Reconsideration on the concept of the critical nucleus for single component systems leads to the distinction between the thermodynamic and the kinetic critical nuclei, the kinetically stable critical nucleus and the runaway nucleation. By the numerical simulation, it is found that the existance of the kinetically stable critical nucleus does not necessarily mean a peak in the cluster number density. This is due to that the attachment and the detachment rates take close values when the stable cluster size appreciable. Conventional expression for the so-called nucleated cluster size is numerically shown to satisfy its definition.

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Relaxation of a metastable phase to a more stable phase necessarily accompanies nucleation, I.e., the formation of a nucleus that can serve as an embryo of the new phase. Despite a long-standing history of the theory of nucleation that dates back to Gibbs, it is only recently that we have begun to appreciate true complexities of the phenomenon by virtue of molecular level approaches. We present a brief overview that spans from the widely used classical nucleation theory to the recent development of molecular theories. In the first half of the review, key concepts of classical theory are addressed and the various shortcomings of the theory are shown to arise from its essentially macroscopic nature. The latter half of the review discusses basic ideas, major findings, and the current status of the molecular level approaches, I.e., the statistical mechanical density functional theory and molecular simulation.

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Recnt developments of the molecular theoretical study of the solid-liquid interface are reviewed. On the basis of the phenomenological model Cahn succesfully predicted the growth mode change between the activation one and the activationless one. A molecular theoretical formulation has recently been extended to describe the behavior of the thickness of the inteface, the intefacial tension as well as the demarcation line of the growth mode change.

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We carry out the simulation of two component A-B crystals to obtain the critical nucleus size, and show that the nucleus size depends on the surface diffusion of ad atoms on substrate and depends on partial pressure ratio of vapor atoms. We treat two components system for only the case of stoichiometric A-B crystal.

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We review effects of crystal anisotropy in pattern formation of flat interfaces in three systems: an isolated step growing in the surface diffusion field, a flat interface growing from the undercooled melt and a solid-superfluid inter-face of ^4He with a tangential flow. In each system, when the interface becomes unstable, nonlinear effect induced by a large amplitude fluctuation causes a chaotic behavior in the isotropic interface. When anisotropy of the interface exists, the chaotic behavior can be suppressed and a periodic regular pattern may appear.

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We make a brief review on recent development in statistical mechanical approach for quantitative description of the vicinal surface viewed as an assembly of fluctuating steps. As for the equilibrium properties, numerical renormalization group method is succesfully applied to the vicinal surface problems. As for the non-equilibrium properties, the harmonically-interacting-step picture of the coarse-grained vicinal surface is utilized to formulate "quantitative" Ginzburg-Landau-Langevin approach.

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The microscopic mechanism of the current-induced domain conversion phenomena on the Si (001) vicinal surface is discussed on the basis of the microscopic kinetic processes of atoms on the surface. In the migration process of atoms our model takes four effects into account: the anisotropic migration on the Si (001) reconstructed surface, the anisotropy of lateral bond between atoms, the electromigration effect and the Schwoebel effect. Based on the kinetic rates for the migration and evaporation of atoms the kinetic equations for the time evolution of the Si (001) vicinal surface are derived by using the pair approximation of the path probability method (PPM) of non-equilibrium statistical method. The domain conversion mechanisms are explained consistently by the microscopic kinetics of atoms. The results of the PPM calculation are in quantitatively good agreement with those of the Monte Carlo simulation.

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In this year, we suddenly lost our leader (Prof. K. Nishioka) on crystal growth theory. He is also interested in the nucleation of smoke and spontaneous compound formation by reaction between thin film and ultrafine particles. This field is again attracting interest as the mesoscopic physics, nanostructure, quantum dots and chemistry and physics of small many body system. Growth of ultrafine particles may develop not only in material science but also in the fields of dust physics. In this report, brief summary on growth of ultrafine particles and singular character are given on the bases of recent results. By the use of convection flow, the growth in smoke has been elucidated. The summary on the use of convection flow in smoke has been presented. By the simultaneous evaporation of metal and carbon or silicon oxide, the quantum dots covered with carbon and silicon oxide were produced. A-15 type structures of Cr and Fe have been found to be stable structure in cluster sizes. Growth of tetrapod from the cubic nucleus in ZnO has been verified by comparison of infrared spectroscopy among tetrapod, zincblende and wurtzite particles. It has been found that spontaneous compound formation between silicon and carbon film took place at room temperature.

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The relation between the cleavage steps and dislocation etch pits patterns was examined by comparing cleavage step patterns and dislocation etch pit patterns in KCl crystals. The following specimens were used in this study; (1) pure crystal, (2) Sr-doped crystal (0.013 at.%), (3). Sr-doped crystal (0.03at.%), (4) Ca-doped crystal (0.02 at.%). Special attention was paid to the effects of impurities and cleavage temperature on the cleavage step pattern. The results obtained are as follows: (1) Ripple markings (see the section 3) were observed on the cleaved surfaces in all crystals examined in this work, but dislocation nucleation at the ripple markings was strongly affected by the impurities. (2) When the dislocations were nucleated at the ripple markings, a number of cleavage steps were newly generated there. (3) The straightness of the cleavage step lines was strongly dependent on the homogeneity of the dislocations and/or impurities in the crystals. (4) No effect of cleavage temperature on the step pattern was found in the cleavage experiment in liquid nitrogen.

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