Martin Friák

Revealing the Design Principles of High‐Performance Biological Composites Using Ab initio and Multiscale Simulations: The Example of Lobster Cuticle

In the course of evolution nature developed materials based on organic–inorganic nanocomposites with complex, hierarchical organization from A u ngstroms to millimeters tailored via molecular self-assembly. [1–3] Such materials possess outstanding stiffness, toughness, and strength related to their low density, while the mechanical characteristics of their underlying constituents are rather modest. [2,4] This remarkable performance is a consequence of their hierarchical structure, the specific design at each level of organization, and the inherent strong heterogeneity [4] resulting in the accommodation of macroscopic loadings bydifferentdeformationmechanisms at differentlength scales. Therefore, to understand the macroscopic mechanical properties of the tissue, one should take into account its structure–property relations at all length scales down to the molecular level. To date, this key challenge has been only partly addressed due to severe obstacles in obtaining mechanical and structural data at the nanometer scale. The mechanical properties of important proteins and biominerals as well as some details about their exact structure are still unknown. A powerful tool to overcome these difficulties and to better understand the structure–property relationships in biomaterials is multiscale modeling encompassing all length scales. [3,5] Some progress in the development of multiscale structure–property relationships for mineralized tissues has been achieved by combined modeling and experimental approaches applied to bone, [4] nacre, [6] and fish skin armor. [7] However, these approaches do not explicitly integrate a molecular-level description and use continuum mechanics at the meso- and macroscale (e.g., finite element analysis) coupled with experimental data obtained, for example, by nanoindentation. A

Robustness and optimal use of design principles of arthropod exoskeletons studied by ab initio-based multiscale simulations

Recently, we proposed a hierarchical model for the elastic properties of mineralized lobster cuticle using (i) ab initio calculations for the chitin properties and (ii) hierarchical homogenization performed in a bottom-up order through all length scales. It has been found that the cuticle possesses nearly extremal, excellent mechanical properties in terms of stiffness that strongly depend on the overall mineral content and the specific microstructure of the mineral-protein matrix. In this study, we investigated how the overall cuticle properties changed when there are significant variations in the properties of the constituents (chitin, amorphous calcium carbonate (ACC), proteins), and the volume fractions of key structural elements such as chitin-protein fibers. It was found that the cuticle performance is very robust with respect to variations in the elastic properties of chitin and fiber proteins at a lower hierarchy level. At higher structural levels, variations of design parameters such as the volume fraction of the chitin-protein fibers have a significant influence on the cuticle performance. Furthermore, we observed that among the possible variations in the cuticle ingredients and volume fractions, the experimental data reflect an optimal use of the structural variations regarding the best possible performance for a given composition due to the smart hierarchical organization of the cuticle design.

Ab initio and atomistic study of generalized stacking fault energies in Mg and Mg-Y alloys

Magnesium-yttrium alloys show significantly improved room temperature ductility when compared with pure Mg. We study this interesting phenomenon theoretically at the atomic scale employing quantum-mechanical (so-called ab initio) and atomistic modeling methods. Specifically, we have calculated generalized stacking fault energies for five slip systems in both elemental magnesium (Mg) and Mg-Y alloys using (i) density functional theory and (ii) a set of embedded-atom-method (EAM) potentials. These calculations predict that the addition of yttrium results in a reduction in the unstable stacking fault energy of basal slip systems. Specifically in the case of an I2 stacking fault, the predicted reduction of the stacking fault energy due to Y atoms was verified by experimental measurements. Wefind a similar reduction for the stable stacking fault energy of the {11¯

Trends in the elastic response of binary early transition metal nitrides

Motivated by an increasing demand for coherent data that can be used for selecting materials with properties tailored for specific application requirements, we studied elastic response of nine binary early transition metal nitrides (ScN, TiN, VN, YN, ZrN, NbN, LaN, HfN, and TaN) and AlN. In particular, single-crystal elastic constants, Youngs modulus in different crystallographic directions, polycrystalline values of shear and Youngs moduli, and the elastic anisotropy factor were calculated. Additionally, we provide estimates of the third order elastic constants for the ten binary nitrides.

Ab initio calculation of tensile strength in iron

A tensile test in ferromagnetic iron for loading in [001] and [111] directions is simulated by ab initio electronic structure calculations using all-electron full-potential linearized augmented-plane-wave method within the generalized gradient approximation. The theoretical tensile strengths and Youngs moduli of ferromagnetic iron are determined and compared with those of other materials. The magnetic and elastic behaviours of iron under uniaxial tensile loading are discussed in detail and compared with the results for isotropic tension (i.e. for negative hydrostatic pressure). Marked anisotropy of theoretical tensile strength in [001] and [111] direction is explained in terms of higher-symmetry structures present or absent along the deformation paths.

Theory-Guided Materials Design of Multi-Phase Ti-Nb Alloys with Bone-Matching Elastic Properties

We present a scale-bridging approach for modeling the integral elastic response of polycrystalline composite that is based on a multi-disciplinary combination of (i) parameter-free first-principles calculations of thermodynamic phase stability and single-crystal elastic stiffness; and (ii) homogenization schemes developed for polycrystalline aggregates and composites. The modeling is used as a theory-guided bottom-up materials design strategy and applied to Ti-Nb alloys as promising candidates for biomedical implant applications. The theoretical results (i) show an excellent agreement with experimental data and (ii) reveal a decisive influence of the multi-phase character of the polycrystalline composites on their integral elastic properties. The study shows that the results based on the density functional theory calculations at the atomistic level can be directly used for predictions at the macroscopic scale, effectively scale-jumping several orders of magnitude without using any empirical parameters.

Ab initio study of thermodynamic, structural, and elastic properties of Mg-substituted crystalline calcite.

Arthropoda, which represent nearly 80% of all known animal species, are protected by an exoskeleton formed by their cuticle. The cuticle represents a hierarchically structured multifunctional biocomposite based on chitin and proteins. Some groups, such as Crustacea, reinforce the load-bearing parts of their cuticle with calcite. As the calcite sometimes contains Mg it was speculated that Mg may have a stiffening impact on the mechanical properties of the cuticle (Becker et al., Dalton Trans. (2005) 1814). Motivated by these facts, we present a theoretical parameter-free quantum-mechanical study of the phase stability and structural and elastic properties of Mg-substituted calcite crystals. The Mg-substitutions were chosen as examples of states that occur in complex chemical environments typical for biological systems in which calcite crystals contain impurities, the role of which is still the topic of debate. Density functional theory calculations of bulk (Ca,Mg)CO₃ were performed employing 30-atom supercells within the generalized gradient approximation as implemented in the Vienna Ab-initio Simulation Package. Based on the calculated thermodynamic results, low concentrations of Mg atoms are predicted to be stable in calcite crystals in agreement with experimental findings. Examining the structural characteristics, Mg additions nearly linearly reduce the volume of substituted crystals. The predicted elastic bulk modulus results reveal that the Mg substitution nearly linearly stiffens the calcite crystals. Due to the quite large size-mismatch of Mg and Ca atoms, Mg substitution results in local distortions such as off-planar tilting of the CO₃²⁻ group.

Ab initio study of the half-metal to metal transition in strained magnetite

Using density-functional theory, we investigate the stability of the half-metallic ground state of magnetite under different strain conditions. The effects of volume relaxation and internal degrees of freedom are fully taken into account. For hydrostatic compression, planar strain in the (001) plane and uniaxial strain along the [001] direction, we derive quantitative limits beyond which magnetite becomes metallic. As a major new result, we identify the bond length between the octahedrally coordinated iron atoms and their neighbouring oxygen atoms as the main characteristic parameter, and we show that the transition occurs if external strain reduces this interatomic distance from 2.06 A in equilibrium to below a critical value of 1.99 A. Based on this criterion, we also argue that planar strain due to epitaxial growth does not lead to a metallic state for magnetite films grown on (111)-oriented substrates.

Chitin in the Exoskeletons of Arthropoda: From Ancient Design to Novel Materials Science

The Arthropoda use chitin and various proteins as basic materials of their cuticle which is forming their exoskeletons. The exoskeleton is composed of skeletal elements with physical properties that are adapted to their function and the eco-physiological strains of the animal. These properties are achieved by forming elaborate microstructures that are organized in several hierarchical levels like the so-called twisted plywood structure, which is built by stacks of planar arrays of complex chitin-protein fibres. Additionally, the properties are influenced by variations in the chemical composition of the cuticle, for instance by combining the organic material with inorganic nano-particles. From a materials science point of view, this makes the cuticle to a hierarchical composite material of high functional versatility. The detailed investigation of microstructure, chemical composition and mechanical properties of cuticle from different skeletal elements of the crustacean Homarus americanus shows that cuticle can combine different design principles to create a high-performance anisotropic material. Numerical modelling of the cuticle using ab initio and multiscale approaches even enables the study of mechanical properties on hierarchical levels where experimental methods can no longer be applied. Understanding and eventually applying the underlying design principles of cuticle bears the potential for realization of a completely new generation of man-made structural materials.

Ab Initio Based conformational study of the crystalline α‐chitin

The equilibrium structure including the network of hydrogen bonds of an α-chitin crystal is determined combining density-functional theory (DFT), self-consistent DFT-based tight-binding (SCC-DFTB), and empirical forcefield molecular dynamics (MD) simulations. Based on the equilibrium geometry several possible crystal conformations (local energy minima) have been identified and related to hydrogen bond patterns. Our results provide new insight and allow to resolve the contradicting α-chitin structural models proposed by various experiments.