Etsuro Yokoyama

Elementary steps at the surface of ice crystals visualized by advanced optical microscopy

Due to the abundance of ice on earth, the phase transition of ice plays crucially important roles in various phenomena in nature. Hence, the molecular-level understanding of ice crystal surfaces holds the key to unlocking the secrets of a number of fields. In this study we demonstrate, by laser confocal microscopy combined with differential interference contrast microscopy, that elementary steps (the growing ends of ubiquitous molecular layers with the minimum height) of ice crystals and their dynamic behavior can be visualized directly at air-ice interfaces. We observed the appearance and lateral growth of two-dimensional islands on ice crystal surfaces. When the steps of neighboring two-dimensional islands coalesced, the contrast of the steps always disappeared completely. We were able to discount the occurrence of steps too small to detect directly because we never observed the associated phenomena that would indicate their presence. In addition, classical two-dimensional nucleation theory does not support the appearance of multilayered two-dimensional islands. Hence, we concluded that two-dimensional islands with elementary height (0.37 and 0.39 nm on basal and prism faces, respectively) were visualized by our optical microscopy. On basal and prism faces, we also observed the spiral growth steps generated by screw dislocations. The distance between adjacent spiral steps on a prism face was about 1/20 of that on a basal face. Hence, the step ledge energy of a prism face was 1/20 of that on a basal face, in accord with the known lower-temperature roughening transition of the prism face.

Oscillation and Synchronization in the Combustion of Candles

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candles burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

Phase-field simulation for crystallization of a highly supercooled forsterite-chondrule melt droplet

Chondrules are submillimeter-sized and spherical-shaped crystalline grains consisting mainly of silicate material observed in chondritic meteorites. We numerically simulated pattern formation of a forsterite (Mg2SiO4)-chondrule in the melt droplet using a phase-field method. Because of the large surface-to-volume ratio, the surface cooling term was introduced in the framework of this method. We reproduced an unique crystal growth pattern inside the droplet composed of two distinguishable parts; the rim that covers whole droplet surface, and dendrite inside the droplet. It was found that the rim was formed when there is a large temperature difference of ∼100 K between the center and surface of the droplet due to the large cooling flux at the surface. In order to obtain the temperature difference, we derived temperature distribution of the droplet analytically, and concluded that the rim was formed only when the droplet cools rapidly at a rate of Rcool∼103 K s−1. However, when the surface cooling was so lar...

Growth of an ice disk: dependence of critical thickness for disk instability on supercooling of water.

The appearance of an asymmetrical pattern that occurs when a disk crystal of ice grows from supercooled water was studied by using an analysis of growth rates for radius and thickness. The growth of the radius is controlled by transport of latent heat and is calculated by solving the diffusion equation for the temperature field surrounding the disk. The growth of the thickness is governed by the generation and lateral motion of steps and is expressed as a power function of the supercooling at the center of a basal face. Symmetry breaking with respect to the basal face of an ice disk crystal is observed when the thickness reaches a critical value; then one basal face becomes larger than the other and the disk loses its cylindrical shape. Subsequently, morphological instability occurs at the edge of the larger basal face of the asymmetrical shape (Shimada, W.; Furukawa, Y. J. Phys. Chem. 1997, B101, 6171-6173). We show that the critical thickness is related to the critical condition for the stable growth of a basal face. A difference of growth rates between two basal faces is a possible mechanism for the appearance of the asymmetrical shape.

Numerical Experiments on the Turing Instability in the Oregonator Model

Numerical experiments on the Oregonator model of the Belousov-Zhabotinsky reaction with 2 variables (activator and inhibitor) are carried out. Influences of an inhibitory diffusion coefficient and inhibitory initial condition (concentration) on its pattern dynamics are studied for several values of a stoichiometric factor of the model. As a result, several pattern formation processes such as decrementally propagating waves and self replicating processes are found by changing the initial condition of the inhibitor and the stoichiometric factor under the Turing instability. In the self replicating process, new pattern dynamics acting as birth and death of waves is also found.

Oscillations and accelerations of ice crystal growth rates in microgravity in presence of antifreeze glycoprotein impurity in supercooled water

The free growth of ice crystals in supercooled bulk water containing an impurity of glycoprotein, a bio-macromolecule that functions as ‘antifreeze’ in living organisms in a subzero environment, was observed under microgravity conditions on the International Space Station. We observed the acceleration and oscillation of the normal growth rates as a result of the interfacial adsorption of these protein molecules, which is a newly discovered impurity effect for crystal growth. As the convection caused by gravity may mitigate or modify this effect, secure observations of this effect were first made possible by continuous measurements of normal growth rates under long-term microgravity condition realized only in the spacecraft. Our findings will lead to a better understanding of a novel kinetic process for growth oscillation in relation to growth promotion due to the adsorption of protein molecules and will shed light on the role that crystal growth kinetics has in the onset of the mysterious antifreeze effect in living organisms, namely, how this protein may prevent fish freezing.

Observation of Two-Dimensional Brownian Motion by Microscope Image Sequence Processing.

We propose a method to measure Brownian motion based on image sequence processing. Random motion of sub-micron sphere particles is visualized under an inverted microscope with laser light illumination. We analyze a long image sequence of the motion by a spatial-filtering method, which corresponds to dynamic light scattering. We confirm that bigger particle (diameter=1.09 µm) show ideal Brownian motion with an inverse power-law spectrum P ( f )∝ f -2 . In tiny particles (diameter=0.46 and 0.20 µm), however, we observe a deviation from f -2 behavior. When the motion of particles is limited within a two-dimensional plane by use of heavy water, ordinary behavior of f -2 spectrum is recovered. We confirm high reliability and big advantages of the proposed method compared to dynamic light scattering.

Introduction to Phase‐Field Model and Its Applications in the Fields of Crystal Growth and Planetary Science

The growth of crystal induces a change of ambient environment (temperature, concentration, etc.), and the environmental change gives some feedback to the growth of crystal. The interaction between the crystal growth and ambient environment is important to be taken into consideration, also in the crystallization process of cosmic crystals observed in chondritic meteorites. In this lecture, we will introduce the phase‐field simulation, which is one of the powerful numerical methods to treat the crystal growth and diffusion fields (temperature, concentration, etc.) simultaneously. Participants can experience some phase‐field simulations on their own laptop by using a newly developed Java program, which will be distributed at the school.