Ab initio study of single-crystalline and polycrystalline elastic properties of Mg-substituted calcite crystals

Comparative nanoindentation study of biogenic and geological calcite

Biogenic minerals are often reported to be harder and tougher than their geological counterparts. However, quantitative comparison of their mechanical properties, particularly fracture toughness, is still limited. Here we provide a systematic comparison of geological and biogenic calcite (mollusk shell Atrina rigida prisms and Placuna placenta laths) through nanoindentation under both dry and 90% relative humidity conditions. Berkovich nanoindentation is used to reveal the mechanical anisotropy of geological calcite when loaded on different crystallographic planes, i.e., reduced modulus E_r{104} ≥ E_r{108} > E_r{001} and hardness H_{001} ≥ H_{104} ≥ H_{108}, and biogenic calcite has comparable modulus but increased hardness than geological calcite. Based on conical nanoindentation, we elucidate that plastic deformation is activated in geological calcite at the low-load regime (<20 mN), involving r{104} and f{012} dislocation slips as well as e{018} twinning, while cleavage fracture dominates under higher loads by cracking along {104} planes. In comparison, biogenic calcite tends to undergo fracture, while the intercrystalline organic interfaces contribute to damage confinement. In addition, increased humidity does not show a significant influence on the properties of geological calcite and the single-crystal A. rigida prisms, however, the laminate composite of P. placenta laths (layer thickness, ∼250-300 nm) exhibits increased toughness and decreased hardness and modulus. We believe the results of this study can provide a benchmark for future investigations on biominerals and bio-inspired materials.

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.

Biomineralized Materials as Model Systems for Structural Composites: Intracrystalline Structural Features and Their Strengthening and Toughening Mechanisms

Biomineralized composites, which are usually composed of microscopic mineral building blocks organized in 3D intercrystalline organic matrices, have evolved unique structural designs to fulfill mechanical and other biological functionalities. While it has been well recognized that the intricate architectural designs of biomineralized composites contribute to their remarkable mechanical performance, the structural features within and corresponding mechanical properties of individual mineral building blocks are often less appreciated in the context of bio-inspired structural composites. The mineral building blocks in biomineralized composites exhibit a variety of salient intracrystalline structural features, such as, organic inclusions, inorganic impurities (or trace elements), crystalline features (e.g., amorphous phases, single crystals, splitting crystals, polycrystals, and nanograins), residual stress/strain, and twinning, which significantly modify the mechanical properties of biogenic minerals. In this review, recent progress in elucidating the intracrystalline structural features of three most common biomineral systems (calcite, aragonite, and hydroxyapatite) and their corresponding mechanical significance are discussed. Future research directions and corresponding challenges are proposed and discussed, such as the advanced structural characterizations and formation mechanisms of intracrystalline structures in biominerals, amorphous biominerals, and bio-inspired synthesis.

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.

First Steps towards Understanding the Non-Linear Impact of Mg on Calcite Solubility: A Molecular Dynamics Study

Magnesium (Mg2+) is one of the most common impurities in calcite and is known to have a non-linear impact on the solubility of magnesian calcites. Using molecular dynamics (MD), we observed that Mg2+ impacts overall surface energies, local free energy profiles, interfacial water density, structure and dynamics and, at higher concentrations, it also causes crystal surface deformation. Low Mg concentrations did not alter the overall crystal structure, but stabilised Ca2+ locally and tended to increase the etch pit nucleation energy. As a result, Ca-extraction energies over a wide range of 39 kJ/mol were observed. Calcite surfaces with an island were less stable compared to flat surfaces, and the incorporation of Mg2+ destabilised the island surface further, increasing the surface energy and the calcium extraction energies. In general, Ca2+ is less stable in islands of high Mg2+ concentrations. The local variation in free energies depends on the amount and distance to nearest Mg in addition to local disruption of interfacial water and the flexibility of surface carbonate ions to rotate. The result is a complex interplay of these characteristics that cause variability in local dissolution energies. Taken together, these results illustrate molecular scale processes behind the non-linear impact of Mg2+ concentration on the solubility of magnesium-bearing calcites.

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.

Elasticity of Phases in Fe-Al-Ti Superalloys: Impact of Atomic Order and Anti-Phase Boundaries

We combine theoretical and experimental tools to study elastic properties of Fe-Al-Ti superalloys. Focusing on samples with chemical composition Fe71Al22Ti7, we use transmission electron microscopy (TEM) to detect their two-phase superalloy nano-structure (consisting of cuboids embedded into a matrix). The chemical composition of both phases, Fe66.2Al23.3Ti10.5 for cuboids and Fe81Al19 (with about 1% or less of Ti) for the matrix, was determined from an Energy-Dispersive X-ray Spectroscopy (EDS) analysis. The phase of cuboids is found to be a rather strongly off-stoichiometric (Fe-rich and Ti-poor) variant of Heusler Fe2TiAl intermetallic compound with the L21 structure. The phase of the matrix is a solid solution of Al atoms in a ferromagnetic body-centered cubic (bcc) Fe. Quantum-mechanical calculations were employed to obtain an insight into elastic properties of the two phases. Three distributions of chemical species were simulated for the phase of cuboids (A2, B2 and L21) in order to determine a sublattice preference of the excess Fe atoms. The lowest formation energy was obtained when the excess Fe atoms form a solid solution with the Ti atoms at the Ti-sublattice within the Heusler L21 phase (L21 variant). Similarly, three configurations of Al atoms in the phase of the matrix with different level of order (A2, B2 and D03) were simulated. The computed formation energy is the lowest when all the 1st and 2nd nearest-neighbor Al-Al pairs are eliminated (the D03 variant). Next, the elastic tensors of all phases were calculated. The maximum Young’s modulus is found to increase with increasing chemical order. Further we simulated an anti-phase boundary (APB) in the L21 phase of cuboids and observed an elastic softening (as another effect of the APB, we also predict a significant increase of the total magnetic moment by 140% when compared with the APB-free material). Finally, to validate these predicted trends, a nano-scale dynamical mechanical analysis (nanoDMA) was used to probe elasticity of phases. Consistent with the prediction, the cuboids were found stiffer.

Quantum-Mechanical Study of Nanocomposites with Low and Ultra-Low Interface Energies

We applied first-principles electronic structure calculations to study structural, thermodynamic and elastic properties of nanocomposites exhibiting nearly perfect match of constituting phases. In particular, two combinations of transition-metal disilicides and one pair of magnetic phases containing the Fe and Al atoms with different atomic ordering were considered. Regarding the disilicides, nanocomposites MoSi 2 /WSi 2 with constituents crystallizing in the tetragonal C11 b structure and TaSi 2 /NbSi 2 with individual phases crystallizing in the hexagonal C40 structure were simulated. Constituents within each pair of materials exhibit very similar structural and elastic properties and for their nanocomposites we obtained ultra-low (nearly zero) interface energy (within the error bar of our calculations, i.e., about 0.005 J/m 2 ). The interface energy was found to be nearly independent on the width of individual constituents within the nanocomposites and/or crystallographic orientation of the interfaces. As far as the nanocomposites containing Fe and Al were concerned, we simulated coherent superlattices formed by an ordered Fe 3 Al intermetallic compound and a disordered Fe-Al phase with 18.75 at.% Al, the α -phase. Both phases were structurally and elastically quite similar but the disordered α -phase lacked a long-range periodicity. To determine the interface energy in these nanocomposites, we simulated seven different distributions of atoms in the α -phase interfacing the Fe 3 Al intermetallic compound. The resulting interface energies ranged from ultra low to low values, i.e., from 0.005 to 0.139 J/m 2 . The impact of atomic distribution on the elastic properties was found insignificant but local magnetic moments of the iron atoms depend sensitively on the type and distribution of surrounding atoms.

An Ab Initio Study of Pressure-Induced Reversal of Elastically Stiff and Soft Directions in YN and ScN and Its Effect in Nanocomposites Containing These Nitrides

Using quantum-mechanical calculations of second- and third-order elastic constants for YN and ScN with the rock-salt (B1) structure, we predict that these materials change the fundamental type of their elastic anisotropy by rather moderate hydrostatic pressures of a few GPa. In particular, YN with its zero-pressure elastic anisotropy characterized by the Zener anisotropy ratio A Z = 2 C 44 / ( C 11 - C 12 ) = 1.046 becomes elastically isotropic at the hydrostatic pressure of 1.2 GPa. The lowest values of the Young's modulus (so-called soft directions) change from 〈100〉 (in the zero-pressure state) to the 〈111〉 directions (for pressures above 1.2 GPa). It means that the crystallographic orientations of stiffest (also called hard) elastic response and those of the softest one are reversed when comparing the zero-pressure state with that for pressures above the critical level. Qualitatively, the same type of reversal is predicted for ScN with the zero-pressure value of the Zener anisotropy factor A Z = 1.117 and the critical pressure of about 6.5 GPa. Our predictions are based on both second-order and third-order elastic constants determined for the zero-pressure state but the anisotropy change is then verified by explicit calculations of the second-order elastic constants for compressed states. Both materials are semiconductors in the whole range of studied pressures. Our phonon calculations further reveal that the change in the type of the elastic anisotropy has only a minor impact on the vibrational properties. Our simulations of biaxially strained states of YN demonstrate that a similar change in the elastic anisotropy can be achieved also under stress conditions appearing, for example, in coherently co-existing nanocomposites such as superlattices. Finally, after selecting ScN and PdN (both in B1 rock-salt structure) as a pair of suitable candidate materials for such a superlattice (due to the similarity of their lattice parameters), our calculations of such a coherent nanocomposite results again in a reversed elastic anisotropy (compared with the zero-pressure state of ScN).

An Ab Initio Study of Connections between Tensorial Elastic Properties and Chemical Bonds in Σ5(210) Grain Boundaries in Ni₃Si

Using quantum-mechanical methods we calculate and analyze (tensorial) anisotropic elastic properties of the ground-state configurations of interface states associated with Σ 5(210) grain boundaries (GBs) in cubic L1 2 -structure Ni 3 Si. We assess the mechanical stability of interface states with two different chemical compositions at the studied GB by checking rigorous elasticity-based Born stability criteria. In particular, we show that a GB variant containing both Ni and Si atoms at the interface is unstable with respect to shear deformation (one of the elastic constants, C 55 , is negative). This instability is found for a rectangular-parallelepiped supercell obtained when applying standard coincidence-lattice construction. Our elastic-constant analysis allowed us to identify a shear-deformation mode reducing the energy and, eventually, to obtain mechanically stable ground-state characterized by a shear-deformed parallelepiped supercell. Alternatively, we tested a stabilization of this GB interface state by Al substituents replacing Si atoms at the GB. We further discuss an atomistic origin of this instability in terms of the crystal orbital Hamilton population (COHP) and phonon dispersion calculations. We find that the unstable GB variant shows a very strong interaction between the Si atoms in the GB plane and Ni atoms in the 3rd plane off the GB interface. However, such bond reinforcement results in weakening of interaction between the Ni atoms in the 3rd plane and the Si atoms in the 5th plane making this GB variant mechanically unstable.

Strength and Brittleness of Interfaces in Fe-Al Superalloy Nanocomposites under Multiaxial Loading: An ab initio and Atomistic Study

We present an ab initio and atomistic study of the stress-strain response and elastic stability of the ordered Fe3Al compound with the D03 structure and a disordered Fe-Al solid solution with 18.75 at.% Al as well as of a nanocomposite consisting of an equal molar amount of both phases under uniaxial loading along the [001] direction. The tensile tests were performed under complex conditions including the effect of the lateral stress on the tensile strength and temperature effect. By comparing the behavior of individual phases with that of the nanocomposite we find that the disordered Fe-Al phase represents the weakest point of the studied nanocomposite in terms of tensile loading. The cleavage plane of the whole nanocomposite is identical to that identified when loading is applied solely to the disordered Fe-Al phase. It also turns out that the mechanical stability is strongly affected by softening of elastic constants C′ and/or C66 and by corresponding elastic instabilities. Interestingly, we found that uniaxial straining of the ordered Fe3Al with the D03 structure leads almost to hydrostatic loading. Furthermore, increasing lateral stress linearly increases the tensile strength. This was also confirmed by molecular dynamics simulations employing Embedded Atom Method (EAM) potential. The molecular dynamics simulations also revealed that the thermal vibrations significantly decrease the tensile strength.

Plastic deformation and twinning mechanisms in magnesian calcites: a non-equilibrium computer simulation study

Deformation twinning provides a mechanism for energy dissipation in crystalline structures, with important implications on the mechanical response of carbonate biogenic materials. Carbonate crystals can incorporate magnesium, e.g. in the sea, modifying their elastic response significantly. We present a full atom computational investigation of the dependence of the twinning response of calcite with magnesium content, covering compositions compatible with three main structures, calcite, dolomite and magnesite. We find, in agreement with experiments that the incorporation of magnesium disfavors twinning as a dissipation mechanism in ordered structures (dolomite, magnesite), however the response is strongly dependent on the arrangement of the magnesium ions in the crystal structure. We show that structures with a high content of magnesium (>33%) in a disordered arrangement, lead to plastic response before twinning or fracturing. We demonstrate that the position of the magnesium ions plays a key role in the determination of the crystal deformation mode. This observation is correlated with the formation of percolation clusters of magnesium in magnesian calcites.

Tensorial elastic properties and stability of interface states associated with Σ5(210) grain boundaries in Ni3(Al,Si)

Grain boundaries (GBs) represent one of the most important types of defects in solids and their instability leads to catastrophic failures in materials. Grain boundaries are challenging for theoretical studies because of their distorted atomic structure. Fortunately, quantum-mechanical methods can reliably compute their properties. We calculate and analyze (tensorial) anisotropic elastic properties of periodic approximants of interface states associated with GBs in one of the most important intermetallic compounds for industrial applications, Ni₃Al, appearing in Ni-based superalloys. Focusing on the Σ5(210) GBs as a case study, we assess the mechanical stability of the corresponding interface states by checking rigorous elasticity-based Born stability criteria. The critical elastic constant is found three-/five-fold softer contributing thus to the reduction of the mechanical stability of Ni₃Al polycrystals (experiments show their GB-related failure). The tensorial elasto-chemical complexity of interface states associated with the studied GBs exemplifies itself in high sensitivity of elastic constants to the GB composition. As another example we study the impact caused by Si atoms segregating into the atomic layers close to the GB and substituting Al atoms. If wisely exploited, our study paves the way towards solute-controlled design of GB-related interface states with controlled stability and/or tensorial properties.

Functional adaptation of crustacean exoskeletal elements through structural and compositional diversity: a combined experimental and theoretical study

The crustacean cuticle is a composite material that covers the whole animal and forms the continuous exoskeleton. Nano-fibers composed of chitin and protein molecules form most of the organic matrix of the cuticle that, at the macroscale, is organized in up to eight hierarchical levels. At least two of them, the exo- and endocuticle, contain a mineral phase of mainly Mg-calcite, amorphous calcium carbonate and phosphate. The high number of hierarchical levels and the compositional diversity provide a high degree of freedom for varying the physical, in particular mechanical, properties of the material. This makes the cuticle a versatile material ideally suited to form a variety of skeletal elements that are adapted to different functions and the eco-physiological strains of individual species. This review presents our recent analytical, experimental and theoretical studies on the cuticle, summarising at which hierarchical levels structure and composition are modified to achieve the required physical properties. We describe our multi-scale hierarchical modeling approach based on the results from these studies, aiming at systematically predicting the structure-composition-property relations of cuticle composites from the molecular level to the macro-scale. This modeling approach provides a tool to facilitate the development of optimized biomimetic materials within a knowledge-based design approach.