On the surface of solution grown crystal, macrosteps are often observed. Macrosteps are produced by bunching of atomic steps on the misoriented surface. Macrostep is composed of atomically flat terraces and an atomically rough riser connecting them. The height of macrostep sometimes reach more than 10 μm. Photoluminescence image of the cleaved cross section of the grown crystal gives various characteristic parameters for the macrostep as well as the behavior of it during the growth. Employing conformal transformation one can solve the solute diffusion equation above the macrostep and can find solute concentration on the surface which enables us to calculate the supersaturation distribution across the macrostep terrace. By observing the grown surface with phase contrast microscope, one sees the train of the atomic steps the shape of which gives the supersaturation distribution across the macrostep terrace. Very good agreement was found between theoretical and experimental supersaturation distribution.
We have reported changes in macrostep structure by various additives in solution growth of 4H-SiC. Typically, solution growth exhibits severe step-bunching that developed large macrosteps in micrometers height. The large macrosteps result in trench-like defects accompanying solvent inclusions. In contrast, Al addition drastically improved surface smoothness by reducing average macrostep height. We have shown that some additives, such as Sc and Sn, also improve surface smoothness, in addition to Al. These results demonstrate that the surface modification by additives is useful to control surface morphology in solution growth. Based on the studies on wetting properties and surface tensions of various solvents, we have shown that the interfacial energy in the 4H-SiC/solvent interface increased by the additives that tend to decrease the macrostep height. We suppose that, owing to the increase in the interfacial energy, reduction of the frequency of 2D nucleation helps to sustain a flat growth surface covered by smooth step-flow patterns.
We carried out measurements of freeze front shapes, temperature and concentration of solute in unidirectional freezing of solutions of antifreeze protein and antifreeze polypeptide in a narrow space of 0.020 mm thickness. It was found that developing pyramidal faces and stable pyramidal faces appear depending on the local concentration of antifreeze protein. High concentration regions of antifreeze protein was found to contribute to the serrated interface by maintaining heat flux to the interface. Both pyramidal faces appeared in the cases of one-hour preheated solutions of antifreeze protein. The aggregates of antifreeze protein interacted with ice surfaces. Consequently, the interface temperature for the preheated solution was lower than that for the unheated solution. The antifreeze polypeptide, inspired with a part of the protein, caused different ice surfaces but showed similar enhancement of supercooling.
Recent experiments on curved crystals have created renewed interest in the properties of vicinal (misoriented from high-symmetry). We begin with a review of results for close-packed, straight steps. While the overall picture is rather familiar, we emphasize various noteworthy subtleties as well as use of a generalization of the Wigner surmise. The curved crystal experiments consider not just these steps but also steps that are fully kinked, zigzagged, half way in polar angle between two orientations with straight steps. The terrace-width distribution (TWD) does not satisfy the scaling relations routinely seen for straight steps. We discuss differences in the stiffness and the issues that arise in extending theoretical analysis of the TWD to these vicinal surfaces. There are several open issues that merit attention to address these questions.
Crystal growth and equilibrium facet shape fluctuations are different problems in nature, but nontrivial similarity between them was recently argued. On the one hand, recent developments on the Kardar-Parisi-Zhang (KPZ) universality class, which describes surface fluctuations during random domain growth (such as crystal growth), unveiled relevance of random matrix theory in the case of one-dimensional interfaces. In particular, it was shown, both theoretically and experimentally, that the distribution of interface height fluctuations is given by that of the largest eigenvalue of certain random matrices. On the other hand, relation to random matrices was also shown to exist in equilibrium crystals, where positions of step trains correspond to eigenvalues of random matrices, and crystal facet edges to their largest eigenvalues. Remarkably, at least in certain cases, fluctuations of growing interfaces and those of equilibrium facet shapes were theoretically shown to exhibit the same random matrix distribution. Here I outline those two developments, emphasizing how they are connected or not, and discuss some perspectives.
Here I review a recent work in our group on Pd nanowire fabrication on MgO(210) facetted templates by shadow deposition. The facetted template was prepared by homoepitaxial deposition of MgO of 150 nm thickness on MgO(210) substrate. Pd was deposited by electron bombardment with a glancing angle of 25 deg on the wider (100) terrace of the template. Moiré patterns of transmission electron microscopy (TEM) images of the samples show that the nanowires are highly crystalline on MgO(210) facetted template. Such effect was not observed on MgO(110) facetted template. I discuss the mechanism of the formation of the well-crystalline structure in the Pd nanowires. One candidate origin is nucleation of the Pd atoms at the step-like defects running perpendicular to the facet edges of the MgO template.
We carry out a phase field simulation to study the formation of a comb–like step pattern induced by a straight adatom source advancing in front of a step. The asymmetry of the suface diffusion field induced by the adatom source causes step wandering and small protrusions are formed. The step pattern is changed by the velocity of the adatom soruce, Vp. When Vp is larger than a critical value Vpc, the step cannot follow the adatom source. A seaweed-like pattern is formed with small ϵ4 and a dendritic pattern is formed with large ϵ4, where ϵ4 represents the strength of the anisotropy of step stiffness. When Vp < Vpc, the protrusions follow the adatom source: the comb-like pattern with straight finger-like protrusions, which is induced by step wandering triggered by noise, is formed. For a small Vp, the period of protrusions depends on the strength of noise, but the dependence of the period on the noise strength is week when Vp is near Vpc. The relation between the period and Vp approaches to that between the width of a channel and the velocity of a needle-like step in the free growth in a channel.
Crystal growth hysteresis and catastrophe are remarkable phenomena induced by impurities. We clarified the fundamental mechanism based on a mean field theory. The mean field theory, however, is too simplified to consider actual crystal growth situations such as non-uniform step spacing and advancing velocities, random impurity adsorption and desorption, and their time fluctuations. To simulate such realistic situations, we developed a numerical scheme based on a phase-field model. We succeeded to reproduce the growth hysteresis and catastrophic behavior as predicted by the mean field theory.
In this report, I outline a series of our theoretical studies relating to the crystal growth hysteresis and catastrophe. I also suggest our numerical scheme as a powerful tool to investigate other impurity-induced crystal growth phenomena.