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Indexed electron diffraction ring positions from a polycrystalline deposit identify candidate phases and give lattice parameters after camera-length calibration. Spot patterns from a small selected area establish zone axis directions, epitaxial orientation relationships or crystal twinning. Nanobeam mapping can reveal grain orientation changes, while systematic spot shifts can measure relative strain if lens distortions and scan drift are controlled. Spot or ring broadening can reflect finite coherent size, but also strain and instrumental broadening, so it is not an unqualified particle-diameter measurement. Use a calibration standard and an empty support region, vary dose to check electron beam damage, and combine spacing information with elemental analysis when chemically distinct phases have similar lattice parameters.

In a polyol process, a hot polyol such as ethylene glycol acts as solvent and reductant for a silver precursor. Nucleation creates seeds; controlled reduction supplies atoms for their subsequent growth, while polyvinylpyrrolidone adsorption and seed crystal twinning favour anisotropic growth. For the common silver nanowire route, a fivefold-twinned seed can develop into a pentagonal wire with predominantly $\{100\}$ side faces and growth at less-passivated ends. Cross-sectional microscopy and diffraction of microtomed wires provide evidence for that twinned structure rather than an inference from a long outline alone.^[ref]

The aspect ratio depends on seed population and twin survival, relative end/side growth rates, precursor feed and reduction rate, PVP coverage, temperature, trace halides, dissolved oxygen and growth time. High aspect ratio requires a suitable population of twinned seeds, suppression of competing particle nucleation and continued atom supply while sidewall thickening is restrained. These variables must be controlled together; adding more capping polymer alone is not a universal recipe. Advantages are solution processing, substantial yield and tunable dimensions without an etched hard template. Disadvantages include sensitive batch reproducibility, particle by-products, residual insulating ligand, purification, oxidation/tarnish and nanowire junction resistance in later films. Compare seed/capping/halide controls using microscopy and size distributions, not only solution colour.

Three suitable examples are cubes bounded mainly by $\{100\}$ facets, octahedra bounded by $\{111\}$ facets, and truncated octahedra bounded by both $\{111\}$ and $\{100\}$ facets. These are crystallographically distinct shapes rather than three arbitrary rounded particle outlines.

At fixed volume the thermodynamic equilibrium shape minimizes $G_{\mathrm{surf}}={\sum }_i{\gamma }_i{A}_i$, with an edge/corner correction when particles are very small. In the Wulff construction, facet support-plane distances scale as their interfacial free energies. Silver's clean low-index energies, selective adsorption of ligands or ions, solvent chemical potential and possible support contact alter those energies. Crystal twinning and elastic strain can add further costs or stabilize multiply twinned forms. A face with slow attachment kinetics can also survive during growth even when that morphology is not the thermodynamic equilibrium Wulff shape. Homogeneous nucleation describes where nuclei form; it does not guarantee an thermodynamic equilibrium final shape.

Symmetry breaking in nanocrystal growth makes growth rates along initially equivalent crystallographic directions unequal, so the final shape has lower symmetry than an unperturbed seed. It need not change the underlying face-centered cubic lattice. A cubic lattice does not require a cubic external shape.

Anisotropy can originate in a twin or stacking fault, unequal ligand coverage of nominally equivalent sites, selective adsorption or etching, a substrate or external field, or a local fluctuation amplified because newly deposited material changes subsequent growth. Facet-selective binding suppresses some normal growth rates; concentration and reduction kinetics determine whether atoms can redistribute towards a near-equilibrium shape or remain in a kinetically selected one. A facet with slow normal growth tends to remain exposed, while a fast-growing facet can disappear.

For a one-dimensional silver example, begin with a small seed with multiple regions related by crystal twinning containing five sectors around a common axis. Ligand-protected lateral faces and more active ends favour axial addition, producing an elongated pentagonal rod and then a wire. The defect geometry and surface kinetics jointly distinguish the axial direction. Fivefold twinning is a composite structure with strain accommodation, not a perfect single fcc crystal with forbidden fivefold lattice symmetry.

For a two-dimensional example, begin with a seed containing a planar twin or stacking fault. Basal-face protection and enhanced incorporation at suitable edges favour lateral extension over thickening, producing a thin triangular or hexagonal plate. The accompanying schematic emphasizes seed, symmetry-breaking event and anisotropic growth stages. These are representative routes, not universal requirements for every rod or plate. Experimentally, silver-seed growth can also be redirected into lower-symmetry forms by controlling reduction kinetics.^[ref]

The low-temperature zirconium matrix has a hexagonal close packing structure. Its crystallographic $a$ and $c$ directions therefore have different elasticity, thermal expansion and available slip systems. Producing tubing also develops a crystallographic texture, so averaging over grains does not necessarily remove these directional effects.

Different expansion along the crystal axes produces intergranular thermal stresses during temperature changes. Under load, easy dislocation glide modes may accommodate some strains much more readily than others; additional slip or crystal twinning is needed for general compatibility. Consequently strength and ductility can depend on the axial, circumferential and radial orientation of the tube.

Irradiation creates vacancies and self-interstitials that cluster into dislocation loops with different crystallographic orientations. Their anisotropic accumulation can produce irradiation growth even without external stress. Different directions can elongate or contract while the net volume change remains small. Texture turns these grain-scale strains into macroscopic length and diameter changes, bowing and stresses between constrained components. This mechanism is distinct from the added cavity volume of void swelling.

The crystallographic character of irradiation loops matters: atomistic calculations by Rory Hulse and Christopher P. Race examine several possible loop types and show that loop energy and shape depend on orientation and size. A single generic spherical-defect description therefore misses important aspects of zirconium's dimensional response.^[ref]

Hydrogen also produces direction-sensitive damage. Zirconium hydrides are brittle precipitates whose preferred orientation depends on crystal texture and stress history. Radially oriented hydrides can offer crack paths across a thin tube wall under circumferential tension. Controlling texture, hydrogen pickup and hydride orientation helps manage that risk; changing the hexagonal structure's orientation cannot by itself eliminate corrosion or irradiation damage.