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We demonstrated numerical simulations of impurity-induced crystal growth hysteresis in spiral growth. The numerical scheme combines two different methods: the phase-field method for step dynamics and the Monte Carlo method for random impurity adsorption. We manually changed the supersaturation (down and up) and repeated this cycle to monitor the time variation of the normal growth rate. We found that the growth rate suddenly drops to almost zero as the supersaturation decreases, and it swiftly recovers as the supersaturation subsequently increases. We confirmed that the critical supersaturation at which the growth rate recovered is distinguishably larger than that at which the crystal growth stopped. The critical supersaturations were found to be consistent with those predicted by the mean field theory for spiral growth if the period of the down-and-up cycle of supersaturation was chosen appropriately. We also applied the mean field theory to the observed hysteresis loops to evaluate some physical quantit...

Growth hysteresis is one of the remarkable phenomena of crystal growth induced by impurities; namely, the growth rates of crystal take different values between when supersaturation is decreased and is increased. The appearance of hysteresis has been explained on the basis of the mean field theory, in which the physical quantities such as step velocity, step interval, and density of impurities adsorbed on the crystal surface are averaged over space and time. Here, we propose a new method for the numerical simulation of step dynamics with impurity adsorption–desorption kinetics on a growing crystal surface. We numerically reproduce the growth hysteresis in a more realistic situation, in which the physical quantities fluctuate. The calculated hysteresis agrees with the prediction of the mean field theory. We have also found that the supersaturation should be changed within a period that is similar to the impurity adsorption time scale or slightly longer in order to observe obvious growth hysteresis. Measurem...

The normal growth rates R and apparent step velocities (lateral growth rates of a spiral hillock) V of tetragonal hen egg-white lysozyme (HEWL) crystals were for the first time measured by Michelson interferometry in the international space station (as part of the NanoStep project) using commercialized HEWL samples containing 1.5% impurities. A significant increase in V under microgravity was confirmed compared to step velocities Vstep on the ground, while a decrease in R was also confirmed compared to that in the purified solution under microgravity as expected. Because of exact measurement of growth rates, kinetic analyses of R were conducted as a function of supersaturation, σ (σ ≡ ln(C/Ce), where C is the concentration; Ce is the solubility), using a spiral growth model and a two-dimensional (2D) nucleation growth model. For both models over a wide range of σ, R in the impure solution was significantly lower than that in the purified solution. The degree of the suppression of impurity effects was also...

The step pinning hypothesis is widely accepted as an explanation for the inhabitation of crystal growth by impurity molecules. This hypothesis enables us to evaluate the average step velocity and the critical impurity density above which no step can move on the crystal surface polluted by impurities. The average step velocity and the critical impurity density were obtained analytically in some literature; however, they have not been verified with other approaches. Here, we propose a new method for the numerical simulation of the step pinning by impurities in the framework of a phase-field technique and report a quantitative study on the average step velocity and critical impurity density for the first time. Our results clarify the limitations of the physical assumptions of the analytical formulas and their applications. Our phase-field method provides a good numerical tool for the quantitative investigation of the effect of impurities on step dynamics if step pinning works as described in the Cabrera–Verm...

We propose a new formulation for numerically simulating step dynamics on growing crystal surfaces in the framework of a phase-field technique. The step advancement rate is proportional to a supersaturation at the crystal surface when the growth units in the ambient phase are integrated to the step front directly (direct integration hypothesis). We conduct numerical simulations of some standard step dynamics problems: the advancement of a straight step, the growth or dissolution of a two-dimensional island, and the vertical growth of the crystal surface due to single or multiple screw dislocations. During evaluations, our phase-field model accurately calculated the rate of advancement of a straight step for various supersaturations. The calculated time variation of the radius of the two-dimensional island showed good agreement with the exact solution. The vertical growth rate due to screw dislocations qualitatively agreed with the predictions of the classical theory of Burton, Cabrera, and Frank. Our simpl...

Chiral symmetry breaking during the chiral crystallization from a sodium chlorate (NaClO3) aqueous solution is an intriguing phenomenon because it provides insights into the prebiotic process of biohomochirality. However, a mechanism of the emergence and amplification of chirality remains controversial, especially for crystallization from highly supersaturated solution, and one of the hypotheses proposed before is a transition toward the homochiral state during the early stages of crystallization. In this contribution, we directly examined the early stage of crystallization by in situ polarized-light microscopy. The observation revealed that achiral crystals, which appear prior to the formation of chiral crystals, transform to the chiral crystal through two kinds of polymorphic transformations: (1) martensitic transformation (MT) and (2) solution-mediated phase transition (SMPT). The SMPT is remarkably facilitated by contact with a chiral crystal. Notably, the resulting enantiomorph through contact-facili...

Chiral symmetry breaking in NaClO3 crystallization from an aqueous solution with perturbations has been of great interest. To understand the mechanism, several models focusing on the early stage of the crystallization have been proposed. However, they are ambiguous because the early stage has been barely explored directly. Here, we investigate the early stages of the crystallization process driven by droplet evaporation using a combination of direct in situ microscopic observations and cryogenic single-crystal XRD experiments. We demonstrate that an achiral crystal having P21/a symmetry, which is newly discovered for a solution growth, first appears in the droplet and then transforms into the chiral crystals. Additionally, determination of the lattice constants by XRD experiments (a = 8.42 A, b = 5.26 A, c = 6.70 A, β = 109.71°) revealed that the achiral phase should be identical to Phase III (a = 8.78 A, b = 5.17 A, c = 6.83 A, β = 110°), which is a high-temperature phase from a melt growth of NaClO3. We...

We proposed a simple physical model of growth hysteresis and oscillatory growth in a crystallization system with impurities. The model is based on two fundamental mechanisms: (i) removal of impurities adsorbed on the growing crystal surface by step advancement and (ii) retardation of step advancement by the adsorbed impurities (the pinning mechanism). We found that the coupling of these two mechanisms causes a cyclic feedback on the kinetics of impurity adsorption and step advancement. We revealed a growth hysteresis on the step velocity, namely, the history of the step velocity when the supersaturation is decreased is different from that when the supersaturation is increased. The critical supersaturation at which the growth hysteresis appears is given by definite physical parameters such as step free energy, number density of the adsorbed impurities, and time scale of impurity adsorption. The feedback loop also results in the oscillatory growth of crystals when the transportation of constituent molecules...

We examined the homogeneous condensation of thermally evaporated manganese vapor in an atmosphere of argon gas and determined the temperature and concentration during homogeneous nucleation in the vapor phase by using a Mach–Zehnder type interferometer. Condensation occurred at 660–785 K below the equilibrium temperature and the degree of supersaturation was as high as ∼5 × 104. Using the condensation temperature and size of the condensed particles, which were measured by transmission electron microscopy, we determined the surface free energy and sticking coefficient of Mn at 1106 ± 50 K to be 1.55 ± 0.10 J/m2 and 0.39–0.20+0.39, respectively, by classical nucleation theory (CNT) and 1.57 ± 0.35 J/m2 and 0.42–0.21+0.42, respectively, by a semiphenomenological theory (SP). The nucleation theories predict that the critical nucleus contains only three and six atoms for CNT and SP, respectively, which are fewer than the number of atoms in a unit cell of Mn. This suggests that the polymorphic form of manganese...