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Choose the orientation relation $(0001{)}_{\mathrm{hcp}}\parallel (111{)}_{\mathrm{ccp}}$ with aligned close-packed rows, for example $[11\bar{2}0{]}_{\mathrm{hcp}}\parallel [1\bar{1}0{]}_{\mathrm{ccp}}$. The two phases then share matching triangular layers at the broad faces. The stacking changes from $ABCABC\dots$ to $ABAB\dots$ across the phase region, so broad coherent crystal interfaces can be made by a local change of stacking, with small mismatch if the in-plane atomic spacings are similar.

At the cylindrical edge, different layer sequences terminate against one another. Registry cannot generally be maintained everywhere, so ledges, stacking defects and possibly misfit dislocations are needed; this interface is less coherent and often more costly. Thus a low-energy basal/$(111)$ face and a higher-energy edge favour a thin plate. An ideal same-element stacking change need not imply zero edge energy or exactly zero face energy.

The upper island has lower contrast than the rod in HAADF imaging, consistent with a lighter Zn-containing region above a Ru-rich support. Thickness, orientation and detector conditions also affect contrast, so intensity alone is not a compositional assay. The island is a flattened supported cap, not an isolated regular bulk crystal.

Using the 2 nm scale bar as a ruler gives a projected lateral size of order 4–6 nm and height of order 1–2 nm, depending on placement of the diffuse edges. These are approximate image estimates, not a three-dimensional diameter or size distribution. The height/width ratio is roughly $0.2$–$0.5$, and only a few atomic rows span the height. Thus surface and interface atoms form a substantial fraction of the particle. The truncated, irregular cap and weak edge order depart from an infinite, fully coordinated, perfectly periodic wurtzite crystal.

Adhesion can favor spreading across the rod. epitaxy can orient ZnO against a compatible surface repeat of the rutile structure, despite the different bulk symmetries. Coherent growth initially introduces strain; free edges allow relaxation, while larger islands may develop misfit dislocations. Facet-dependent attachment, polar surface energies, ligand coverage and unequal precursor delivery can further alter the cap. A final image does not uniquely reveal which kinetic pathway operated.

To measure strain, first index the zone axis and projected lattices. For pixel spacing $s$ and scale-bar length $s_{\mathrm{bar}}$, $d_{\mathrm{image}}=2s/s_{\mathrm{bar}}\mathrm{nm}$. Compare an indexed spacing with its unstrained reference:The latter is the hexagonal wurtzite relation. An ideal tetrahedral geometry has $c/a=\sqrt{8/3}$ and internal coordinate $u=3/8$; real bulk ZnO itself need not attain those ideal values. Measure several periods and compare interface and free-edge regions to distinguish strain from tilt and calibration errors.

A unique numerical lattice strain, vacancy concentration or phase assignment is not established by this unindexed single projection. Oxygen columns are weak, so a missing bright spot does not prove an oxygen vacancy. Tilted images, electron diffraction, chemical mapping and thickness-aware simulations would test those claims. The full rutile structure is primitive tetragonal with a basis: its metal positions can appear body-centered in a conventional cell, but the oxygen basis prevents calling the entire structure a body-centered tetragonal Bravais lattice.

An interface with largely matched regions separated by a network of misfit dislocations.