A review is given on the surface melting of an ice crystal and the physical properties of the quasi-liquid layer (surface melting layer). The thermodynamics of surface covered with the q.1.1. Is first briefly described and then the recent experimental works about the q.1.1. On ice surface are summarized. An ellipsometric study indicates that the critical temperatures of surface melting are -2℃ and -4℃ for {0001} and {101^^-0} faces, respectively, and the temperature dependences of q.1.1. Thickness for both faces are fundamentally different from each other. This result is discussed in conjunction with both the thermodynamic consideration and the structure of ice/quasi-liquid inter-face. On the other hand, the physical properties of q.1.1. Are discussed on the basis of the results obtained by some experimental methods, that is, the ellipsometry, X-ray diffraction, NMR and so on.

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Strarting from a spherical single crystal of ice, the pattern of snow crystals grown from supersaturated vapor in clouds first becomes an hexagonal prism bounded by two basal and six prism faces. At low supersaturation, such a hexagonal prism can grow in a stable manner and retains its form. For higher supersaturations, however, it changes form by means of preferred growth of edges and corners, becoming a needle crystal for temperature between -4℃ and -10℃ and becoming a dendrite for temperatures between -10℃ and -22℃. Recently, a numerical model of the formation of patterns during the growth of snow crystals was developed by Yokoyama and Kuroda (1990). In the present article, we review briefly studies of the formation of patterns of snow crystals, and present a model that takes into account the following elementary processes relevant to the growth: (1) A surface kinetic process for incorporating molecules into a crystal lattice, and (2) a process for diffusing molecules through air toward the crystal surface. Our numerical calculations give hexagonal pat-terns, dendritic patterns and circular patterns starting from a circular crystal under various growth conditions. We discuss the transition from the hexagonal to the dendritic pattern and the conditions for kinetic roughening that lead to a circular pattern. Finally, we show that the dimensionless crystal size, relative to the mean free path of a water molecule, plays an important role in the formation of patterns during the growth of snow crystals.

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Condensation, metamorphism and evaporation of water ice and mixtures containing CO, CO_2 and CH_4 are thought to be important for the evolution of cometary ice. Based on recent laboratory studies, an overview is given on the physical properties of amorphous ice and on condensation, metamorphism and evaporation of various ices. It is shown that the macroscopic defect structures in amorphous ice play an important role not only in the retention of other volatile molecules but also in the thermal properties. Discussions of the influence of the physical properties of amorphous ices on the origin and thermal evolution of comets are presented. The formation conditions for amorphous ice by vapor deposition are also discussed.

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When a porous material such as soil is exposed to the subzero temperature and freezes partially, water is induced to flow from the unfrozen zone to the frozen zone and ice segregates as lens around the freezing front. The ice lens segregation causes the expansion of the soil volume. This is known as a frost heave phenomenon. This phenomenon is also observed during the solidification of nitrobenzen and liquid helium in porous material. A unique property of frozen soil is the existence of unfrozen water. The unfrozen water exists because of its low chemical potential due to soil particle adsorption. It alows the water movement in the frozen soil and induces ice segregation. When the soil freezes under the confined condition, the frost heaving pressure is built up. The relation-ship between the maximum frost heaving pressure and temperature condition agrees well with the generalized Clausius-Clapeyron equation. Several frost heave model have been proposed on the basis of different viewpoints. In this report, the frost heave model by the late Dr. Kuroda is introduced.

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The periodic change of the structure and the flatness of a growing surface under MBE conditions are theoretically investigated. The growth of the (001) face of the simple cubic lattice is simulated by using Gilmer and Bennema's model for vapor growth. We discuss the properties of the RHEED oscillation by combining this simulation and a kinematical formula for RHEED intensity. In MBE growth, lifetime τ, of an adatom before evaporation is much larger than the life time τ, of an adatom before capture by another adatom. If J is the incident beam flux and D_5, is the surface diffusion coefficient of adatoms, τ_c = (JD_5)^<-1/2>. The results of the Monte Carlo simulation and RHEED intensities calculated for the simulated growth are interpreted in term of lifetime τ_c and the mean diffusion length λ_c inτ_c. We obtain a diagram predicting the growth conditions under which the periodic change of a growing surface causing RHEED oscillation occurs, and the conditions for oscillations of RHEED intensity for stepped surfaces.

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Thermodynamics of interface is extended for small fluid nuclei including those that do not possess homogeneous bulk properties even at their centers. Employing a mathematical boundary to define the system, interaction between the molecules in the system and in the surroundings is taken into account. It is found that the formula for macroscopic systems are rigorously valid for small nuclei without limitation of the size. The meaning of the bulk and the interface terms in the reversible work of forming a critical nucleus is clarified by employing the thought pocess due to Gibbs.

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Interface controlled models of phase-boundaries are considered. Evolving phase-boundaries may develop singularities in a finite time. A level set approach developed by Chen-Giga-Goto and Evans-Spruck is explained for nonmathematicians. This method is usefel to track the evolution of the phase-boundary after it experiences singularities. A key mathematical tool is the theory of viscosity solutions which are generalized solutions of the second order degenerate elliptic and parabolic equations. This important theory is also explained without touching technical details.

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Dendritic crystal growth is one of the most typical phenomena of the spontaneous pattern formation in nature. In order to understand these phenomena in macroscopic level, simple phase field models for one component melt growth are presented. These models are written by the system of partial differential equations which is called reaction diffusion systems. They include thermo-dynamical driving force, surface tension and anisotropy as local dynamics, and temperature field as non-local effect. They can simulate the formation of various dendritic patterns in both two dimensional and three dimensional spaces. Some qualitative relations between the shapes of crystals and some physical parameters are discussed.

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The frost heave phenomena of ^4He on porous glasses are reported. When a boundary between bulk solid and liquid in the porous glass is cooled below bulk melting point, in equilibrium the pressure of the bulk solid surpasses that of the liquid across the boundary. This pressure jump in equilibrium condition is called maximum frost heave pressure. The maximum frost heave pressure was measured at constant pressure in the range 26-60 bars and at temperatures above 1.3 K, using two kinds of porous glasses with pore diameters of 40Å and 140Å. The maximum frost heave pressure obtained for samples above 28.5 bar was in good agreement with the formula, so-call-ed modified Clausius-Clapeyron equation, which is deduced by assuming that the chemical potantial in the solid and liquid phase is the same. For samples below 28 bar, the measured maximum frost heave pressure became less than that of the prediction of the above formula.

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Crystal growing in a diffusion field takes various patterns. Only with the diffusional instability, the aggregation grown has a self-similar structure, called fractal, up to a diffusion length. The growth rate is determined by the fractal dimension and the gas density. With the anisotropic surface tension, the regular dendritic morphology is stabilized, and the growth rate and the tip radius satisfies a universal scaling relation. Below a rounghening temperature of a certain interface, the singularity in the surface kinetics governs the growth and the crystal shape becomes polygonal.

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The growth of emerald (Be_3Al_2Si_6O_<18>: Cr) crystals by slow cooling in the PbO-V_2O_5 flux is reported. The crystal growth was conducted by heating mixtures at 1200℃ for 10h, followed by cooling to 600℃ at a rate of 5℃/h. The emerald crystals exhibited the typical emerald-green color, were up to 2.2 mm in size and transparent. Their form was a regular hexagonal rod bounded by the well-developed {0001} and {101^^-0} faces. The aspect ratio (L/W) of emerald crystals grown at the respective runs was approximately 1. Batch containing the oxide dopant (Cr_2O_3) added as 1.0 or 1.5 wt% of the beryl mixture produced the emerald crystals of good quality. The most suitable com-position of flux was found to be PbO (50 mol%)-V_2O_5(50 mol%). The larger volume batches produced emerald crystals of smaller size and also unwanted crystal phases such as SiO_2 and Be_2SiO_4.

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