Steps in solution growth: dynamics of kinks, bunching and turbulence

Abstract

New findings on calcium oxalate monohydrate, monoclinic lysozyme and potassium dihydrophosphate crystal growth are presented and discussed. Atomic force microscopy was applied to measure step rates on CaOx and monoclinic lysozyme faces to understand kink kinetics. High precision Michaelson interferometry allowed to discover step splitting on the (1 0 1) KH 2PO 4 face growing from turbulent solution. In all three cases, aqueous solutions at room temperature were used. CaOx was grown from solution in which the ion concentration ratio ξ ≡ [ Ox ] / [ Ca ] = 5 × 1 0 - 2 , 10 −1, 1, 10, 20. The rate v of steps one lattice spacing high on the (1 0 0) face reach maximum at ξ=1. Attachment and detachment statistics of two types of particles (Ca and Ox) to a kink on the step of a non-Kossel crystal predicted the reciprocal kink propagation rate to be 1/ v ∼ ξ 1/2+ ξ −1/2, consistent with experiment. Step morphology on the (1 0 1) face of monoclinic lysozyme suggests rhombic, about rectangular 2D critical nucleus. In such a nucleus, two mutually parallel, though crystallographically different steps making the opposite edges, are supposed to be equal. The segment lengths pinned at dislocation outcrop are found to be very different and experience huge scattering. These phenomena, treated as a result of different kink nucleation rates on parallel nearly kink-free steps “looking” to the opposite directions, are of kinetic rather than of thermodynamic origin. Contrary to conventional observations, in a turbulent solution flow the average step bunch width and height were found to reach limits as bunches propagate along the face. These limits decrease when the flow rate increases from ∼60 to 200 cm/s. The phenomenon is explained by the turbulent nature of the solution flow. In this flow, due to penetration of turbulent eddies, diffusivity within the viscous solution boundary layer, D= D 0+0.5 u τ y , quickly increases with the distance y from the interface since the friction velocity, u τ, reaches several cm/s. Therefore, molecular diffusivity, D 0 ≅ 10 −5 cm 2/s, is significant only within the ∼20–40 nm thick solution layer over the interface. As the flow rate increases, the turbulent mixed solution approaches the growing stepped crystal face closer and shrinks the range within which steps interact with one another through their diffusion fields. This weak interaction results in step splitting.