GRAIN-SIZE PIEZOMETRY: SUBGRAINS AND NEW GRAINS IN THEORY AND IN PRACTICE

Experimental evidence shows that recrystallized grain size in plastically deformed crystalline materials is related to differential stress. The theoretical basis for this has not been established, and different recrystallization mechanisms may lead to different relationships. I suggest a revised theoretical basis for the three main mechanisms.

Rotation recrystallization (SGR) is directly related to subgrain size. Subgrain size becomes stable when the dislocation energy density in the wall equals the dislocation energy density in the grain as a whole, and is related to the density of geometrically necessary dislocations at that time. If the density of geometrically necessary dislocations is related to the total density by a proportionality factor P, then the subgrain diameter d_s has an inverse linear relationship to stress σ, as is widely observed in metals and rock-forming minerals: d_s ~ 3Gb/Pσ, where G is the shear modulus and b the Burgers vector. For P = 0.05, the subgrain piezometer intersects the experimental grain-size piezometer at 50 MPa, and a dynamically recrystallized grainsize d_g of 27 µm. If the surface energy is 0.25 J/mole, appropriate for quartz, the line for the minimum grainsize D_min that can survive the effects of surface-energy-driven grain boundary migration (γGBM) intersects at the same point. These relationships suggest that at stresses below this intersection, new grains form by rotation recrystallization (SGR) along the subgrain piezometer, and then grow up towards the D_min line; at stresses above the intersection, new grains form by both the bulging (BLG) and SGR mechanisms. In this case, new grains will form between the subgrain piezometer and the D_min line, and they won’t change size after nucleation. In both cases, the new grain-sizes will scatter along the experimental grain-size piezometer.

High-temperature recrystallization by the migration mechanism (GBM) does not involved nucleation. Grains grow by γGBM until they reach the D_min line, and then the characteristic lobes form by strain-energy-driven grain boundary migration (ρGBM). The size of the lobes may be controlled by the subgrain size – experimental evidence from deformed ice suggests that lobe size has an inverse linear relationship to stress.