A conceptual change in crystallisation mechanisms of oxide materials from solutions in closed systems

Atomic and molecular level interactions in solutions dictate the structural and functional attributes of crystals. These features clearly dictate the properties of materials and their applicability in technologies. However, the microscopic phenomena of particle formation—nucleation and growth—in real systems are still not fully understood. Specifically, crystallisation occurring in closed systems are largely unproven. Combining coherent experimental data, we here demonstrate a fundamental nucleation-growth mechanism that occurs in a model zinc oxide system when particles are formed under continuous, rapid heating under closed reaction conditions. Defying all previous reports, we show that the nucleation commences only when the heating is terminated. A prenucleation clusters pathway is observed for nucleation, followed by crystallite assembly-growth. We show that the nucleation-growth processes result from temporal and dynamic activity of constituent ions and gaseous molecules in solution and by the irreversible expulsion of the dissolved gaseous molecules. We suggest that this nucleation process is generic to most closed systems that go through precipitation, and, therefore, important for the crystallisation of a variety of metal oxides, composites and minerals. We anticipate that the work may be a platform for future experimental and theoretical investigation promoting deeper understanding of the nucleation-growth phenomena of a variety of practical systems.


SI1. MW set up and XRD instrumental broadening
presents photograph of the modified MW set up employed for this work. The CEM Technology Discover system utilizes a self-tuning microwave cavity, which ensures that the reaction vessel is uniformly exposed to microwaves from every direction. In addition, the penetration depth of microwaves in water at 95 °C is 5.7 cm, which is greater than the diameter of the reaction vessel and, therefore, uniformly providing energy to the reagents.
To estimate the effect of MWs on the process, MW absorptivity of water, urea and their decomposition products must be considered. Water is only a medium MW absorber with tan  = 0.123, where tan  is the dielectric loss tangent; a ratio between dielectric loss  ‫״‬ , representing the efficiency with which electromagnetic radiation is converted into heat and dielectric constant  ‫׳‬ , describing the ability to be polarized by the electric field such that tan  =  ‫״‬   ‫׳‬ . This loss factor provides a measure of the ability of a material to convert electromagnetic energy into heat at a given frequency and temperature. The tangent loss is similar for water and urea 1 .  Before 20 min, the complete dissociation of urea into the smallest components is not facilitated as per the FTIR and EDX data. Therefore, below 20 min of MW irradiation, as the number of growth units are less, the resultant inhomogeneity of the system would lead to competing and inhomogeneous crystallite assembly driven growth process producing particles with a wide size range. The complete dissociation of urea at higher MW times would lead to more of a homogeneous-like PNC system and resultant particles will be more homogeneous with small size distribution. This is the reason for the larger error bar for the a c components will appear in the IR spectrum. Additionally, each of the six non-degenerate modes (A species) of the CO3 2− ion could split into two IR active components Au and Bu under C2h symmetry, as a result of the correlation field splitting. Furthermore, when more than one carbonate ion exists in the lattice, more sets of the internal modes will appear in the spectra, corresponding to the number of crystallographically different carbonate ions.

Supplementary
The splitting of 3 and 4 modes in the current samples The lifting of degeneracy of the unperturbed free carbonate ions on coordination to Zn moieties (on changing the symmetry) will be reflected as splits in its 3 and 4 modes as (Au + Bu) components around its uncoordinated frequency of 1400 cm −1 and 770 cm −1 respectively. When more than one carbonate ion exists in the particle (at the crystallite or grain boundaries or even associated within the lattice), more sets of the internal modes can appear in the spectra, corresponding to the number of crystallographically different carbonate ions 4 . The frequency difference upon coordination, Δ, is a measure of the interaction with the surface. Hence, the Δ values calculated can be used to assign coordinated carbonate to mono-, bi-, tri and bridged configurations (Δ3 = <100 cm −1 , 100 < Δ3 < 300 cm −1 and Δ3 > 400 cm −1 , respectively). owing to sequential decomposition events, and the pH increases on increasing MW reaction time. When the MWs are stopped and the temperature and pressure drop, the dissolved gaseous molecules (CO2 and NH3) start expelling from the system. This will force the system that maintains its supersaturation until that time to undergo nucleation and follow up growth. During such a growth process, the species available at the interface of crystallites and grains at that phase of the reaction can also become integrated into the particle structure dictated by the interfacial and thermodynamic compatibility. By comparing all experimental data, it can be assumed that by increasing the MW time, hence, on increasing the solution pH, the particle nucleation-growth process undergo some refinement in terms of the Zn, O and C content and the crystal structure is refined in terms of the organic content, as suggested by FTIR and EDX; i.e. the organic content appears to be reduced on increasing the MW time. This refinement may be driven by the pH/pKa defined speciation events, where the gaseous species like ammonia and CO2 may be formed, dissolved in the solution due to the closed nature of the system, and expelled when the MW irradiation is stopped.  stabilizing groups) high energy c-axial planes. To reduce its energy, the c-axes of particles will be grown further by atomic deposition of Zn and OH, and as the concentrations of these species are limited, the system tries to achieve the highest stability structures possible by forming tapered ends.  Crystallite size evolution, together with EDX, FTIR and pH data suggest that the crystallization process becomes consistent above 20 min of MW irradiation. All data indicate to an incomplete dissociation of urea below 20 min. Above 20 min, as urea is dissociated completely into its smallest components, the system becomes homogeneous-like and the PNC-mediated crystallization becomes more consistent.

SI7. Schematic of crystallites formed from PNCs
Specifically, above 20 min, the limited growth of lateral crystal planes indicates to a possible lateral linkage between PNCs. However, as PNCs allow diffusion of growth units through them, although limited, certain lateral planes still show limited modifications.
Thus, the crystallization process, despite through PNC mediated mechanism, show a clear division above and below 20 min of MW irradiation. Below 20 min, the PNCs form, then nucleation and follow up aggregation-growth occurs on stopping the MW reaction. Above 20 min, according to all available data, the complete dissociation of urea, the homogeneous-like nature of the system and the time available would lead to a possible lateral linkage of PNCs. On stopping MW reaction, these laterally linked PNCs