Diffusion-induced stress in crystals: Implications for timescales of mountain building

Abstract

Intracrystalline chemical diffusion offers valuable insights into the durations of metamorphic and igneous processes. However, it can yield timescale estimates for orogenic and subduction zone events that are considerably shorter than those obtained via isotopic geochronology. One potential explanation that has been offered for the discrepancy is that the interdiffusion of species with different atomic or ionic radii may generate intracrystalline, compositional stresses that alter or limit diffusional relaxation. In this study we test this idea by developing and applying the compositional stress theory of materials scientists F. Larché and J. Cahn to garnet from the Barrovian sillimanite zone, Scotland. Relaxed contacts from the garnet, independent diffusion chronometers, and thermal modeling all indicate a > 100 kyr duration for peak temperature metamorphism. Nonetheless, the garnet records sharp, μm-scale variations in calcium and iron contents that standard diffusion treatments predict should relax in 1–10 kyr at peak temperature conditions. Our results show that the development of compositional stress during diffusional relaxation can explain the preservation of the observed short wavelength compositional oscillations at a > 100 kyr timescale. Thus, it may be necessary to account for compositional stress when modeling diffusion in solid solutions with appreciable differences in their endmember molar volumes. This will be particularly relevant when considering sharp, μm-scale chemical gradients involving grossular, the garnet endmember with the largest molar volume relative to pyrope, almandine, and spessartine. Neglecting compositional stress in such cases could result in the underestimation of the timescales of lithospheric processes by potentially orders of magnitude. The effects of compositional stress in garnet are predicted to be the most pronounced under amphibolite and blueschist–eclogite facies conditions. At lower temperatures diffusion is limited, and at higher temperatures both plastic deformation and more ideal solid solution behavior will act to diminish the impact of stress.