On the co-evolution of dislocations and grains in deforming rocks

Abstract

Deformation at tectonic plate boundaries is governed by the mechanical properties of crustal and lithospheric rocks, which evolve through changes in the microstructure of their constituent minerals. Geological observations of microstructure can, therefore, provide estimates of the rock's deformation conditions through various piezometers (e.g., the relationship between stress and grain size or dislocation density). However, grain size and dislocation density do not evolve independently, and thus their associated piezometers are unlikely to be decoupled. We present a new theoretical model coupling the evolution of grain boundaries and dislocations in a deforming rock and make a novel prediction that the equilibrium dislocation density at a given stress (the dislocation piezometer) can be non-unique, with co-existing deformation states or piezometric branches. One stable piezometric branch exists at high stress and large grain-size, for which the steady state dislocation density is large and dictated by stress, in agreement with experimental observations and earlier theoretical models. However, another stable branch exists at low stress and small grain-size, in which case dislocation density is small, weakly stress-dependent, and is governed by the balance between dislocation sinks and sources at grain boundaries. The contrast in dislocation density between grains of different sizes induces grain boundary migration from smaller grains into larger grains. Dislocation-induced grain boundary forces thus act in the opposite direction to those dictated by surface energy, for which grain boundaries migrate from larger grains into smaller ones. When forces due to surface and dislocation energies are balanced, the system reaches a stable microstructural equilibrium, thereby halting grain growth and helping preserve plate boundary weakness. When the forces are not in balance, unstable and oscillatory behavior can ensue, with oscillation periods on the order of decades. Finally, the new theory provides a microphysical model for transient rheological behavior, which is particularly relevant to tectonic activity in which deformation is relatively rapid and where the steady state flow laws are a poor approximation, such as during postseismic relaxation or postglacial rebound.