Chiral symmetry breaking is often observed in crystalline shape or organic molecules in life. We introduce a simple model, motivated by the enantiomeric excess (ee) amplification observed in the organic molecule production, called the Soai reaction. We review results obtained by the reaction rate theory and by the stochastic method. The model contains autocatalytic processes in the production of two chiral enantiomers, R and S, from an achiral substrate A. It may also include decomposition processes from the chiral products to the achiral substrate. According to the rate equations for average concentrations of R and S enantiomers, it is found that an initially small ee is amplified by the second order autocatalytic process. With the back decomposition, a unique final state is chosen, and the chiral symmetry breaking takes place. However, if the inital state is chirally symmetric without any chiral impurities, the system cannot escape from the racemic fixed point even though it is unstable. To escape from an unstable fixed point, fluctuation has to be granted. We consider a probability distribution for the numbers of two enantiomeric molecules R and S. Its stochastic time evolution is governed by the master equation. With the back decomposition, the final probability distribution P_f is found independent of the initial state. With a second order autocatalytic process, P_f has double peaks at two states with an excess of R or S enantiomers. Without back decomposition, the profile of the final probability depends on the initial condition. In the case with a spontaneous production and the second order autocatalysis, it is found to depend furthermore on the total number of reactant molecules N. On starting from a completely achiral initial state with a small N, final probability has only a single racemic peak, because two enantiomers are randomly produced by the spontaneous process. On the contrary, with a large N the second order autocatalysis dominates the spontaneous production and the final probability has two peaks with an excess of one of the enantiomers. Similar double peaks are observed in the histogram of the final ee value in the experiment performed by Soai's group starting from a completely achiral initial condition.

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Spontaneous chiral symmetry breaking in crystallization is briefly reviewed. Experimentally, crystallization of several substances such as NaClO_3 from supersaturated solution with stirring produces strong chiral symmetry breaking. In addition, stiring and grinding of racemic mixture of chiral crystals in solution results in chirality transformation, and complete symmetry breaking is realized. Several models to explain these experiments are introduced, and the mechanism of autocatalytic processes is discussed at a phenomenological level.

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Some models have been proposed for the origin of homochirarity of amino-acids and proteins in nature not only on the Earth but also in space. A model has been proposed on the basis of the effect of circular polarized light on the selection of chiral molecules. The strong circular light of ultraviolet is emitted from a heavier start than the Sun. Experimentally this circular polarized light is confirmed to destroy one type of chiral amino acids, leading to homochirality in space. Another model is based on the selective adsorption of one chiral molecules on mineral surfaces. Recent experimental data show that the chiral selection is caused not by structural conformation of the chiral molecules at the step fronts but by some complex kinetic processes, One example will be shown for the case of L-ASP adsorption on calcite.

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The influence of biomolecules on crystallization in living systems leads to dramatic control over crystal shapes, growth rates and properties. AFM studies of crystal growth in which both synthetic and naturally occurring biomolecules are introduced during growth, in combination with computational modeling of modifier-crystal interactions, have led to new insights into mechanisms of biomolecule-driven growth modification. Amongst the important factors that have emerged are the stereochemical relationship between modifier and step edge, the strength of binding to terrace and step edge sites, and the effect of biomolecules on crystal and solute solvation state. Here we illustrate these factors using examples from the calcite and calcium oxalate monohydrate systems, in which carboxyl-rich biomolecules are used to influence growth.

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We review two methods of optical resolution using the crystal size difference between D- and L-crystals. As a first optical resolution technique, seeded cooling crystallization was performed with the L-Asn seeds of large size and the D-Asn seeds of small size. This method was experimentally proved as a useful method. The product crystals had a bi-modal distribution. The large crystals were L-Asn of 100 % purity and the small crystals were D-Asn of 100 % purity. As a second optical resolution technique, a "tailor-made" additive was used as a separation agent. As a model chiral compound, the conglomerate of asparagine was examined. By a batch cooling operation, the primary nucleation of L-Asn was delayed significantly by adding L-Cysteine at 5 mol %, while that of the other enantiomer, D-Asn, remained almost unchanged. The distribution of the product crystals was found to be bi-modal. The large crystals were D-Asn with 100 % optical purity.

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In this review, preparation process, morphology, microstructure, growth mechanism and some properties of vapor grown carbon microcoils (CMC) are reviewed. The CMCs are obtained by the metal-catalyzed pyrolysis of acetylene containing a small amount of sulfur impurity at 750-800 ℃. The CMCs with various coiling morphology; regular coils, irregular coils, double coils, single coils, circular coils, flat coils, etc. can be obtained depending on the reaction conditions. The vapor grown carbon fibers grow from a catalyst grain to an opposite direction and continuously curl, caused by the catalytic anisotropy of the catalyst grain, to form double-helix carbon coils. There are two coiling-directions (coiling-chirality) in CMC; clock-wise and unticlock-wise, and the ratio are nearly the same. However, the change in coiling-chirality was sometimes observed for carbon nanocoils with smaller coil diameter than 1 μm.

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