Solution (source code)

= Solution

\b[<Material creep> is time-dependent permanent deformation under sustained <stress>.] Its rate is often appreciable at a large <homologous temperature> $T/T_m$, because <diffusion> and obstacle-escape processes become rapid. In an activated regime a useful form is
$$
\dot\varepsilon=A\sigma^n d^{-p}\exp[-Q_c/(RT)],
$$
with additional elastic, geometric and <temperature> prefactors absorbed into $A$ for the chosen approximation. The <activation energy> belongs to the rate-controlling process: bulk <diffusion>, grain-boundary <diffusion> and <dislocation> motion need not have the same value.

* \b[A: power-law <dislocation> <material creep>.] <Dislocations> glide and climb around obstacles; vacancy transport enables climb and recovery. The rate is strongly stress-dependent, typically with $n$ several times greater than one. It dominates the higher-stress, hot field below the glide-strength boundary.
* \b[B: <Nabarro-Herring creep>.] Stress-directed <vacancy diffusion> through the grain interiors transfers material between differently stressed boundaries, extending grains along tension. In the simple equiaxed-grain model $\dot\varepsilon\propto D_V\sigma/(Td^2)$. It occupies the high-temperature, low-stress field.
* \b[C: <Coble creep>.] The analogous transport runs predominantly along <grain boundaries>. The characteristic scaling is $\dot\varepsilon\propto\delta D_{GB}\sigma/(Td^3)$, where $\delta$ is an effective boundary thickness. The lower activation cost of boundary <diffusion> makes it competitive at lower <temperature> than bulk-diffusion <material creep>.

Boundary sliding can accommodate grain-shape changes during diffusional <material creep>; it is not a reason to identify either <diffusion> field as <dislocation glide>. The supplied map's A/B/C placement, including the boundary between B and C, determines these assignments. Its numerical contours apply to the material state used to construct that map, not to arbitrary <grain sizes>.