Architected materials can actively respond to external stimuli—such as mechanical forces, hydration and magnetic fields—by changing their geometries and thereby achieve novel functionalities. Such transformations are usually binary and volatile because they toggle between ‘on’ and ‘off’ states and require persistent external stimuli. Here we develop three-dimensional silicon-coated tetragonal microlattices that transform into sinusoidal patterns via cooperative beam buckling in response to an electrochemically driven silicon-lithium alloying reaction. In situ microscopy reveals a controllable, non-volatile and reversible structural transformation that forms multiple ordered buckling domains separated by distorted domain boundaries. We investigate the mechanical dynamics of individual buckling beams, cooperative coupling among neighbouring beams, and lithiation-rate-dependent distributions of domain sizes through chemo-mechanical modelling and statistical mechanics analysis. Our results highlight the critical role of defects and energy fluctuations in the dynamic response of architected materials. We further demonstrate that domain boundaries can be programmed to form particular patterns by pre-designing artificial defects, and that a variety of reconfigurational degrees of freedom can be achieved through micro-architecture design. This framework enables the design, fabrication, modelling, behaviour prediction and programming of electrochemically reconfigurable architected materials, and could open the way to beyond-intercalation battery electrodes, tunable phononic crystals and bio-implantable devices.
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Dynamic morphological transformations in soft architected materials via buckling instability encoded heterogeneous magnetization
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We thank D. Tozier, O. A. Tertuliano, W. L. Johnson, J. Y. Chen, K. Bhattacharya, P. W. Voorhees and D. J. Srolovitz for helpful discussions, and N. S. Lee, M. S. Hunt, A. R. Wertheim, G. A. DeRose, H. A. Atwater, N. S. Lewis, B. S. Brunschwig, J. Shi and A.H. Shih for support and assistance with experiments and instruments. We gratefully acknowledge the facilities and infrastructure provided by the Kavli Nanoscience Institute and the Molecular Materials Research Center at Caltech. J.R.G. acknowledges financial support from the Department of Defense through a Vannevar-Bush Faculty Fellowship, a Caltech Innovation Initiative Grant (CI2), and a Samsung Global Research Outreach Grant. C.V.D.L. acknowledges support from the National Science Foundation Division of Civil, Mechanical, and Manufacturing Innovation (CMMI-1825132). D.M.K. acknowledges financial support from the Office of Naval Research (N00014-16-1-2431).
The authors declare no competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Sn microlattices before and after lithiation-induced cooperative beam buckling.
a, b, SEM images of representative as-fabricated Sn microlattices. c–f, SEM images of representative Sn microlattices after lithiation, exhibiting a similar cooperative beam buckling behaviour. Images in b, d and f are taken at a tilt angle of 52°.
a, Illustration of modified CR2032 coin cells consisting of a stainless steel (SS) casing, a SS spring, a SS spacer, a separator, electrolyte, a polyethylene washer, paraffin wax, a Si microlattice sample on a glass substrate coated with Ni, and a Li counter electrode. b, c, Images of the in situ optical microscopy set-up and the custom electrochemical cell with a quartz viewing window. See Methods section ‘Electrochemical testing’ for details.
a–c, SEM images of periodically arranged artificial defects. Each artificial defect is a 5-µm-long, 100-nm-thick patch on one side of a horizontal beam, as illustrated in red in a. d, Image of the Caltech icon. e, Processed domain map based on the Caltech icon. f, SEM image of programmed domain boundaries of the Caltech icon shape after lithiation, produced by pre-designing artificial defects. The Caltech icon is used with permission.
a, SEM image of a representative domain. b, Tracing the domain boundary (red dashed line) in a through mode-II buckled beams. c, SEM image of a representative lithiated Si microlattice sample with multiple domains. d, Tracing of domain boundaries on the original SEM image in c. e, An example of digitally processed domain maps with red and blue square pixels indicating each node being in one of the two bistable domain phases. f, An example of digitally processed node rotation maps with red and blue square pixels indicating respectively clockwise and anticlockwise rotation of each node, which can be represented mathematically by an 80 × 80 array of si = ±1 for clockwise and anticlockwise node rotations. From this array, we can calculate the correlation of pairwise node rotation directions as a function of their separation in terms of the nearest integer number of unit cells.
Extended Data Fig. 5 Domain maps and correlation functions for various lithiation rates at room temperature.
a–f, Representative domain maps (top row) and SEM images (bottom row) of Si microlattice samples lithiated at different rates at room temperature. Panels c and d show two samples for C/6, illustrating that nominally identical Si microlattices at the same lithiation conditions produce different domain patterns. g, Correlation functions at different lithiation rates with two samples per rate at room temperature. h, A zoomed-in plot of part of g, focusing on the initial decay of the correlation functions. i, Averaged correlation function at different lithiation rates from two samples per rate at room temperature. Data points in g–i are connected by straight lines.
Extended Data Fig. 6 Influence of defect distributions and energy fluctuations in Monte Carlo simulations of domain formation dynamics.
a–c, Variations in correlation length ξ with coupling ramp rate R from MC simulations with different energy fluctuations QEC (from 0.00001 to 0.002) and defect distributions hi (from a standard deviation of 0.05 to 0.2). Data points are connected by straight lines. d, Relation between correlation length ξ and normalized coupling ramp rate R/QEC following the same trend for different levels of electrochemical energy fluctuations QEC.
a, First Brillouin zone (reciprocal space, black outline) and irreducible Brillouin zone (yellow) of the as-fabricated tetragonal lattice. The real-space coordinate system is shown in blue. b, Lithiated unit cell with buckled beams approximated by sinusoidal functions, resembling an 80% state of charge corresponding to a Li3Si phase. c, Delithiated unit cell with a 70% Coulombic efficiency and a 0.6 V cutoff voltage corresponding to Li0.9Si. d, Comparison of dispersion relations (point Γ to point Χ) of buckled and partially unbuckled Si microlattices with the same curvature as the lithiated and delithiated microlattice, isolating the effects of geometric transformations from those of material property changes. e–g, Extended dispersion relations of as-fabricated, lithiated and delithiated Si microlattices traversing through the Brillouin zone in 3D. Insets in d–g represent the chemical composition and the degree of buckling for each simulation.
This Supplementary Information file contains Sections I-XII, Supplementary Figures 1-23, Supplementary Tables 1-2 and Supplementary References.
In situ lithiation of a Si microlattice at a constant current.
In situ delithiation of a Si microlattice at a constant current.
In situ lithiation of a Si microlattice with a resistor load.
In situ cycling of a Si microlattice at high rates.
In situ lithiation of a Si microlattice with programed artificial defects.
FEA simulation of a 3D beam that buckles upon lithiation.
FEA simulation to compare different deformation mechanisms.
FEA simulation to compare beams with different slenderness ratios.
FEA simulation of cooperative buckling of 2D extended unit cells.
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Xia, X., Afshar, A., Yang, H. et al. Electrochemically reconfigurable architected materials. Nature 573, 205–213 (2019). https://doi.org/10.1038/s41586-019-1538-z
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