Strong, lightweight, and recoverable three-dimensional ceramic nanolattices

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Science  12 Sep 2014:
Vol. 345, Issue 6202, pp. 1322-1326
DOI: 10.1126/science.1255908

Compressive, ductile ceramic nanolattices

Ceramics are strong and stiff, but their limited ability to stretch like putty or steels makes them unsuitable for many engineering applications. Meza et al. constructed ceramic nanolattices from aluminum oxide, in which the beams are designed to stretch rather than bend. A key parameter in lattice design is the ratio of the wall thickness to the beam radius. When that ratio is small enough, compressing the beams does not break them. That way, the nanolattices can be highly compressed and recover to something close to their original shape when the stress is removed.

Science, this issue p. 1322


Ceramics have some of the highest strength- and stiffness-to-weight ratios of any material but are suboptimal for use as structural materials because of their brittleness and sensitivity to flaws. We demonstrate the creation of structural metamaterials composed of nanoscale ceramics that are simultaneously ultralight, strong, and energy-absorbing and can recover their original shape after compressions in excess of 50% strain. Hollow-tube alumina nanolattices were fabricated using two-photon lithography, atomic layer deposition, and oxygen plasma etching. Structures were made with wall thicknesses of 5 to 60 nanometers and densities of 6.3 to 258 kilograms per cubic meter. Compression experiments revealed that optimizing the wall thickness-to-radius ratio of the tubes can suppress brittle fracture in the constituent solid in favor of elastic shell buckling, resulting in ductile-like deformation and recoverability.

The ability to decouple properties such as strength and stiffness from density requires the use of advanced processing techniques combined with materials optimized for superior mechanical performance per unit weight. Many monolithic materials with high strength-to-weight (σys/ρ) and stiffness-to-weight (E/ρ) ratios—such as technical ceramics, diamond, and metallic glasses—have excellent potential for use as strong and lightweight structural materials but are suboptimal because of their low toughness and brittle, flaw-sensitive nature. Some of these materials exhibit size effects in mechanical properties when reduced to nanoscale dimensions, such as improved strength (1, 2), flaw tolerance (3), and enhanced ductility (4, 5). Architected lightweight structures made from high-strength nanoceramics (1, 6, 7) and nanoceramic composites (8) have been reported to have enhanced strengths and stiffnesses, but they still suffer from brittle, catastrophic failure. Efforts to toughen fully dense brittle materials have focused primarily on using microstructural features to impede crack motion (911) and on forming composites (12, 13), but these approaches have seen limited success in lightweight structures. Many natural hard materials such as sea sponge skeletons (14) and diatom shells (15) are simultaneously stiff, tough, and lightweight, a combination of properties that is thought to be attained by a hierarchical design of components within their bodies (16).

Lightweight structures that are both strong and tough may be engineered by utilizing such hierarchical design principles. The yield strength and stiffness of cellular structures scale as Embedded Image and Embedded Image, where Embedded Image is the relative density, σys and Es are the yield strength and stiffness of the parent solid, and exponents n and m are functions of the architecture (17). Cellular geometries that typically lead to the highest strength are stretching-dominated, meaning that they have no intrinsic mechanisms that allow for bending of the individual truss members (18, 19). The yield strength and stiffness of an ideal stretching-dominated structure scale linearly with relative density as Embedded Image and Embedded Image (20). This is in contrast to architectures that are either periodic and bending-dominated, whose modulus scales as Embedded Image, or stochastic, with Embedded Image scaling (21).

We created a strong, stiff, and energy-absorbing hollow-tube nanolattice with an octet-truss geometry (Fig. 1) that consists solely of a brittle ceramic, aluminum oxide (alumina), and exhibits nearly full recoverability after compressions in excess of 50% strain. Nanomechanical experiments reveal that the Young’s modulus of our nanolattices scales with relative density as Embedded Image, and failure strength scales as Embedded Image, which differ from the analytical scaling for both stretching- and bending-dominated structures because of the hollow tubes and nodes.

Fig. 1 Architecture, design, and microstructure of alumina nanolattices.

(A) CAD image of the octet-truss design used in the study. The blue section represents a single unit cell. (B) Cutaway of hollow octet-truss unit cell. (C) Hollow elliptical crosssection of a nanolattice tube. (D) SEM image of alumina octet-truss nanolattice. (E) Zoomed-in section of the alumina octet-truss nanolattice. The inset shows an isolated hollow tube. (F) TEM dark-field image with diffraction grating of the alumina nanolattice tube wall.

Creation of ceramic nanolattices begins with the design and writing of a three-dimensional (3D) polymer scaffold using two-photon lithography direct laser writing. A thin alumina film is then deposited onto the polymer scaffold by atomic layer deposition (ALD), so that it coats the entire surface. The outermost walls of the coated structure are then removed by focused ion beam milling (FIB), and the internal polymer is etched away in O2 plasma. The resulting 3D freestanding ceramic nanolattice consists of a network of hollow tubes, as shown in Fig. 1. This fabrication method enables the creation of 3D structures with numerous geometries (8, 22). Further fabrication details and a schematic of the deposition process can be found in (23) and are shown in fig. S1.

Nanolattices in this work were designed with relative densities spanning Embedded Image = 0.21 to 8.6%. Using a reported value for the density of ALD alumina, ρs = 2900 kg/m3 (24), the absolute densities of nanolattices were calculated to be ρ = 6.1 to 249 kg/m3, which places the lightest ones into the ultralight regime, defined as materials with densities ≤10 kg/m3 (21). This density range is comparable to that of aerogels (25) and other ultralight materials (7, 21). In this work, nanolattices were designed to have tube wall thicknesses t of 5 to 60 nm, tube major axis a of 0.45 to 1.38 μm, and unit cell widths L of 5 to 15 μm (Fig. 1, B and C), spanning length scales that can be controlled across four orders of magnitude. Transmission electron microscopy (TEM) analysis revealed ALD alumina to contain 2- to 10-nm nanocrystalline precipitates intermixed in an amorphous matrix (Fig. 1F). A list of the parameters and relative densities is provided in Table S1.

Monotonic and cyclical uniaxial compression experiments were performed on nanolattices in a G200 XP Nanoindenter (Agilent Technologies). In the first set of experiments, structures were compressed uniaxially to ~50% strain at a rate of 10−3 s−1 to determine their yield stress and overall deformation characteristics (Figs. 2; 3, A to D; and 4, B and D; and fig. S2A). In the second set of experiments, structures were cyclically loaded and unloaded three times to ~70% of their failure load, and unloading slopes from each cycle were averaged to estimate Young’s modulus (Fig. 4, A and C, and fig. S2B). Unloading rather than loading moduli were used to mitigate the possible effects of loading imperfections such as misalignment and partial initial contact (fig. S2B). Additional samples were compressed in an in situ nanomechanical instrument, InSEM (Nanomechanics Inc.), to observe local and global deformation characteristics and to investigate the failure modes that occurred during deformation (movies S1 to S3). Stress-strain data and still frames of the in situ compression experiments are shown in Fig. 2.

Fig. 2 Compression experiments on thick- and thin-walled nanolattices.

(A to E) Mechanical data and still frames from the compression test on a thin-walled (L = 5 μm, a = 650 nm, t = 10 nm) nanolattice demonstrating the slow, ductile-like deformation, local shell buckling, and recovery of the structure after compression. (F to J) Mechanical data and still frames from the compression test on a thick-walled (L = 5 μm, a = 790 nm, t = 50 nm) nanolattice showing catastrophic brittle failure and no post-compression recovery.

Fig. 3 Mechanical tests on varying wall thickness and relative density samples.

(A to D) Stress-strain plots of structures with varying wall thicknesses in showing the transition from brittle to ductile-like deformation in thinner-walled structures. (E to J) Post-compression images of the nanolattices showing the recoverability as wall thickness is reduced.

Fig. 4 Strength and stiffness versus density of alumina nanolattices.

(A and B) Stiffness and strength plotted against relative density for all tested samples. Data clearly obey a power law, with little deviation across wall thicknesses and failure modes. (C and D) Material property plots (Materials Property CES Selector software by Granta Design) of the experimental stiffness and strength data against density for existing materials, showing that the materials created in this work reach a new niche in the high-strength and -stiffness lightweight material parameter space.

Two distinct deformation signatures were observed during nanolattice compressions. These are best characterized using the thickness-to-radius ratio of the tubes, t/a, as a figure of merit. Structures with t/a ≥ 0.03, referred to as thick-walled, demonstrate linear elastic loading followed by catastrophic brittle failure (Fig. 3, A, B, E, and F). An example of a typical deformation and corresponding stress-strain data are shown in Fig. 2, F to J, and movie S3. Compressive stress-strain data for thick-walled structures show large strain bursts, with burst magnitude increasing at greater t/a; structures with t/a = 0.032 have bursts of ~10% strain (Fig. 3B), whereas structures with t/a = 0.067 show bursts of ~80% strain (Fig. 3A). This observed increase in burst magnitude is probably driven by greater elastic strain energy stored in thicker-walled structures during deformation. Each strain burst corresponds to a discrete brittle failure event, which leads to permanent damage of the structure (Figs. 2J and 3, E and F). This type of catastrophic failure has been observed in previous experiments on hollow ceramic nanolattices (6) and ceramic composites (8) and is generally typical of ceramic foams (17).

Thin-walled nanolattices, defined as those with t/a ≤ 0.02, did not exhibit catastrophic failure or discrete strain bursts. Samples in this regime first deformed elastically, where stress increased linearly with strain, followed by a ductile-like, controlled deformation, with stress plateauing after yielding (Fig. 3, C and D). An example of a typical deformation and corresponding stress-strain data are shown in Fig. 2, A to E, and movie S1. As the t/a of the samples decreased, the serrated burst behavior seen in the thick-walled structures was suppressed, and stress-strain data became smooth (Fig. 3, C and D). After yielding, all ensuing deformation was accommodated through wrinkling and local buckling of the tube walls (Fig. 2, D and E, and movie S1). All thin-walled ceramic nanolattices exhibited notable recovery after deformation, with some recovering up to ~98% of their original height after compression to 50% strain (Figs. 2E and 3H) and others recovering by ~80% after compression to 85% strain (fig. S4). Structures with smaller unit cells demonstrated greater recoverability, each recovering to at least 95% of its original height. Nanolattices with larger unit cells recovered less on average, but all recovered to at least 75% of their original height (fig. S3). SEM images of post-deformed structures revealed localized cracking on and around the nodes (Fig. 3J), implying that the failure of ALD alumina remained brittle and that the observed deformability and recoverability probably emerged from structural effects.

Nanolattices with 0.02 ≤ t/a ≤ 0.03 exhibited a combination of the two described deformation signatures. In these samples, both brittle and ductile-like deformation took place; several minor strain bursts were present, and marginal recovery occurred after compression to 50% strain (Fig. 3, C, G, and I, and movie S2). The in situ deformation movie S2 shows that each strain burst correlates with discrete local brittle fracture events in the tubes, and post-yield ductile-like behavior corresponds to buckling and wrinkling of the tube walls. The transition between these two deformation modes is probably driven by an energetic competition between elastic and brittle failure.

Three competing failure mechanisms exist for hollow-tube lattice structures: fracture of the tube wall, Euler (beam) buckling of a truss member, and local (shell) buckling of the tube wall (26). We define a failure mechanism (or failure mode) here to be any event that causes a loss of structural integrity of the nanolattice. Different combinations of these mechanisms can occur during deformation, depending on the stress state that arises in the beams during loading. Elastic deformation and potentially recoverability will occur in a structure when the stress necessary to initiate these processes is below the critical stress required for fracture. The condition for elastic deformation can be determined by calculating the transition point between two pairs of failure modes: shell buckling versus fracture, and Euler buckling versus fracture. Equating the stresses necessary to initiate each individual failure mechanism, we obtain an expression for the critical transition point between fracture and elastic failure [see (23) for the full derivation]

Embedded Image(1)

Embedded Image(2)

Both of these functions depend on the constituent material properties: Young’s modulus (E), fracture strength (σfs), and Poisson’s ratio (ν). Equation 1 represents the critical ratio between the wall thickness (t) and the major radius (a) that is necessary to induce a transition between local buckling and fracture in the tubes. Equation 2 represents the critical ratio between the major radius (a) and length (L) of the tubes that describes a similar transition from Euler buckling to fracture.

Using mechanical property data reported for 75-nm-thick ALD alumina, E = 164 GPa, σfs = 1.57 to 2.56 GPa, ν = 0.24 (27), and Eqs. 1 and 2, the critical thickness-to-radius ratio that induces a transition from yielding to shell buckling in the nanolattices was calculated to be between (t/a)crit ≈ 0.0161 and 0.0262, and the critical radius-to-length ratio that denotes transition from yielding to Euler buckling was between (a/L)crit ≈ 0.0591 and 0.0755. The property space of all nanolattices studied here, along with their t/a, a/L, and predicted failure modes, are shown in table S1. The experimentally observed deformation behavior of each sample is also noted in the table.

The radius-to-length ratios, a/L, for nanolattices studied here ranged from 0.0750 to 0.180. All of these values are greater than or equal to (a/L)crit predicted by Eq. 2, which means that in an ideal structure, the beams will fracture before the Euler buckling condition is met. This prediction is consistent with our experimental results; no Euler buckling was observed in our in situ compression experiments (Fig. 2 and movies S1 to S3). This model is not capable of capturing local-scale stress concentrations, nor does it account for structures with a high degree of misalignment or pre-bending of the beams, which have been reported to reduce the critical load required to initiate buckling (6). The a/L values of the nanolattices are close to (a/L)crit, suggesting that Euler buckling may occur in the samples with a large degree of misaligned or pre-bent beams, but it is not observed experimentally to be a dominant deformation mechanism.

The thickness-to-diameter ratios, t/a, of the nanolattices ranged from 0.0059 to 0.0862, which overlaps the range of (t/a)crit predicted by Eq. 1. For thick-walled structures, whose t/a ≥ 0.030 > (t/a)crit, the model predicts that failure of the beams is dominated by brittle fracture within the alumina tubes. Fractured segments of tubes are unable to carry any load, so every failure event will cause a strain burst whose magnitude depends on the amount of strain energy stored in the system before failure. These predictions are corroborated by experimental stress-strain data for the thick-walled structures (Figs. 2, I and J, and 3, E and F, and movie S3).

Failure in the thin-walled structures, whose t/a(t/a)crit ≤ 0.020, is predicted to occur primarily via shell buckling, which is an elastic failure mode. This type of failure corresponds to a plateau in the stress-strain data caused by a gradual drop in load-carrying capacity of the beams (28), in contrast to the immediate drop in load-carrying capacity associated with fracture. Bending of an isolated thin-walled hollow beam often leads to shell buckling bifurcation, which can cause a jump in displacement (29). In a truss structure, the interactions and nodal support among all the beams delay the onset of bifurcation and allow the beams to gradually settle into a new mode. Shell buckling in thin-walled nanolattices is manifested as wrinkling and warping of the tubes near the nodes (Figs. 2, D and E; and 3, H and J; and movie S1). The ductile-like deformation and recoverability observed in our experiments on the thin-walled nanolattices probably arise as a result of such shell buckling.

The proposed shell buckling model does not take into account the microstructural or material details, nor is it capable of predicting the deformation of structures in the transition regime of 0.020 ≤ t/a ≤ 0.030. It is helpful in qualitatively explaining deformation in this regime, where nanolattices experience a complex stress state with compressive, tensile, and shear components. Fracture occurs primarily under tension, and shear and buckling occur only in compression, which means that the stress state within the beams can simultaneously satisfy fracture and buckling conditions. This is observed experimentally as a mixing of fracture and buckling failure modes, along with suppressed strain burst behavior and some recoverability (Fig. 3, G and I, and movie S2).

Elastic recovery has been studied previously in metallic and polymer lattices, and models have been proposed for their recoverability (21, 3032). None of these works account for the observed ductile-like behavior of the ceramic nanolattices, and elastically deformable structures composed of intrinsically brittle materials such as ceramics are virtually unexplored. We postulate that reducing the t/a ratio to below (t/a)crit derived in Eq. 1 enables failure via shell buckling, an elastic failure mode that causes minimal damage to the beams and nodes and allows the structure to recover. The transition to elastic failure is a necessary condition to prevent initial yielding or fracture of the constituent material but not a sufficient condition to ensure recovery of the structure. Figure 2D shows that during shell buckling, the global deformation is accompanied by localized wrinkling and warping of the tube walls. This results in confined regions of high stress that can subsequently lead to localized fracture (Figs. 2E and 3J). The propagation of these localized microcracks depends on the overall stress landscape and flaw distribution. If a crack extends into a region of high tensile stresses, or if numerous flaws reside near a crack tip, it is likely to propagate through the node and can potentially result in fracture of the tube. If an existing crack extends into a region of compressive stress, or if the stress field is insufficient to continue the crack extension, its propagation will be suppressed so that the tubes may never fully fracture. In this mechanism, a sufficient number of nodal connections remain intact to enable the structure to recover nearly fully to its original shape. The applied compressive load reduces the local tensile stresses within the tube walls that are generated by bending of the beams, which generates a compressive stress state at the nodes that can impede the propagation of a crack. As the t/a is reduced, shell buckling will commence at a lower applied load (Eq. 1), which lowers the probability of initiating and/or propagating an existing crack. The wall thicknesses of alumina are on the order of tens of nanometers, a length scale that has been shown to exhibit enhanced strengths and damage tolerance caused by a statistically lower probability of finding a weak defect (1). These are some of the phenomena that collectively give rise to recoverability of the alumina nanolattices (Figs. 2E and 3H and figs. S3 and S4).

We discovered that the strength and Young’s modulus of all our octet-truss nanolattices follow a power law scaling with relative density as Embedded Image and Embedded Image (Fig. 4, A and B). This scaling outperforms traditional lightweight and ultralight bending-dominated structural materials, whose properties scale as Embedded Image or Embedded Image (21), but does not follow the analytic prediction for an ideal stretching-dominated structure, Embedded Image and Embedded Image (20). Such a deviation from the analytic prediction can be explained, in part, by factors such as the ellipticity of the tubes, structural imperfections, and non-idealities of the experimental setup. We attribute this deviation primarily to the hollowness of the tubes, which affects the structural integrity of the nodes, where the highest stress concentrations will occur (30, 31).

The strength and deformation of an ideal, monolithic, stretching-dominated cellular solid is governed by stretching of the beams, with the nodes acting as rigid pin-jointed elements that perfectly transfer load between truss members (20). In a hollow lattice, the nodes are constrained only by the shell walls, which has a detrimental effect on strength and stiffness because load transfer at the nodes occurs via shell wall bending. This, together with the sharp angles between the tubes, leads to an uneven distribution of stress and induces large stress concentrations in the vicinity of the nodes (Fig. 1, B and E). Bending of the tubes also causes large deflections and additional ovalization at the nodes, which further increases the compliance and stress concentrations. In situ experiments and postcompression analysis revealed that most of the deformation is localized to the nodes (Figs. 2, D and E, and 3J), which implies that improving nodal strength is a critical factor in enhancing the scaling of strength and stiffness with density.

We demonstrated the creation of ultralight hollow ceramic nanolattices that absorb energy, recover after significant compression, and reach an untapped strength and stiffness material property space. This is achieved using high-strength ALD alumina engineered into a thin-walled nanolattice that is capable of deforming elastically via shell buckling. The ultralight ceramic nanolattices represent the concept of materials by design, where it is possible to transform a strong and dense brittle ceramic into a strong, ultralight, energy-absorbing, and recoverable metamaterial. These results serve to emphasize the critical connection between material microstructure, hierarchical architecture, and mechanical properties at relevant length scales.

Supplementary Materials

Materials and Methods

Figs. S1 to S6

Table S1

Reference (33)

Movies S1 to S3

References and Notes

  1. See the supplementary materials.
  2. Acknowledgments: The authors gratefully acknowledge the financial support from the Defense Advanced Research Projects Agency under the Materials with Controlled Microstructure and Architecture program managed by J. Goldwasser (contract no. W91CRB-10-0305) and to the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S. Army Research Office. The content of the information does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. The authors are grateful to the Kavli Nanoscience Institute at Caltech for the availability of critical cleanroom facilities, and to R. Liontas and C. Garland for TEM assistance. Part of this work was carried out in the Lewis Group facilities at Caltech.

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