Makio Uwaha

A Model for Complete Chiral Crystallization

A simple reaction-type model that produces complete chiral symmetry breaking in crystallization is proposed. Crystals of homochirality are formed from achiral molecules. The model assumes i) perpetual mixing of the solution and abrasion of the crystals, ii) existence of chiral units smaller than the critical nucleus, iii) all processes have their counterparts, that is, decay of chiral units and crystals also occurs. We show that autocatalysis arises from the reaction of the chiral units so that chiral asymmetry is amplified as crystallization proceeds. Homochirality is achieved via slow relaxation in a later stage of crystallization.

Simple Models for Chirality Conversion of Crystals and Molecules by Grinding

By grinding crystals in a solution, the chirality conversion of the crystal structure and the resultant conversion of molecular chirality have been realized recently. Reaction-type models that enable the reproduction of these phenomena are studied. In the models, chiral clusters are assumed to be formed by grinding and that these clusters can be integrated into crystals of the same chirality. An initial chirality imbalance is amplified exponentially, and the rate is approximately proportional to the grinding strength and to the molecular racemization rate in a relevant parameter range.

Growth of step bunches formed by the drift of adatoms

Abstract We study power-law growth of step bunches produced by the drift of adatoms. When evaporation of the adatoms is neglected (conserved system), the terrace width between the bunches increases as L ∝ t β with β ≈1/2 through a hierarchical bunching. The time dependence of L is not affected by the form of step repulsion. When the adatoms evaporate to the atmosphere (non-conserved system), the motion of the steps changes drastically: isolated steps are always present in large terraces, and collision of the steps with the bunches is repeated. When the drift of adatoms is fast, the terrace width grows by ‘effective coalescence’ of the bunches as L ∝ t 1/2 , similarly to the bunching in the conserved system. When the drift of adatoms is slow, the bunches grow by ‘bunch size exchange’ with β smaller than 1/2 and the terrace width saturates in a late stage. The exponent β increases with increasing drift velocity and approaches β ≈1/2.

Relaxation of Crystal Shapes Caused by Step Motion

Shape relaxation of a crystal faces and of vicinal faces is theoretically studied interms of step movement. When a flat vicinal surface is perturbed, the power of wave number dependence in the relaxation time τ is determined by the bottleneck process, step movement or diffusion, and the proportionality constant depends on the relative angle of the wave vector and the steps. If a small crystal is quenched through a roughening transition, a new equilibrium shape with a facet emerges when the step loops shrink or expand. If diffusion is fast, D s →∞, gradual flattening occurs with τ∝ R c 2 ( R c : radius of the 2D critical nucleus). If the step mobility is large, η s →∞ and the transport relies on slow diffusion, a small facet appears on the top of the crystal and the facet size expands as R f ∝ t 1/5 .

Fluctuations and instabilities of steps in the growth and sublimation of crystals

Abstract Asymmetry in step kinetics (Schwoebel effect) has drastic effects on the motion of steps, and we study them theoretically and by simulation. With asymmetric step kinetics a step becomes smooth when it melts, whereas it becomes increasingly rough when it grows. When the Mullins-Sekerka type of instability takes place, the step does not form any stable pattern but shows a chaotic behavior although the crystal anisotropy influences the morphology. For a vicinal face consisting of equidistant steps, a similar enhancement of the step fluctuation in growth occurs while the fluctuation of step separation (terrace width) is suppressed because of the interference of the diffusion field. In sublimation, on the other hand, the step width is reduced but the fluctuation of the terrace width is enhanced. This leads to a bunching instability of steps. With one-sided step kinetics, steps always form pairwise bound states which have a hierarchical structure. In general various types of bound states appear, some of which lead to a morphological instability of the vicinal face.

Fractal-to-Compact Transition and Velocity Selection in Aggregation from Lattice Gas

Velocity selection has been studied for aggregate growth from a lattice gas, which interpolates between the diffusion-limited aggregation (DLA) and the Eden model. At a low gas density n g , the aggregate is fractal and similar to the DLA up to a length ξ, beyond which it becomes compact and uniform. The growth rate V is expected to follow as V ∼ξ -1 ∼ n g 1/( d - D f ) , where D f =1.71, being the fractal dimension of the DLA. The above theoretical hypothesis is confirmed by Monte Carlo simulations.

Anisotropy Effect on Step Morphology Described by Kuramoto-Sivashinsky Equation

A step growing in a diffusion field is unstable due to the Schwoebel effect when it advances too fast. A continuum model equation is derived for morphological evolution of the unstable step by taking account of the anisotropy effect in the stiffness. The anisotropy brings up an additional term (∂ H /∂ X ) 2 ∂ 2 H /∂ X 2 in the Kuramoto-Sivashinsky equation that describes an isotropic step. Unless direction of the growth corresponds to the one with the stiffness minimum, the morphology is chaotic in space and time. When the step advances in the direction of the stiffness minimum and the anisotropy is sufficiently strong, the step takes a periodic structure.

Step Bunching as Formation of Soliton-Like Pulses in Benney Equation

We study the morphological evolution of a vicinal face that consists of repulsive straight steps moving in a surface diffusion field. Numerical integration of the equations of motion for steps shows that, above the critical undersaturation (or supersaturation, depending on the asymmetry in the step kinetics), unstable density fluctuation grows into periodic step bunches. We construct a continuum model by deriving a non-linear evolution equation for step density from the equations of step motion. Near above the critical point the step density obeys the Benney equation with a large dispersion term, numerical solutions of which reproduce basic features found in the original discrete step model.

Interpretation of the epitaxial orientation relationship at bcc(110)/fcc(111) interfaces

Abstract By using a simple interaction potential, the interfacial energy between bcc(110) and fcc(111) surfaces was calculated. Energy minima appear at specific values of the atomic diameter ratio of bcc to fcc for the Nishiyama-Wassermann orientation relationship (NW), [1 1 0]fcc|[001]bcc, and the Kurdjumov-Sachs relationship (KS), [1 1 0]fcc|[1 1 1]bcc. The reason for the appearance of energy minima is well understood by considering the relative atomic arrangements of the two lattices at the interface. From the calculation and from geometrical considerations, one can predict the preferred orientation relationship for epitaxy, namely the NW, and KS or a new [2 1 1 ]fcc|[001]bcc relationship, from the variation of the atomic diameter ratio of bcc to fcc.

Repulsion-mediated step wandering on a Si(001)vicinal face

With a Si(001) vicinal surface in mind, we study step wandering instability on a vicinal surface with an anisotropic surface diffusion whose orientation dependence alternates on each consecutive terrace. In a conserved system step wandering takes place with step-up adatom drift. Repulsive interaction between steps is found indispensable for the instability. Monte Carlo simulation with a strong repulsive step interaction confirms the result of linear stability analysis, and further shows that in-phase step wandering produces straight grooves. Grooves widen as their amplitudes increase in proportion to the square root of time.