A process-based theory for subgrain-size and grain-size piezometry

A piezometric relationship is derived between subgrain size and stress in plastically deformed crystalline materials, based on the assumption that subgrain boundaries become stabilized once their strain energy per unit area exceeds that in the adjacent lattice. The subgrain diameter at this point depends on the density of geometrically necessary dislocations (GND), many of which are housed in the subgrain walls, and on their spacing in the walls. Subgrains grow by merging, which results in a linear relationship between size and misorientation. The piezometric relationship for any given misorientation has a stress exponent close to unity. The subgrain piezometer can be calibrated using literature-based estimates of the size of dynamically recrystallized grains produced by subgrain rotation (SGR) for different minerals. Grain-size piezometers reflect processes of nucleation and post-nucleation modification during dynamic recrystallization. New grains formed by these different processes occupy different regions in grain-size/stress space. These regions are bounded by the subgrain piezometer and the Dmin line, which marks the smallest size that newly formed grains can have without being eliminated by surface-energy driven grain-boundary migration. The piezometers are statistically defined by the scatter of grain-sizes produced by these different processes. Piezometers defined in this way for quartz, olivine, and calcite correspond well within uncertainties to experimentally determined piezometers. No experimental piezometer exists for feldspars; a piezometer based on the concepts advanced in this paper is suggested that can be tested by experiment.