Crystal growth in confinement

Abstract

The growth of crystals confined in porous or cellular materials is ubiquitous in Nature and forms the basis of many industrial processes. Confinement affects the formation of biominerals in living organisms, of minerals in the Earth's crust and of salt crystals damaging porous limestone monuments, and is also used to control the growth of artificial crystals. However, the mechanisms by which confinement alters crystal shapes and growth rates are still not elucidated. Based on novel in situ optical observations of (001) surfaces of NaClO₃ and CaCO₃ crystals at nanometric distances from a glass substrate, we demonstrate that new molecular layers can nucleate homogeneously and propagate without interruption even when in contact with other solids, raising the macroscopic crystal above them. Confined growth is governed by the peculiar dynamics of these molecular layers controlled by the two-dimensional transport of mass through the liquid film from the edges to the center of the contact, with distinctive features such as skewed dislocation spirals, kinetic localization of nucleation in the vicinity of the contact edge, and directed instabilities. Confined growth morphologies can be predicted from the values of three main dimensionless parameters.

Fig. 1. Experimental setup.

A Sketch of experiment chamber with crystal in solution and high-resolution microscope objective. B Vertical cut of crystal. C Reflection of light from crystal and confining surface enables interferometric determination of the distance ζ(r) between the crystal and the glass surface and schematic of molecular steps of layered growth from outer edge. D Interferometric image of part of a growth rim of a crystal surface. E Reconstruction of local crystal height relative to the time-averaged interface $z=\zeta -\overline{\zeta }$, with $\overline{\zeta }=53$ nm from the image intensity in (D). The measured 0.33 nm height of the steps corresponds to single molecular layers of the NaClO₃ crystal. B, C, E The color intensity indicates the solution supersaturation from high (red) in the bulk to zero (white) at the center. The red arrows indicate the growth direction of the steps as interpreted from the time-lapse movies S1–S5 in the Supplementary Information.

Fig. 2. Nucleation of molecular layers.

A Time series (0.1 s interval) of average subtracted RICM images of nucleation and spreading of a new layer (darker gray) at σ = 0.051. B Temporal evolution of mean distance, $\overline{\zeta }$, for a small crystal (L = 48 μm) showing sudden nucleation events (steep negative slopes of one unit cell height, 0.66 nm) followed by a relaxation towards equilibrium distance. C Nucleation rate as function of supersaturation. The nucleation rate was determined by counting of new layers in distance–time curves like (B). The error bars are standard deviations. The red line is a fit of nucleation theory to the data. D Localization of nucleation at different supersaturations. Position of nucleation events at σ≤0.051 (blue) showing random, homogeneous nucleation and a weak tendency of heterogeneous nucleation at three locations, and σ > 0.051 (red) showing strong localization at the edge. E Enhanced RICM image from Supplementary Movie 2 of crystal at $\overline{\zeta }=53$ nm, σ = 0.057 showing four molecular layers (different gray levels) with step fronts of height 0.33 nm advancing inwards. Nucleation at the crystal edges and faster step front propagation in the vicinity of the crystal edge are caused by concentration gradients between the edges and the center.

Fig. 3. Spiral growth in nanoconfinement.

A–C Average subtracted RICM image series at a bulk supersaturation σ = 0.002 with 3-s intervals. The areas outside the crystal and inside the cavity are marked in respectively red and light red colors. The oval regions of different intensities (gray levels) are molecular layers 0.33 nm in height each. The regions a and b in (C) have been selected for the determination of the step flow velocities along the outer rim boundaries. The green region c in (C) was selected to determine position (concentration) dependencies of step fronts shown in (D): position dependence of the step front propagation velocity in region c. The dashed and the dotted lines are linear fits to the data. E Kinetic anisotropy ratios of the two half layers A (blue) and B (green) corresponding to the fronts shown in (D). F, G Evolution of the A and B step fronts simulated by simple forward step algorithm using a linear supersaturation gradient and kinetic anisotropy ratios displayed in (E). One observes close correspondence with the step front shapes in the images (A–C).

Fig. 4. Step front instability.

Average subtracted RICM images of corner of a 700 × 700 μm² crystal with σ = 0.053 and $\overline{\zeta }$ = 22 nm. Areas outside the crystal are marked in red. The dark areas correspond to a smaller distance to the confining glass and thus to the newly formed layer showing instabilities at the front. A–C Time lapse of the same step front at 0.45 s intervals. C–F Four consecutive step fronts nucleated at opposite sides with a time delay of 54 ± 7 s. The black arrow indicates the direction from which the layer originates. The orientation-dependent growth kinetics of the respective layer is indicated by the white arrows.

Fig. 5. Nonequilibrium morphology diagram of confined growth morphologies.

The stable step front morphologies (above the blue line) and the transition from no cavity to cavity (crossing the red line) have been observed both for NaClO₃ and CaCO₃ crystals. The finger-like instability to the upper left has only been observed on NaClO₃ and the growth rim roughening depicted to the upper right has been observed for both NaClO₃ and CaCO₃ crystals.