Toshio Kuroda

Growth kinetics of ice from the vapour phase and its growth forms

A new interpretation of the habits of ice growing from vapour is proposed. The basic habits of ice alternate three times: plates (A) → -4°C → columns (B) → -10°C → plates (C) → between -20°C and -35°C → columns (D). The theory is based on a view- that the surface of ice just below 0°C is covered with a quasi-liquid layer, whose thickness ϑ or coverage δ decreases with falling temperature, and therefore the growth mechanism of a crystal face changes also as follows: (I) Vapour—Quasi-Liquid— Solid mechanism (δ > 1), (II) Adhesive Growth on a surface strongly adsorbed by H2O molecules (0.02 < δ < 1) and (III) Two- Dimensional Nucleation Growth on a surface with low eigen adsorption (δ < 0.02). The type of surface structure and consequently the growth mechanism depends on the surface orientation and the temperature. The complicated habit change is caused mainly by the combination of surface kinetics of the {0001} and {10110} face. The first and second conversion temperature (TAB, TBC) are expected to be independent of the absolute supersaturation δP as found in experiments. On the other hand, the third (TCD) is the temperature where the usual two-dimensional nucleation growth rate of the {0001} face reaches the one of the {1010} face, and exceeds it by the effect of diffusion field, so that the third conversion temperature falls with decreasing δP. The marked columnar crystals observed at -7°C can be explained only by taking into account the spherical volume diffusion field near the {0001} face and a cylindrical one near the {10110} face. For plate-like crystals between -10°C and -20°C to -35°C the surface diffusion from {0001} to {1010} and volume diffision with cylindrical symmetry near {10110} faces is very important.

Ellipsometric study of the transition layer on the surface of an ice crystal

The purpose of this work is to examine the properties of the transition layer (quasi-liquid layer, QLL) on the surface of an ice crystal at temperatures just below its bulk melting point (0°C) using ellipsometry. The refractive index n 1 and thickness d of the transition layer were measured on both basal {0001} and prismatic 1 0 1 1 ¯ faces of ice crystals. The ice surface sample used was a slice section of a negative crystal, which is a hole growing to the shape of a sharp hexagonal prism in an ice single crystal. The surface prepared in this way was molecularly smooth and free from contaminations. Transition layers were detected on the {0001} and 1 0 1 1 ¯ faces at the condition of equilibrium vapor pressure. The measured n 1 was 1.330 for both faces, which is quite close to the refractive index of bulk water at 0°C ( n w = 1.3327) rather than that of ice ( n 1 = 1.3079). Consequently, the transition layer should be water-like (namely, QLL), and this result gives direct evidence of surface melting. The critical temperatures ( T w ) at which the QLL was detected on the surface were −2°C for the {0001} face and −2 to −4°C for the 1 0 1 1 ¯ face. The thickness of the layer steeply increases as the temperature approached the melting point. However, the temperature dependences of the layer thickness showed a systematic difference between the {0001} and 1 0 1 1 ¯ faces. That is, T w (0001)> T w 1 0 1 1 ¯ and d (0001) d 1 0 1 1 ¯ for a given temperature above −4°C. These characteristics were qualitatively explained by theoretical arguments on the basis of the thermodynamics of the surface. Finally, it was indicated that the structure of the interface between the QLL and the ice crystal on the 1 0 1 1 ¯ face changes from smooth to rough at a temperature of −2°C, and that the roughening transition temperature ( T r ) at which the facets disappear from the growing negative crystals or snow crystals is higher than T w .

Periodic changes in the structure of a surface growing under MBE conditions

Abstract Periodic changes in the structure of a surface growing by the process of MBE are investigated theoretically by means of a Monte Carlo simulation. The conditions for oscillations of the RHEED intensity are obtained for singular and stepped surfaces.

Growth of a crystal surface with non-uniformity in supersaturation due to laminar flow of solution along the surface

Abstract The rate of crystal growth from solution under the influence of laminar flow is derived by taking into account the following three processes: (1) Volume diffusion of growth units, (2) kinetic process at the surface with non-uniformity in supersaturation and (3) conduction of crystallization heat. The growth rate is expressed as a function of the supersaturation at an infinite distance from the surface, which is a driving force for crystal growth, and the sum of resistances for individual processes. By estimating the values of the resistances in the case of growth of Rochelle salt, we investigated the role of each process as a rate determining process, and discussed the microscopic shape of the growing surface. The obtained results are as follows: (1) A non-linear dependence of growth rate on supersaturation of bulk solution is expected at such low supersaturation that the resistance of surface kinetic process cannot be ignored in the total resistance, (2) the resistance of volume diffusion increases with crystal size and with decreasing flow velocity, (3) the resistance of heat conduction is much smaller than that of volume diffusion because of the larger thermal conductivity of solution, and (4) the microscopic shape of the surface determined by the step distribution is expected to be non-symmetrical to compensate the non-uniformity in surface supersaturation caused by the laminar flow along the surface.

Recent developments in theory and experiment of growth kinetics of ice crystals from the vapour phase and their growth forms

Abstract During the last ten years progress has been made in understanding the surface growth kinetics, habit change and morphological stability of snow single crystals, and structure and formation mechanism of snow polycrystals. These works are surveyed.

Vapor growth mechanism of a crystal surface covered with a quasi-liquid layer — Effect of self-diffusion coefficient of the quasi-liquid layer on the growth rate

Abstract For several years, progress has been made in understanding surface melting as well as surface roughening of various crystals such as ice, lead, rare gases etc. A so-called quasi-liquid layer (QLL), caused by surface melting, is expected to influence the vapor growth mechanism of crystals at temperatures not far below their melting points. The effect of the self-diffusion coefficient D of a QLL on the growth rate is investigated in this study. It is shown that the condensation coefficient α QLL involved in the Hertz-Knudsen equation decreases with a decrease in D because of difficulty of rearrangement of molecules from QLL to crystal and this effect appears more clearly for crystals with larger equilibrium vapor pressure. The expression for the rate of spiral growth of the surface covered with QLL is also derived as a function of supersaturation.

Critical thickness for growth of epitaxial grains in silicon film deposited on superlattice surface of silicon (111)

Abstract When Si film is grown on the 7X7 surface of Si(111) held at temperatures ( T s ) below 300°C, some epitaxial grains grow in the film deposited at thicknesses ( d ) below a certain value, d C . The value of d C depends on T s and the growth rate of the film . This could be explained qualitatively by the nucleation process of two-dimensional crystalline nuclei on the growing surface which becomes rough with approaching d C . Some consideration is also given to the film which is initially in an amorphous state, and is rearranged to crystallize during the film growth.

Periodic changes in the structure of a surface growing under MBE conditions and RHEED oscillation

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 Bennemas 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, the lifetime τs of an adatom before re-evaporation is much larger than the lifetime τc of an adatom before capture by another adatom. If J is the incident beam flux and Ds is the surface diffusion coefficient of adatoms, τc = (JDs)−12. The results of the Monte Carlo simulation and the RHEED intensities calculated for the simulated growth are interpreted in terms of the lifetime τu and the mean diffusion length λc inτc. We obtain a diagram predicting the growth conditions under which the periodic change of a growing surface causing RHEED oscillation occurs.

Periodic Changes in the Structure of the Growing Crystal Surface

Periodic changes in the structure of a growing crystal surface are investigated theoretically by means of a Monte-Carlo simulation. The conditions for occurrence of the periodic changes in the structure of the growing crystal surface are obtained for singular surfaces.