Morphology and rate of fracture in chemical decomposition of solids

Single-chirality nanotube synthesis by guided evolutionary selection

Bringing to fruition the tantalizing properties, foreseen since the discovery of carbon nanotubes, has been hindered by the challenge to produce a desired helical symmetry type, single chirality. Despite progress in postsynthesis separation or somewhat sporadic success in selective growth, obtaining one chiral type at will remains elusive. The kinetics analysis here shows how a local yet moving reaction zone (the gas feedstock or elevated temperature) can entice the tubes to follow, so that, remotely akin to proverbial Lamarck giraffes, only the fastest survive. Reversing the reaction to dissolution would further eliminate the too fast-reactive types so that a desired chirality is singled out in production.

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.

Crack formation during solid pyrolysis: evolution, pattern formation and statistical behaviour

As solids pyrolyse during combustion, they lose chemical and structural integrity by gradually degrading into residual char and forming defects such as voids, fissures and cracks. The material degradation process, which is coupled to the crack formation process, is described using a theoretical model and is numerically simulated using the finite-element method for a generic, charring, rubber-like material. In this model, a slab of material is subjected to an external, localized heat flux and, as the material degrades, cracks form when the local principal stress exceeds a defined cracking threshold. The magnitude of the cracking threshold σ _c is systematically varied in order to examine its influences on crack initiation, evolution, distribution and behaviour over time. When σ _c exceeds the maximum principal stress for the entire process, σ _m , then no cracks are generated. We quantify how the average crack spacing, total crack length and crack initiation time depend upon the ratio σ _c /σ _m . Two characteristic domains of crack formation behaviour are identified from the crack initiation behaviour. Correlations are produced for the crack length evolution and final crack length values as functions of σ _c /σ _m . Crack intersection patterns and behaviour are described and characterized.

Spatially-ordered nano-sized crystallites formed by dehydration-induced single crystal cracking of CuCl2·2(H2O)

The dehydration of CuCl₂·2(H₂O) crystals is studied as an example of a fracture-assisted chemical reaction. The structure of the combined reaction–fracture front undergoes a spontaneous morphology transition, leading to spatial ordering and 8-fold acceleration of the reaction.

Self-similarity and scaling of thermal shock fractures

The problem of crack pattern formation due to thermal shock loading at the surface of half space is solved numerically using the two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such a process of pattern formation with quasistatic crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest cracks. This single-crack scenario should be understood in a local sense. There could be other unstable cracks far away that together can form a new pattern. The onset of instability has also been determined from numerical results.

Crack front dynamics across a single heterogeneity

We study the spatiotemporal dynamics of a crack front propagating at the interface between a rigid substrate and an elastomer. We first characterize the kinematics of the front when the substrate is homogeneous and find that the equation of motion is intrinsically nonlinear. We then pattern the substrate with a single defect. Steady profiles of the front are well described by a standard linear theory with nonlocal elasticity, except for large slopes of the front. In contrast, this theory seems to fail in dynamical situations, i.e., when the front relaxes to its steady shape, or when the front pinches off after detachment from a defect. More generally, these results may impact the current understanding of crack fronts in heterogeneous media.

Numerical study of drying process and columnar fracture process in granule-water mixtures

The formation of three-dimensional prismatic cracks in the drying process of starch-water mixtures is investigated numerically. We assume that the mixture is an elastic porous medium which possesses a stress field and a water content field. The evolution of both fields is represented by a spring network and a phenomenological model with the water potential, respectively. We find that the water content distribution has a propagating front which is not explained by a simple diffusion process. The prismatic structure of cracks driven by the water content field is observed. The depth dependence and the coarsening process of the columnar structure are also studied. The particle diameter dependence of the scale of the columns and the effect of the crack networks on the dynamics of the water content field are also discussed.

Fracture patterns generated by diffusion controlled volume changing reactions

A simple two-dimensional model was developed for the growth of fractures in a chemically decomposing solid. Simulations were carried out under rapid chemical decomposition conditions for which the kinetics of fracture growth is controlled by diffusion of the volatile reaction product or the kinetics of evaporation. The growth of the fracture pattern is self-sustaining due to the volume reduction associated with the decomposition process. Consistent with the theoretical analysis of Yakobson [Phys. Rev. Lett. 67, 1590 (1991)10.1103/PhysRevLett.67.1590], the fracture front propagates with a constant velocity v approximately=k2/3(Dl0)1/3 under evaporation controlled conditions and v approximately=D/l0 under diffusion controlled conditions, where k is the evaporation rate constant, D is the diffusion constant for the volatile reaction product in the solid, and l0 is the critical stable crack length. Under diffusion controlled conditions, the front width w scales as w approximately=(kl0/)D.

Directional crack propagation of granular water systems

Pattern dynamics of directional crack propagation phenomena observed in drying process of starch-water mixture is investigated. To visualize the three-dimensional structure of the drying-fracture process two kinds of experiments are performed, i.e., resin solidification planing method and real-time measurement of water content distribution with MR instruments. A cross section with polygonal structure is visualized in both experiments. The depth dependency of cell size is measured. The phenomenological model for water transportation is also discussed.

Kinetic theory of symmetry-dependent strength in carbon nanotubes

Carbon nanotubes yield to mechanical force by a primary dislocation dipole whose formation energy describes the thermodynamic stability of the tubule. However, the real-time strength is determined by the rate of defect formation, defined in turn by the activation barrier for the bond flip. First extensive computations of the kinetic barriers for a variety of strain-lattice orientations lead to predictions of the yield strength. Its value depends on nanotube chiral symmetry, in a way very different from the thermodynamic assessment.

Accelerated hydration of the Earth's deep crust induced by stress perturbations

The metamorphic cycle associated with the formation of mountain belts produces a lower crust containing little or no free fluid. The introduction of external fluids to dry and impermeable volumes of the Earth's crust is thus a prerequisite for the retrogressive metamorphism later observed in such regimes. Such metamorphism can cause significant changes in the crust's physical properties, including its density, rheology and elastic properties. On a large scale, the introduction of fluids requires the presence of high-permeability channels, such as faults or fractures, which are the result of external tectonic stresses. But extensive interaction between externally derived fluids and the fractured rock requires efficient mass transport away from the initial fractures into the rock itself, and this transport often occurs over distances much longer than expected from grain-boundary diffusion. Here we present both field observations and a simple network model that demonstrate how the transport of fluids into initially dry rock can be accelerated by perturbations in the local stress field caused by reactions with fluids. We also show that the morphology of reaction fronts separating 'dry' from 'wet' rocks depends on the anisotropy of the external stress field.