Step and Kink Dynamics in Inorganic and Protein Crystallization
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Step and Kink
Dynamics in Inorganic and Protein Crystallization
A.A. Chernov, J.J. De Yoreo, L.N. Rashkovich, and P.G.Vekilov Abstract Revived interest in crystal growth from solutions is driven by a variety of demands, including the need to develop an understanding of biomineralization processes in bones, teeth, and shells; and efforts to characterize large optically nonlinear crystals, perfect crystals of proteins, nucleic acids, and complexes such as viruses. Producing and purifying drugs, food, paint, fertilizers, and other polycrystalline materials in industry are other expanding areas that rely on crystal growth from solution. These general practical incentives have activated in-depth studies that revealed new phenomena and raised new fundamental questions: Are thermal fluctuations of steps on a crystal face always fast enough to assure the step propagation at the rate controlled just by molecular incorporation at kinks? Is the Gibbs–Thomson capillarity shift of thermodynamic equilibrium always applicable to evaluate the crystallization driving force of polygonized steps? Is it possible to eliminate the step bunching on a growing crystal face that compromises crystal homogeneity, or at least to mitigate it? In this overview, we will discuss experimental findings and provide state-of-the-art answers to these questions. Keywords: atomic force microscopy, crystal growth, crystal perfection, kinetics, proteins.
Crystal Surfaces, Steps, and Kinks All crystallization processes occur at the interface between the crystal and its surroundings. Any crystal interface may be either ordered or disordered. On an ordered crystal face, the species building the crystal occupy positions mainly coinciding with that in the bulk lattice. If such an ordered interface is only slightly (less than 0.1 rad) tilted relative to the nearest close-packed crystallographic plane, this interface may be viewed as a staircase of parallel steps, usually one lattice spacing high, although spacings of 1/2, 1/3, and 1/4 of the lattice height are also known. Each step is the termination of an uncompleted lattice layer. The steps are separated by terraces that are pieces of the ordered close-packed planes.
MRS BULLETIN/DECEMBER 2004
Similarly, two ends of an uncompleted row along a step are positive or negative “kinks” (the signs are usually chosen arbitrarily). Species belonging to a disordered interface occupy a layer several lattice spacings thick, within which the lattice long-range order is gradually transferred to the disordered liquid or gas.1 Disordering comes from thermal fluctuations of the interface. These fluctuations are strong, for example, when a metal crystal is in contact with its own melt (see article by Hoyt et al. in this issue) and in other cases when interfacial free energy per area of one surface species is less than the thermal energy. Disordered interfaces have a nearly isotropic specific free energy and growth rate, resulting in
rounded crystal shapes. In what follows, we consider the ordered interfaces of wellfacete
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