Synthesis of nanolattices from mechanically strong and stiff ceramics or metals requires sophisticated multi-step processes that are complicated to apply to closed-cell topologies and have, so far, mostly been limited to non-optimal beam-lattice designs. High-resolution 3D additive manufacturing processes are generally limited to viscoelastic polymers, but demonstration of nanolattice performance at the Hashin-Shtrikman upper bound requires linear elastic material properties19,21 like those of ceramics and metals (Supplementary Note 5). Ceramic and metallic nanolattices are manufacturable by conversion1 from polymer templates such as those printed by TPP-DLW. However, closed-cell designs impose process restrictions, complicating the adoption of atomic-layer-deposited ceramics32,34 as well as electroless36 and electro-plated40 metals, even for the synthesis of composites34,35,36 where templates are not removed. Pyrolysis is the only alternative, and requires structures to be fabricated such that they survive extreme linear shrinkage of up to 90%6.

Here, we overcame several critical manufacturing challenges, leading to fabrication of highly efficient virtually closed-cell ceramic plate-topologies (Supplementary Note 1). As with most additive manufacturing techniques, TPP-DLW-printing of fully enclosed cellular geometries results in trapped excess liquid monomer and/or rupture of thin membranes during post-print development. We show that nanometer-size pores are sufficient to eliminate residual monomer from assemblies of even tens of micrometer-size cells, while retaining mechanical performance on par with fully closed cell topologies. In contrast to TPP-DLW-derived beam-nanolattices, plate-nanolattices cannot simply be printed from individual line features in one three-dimensional trajectory pattern. To address this challenge, we developed an orientation-specific layer-by-layer hatching strategy (Supplementary Fig. 2) to combine the highest surface quality with smallest possible wall thicknesses, and fully exploited size-dependent strengthening of the constituent material. Material properties of hatched TPP-DLW-derived structures are highly sensitive to printing parameters46; thus, carefully selected combinations of laser average power, scan speed and hatching distances were adopted herein to ensure identical constituent properties throughout our nanoarchitected material (Supplementary Fig. 3). To demonstrate property uniformity, for each plate orientation, micro-Raman spectroscopy measured nearly identical degree of conversion (DC) of pre-pyrolysis polymeric structures and nearly identical degree of graphitization (DG) for all pyrolytic carbon structures (Supplementary Figs. 3, 5; Supplementary Tables 1, 2). While pyrolysis of TPP-DLW printed beam-lattices has been demonstrated, the much larger ratio of unit cell dimensions to feature size in plate-lattices drastically complicates this conversion by pyrolysis, e.g., the overall size of our CO plate-nanolattices is up to 5 times larger than that of same-\(\bar \rho\) octet beam-lattices6,23 with comparable feature sizes. Given structures with larger surface areas tend to shrink more during pyrolysis, support pillars were coarsely hatched to introduce controlled porosity to lessen the shrinkage mismatch between the large surface area cubic+octet plate-nanolattices and the monolithic support pillars.

Despite the variability in the properties of pyrolytic carbon at small scales, our cubic+octet plate-nanolattices clearly reside within the bound bands of Fig. 4. Size effects strongly increase both the strength and stiffness of pyrolytic carbon, with decreasing characteristic length27,28,47. In the range of 1 µm and 5 nm, Young’s moduli around 40 GPa28 and 62 GPa27 are reported, respectively; the former agrees well with our 6 µm-diameter micro-pillar compression results (Supplementary Fig. 6). Consequently, the Young’s moduli of the constituent material in our plate-nanolattices, with wall thicknesses of 150–260 nm, are expected to lie within the above upper and lower limits. Nonlinear least square fitting of the stiffnesses of our most pristine specimens (\(\bar \rho \ge 37.5\%\)) with Eq. (1), assuming a Poisson’s ratio v = 0.1748 and considering a correction function to account for the structure’s face holes (Supplementary Note 4), estimated a constituent material stiffness (E s ) of 62 GPa. This agrees remarkably well with the literature utilized upper limit in Fig. 4a, confirming performance of our plate-nanolattices at the HS upper bound. Regarding strength, literature-reported compressive properties28 of pyrolytic carbon with characteristic dimensions down to 600 nm agree well with our pillar experiments. Literature-reported ultimate tensile strengths of 2 µm-size specimens of up to 2.75 GPa29 are also in good agreement, indicating that our pillar-measured yield strengths represent the constituent yield strength of our plate-nanolattices well.

Plate-nanolattices fully exploit the topological advantages of their plate architecture in the higher relative density range. Although all details of the computer models are not fully reflected in our high-\(\bar \rho\) plate-nanolattices given the limitations of nano-manufacturing, numerical results confirmed that the structural quality of these lattices was sufficient to perform on par with theoretical and numerical predictions, albeit with some experimental scatter. Correspondingly, experiments with polymeric cubic+octet plate-microlattices with near-ideal geometries (Supplementary Note 5) correlated well with the pyrolytic carbon results, but with less scatter. Despite manufacturing imperfections, our pyrolytic carbon data has one of the lowest variabilities among the nanolattices presented in Fig. 6. Outliers in stiffness remain within ±6.9% of the average upper bound predictions.

While plate-lattices clearly outperform beam-lattices in the higher relative density range, our results reveal a tradeoff between performance and manufacturability at lower relative densities. Finite element analyses (Fig. 5) showed that the underperformance of the low-\(\bar \rho\) plate-nanolattices with respect to the theoretical upper bounds in Fig. 4 is related to small plate thickness-to-size ratios which promote warping during pyrolysis and hence introduce plate curvature via pyrolysis-induced buckling (Fig. 1). Simulations showed that pre-curvature is the key mechanism diminishing stiffness, with a yielding-to-buckling transition at \(\bar \rho \approx 37.5\%\) also having a strong effect on the strength. As buckling ideally should not affect stiffness measurements, this explains the notably stronger reduction in yield strength compared to stiffness for the low-\(\bar \rho\) plate-nanolattices. In agreement with the simulations, near-ideal polymer plate-microlattices did not show a transition to worse stiffness scaling at lower relative densities, although the lowest relative density sample displayed reduced strength (Supplementary Note 5). The combination of imperfections and premature buckling of low-\(\bar \rho\) plate-nanolattices led to convergence of our data with theoretically less efficient pyrolytic carbon beam-nanolattices6, particularly in terms of strength (Fig. 6). While the manufacturing complexity of nano-architected materials may amplify these effects, low-\(\bar \rho\) plate-lattices are, regardless of scale, far more difficult to manufacture without significant geometric defects than beam-lattices due to the more extreme aspect ratios of individual features. Moreover, the theoretical performance of plate-lattices improves as the number of plate elements per unit cell is increased (as in the simple cubic + body centered cubic (SC-BCC) design18); however, in practice each additional plate element further reduces the lowest manufacturable relative density, and the simplest topologies like the cubic+octet design may be most practical.

Plate curvature may mitigate brittle failure in plate-lattices. While our high-\(\bar \rho\), pre-deformation-free specimens failed in a brittle manner, increasing plate curvature at low \(\bar \rho\) coincided with a more progressive failure behavior, albeit at the cost of reduced mechanical properties (Fig. 3). In previous work, highly curved, thin shell topologies made of brittle constituent materials, such as pyrolytic carbon, have been shown to exhibit progressive failure with high stress plateaus up to 80% strain45. This behavior arises from an advantageous crack propagation mechanism displayed by shells with high radius of curvature-to-thickness ratios. In plate-nanolattices, plate curvature induced during pyrolysis also produces such behavior. Interestingly, non-pre-deformed polymer cubic+octet plate-microlattices exhibited the same transition from catastrophic to progressive failure (Supplementary Fig. 12) as a result of the introduction of plate curvature by post-yield buckling. Therefore, pre-existent plate curvature is not necessary to induce progressive failure, and elastic buckling may well have contributed to progressive failure in our pyrolytic carbon structures. The implication is that non-pre-deformed thin-walled pyrolytic carbon plate-nanolattices, if manufacturable, may potentially still exhibit beneficial progressive failure without compromising stiffness and yield strength. Plate-designs with more plate elements per unit cell and thinner features, such as the SC-BCC design, may exploit post-buckling curvature-induced progressive failure most efficiently. At the same time, though, thin wall design is complicated by manufacturing limitations and potentially exacerbates defect-induced buckling strength reductions. Ultimately, both pre-existing and buckling-induced curvature are expected to produce a trade-off between compressive strength and deformability.

The combination of an optimal topology at the HS and Suquet upper bounds, and ultra-high strength nanoscale constituent pyrolytic carbon, makes our plate-nanolattices the only cellular material to lie above the theoretical specific strength limit for all bulk materials, as well as outperform all other architected materials in stiffness (Fig. 6). Beam-lattices, such as the octet truss, in practice perform on the order of 25 and 20% of the HS and Suquet upper bounds, respectively; which is in good agreement with the found five-fold and six-fold improvement, respectively, of our plate-nanolattices over TPP-DLW-derived pyrolytic carbon octet truss and isotropic truss nanolattices23 in the density range of 0.35–0.79 g/cm³.

In summary, we demonstrated closed-cell plate-nanolattices manufacturable via TPP-DLW and pyrolysis by applying nanometer-size face holes, which we showed to impose only small reductions in mechanical performance, orientation specific hatching strategies and optimization of support structures to minimize shrinkage mismatch with specimens during pyrolysis. This study experimentally demonstrates a cellular material reaching the theoretical strength and stiffness limits of an isotropic voided topology. At the same time, the constituent pyrolytic carbon approaches the theoretical material strength limit, thanks to mechanical size-effects. This combination of both optimal topology and ultra-strong constituent material culminates in the strongest and stiffest existing architected material, with up to 639% average performance improvement over the most efficient beam-nanolattices. While beam-based lattices have dominated structural metamaterials1 for the past two decades, this study’s comprehensive experimental characterization of plate-lattices provides important, scale-independent and process-independent groundwork to establish plate-architecture as a superior design principle. Our results provide understanding of density-dependent performance and deformation behaviors in light of previous theoretical studies and highlight several critical areas of interest for future work, including imperfection sensitivity, and design-dependent manufacturing limitations.

Although the TPP-DLW/pyrolysis fabrication route developed in this work is limited to small specimens, plate-lattices with exceptional size-strengthened constituent materials may be manufactured by more scalable techniques (e.g., projection micro-stereolithography49) using preceramic resins which exploit size effects into the micrometer range coupled with dramatically reduced shrinkage during pyrolysis43. Hence, plate-nanolattices deserve strong attention in the development of scalable high-resolution additive manufacturing processes50,51, which might in the future make carbon-based nanoarchitected metamaterials as ubiquitous as carbon composites have become in modern engineering applications.