Evaluation of the effects of 3D diffusion, crystal geometry, and initial conditions on retrieved time-scales from Fe-Mg zoning in natural oriented orthopyroxene crystals

Volcano petrologists and geochemists increasingly use time-scale determinations of magmatic processes from modeling the chemical zoning patterns in crystals. Most determinations are done using one-dimensional traverses across a two-dimensional crystal section. However, crystals are three-dimensional objects with complex shapes, and diffusion and re-equilibration occurs in multiple dimensions. Given that we can mainly study the crystals in two-dimensional petrographic thin sections, the determined time-scales could be in error if multiple dimensional and geometrical effects are not identified and accounted for. Here we report the results of a numerical study where we investigate the role of multiple dimensions, geometry, and initial conditions of Fe-Mg diffusion in an orthopyroxene crystal with the view towards proper determinations of time scales from modeling natural crystals.We found that merging diffusion fronts (i.e. diffusion from multiple directions) causes 'additional' diffusion that has the greatest influence close to the crystal's corners (i.e. where two crystal faces meet), and with longer times the affected area widens. We also found that the one-dimensional traverses that can lead to the most accurate calculated time-scales from natural crystals are along the b- crystallographic axis on the ab-plane when model inputs (concentration and zoning geometry) are taken as measured (rather than inferred from other observations). More specifically, accurate time-scales are obtained if the compositional traverses are highly symmetrical and contain a concentration plateau measured through the crystal center. On the other hand, for two-dimensional models the ab- and ac-planes are better suited if the initial (pre-diffusion) concentration and zoning geometry inputs are known or can be estimated, although these are a priory unknown, and thus, may be difficult to use in practical terms.We also found that under certain conditions, a combined one-dimensional and two-dimensional model performed on the ab-section can reveal the initial (pre-diffusional) concentration, and thus, offer a unique opportunity to recover lost petrologic information. The influence of three-dimensional diffusion on the one-dimensional two-dimensional model estimates is the combined result of the crystal shape, in particular the presence of facets, and somewhat of the aspect ratio. Our study focuses on Fe-Mg in orthopyroxene, but many of the effects we report are also applicable to other minerals and elements.