Evolution of chemically induced cracks in alkali feldspar: thermodynamic analysis.

A system of edge cracks was applied to polished (010) surfaces of K-rich gem-quality alkali feldspar by diffusion-mediated cation exchange between oriented feldspar plates and a Na-rich NaCl-KCl salt melt. The cation exchange produced a Na-rich layer at and beneath the specimen surface, and the associated strongly anisotropic lattice contraction lead to a tensile stress state at the specimen surface, which induced fracturing. Cation exchange along the newly formed crack flanks produced Na-enriched diffusion halos around the cracks, and the associated lattice contraction and tensile stress state caused continuous crack growth. The cracks nucleated with non-uniform spacing on the sample surface and quickly attained nearly uniform spacing below the surface by systematic turning along their early propagation paths. In places, conspicuous wavy cracks oscillating several times before attaining their final position between the neighboring cracks were produced. It is shown that the evolution of irregularly spaced towards regularly spaced cracks including the systematic turning and wavyness along the early propagation paths maximizes the rate of free energy dissipation in every evolutionary stage of the system. Maximization of the dissipation rate is suggested as a criterion for selection of the most probable evolution path for a system undergoing chemically induced diffusion mediated fracturing in an anisotropic homogeneous brittle material. Supplementary Information: The online version contains supplementary material available at 10.1007/s00269-022-01183-9.

Surface Energy of Au Nanoparticles Depending on Their Size and Shape.

Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to a value for ( 0 0 1 ) facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface is hugely reduced if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.

Damage tolerance of lamellar bone.

Lamellar bone is known to be the most typical structure of cortical bone in large mammals including humans. This type of tissue provides a good combination of strength and fracture toughness. As has been shown by John D Currey and other researchers, large deformations are associated with the appearance of microdamage that optically whitens the tissue, a process that has been identified as a contribution to bone toughness. Using finite-element modelling, we study crack propagation in a material with periodic variation of mechanical parameters, such as elastic modulus and strength, chosen to represent lamellar bone. We show that a multitude of microcracks appears in the region ahead of the initial crack tip, thus dissipating energy even without a progression of the initial crack tip. Strength and toughness are shown to be both larger for the (notched) lamellar material than for a homogeneous material with the same average properties and the same initial notch. The length of the microcracks typically corresponds to the width of a lamella, that is, to several microns. This simultaneous improvement of strength and toughness may explain the ubiquity of lamellar plywood structures not just in bone but also in plants and in chitin-based cuticles of insects and arthropods.

Surface energy of nanoparticles - influence of particle size and structure.

The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.

Au55, a stable glassy cluster: results of ab initio calculations.

Structure and properties of small nanoparticles are still under discussion. Moreover, some thermodynamic properties and the structural behavior still remain partially unknown. One of the best investigated nanoparticles is the Au55 cluster, which has been analyzed experimentally and theoretically. However, up to now, the results of these studies are still inconsistent. Consequently, we have carried out the present ab initio study of the Au55 cluster, using up-to-date computational concepts, in order to clarify these issues. Our calculations have confirmed the experimental result that the thermodynamically most stable structure is not crystalline, but it is glassy. The non-crystalline structure of this cluster was validated by comparison of the coordination numbers with those of a crystalline cluster. It was found that, in contrast to bulk materials, glass formation is connected to an energy release that is close to the melting enthalpy of bulk gold. Additionally, the surface energy of this cluster was calculated using two different theoretical approaches resulting in values close to the surface energy for bulk gold. It shall be emphasized that it is now possible to give a confidence interval for the value of the surface energy.

A kinetic model of the transformation of a micropatterned amorphous precursor into a porous single crystal.

Biogenic single crystals with complex shapes are believed to be generated by the crystallization of an amorphous precursor. Recent biomimetic experiments on the crystallization of calcite via amorphous-to-crystalline transition point to the fact that the transformation kinetics may be controlled by the micropattern and the macroscopic shape of the amorphous precursor phase. Here we analyse a simple kinetic model, based on thermodynamic considerations, showing that the presence of cavities in the micropatterned precursor phase might interfere with the transformation process and control its kinetics. The size of the cavities couples to the total surface energy and, hence, to crystal nucleation and growth, while the spacing of the cavities, as compared to the typical diffusion path, controls the possible nucleation of competing crystals.

Switching mechanics with chemistry: a model for the bending stiffness of amphiphilic bilayers with interacting headgroups in crystalline order.

Bilayer structures in catanionic systems experimentally showed peculiar mechanical behavior. The observed increase in the bending stiffness is supposedly connected to additional hydrogen bonds forming between anionic headgroups. With a simple model, we can explain the extreme sensitivity of the bending stiffness of the membrane on the molar ratio of the charged molecules. This effect is further amplified by the sandwichlike structure of the membrane, where the apolar core separating the headgroups acts via a kind of lever-arm principle. As a consequence of these combined effects, the model membrane changes from a soft behavior with bending rigidities on the order of 10k(B)T to an extremely stiff membrane with a bending stiffness more than 2 orders of magnitude larger where most of this change occurs within a molar ratio interval smaller than 0.1.

Energy dissipation and stability of propagating surfaces.

Thermodynamic equilibrium states are given by the minimum of a convex free energy function with suitable boundary conditions. Nonconvexity may lead to the coexistence of several phases and the classical Gibbs phase rule allows constructing their equilibrium properties (e.g., density or pressure). Within the framework of nonequilibrium thermodynamics, the maximization of energy dissipation (under suitable boundary conditions) can be used as an extremal principle to find stationary states. We show that stationary states generally exist for convex energy dissipation functions and that nonconvexity leads to metastable and unstable states. A geometric argument, similar in spirit to Gibbs' double-tangent construction, yields the stability limits of stationary states. This argument is applied to study a classical problem of materials science, namely the motion of a grain boundary under the influence of solute drag.

Fracture statistics of brittle materials: Weibull or normal distribution.

The fit of fracture strength data of brittle materials (Si(3)N(4), SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si(3)N(4), the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.