= Solution
\b[<thermal cycling growth> is permanent dimensional change remaining after a <temperature> cycle; <irradiation growth> is a radiation-driven change of shape that need not require an applied load.] Neither is simply the reversible increase in dimensions of a warm specimen.
For a crystal in its principal axes, a small unconstrained thermal <strain> is
$$
\boldsymbol\varepsilon^{\rm th}=\boldsymbol\alpha\Delta T.
$$
<anisotropic thermal expansion> means that the principal components of $\boldsymbol\alpha$ differ. Adjacent <crystal grains> with different orientations therefore demand different <strain> tensors during the same <temperature> change. Their bonded boundaries impose compatibility and generate internal <stresses>. <plasticity (physics)>, <creep (deformation)>, boundary motion or microcracking can accommodate this mismatch irreversibly; when the accommodation fails to cancel on cooling, a residual <strain> remains. Repeated cycles can accumulate directional <thermal ratcheting>, surface roughening or distortion. <crystallographic texture>, constraints, cycle amplitude and the <temperature> dependence of yielding and recovery determine the outcome.
\b[Anisotropy alone is insufficient.] A freely expanding <single crystal> under spatially uniform, fully reversible heating returns to its original dimensions. Even cyclic <plasticity (physics)> can settle into a stabilised response rather than ratchet indefinitely. Demonstrating <thermal cycling growth> means comparing dimensions at the same reference <temperature> after successive cycles, while controlling external loads, <temperature> gradients and phase changes. <uranium> dimensional instability under cycling was investigated directly in the early reactor-materials programme.<Thermal Cycling of Uranium by Nathaniel Stetson and Melbourne L. Winton>[ORNL-1386, 1952, opening discussion of dimensional instability, preferred orientation and observed distortion]{ref}
<irradiation growth> has a different source of irreversibility. <displacement cascades> create <vacancies> and <self-interstitials>; anisotropic migration, clustering and capture at oriented <dislocations> and boundaries can produce unequal <strains> along crystal directions. For approximately volume-conserving growth,
$$
\varepsilon_1^{g}+\varepsilon_2^{g}+\varepsilon_3^{g}\simeq0,
$$
although a rod may elongate substantially in one direction. The effect can occur at constant <temperature> without an external <stress>. Distinguish it from \b[<void swelling>], which increases volume through cavities, and \b[<irradiation creep>], whose directional deformation is stress-dependent. Experiments should therefore measure axial and transverse dimensions, <density> and the applied <stress> rather than identifying every increase in length as one mechanism.
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