2D companion to the 3D hydrothermal ZnO model: the same facet-selective growth race, read off four live views instead of a rendered rod array. Wurtzite ZnO's polar (0001) tip accepts Zn(OH)₄²⁻ growth units far faster than the six nonpolar {10-10} side facets, so a seeded crystallite elongates along c much faster than it thickens.
Both facet rates follow Arrhenius kinetics driven by the bath's supersaturation ratio S = C/Ceq − 1:
dL/dt = A_axial · exp(−Ea_axial / RT) · S^1.5 (tip, polar facet)
dD/dt = A_radial · exp(−Ea_radial / RT) · S^1.5 · (1 − 0.9·θ_cap) (sides, nonpolar facets)
- Side profile (top-left) — a schematic row of hexagonal rods growing on the substrate, coloured by local aspect ratio.
- Arrhenius curve (top-right) — both facet rates vs. bath temperature at the current concentration, with the live point marked; the radial facet's higher activation energy makes it climb faster with heat.
- Supersaturation curve (bottom-left) — both rates vs. precursor concentration at the current temperature; below the equilibrium concentration (S≈0) growth stalls entirely.
- Length & diameter vs. time (bottom-right) — the live growth trace for this run; the gap between the two curves is the aspect ratio building up.
Real-world relevance: this seeded hydrothermal route (zinc nitrate + HMTA, 60–200 °C, aqueous, no vacuum) is the standard low-cost way to grow the vertical ZnO nanorod arrays used in dye-sensitized solar cells, piezoelectric nanogenerators and UV photodetectors.