Stress and temperature dependence of recrystallized grain size: A subgrain misorientation model

The steady‐state grain size of Earth materials undergoing solid state flow is estimated based on a nucleation‐and‐growth model of dynamic recrystallization. Assuming a nucleation mechanism of subgrain rotation, the mean diameter d of recrystallized grains is obtained as d/b = A(σ/µ)−p exp[‐((Qgb ‐ Qv)/mkT)], where b is the length of the Burgers vector, σ is differential stress, µ is the shear modulus, Qgb is the activation energy for the jump of an atom across the grain boundary, Qv is that for self‐diffusion in the grain volume, k is the Boltzmann constant, T is temperature, A is a constant, p = 1.25 and m = 4 for intracrystalline nucleation, and p = 1.33 and m = 3 for grain‐boundary nucleation. The exponent p = 1.25 ∼ 1.33 agrees well with available data for high‐ temperature dislocation creep of rock‐forming minerals. A weak negative dependence of grain size on temperature is expected from this theory.