiAl-Mo or Al 2 O 3 -ZrO 2 to form mechanical

microlattices^10 ,^11. It is important to keep in mind that the template can

provide additional functionality (for example, being formed from a

y x

z

a b

cdO = 1,352 nm O = 676 nm eO = 450.67 nmfgO = 338 nm O = 270.4 nmhO = 225.33 nmiO = 193.14 nm

jkl mno p

Fig. 2 | Patterns observed in phase-f ield simulations. a, b, Three-dimensional
views of the phase-field simulation domain showing the evolution of the initial
lamellar seed (a; cross-section shown in h) into the hexafoil structure (b; cross-
section shown in o). The solidification direction in a and b is along the z axis.
c–i, Images of the initial conditions of simulations performed using the given
lamellar spacing. j–p, Images showing the corresponding steady-state

patterns: j, no-foil; k–m, trefoil; n, cinquefoil; o, p, hexafoil. The solidification

direction in c–p is out of the image (z axis), as indicated by the red dotted

circles. The images in c–p show the x–y plane cross-section of the simulation

domain repeated once in each direction. The template pillars are displayed as

semitransparent grey in a and b, and as black in c–p, while AgCl is shown as

yellow, and KCl as blue. All scale bars, 1 μm.

λ

Fig. 3 | Mesostructure phase map. Map of experimentally observed (red) and
phase-field simulated (black) mesostructures (shown on the vertical axis) as a
function of g/λ. The plotted data are displayed in Fig.  2 and in Extended Data
Figs. 3 and 4.

a c

d

b

d

Fig. 4 | Pattern formation by a monolayer colloidal crystal template. a, SEM

image of the monolayer silica colloidal crystal (sphere diameter d = 560 nm)

template. b, Schematic of eutectic-infilled monolayer colloidal crystal

template (see Methods for details). c, SEM image of the trefoil pattern (a

schematic of the Archimedean kagome lattice is overlaid on the image at

bottom left) obtained when λ ≈ d (λ = 500 nm). d, SEM image of the hexafoil

pattern obtained when λ < d (λ = 160 nm). The solidification direction in c and

d is into the image (z axis), as indicated by the black crossed circle. All scale

bars, 1 μm.