Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals.

Unlike crystalline atomic and ionic solids, texture development due to crystallographically preferred growth in colloidal crystals is less studied. Here we investigate the underlying mechanisms of the texture evolution in an evaporation-induced colloidal assembly process through experiments, modeling, and theoretical analysis. In this widely used approach to obtain large-area colloidal crystals, the colloidal particles are driven to the meniscus via the evaporation of a solvent or matrix precursor solution where they close-pack to form a face-centered cubic colloidal assembly. Via two-dimensional large-area crystallographic mapping, we show that the initial crystal orientation is dominated by the interaction of particles with the meniscus, resulting in the expected coalignment of the close-packed direction with the local meniscus geometry. By combining with crystal structure analysis at a single-particle level, we further reveal that, at the later stage of self-assembly, however, the colloidal crystal undergoes a gradual rotation facilitated by geometrically necessary dislocations (GNDs) and achieves a large-area uniform crystallographic orientation with the close-packed direction perpendicular to the meniscus and parallel to the growth direction. Classical slip analysis, finite element-based mechanical simulation, computational colloidal assembly modeling, and continuum theory unequivocally show that these GNDs result from the tensile stress field along the meniscus direction due to the constrained shrinkage of the colloidal crystal during drying. The generation of GNDs with specific slip systems within individual grains leads to crystallographic rotation to accommodate the mechanical stress. The mechanistic understanding reported here can be utilized to control crystallographic features of colloidal assemblies, and may provide further insights into crystallographically preferred growth in synthetic, biological, and geological crystals.

Mechanical design of the highly porous cuttlebone: A bioceramic hard buoyancy tank for cuttlefish.

Cuttlefish, a unique group of marine mollusks, produces an internal biomineralized shell, known as cuttlebone, which is an ultra-lightweight cellular structure (porosity, ∼93 vol%) used as the animal's hard buoyancy tank. Although cuttlebone is primarily composed of a brittle mineral, aragonite, the structure is highly damage tolerant and can withstand water pressure of about 20 atmospheres (atm) for the species Sepia officinalis Currently, our knowledge on the structural origins for cuttlebone's remarkable mechanical performance is limited. Combining quantitative three-dimensional (3D) structural characterization, four-dimensional (4D) mechanical analysis, digital image correlation, and parametric simulations, here we reveal that the characteristic chambered "wall-septa" microstructure of cuttlebone, drastically distinct from other natural or engineering cellular solids, allows for simultaneous high specific stiffness (8.4 MN⋅m/kg) and energy absorption (4.4 kJ/kg) upon loading. We demonstrate that the vertical walls in the chambered cuttlebone microstructure have evolved an optimal waviness gradient, which leads to compression-dominant deformation and asymmetric wall fracture, accomplishing both high stiffness and high energy absorption. Moreover, the distribution of walls is found to reduce stress concentrations within the horizontal septa, facilitating a larger chamber crushing stress and a more significant densification. The design strategies revealed here can provide important lessons for the development of low-density, stiff, and damage-tolerant cellular ceramics.

Lightweight lattice-based skeleton of the sponge Euplectella aspergillum: On the multifunctional design.

The glass sponge, Euplectella aspergillum, possesses a lightweight, silica spicule-based, cylindrical lattice-like skeleton, representing an excellent model system for bioinspired lattices. Previous analysis suggested that the E. aspergillum's skeletal lattice exhibits improved buckling resistance and suppressed vortex shedding. How the sponge's skeletal lattice with diagonally-oriented reinforcing bundle of fused spicules and the ridge system behaves under different loading conditions and achieves dual mechanical and fluidic transport performance requires further investigation. Here, we first quantified the structural descriptors such as length and thickness of the bundles of fused spicules and hole opening diameter of the sponge skeletons with and without the soft tissue covered. Secondly, parametric modeling and simulations of the sponge lattice in comparison with other bioinspired designs under different loading conditions were implemented to obtain the structure-mechanical property relationship. Our results reveal that the double-diagonal reinforcements of the E. aspergillum's lattices show i) tendency to maximize the torsional rigidity in comparison to longitudinal and radial modulus and flexural rigidity, and ii) independency of mechanical properties on the diagonal spacing, leaving freedom to control the hole-opening position for the sponge's fluid transport. Furthermore, our coupled fluid-mechanical simulations suggest that the ridge system spiraling the cylindrical lattice simultaneously improves the radial stiffness and fluid permeability. Finally, we discuss the general mechanical strategies and design flexibility in the sponge's skeletal lattice. Our work provides understanding of the mechanical and functional trade-offs in E. aspergillum's skeletal lattice which may shed light on the design of lightweight tubular lattices.

High strength and damage-tolerance in echinoderm stereom as a natural bicontinuous ceramic cellular solid.

Due to their low damage tolerance, engineering ceramic foams are often limited to non-structural usages. In this work, we report that stereom, a bioceramic cellular solid (relative density, 0.2-0.4) commonly found in the mineralized skeletal elements of echinoderms (e.g., sea urchin spines), achieves simultaneous high relative strength which approaches the Suquet bound and remarkable energy absorption capability (ca. 17.7 kJ kg-1) through its unique bicontinuous open-cell foam-like microstructure. The high strength is due to the ultra-low stress concentrations within the stereom during loading, resulted from their defect-free cellular morphologies with near-constant surface mean curvatures and negative Gaussian curvatures. Furthermore, the combination of bending-induced microfracture of branches and subsequent local jamming of fractured fragments facilitated by small throat openings in stereom leads to the progressive formation and growth of damage bands with significant microscopic densification of fragments, and consequently, contributes to stereom's exceptionally high damage tolerance.

A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus.

Cellular solids (e.g., foams and honeycombs) are widely found in natural and engineering systems because of their high mechanical efficiency and tailorable properties. While these materials are often based on polycrystalline or amorphous constituents, here we report an unusual dual-scale, single-crystalline microlattice found in the biomineralized skeleton of the knobby starfish, Protoreaster nodosus. This structure has a diamond-triply periodic minimal surface geometry (lattice constant, approximately 30 micrometers), the [111] direction of which is aligned with the c-axis of the constituent calcite at the atomic scale. This dual-scale crystallographically coaligned microlattice, which exhibits lattice-level structural gradients and dislocations, combined with the atomic-level conchoidal fracture behavior of biogenic calcite, substantially enhances the damage tolerance of this hierarchical biological microlattice, thus providing important insights for designing synthetic architected cellular solids.

Quantitative 3D structural analysis of the cellular microstructure of sea urchin spines (I): Methodology.

The mineralized skeletons of echinoderms are characterized by their complex, open-cell porous microstructure (also known as stereom), which exhibits vast variations in pore sizes, branch morphology, and three-dimensional (3D) organization patterns among different species. Quantitative description and analysis of these cellular structures in 3D are needed in order to understand their mechanical properties and underlying design strategies. In this paper series, we present a framework for analyzing such structures based on high-resolution 3D tomography data and utilize this framework to investigate the structural designs of stereom by using the spines from the sea urchin Heterocentrotus mamillatus as a model system. The first paper here reports the proposed cellular network analysis framework, which consists of five major steps: synchrotron-based tomography and hierarchical convolutional neural network-based reconstruction, machine learning-based segmentation, cellular network registration, feature extraction, and data representation and analysis. This framework enables the characterization of the porous stereom structures at the individual node and branch level (~10 µm), the local cellular level (~100 µm), and the global network level (~1 mm). We define and quantify multiple structural descriptors at each level, such as node connectivity, branch length and orientation, branch profile, ring structure, etc., which allows us to investigate the cellular network construction of H. mamillatus spines quantitatively. The methodology reported here could be tailored to analyze other natural or engineering open-cell porous materials for a comprehensive multiscale network representation and mechanical analysis. STATEMENT OF SIGNIFICANCE: The mechanical robustness of the biomineralized porous structures in sea urchin spines has long been recognized. However, quantitative cellular network representation and analysis of this class of natural cellular solids are still limited in the literature. This constrains our capability to fully understand the mechanical properties and design strategies in sea urchin spines and other similar echinoderms' porous skeletal structures. Combining high-resolution tomography and computer vision-based analysis, this work presents a multiscale 3D network analysis framework, which allows for extraction, registration, and quantification of sea urchin spines' complex porous structure from the individual branch and node level to the global network level. This 3D structural analysis is relevant to a diversity of research fields, such as biomineralization, skeletal biology, biomimetics, material science, etc.

Quantitative 3D structural analysis of the cellular microstructure of sea urchin spines (II): Large-volume structural analysis.

Biological cellular materials have been a valuable source of inspiration for the design of lightweight engineering structures. In this process, a quantitative understanding of the biological cellular materials from the individual branch and node level to the global network level in 3D is required. Here we adopt a multiscale cellular network analysis workflow demonstrated in the first paper of this work series to analyze the biomineralized porous structure of sea urchin spines from the species Heterocentrotus mamillatus over a large volume (ca. 0.32mm3). A comprehensive set of structural descriptors is utilized to quantitatively delineate the long-range microstructural variation from the spine center to the edge region. Our analysis shows that the branches gradually elongate (~50% increase) and thicken (~100% increase) from the spine center to edge, which dictates the spatial variation of relative density (from ~12% to ~40%). The branch morphology and network organization patterns also vary gradually with their positions and orientations. Additionally, the analysis of the cellular network of individual septa provides the interconnection characteristics between adjacent septa, which are the primary structural motifs used for the construction of the cellular structure in the edge region. Lastly, combining the extracted long-range cellular network and finite element simulations allows us to efficiently examine the spatial and orientational dependence of local effective Young's modulus across the spine's radius. The structural-mechanical analysis here sheds light on the structural designs of H. mamillatus' porous spines, which could provide important insights for the design and modeling of lightweight yet strong and damage-tolerant cellular materials. STATEMENT OF SIGNIFICANCE: Previous investigations on the cellular structures of sea urchin spines have been mainly based on 2D measurements or 3D quantification of small volumes with limited structural parameters. This limits our understanding of the interplay between the 3D microstructural variations and the mechanical properties in sea urchin spines, which hence constrains the derivation of the underlying principles for bio-inspired designs. This work utilizes our multiscale 3D network analysis, for the first time, to quantify the 3D cellular network and its variation across large volumes in sea urchin spines from individual branch and node level to the cellular network level. The network analysis demonstrated here is expected to be of great interest to the fields of biomineralization, functional biological materials, and bio-inspired material design.

Strategies for simultaneous strengthening and toughening via nanoscopic intracrystalline defects in a biogenic ceramic.

While many organisms synthesize robust skeletal composites consisting of spatially discrete organic and mineral (ceramic) phases, the intrinsic mechanical properties of the mineral phases are poorly understood. Using the shell of the marine bivalve Atrina rigida as a model system, and through a combination of multiscale structural and mechanical characterization in conjunction with theoretical and computational modeling, we uncover the underlying mechanical roles of a ubiquitous structural motif in biogenic calcite, their nanoscopic intracrystalline defects. These nanoscopic defects not only suppress the soft yielding of pure calcite through the classical precipitation strengthening mechanism, but also enhance energy dissipation through controlled nano- and micro-fracture, where the defects' size, geometry, orientation, and distribution facilitate and guide crack initialization and propagation. These nano- and micro-scale cracks are further confined by larger scale intercrystalline organic interfaces, enabling further improved damage tolerance.