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At fixed transformed volume, an equilibrium solid-state precipitate seeks a low total free energy, including the orientation-dependent interfacial energy and elastic strain energy associated with misfit and applied stress. Low-energy interface orientations occupy large faces. The Wulff construction captures surface-energy anisotropy when strain and other contributions can be neglected; a solid-state precipitate generally also pays coherency strain energy, and its optimum shape can change with size.

During formation, growth kinetics and diffusion may prevent the equilibrium shape being reached. Coherent, semicoherent and incoherent interfaces have different bonding and defect structures, so their energies and attachment rates differ. The disc shape is consistent with much cheaper broad faces than edges, but morphology alone does not uniquely measure the energies or prove equilibrium.

The disc volume is $\pi d^{2}h/4$, the combined area of its two flat faces is $\pi d^2/2$, and its cylindrical edge area is $\pi dh$. With the signed bulk driving term $\Delta G$ per volume,For favourable transformation $\Delta G$ is negative and the interfacial terms are positive. This classical nucleation theory expression neglects a separate elastic term; if coherency strain is important, its appropriate energy must be added or included explicitly in the effective volume term. $W_n$ has energy units, whereas $\Delta G$ here has energy-per-volume units.

The main strengthening architecture is a high volume fraction of fine, thermally stable ordered gamma prime phase precipitates in the ductile nickel-rich matrix. Their nearly matching crystal parameters allow coherent crystal interfaces, but coherence does not make them transparent to a moving dislocation: cutting disrupts chemical order and costs antiphase-boundary energy. Pairing of cutting dislocations and their interactions with narrow matrix channels raise the stress needed for deformation. For particles that are bypassed, bowing and high-temperature climb are also impeded by the precipitate spacing and interface dislocation structures.

coherency strain and differences in elastic response provide additional obstacles. Refractory substitutional solutes contribute solid-solution strengthening and can slow diffusion-controlled deformation. Single-crystal manufacture suppresses grain-boundary creep and grain-boundary cavitation. Together these mechanisms permit useful strength at temperatures where an unstrengthened nickel matrix would deform much faster. Protective oxide scales and coatings preserve load-bearing material against environmental attack; they complement, rather than replace, the internal strengthening mechanisms.

A concrete microscopic observation is the paired dislocation loops around fine precipitates in the Cambridge C263 creep micrograph: the observed defect structure supports the importance of precipitate–dislocation interactions, though one image does not by itself separate every strengthening contribution.^[ref] In-situ diffraction during stress-jump tests of a rafted AM1 single crystal also resolves evolving load partition and deformation in matrix channels, demonstrating why channel width and interface interactions matter.^[ref] Long exposure can coarsen or change the precipitate morphology and alter channel widths, so high strength is conditional on temperature, time and microstructural stability.

A new solid phase formed within an existing solid matrix. Its morphology reflects anisotropic interfacial energy, coherency strain and growth kinetics.