A geometric model for anisotropic crystal growth

Morphological Attractors in Natural Convective Dissolution

Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle-a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.

Probing the growth and melting pathways of a decagonal quasicrystal in real-time

How does a quasicrystal grow? Despite the decades of research that have been dedicated to this area of study, it remains one of the fundamental puzzles in the field of crystal growth. Although there has been no lack of theoretical studies on quasicrystal growth, there have been very few experimental investigations with which to test their various hypotheses. In particular, evidence of the in situ and three-dimensional (3D) growth of a quasicrystal from a parent liquid phase is lacking. To fill-in-the-gaps in our understanding of the solidification and melting pathways of quasicrystals, we performed synchrotron-based X-ray imaging experiments on a decagonal phase with composition of Al-15at%Ni-15at%Co. High-flux X-ray tomography enabled us to observe both growth and melting morphologies of the 3D quasicrystal at temperature. We determined that there is no time-reversal symmetry upon growth and melting of the decagonal quasicrystal. While quasicrystal growth is predominantly dominated by the attachment kinetics of atomic clusters in the liquid phase, melting is instead barrier-less and limited by buoyancy-driven convection. These experimental results provide the much-needed benchmark data that can be used to validate simulations of phase transformations involving this unique phase of matter.

Ordered Self-Similar Patterns in Anisotropic Stochastic Growth

We propose an anisotropic stochastic growth model to rationalize the anisotropic self-assembly of supramolecules to form elongated two-dimensional ribbon structures in a recent experiment. The model exhibits distinct growth scenarios that are critically controlled by the ratio of the transverse and the longitudinal growth rate. In the regime of suppressed transverse growth, the model generates the experimentally observed elongated structures through layer-by-layer growing. We further observe the convergence of rough clusters toward smooth regular elliptic patterns by averaging over a number of independent growth processes. Remarkably, these resulting elliptic clusters are self-similar in each instantaneous moment in the growth process. Statistical analysis suggests that the realization of such ordered patterns does not rely on the delicate coordination of different parts in the cluster growth. The self-similarity phenomenon derived from this idealized model may have wider implications, notably in the designed clustering of various elementary building blocks with anisotropic interactions.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Solidification of a disk-shaped crystal from a weakly supercooled binary melt

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapor phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid-liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase, and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10-100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.

New insights into ice growth and melting modifications by antifreeze proteins

Antifreeze proteins (AFPs) evolved in many organisms, allowing them to survive in cold climates by controlling ice crystal growth. The specific interactions of AFPs with ice determine their potential applications in agriculture, food preservation and medicine. AFPs control the shapes of ice crystals in a manner characteristic of the particular AFP type. Moderately active AFPs cause the formation of elongated bipyramidal crystals, often with seemingly defined facets, while hyperactive AFPs produce more varied crystal shapes. These different morphologies are generally considered to be growth shapes. In a series of bright light and fluorescent microscopy observations of ice crystals in solutions containing different AFPs, we show that crystal shaping also occurs during melting. In particular, the characteristic ice shapes observed in solutions of most hyperactive AFPs are formed during melting. We relate these findings to the affinities of the hyperactive AFPs for the basal plane of ice. Our results demonstrate the relation between basal plane affinity and hyperactivity and show a clear difference in the ice-shaping mechanisms of most moderate and hyperactive AFPs. This study provides key aspects associated with the identification of hyperactive AFPs.

Modelling the influence of antifreeze proteins on three-dimensional ice crystal melt shapes using a geometric approach

The melting of pure axisymmetric ice crystals has been described previously by us within the framework of so-called geometric crystal growth . Non-equilibrium ice crystal shapes evolving in the presence of hyperactive antifreeze proteins (hypAFPs) are experimentally observed to assume ellipsoidal geometries (‘lemon’ or ‘rice’ shapes). To analyse such shapes, we harness the underlying symmetry of hexagonal ice I h and extend two-dimensional geometric models to three-dimensions to reproduce the experimental dissolution process. The geometrical model developed will be useful as a quantitative test of the mechanisms of interaction between hypAFPs and ice.

Dynamic pressure-induced dendritic and shock crystal growth of ice VI

Crystal growth mechanisms are crucial to understanding the complexity of crystal morphologies in nature and advanced technological materials, such as the faceting and dendrites found in snowflakes and the microstructure and associated strength properties of structural and icy planetary materials. In this article, we present observations of pressure-induced ice VI crystal growth, which have been predicted theoretically, but had never been observed experimentally to our knowledge. Under modulated pressure conditions in a dynamic-diamond anvil cell, rough single ice VI crystal initially grows into well defined octahedral crystal facets. However, as the compression rate increases, the crystal surface dramatically changes from rough to facet, and from convex to concave because of a surface instability, and thereby the growth rate suddenly increases by an order of magnitude. Depending on the compression rate, this discontinuous jump in crystal growth rate or "shock crystal growth" eventually produces 2D carpet-type fractal morphology, and moreover dendrites form under sinusoidal compression, whose crystal morphologies are remarkably similar to those predicted in theoretical simulations under a temperature gradient field. The observed strong dependence of the growth mechanism on compression rate, therefore, suggests a different approach to developing a comprehensive understanding of crystal growth dynamics.

Growth-melt asymmetry in crystals and twelve-sided snowflakes

It is in the lexicon of crystal growth that the shape of a growing crystal reflects the underlying microscopic architecture. Although it is known that in weakly nonequilibrium conditions the slowest growing orientations ultimately dominate the asymptotic shape, is the same true for melting? Here we observe and show theoretically that while the two-dimensional steady melt shapes of ice are bounded by six planes, these planes are not proper facets but instead are rotated 30 degrees from the prism planes of ice. Finally, the transient melting state exposes 12 apparent crystallographic planes thereby differing substantially from the transient growth state.

Shocks preempt continuous curvature divergence in interface motion

The dichotomy between two approaches to interface motion is illustrated in the context of two-dimensional crystal growth. Analyzing singularity formation based on the curvature of the interface predicts a continuous divergence of curvature in contrast to the discrete loss of orientations predicted when the evolution is described by an equation for the two-vector of the interface. We prove that the formation of a shock in the latter approach preempts continuous curvature divergence predicted in the former approach. The results are broadly applicable to kinematic interface motion problems, and we connect them with experiments reported by Maruyama et al. [Phys. Rev. Lett. 85, 2545 (2000)].

Shocks and curvature dynamics: A test of global kinetic faceting in crystals

We investigate the microscopic mechanisms underlying the dynamical faceting of crystals. Partially faceted crystal shapes of CCl4 are formed from a melt contained in a Bridgman apparatus and pressure is used to control growth which is observed using optical microscopy. In contrast to predictions of models in which the local interfacial motion is greatest where the step density is the highest, the loss of rough orientations is observed to occur via a local decrease in curvature which results in the formation of discontinuities-shocks-in the surface of the growth forms, a feature predicted by a recent theory of kinetic faceting.