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The growth rate of a crystal in the presence of impurity depends on the history of supercooling. This behavior is called growth rate hysteresis (GRH). In this paper, GRH is described by using a mathematical model. This mathematical model is devised by considering the pinning mechanism of Cabrera and Vermilyea, the two-dimensional Gibbs−Thomson effect on step movement and slow adsorption of impurity species on a crystal surface. The model explains, reasonably but qualitatively, experimental literature data on GRH that its magnitude becomes large as the supercooling-changing rate R is decreased or the impurity concentration c is increased. The model also shows a possibility that the reverse effect of these two factors (R and c) on GRH may occur in the range of their small values and it predicts the GRH behavior over a wide range of experimental conditions. Limitations of the model are also discussed.

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Stainless steels are used today in a wide range of applications as a result of their combination of high corrosion resistance and good mechanical properties. In some applications, for example, temporary contact biomedical devices or solar water heaters, corrosion resistance may need further improvement, and surface coatings may be applied for enhanced protection. In this study, AISI 316 stainless steel samples with two different standard industrial finishes were coated using atomic layer deposition (ALD) of Al 2 O 3 /TiO 2 layers. The morphology, composition and corrosion protection was then investigated using different techniques. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to obtain a morphological characterization of coatings and substrates. Glow discharge optical emission spectrometry (GDOES) was used to obtain an in-depth profile of composition. Polarization curves in a 0.2 M NaCl solution were used to evaluate the corrosion protection given by the coatings. The deposited ALD layers were found to be almost flawless. The measured RMS roughness values were compared before and after the ALD, and were around 50 and 370 nm for the two samples. GDOES profiles were strongly influenced by the roughness of the substrate. The corrosion protection obtained on AISI 316 stainless steel by the application of nanometric coatings proved to be very effective in reducing the passive region current density from 10 À7 to less than 10 À9 A/cm 2 and increasing the passive region potential interval from 0.8 to 1.3 V before breakdown.

The growth kinetics of a potassium sulfate crystal was investigated in the presence of traces of chromium(III) impurity (0.5 and 2 ppm) in a flow cell at different rates of change of supercooling (( 0.1 and ( 0.2 °C/min). Hysteresis in crystal growth rates with chromium(III) impurity was induced by decreasing and increasing the supercooling. The rate of supercooling change affected this hysteresis behavior. The cause of hysteresis was hypothesized to occur due to a slow adsorption of impurity at high supercooling.