Reducing epistemic and model uncertainty in ionic inter-diffusion chronology: A 3D observation and dynamic modeling approach using olivine from Piton de la Fournaise, La Réunion
Authors: Couperthwaite Fiona K. , Morgan Daniel J. , Pankhurst Matthew J. , Lee Peter D. , Day James M.D. 
Published: October 2020

Abstract
Modeling of ionic diffusion in natural crystals has been developed over the last three decades to calculate timescales of geological processes. As the number of studies and the size of data sets have expanded, improvements in the precision of the general technique are needed to resolve temporal patterns that would otherwise be masked by large uncertainties. This contribution examines fundamental aspects of timescale calculation uncertainty using Mg-Fe zonation in olivine crystals from a Piton de la Fournaise oceanite erupted in 2002 CE. First, we quantitatively consider the role of geometric uncertainty in data sets from the perspectives of sectioning angle, crystal shape, and crystal agglomeration. Second, we assess how crystal growth and changing boundary conditions during diffusion pose problems for simplistic, 1D, diffusion-only modeling.
An initial database of 104 timescales (7–45 days) was generated using typical, 1D, isothermal diffusion-only methods for profiles taken from 30 compositionally and texturally zoned crystals of olivine. This simplistic modeling yields poor model fits and imprecise timescales; prior to this work, we would have rejected &gt;60% of these data. Universal-stage measurements of crystal boundary angles and three-dimensional (3D) X-ray microcomputed tomography observations of crystal shape address geometric uncertainties. U-stage measurements show that, contrary to expectations of random sectioning, most boundaries modeled initially were close to the ideal sectioning plane. Assessment of crystal morphology from 2D thin sections suggests olivine crystals are dominantly euhedral; however, 3D imaging reveals that they are significantly subhedral and often exist as agglomerates, an observation that underscores both the potential for diverse crystal interactions through time in the magma (Wieser et al. 2019) and out-of-plane effects capable of influencing calculations of diffusion profiles.
Refinements to timescale determination can be made using a dynamic 1D modeling code to resolve growth and changing boundary effects simultaneous with diffusion. We incorporated temperature-dependent crystal growth rates (both linear growth and quadratically increasing, with a peak growth rate ~1.9 ×10–11 ms–1) and temperature-dependent boundary conditions (controlled using a cooling rate of −0.5 ± 0.1 °C/h) to remodel 13 timescales, resulting in significantly improved fits of the diffusion model to the initial data, better agreement between different faces of the same crystal, and less scatter within the whole data set. The use of 3D imaging and the inclusion of changing boundary conditions and crystal growth for diffusion calculations will enable more robust conclusions to be drawn from similar data in the future. Accurately retrieving timescale information from these crystals expands the pool of data available and reduces sampling bias toward “well-behaved” crystals.