Paleowattmeters: A scaling relation for dynamically recrystallized grain size

During dislocation creep, mineral grains often evolve to a stable size, dictated by the deformation conditions. We suggest that grain-size evolution during deformation is determined by the rate of mechanical work. Provided that other elements of microstructure have achieved steady state and that the dissipation rate is roughly constant, then changes in internal energy will be proportional to changes in grain-boundary area. If normal grain-growth and dynamic grain-size reduction occur simultaneously, then the steady-state grain size is determined by the balance of those rates. A scaling model using these assumptions and published grain-growth and mechanical relations matches stress-grain-size relations for quartz and olivine rocks with no fitting. For marbles, the model also explains scatter not rationalized by assuming that recrystallized grain size is a function of stress alone. When extrapolated to conditions typical for natural mylonites, the model is consistent with field constraints on stresses and strain rates.