Upper and Lower limits of timescales accessible by Diffusion Chronometry

Diffusion chronometry makes use of concentration gradients to determine timescales (as examples - durations of residence in thermal reservoirs, rates of cooling or ascent) of geological and planetary processes. The governing relationship that underlies the method is that the diffusion distance (x) scales with the square root of time (t), so that shorter the length scale over which concentration gradients can be measured, the shorter the timescales of processes that may be determined. However, there are some physical effects that set natural lower and upper limits of length and time scales that are accessible using the tool – these will be discussed in this talk. At the lower end, convolution (i.e., spatial averaging) effects in the analytical instrument being used to measure concentration gradients sets a limit. However, as analytical instruments have evolved to measure concentrations on practically atomic scales, some absolute physical boundaries have become relevant. The first one is related to the statistical nature of diffusion itself – at spatial scales on the order of lattice spacings of minerals (~ 10 Å), Fick’s law of diffusion which forms the basis of most applications, ceases to be valid. Secondly, depending on the nature of concentration jumps that drive the process of diffusion (related to chemical affinity) and the nature of the surrounding medium, transient oscillatory zoning may appear instead of smooth diffusion gradients, even when the thermodynamic variables controlling element partitioning (e.g., temperature, pressure) remain constant. These set limits at the shorter end of the timescale (for a given element in a particular mineral). At the upper end, limits are set by processes of diffusive homogenization or the processes of recrystallization (dissolution of old grains to produce new ones). The latter may be caused by processes such as deformation, exposure to large chemical affinity (driving force for dissolution / growth of crystals), textural refinement related to minimization of surface free energies, or coupling between chemical diffusion and lattice strain caused by element partitioning. Specific examples of some of these instances, such as from the iconic 79 AD eruption of Mt. Vesuvius (the “Pompeii eruption”), will be shown.