Transient modes of zeolite surface growth from 3D gel-like islands to 2D single layers

Zeolite crystallization occurs by multifaceted processes involving molecule attachment and nonclassical pathways governed by the addition of amorphous precursors. Here, we use scanning probe microscopy to monitor zeolite LTA crystallization in situ with a spatiotemporal resolution that captures dynamic processes in real time. We report a distinctive pathway involving the formation of gel-like islands from supersaturated solutions comprised of (alumino)silicate molecules. Three-dimensional assembly and evolution of these islands constitutes a unique mode of growth that differs from classical theories. Time-resolved imaging also reveals that growth can occur by (nearly) oriented attachment. At later stages of crystallization, a progressive transition to lower supersaturation shifts growth to a layered mechanism involving two-dimensional nucleation and spreading of layers. Here, we show that LTA crystallization occurs by multiple pathways, thereby reconciling putative hypotheses of growth mechanisms while also highlighting new modes of nonclassical crystallization that may prove relevant to other zeolites and related materials.


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(1) where k is the Boltzmann constant, T is temperature, ∆ is the change in chemical potential per molecule, C is the solute concentration, and Co is the equilibrium concentration (or solubility).
At low  ( Supplementary Fig. 17, Region I), surfaces grow by the direct addition of solute to defect sites (e.g., screw dislocations 2 ), resulting in the formation of hillocks. AFM has proven to be a useful technique for capturing the presence and growth of such features on the surfaces of inorganic 3,4 and organic crystals [5][6][7] . The growth of a crystal surface follows different dynamics depending on the limitations of solute addition. The Damköhler number (Da) is often used to differentiate the rate limiting steps. For instance, when Da << 1 the growth rate is limited by surface integration, and when Da >>1 the growth rate it is limited by bulk transport. In the kinetic regime, the normal growth rate R of a surface 4,8 exhibits a parabolic relationship with : The rate constant C" is a function of several parameters, where a is the step height, st is the kinetic coefficient of step growth, is the volume of a single building unit, and n is the number of dislocations. The parameter is given by where is the mean distance covered by adatoms during their lifetime, and Ds is the surface diffusion coefficient.
At higher supersaturation ( Supplementary Fig. 17, Region II), the rate of 2D nucleation becomes sufficiently high to compete with spiral growth, and there is a crossover to the regime where crystallization occurs by 2D layer nucleation and spreading 9 . This mode of growth has been observed for a wide range of materials that include metals 10 , inorganics 11 , and organics 12 . Nuclei can form on defect free terraces and generate a new layer that advances by monomer addition to steps sites (e.g., kinks). The rate of 2D nucleation determines the mode of growth. At low nucleation rate, the layer extends across the entire crystal surface prior to a new nucleation event. This phenomenon, which is typically referred to as monolayer growth, is more pronounced on small crystal faces at low supersaturation. In this regime, the nucleation rate varies exponentially with supersaturation while the rate of step growth follows a linear trend. Conversely, the formation of new nuclei before the completion of the underlying layer gives rise to multilayer growth 13 . This regime can be subdivided into two categories depending on the growth area and nucleating area. If the growth area is larger than the nucleating area, the layer emanating from a sparse population of nucleating centers will start merging, and the growth rate of the crystal surface is dominated by the step velocity. However, if the rate of nucleation is high enough that steps merge quickly due to a large population of nuclei, it is referred to as the polynuclear regime. Our observations suggest that LTA surfaces exhibit multilayer growth, R2D, ML, via a birth and spread model: The term ∆Gc (α 1/∆μ) is the free energy barrier for 2D nucleation. The constant is expressed as √ Where K1 is a pre-exponential term for 2D nucleation in solution.
As the supersaturation increases further, classical theory posits a transition from smooth (layered) to rough growth. This phenomenon, which is commonly referred to as kinetic roughening, has been observed for various crystalline materials. The transition from smooth to rough growth can be controlled by supersaturation and/or temperature [14][15][16][17][18] . During kinetic roughening, there is a loss of faceting on crystal surfaces owing to rounded step edges, which can have a concomitant effect on the bulk morphology of crystals [19][20][21] . Based on the Gibbs-Thompson inverse correlation between a critical radius and supersaturation, the size of a nucleus in this regime is generally smaller than the critical nucleus size for 2D generation of islands at higher supersaturation. This is attributed to a negligible energetic barrier 22 for solute attachment to crystal surfaces, which renders molecules (i.e., monomers) or small clusters thereof as viable nuclei. Under conditions when barriers to monomer addition are small, there is a high density of nuclei on the surface wherein the average distance between layers is small (e.g., interatomic distances). This, in turn, leads to highly rough surfaces when monomers can attach at all possible binding sites on crystal surfaces.
Various theoretical models 23-26 based on either known or estimated thermodynamic parameters 27,28 have been used to modify the original growth models of Burton, Cabrera, and Frank 29 to account for kinetic roughening. Measurements of crystal growth in the kinetic roughening regime ( Supplementary Fig. 17, Region III) reveal that the normal growth rate of crystal surfaces varies linearly with increasing supersaturation 30 , expressed as where CKR is the kinetic rate constant for kinetic roughening (labelled "KR"). In our study, we show a unique form of roughening at low temperature owing to the formation of gel-like islands.
Our findings indicate that it is possible for 3D nucleation to occur in a cohesive region when there is partial wetting of the surface by solute. This regime requires higher supersaturation than that of 2D nucleation. The fact that we observe gel-like islands in LTA surface growth at sufficiently high  suggests a transition from an adhesive region (2D nucleation) to a cohesive region (3D nucleation).
Supplementary Figure 1│Time-elapsed particle evolution. In situ DLS measurements of supernatant solutions S1 (blue squares) and S2 (red diamonds) heated at 45°C as a function of time. Solutions at initial times do not contain any detectable particles, consistent with SAXS measurements in figure 1d. These growth curves show an induction period that increases with decreased supersaturation. During periods of growth, there is a linear increase in the average hydrodynamic diameter Dh of crystals. The particle size eventually plateaus at longer times as solutions approach equilibrium. Note that the scattering intensity from supernatant solutions S3 and S4 was insufficient for DLS measurements. Also, similar measurements at 35°C (not shown) over a 12 h period showed no sign of crystal nucleation, indicating a much longer induction time at lower temperature, as expected. The hydrodynamic diameters reported here account for the kinematic viscosity of the growth solution, which was ca. 1.13 mm 2 s -1 for both S1 and S2.

Supplementary Figure 2│Determination of particle in growth solution.
Small-angle X-ray scattering patterns of supernatant solutions S2 (blue), S3 (red), and S4 (black) with subtracted background patterns (water). The background subtracted patterns exhibit no trace of nanoparticles for all three growth solutions. It is feasible that the absence of particles may be attributed to the limitations of SAXS analysis, such as low particle number density and/or insufficient solvent-particle contrast.  (Fig. 1f). Crystal growth in region II (moderate ) occurs by the formation and propagation of 2D layers (Fig. 4) via a birth and spread or polynuclear pathway. Growth in region III (high ) occurs by kinetic roughening at high temperature, akin to classical models. At low temperature, growth occurs by a unique nonclassical mode of action wherein roughness derives from the formation of 3D gel-like islands (Fig. 2). 1.0 0.9 Ex situ growth (S2, 35 °C, 2 h) [a] 1.0 0.7 Ex situ growth (S2, 35 °C, 12 h) [a] 1.0 1.1

Supplementary
[a] LTA crystals (ca. 10 mg) were suspended in a S2 growth solutions (ca. 3 g) that was heated to the set point temperature. Samples were removed either after 2 h of heating (i.e., intermediate stage of growth) or after 12 h of heating (i.e., complete growth). The samples were imaged by AFM ( Supplementary Fig. 8a and b) to confirm the presence of rough and layered surface features, respectively.
[b] Energy dispersive X-ray spectroscopy (EDX) data is an estimate of the bulk (overall) crystal composition while X-ray photoelectron spectroscopy (XPS) is a surfacesensitive technique that estimates the composition of exterior regions of the particle.