 Solution

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 isanisotropic thermal expansion means that the principal components of $\mathbf{\alpha }$ 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, creep, 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.

Anisotropy alone is insufficient. A freely expanding single crystal under spatially uniform, fully reversible heating returns to its original dimensions. Even cyclic plasticity 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.^[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,although a rod may elongate substantially in one direction. The effect can occur at constant temperature without an external stress. Distinguish it from void swelling, which increases volume through cavities, and 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.