A 4D view on the evolution of metamorphic dehydration reactions

Metamorphic reactions influence the evolution of the Earth’s crust in a range of tectonic settings. For example hydrous mineral dehydration in a subducting slab can produce fluid overpressures which may trigger seismicity. During reaction the mechanisms of chemical transport, including water expulsion, will dictate the rate of transformation and hence the evolution of physical properties such as fluid pressure. Despite the importance of such processes, direct observation of mineral changes due to chemical transport during metamorphism has been previously impossible both in nature and in experiment. Using time-resolved (4D) synchrotron X-ray microtomography we have imaged a complete metamorphic reaction and show how chemical transport evolves during reaction. We analyse the dehydration of gypsum to form bassanite and H2O which, like most dehydration reactions, produces a solid volume reduction leading to the formation of pore space. This porosity surrounds new bassanite grains producing fluid-filled moats, across which transport of dissolved ions to the growing grains occurs via diffusion. As moats grow in width, diffusion and hence reaction rate slow down. Our results demonstrate how, with new insights into the chemical transport mechanisms, we can move towards a more fundamental understanding of the hydraulic and chemical evolution of natural dehydrating systems.


Llana-Funez et al. (2012) took a dataset of reaction rates from 35 experiments on gypsum
dehydration, using the volume of fluid expelled as a monitor of reaction rate. The maximum rate of fluid expulsion could be used as a measure of reaction rate but, realising that compaction also plays a role in fluid expulsion, they proposed that a reaction rate proxy is more useful: Reaction rate proxy = (maximum expulsion rate)/(volume expelled at that time) This idea can applied in the same way to porosity evolution. Because porosity development should scale with fluid expelled, for our new experiment we can calculate the same proxy using: Reaction rate proxy = (maximum rate of porosity increase)/(porosity at that time) Smoothing the data of Supplementary Figure 1

Determination of the diffusion coefficient
For figure 4 we required individual grain areas but it was not possible to segment bassanite from gypsum reliably: although the eye can distinguish these two minerals, there is too much overlap in grey scale. So, to analyze grain growth we selected individual grains which could be identified through the time series and measured the areas (A) and perimeters (p) of grains and moats in Fiji.
We then calculated average growth and dissolution velocities by from dt dA p u 1  . This approach was chosen because it guarantees the correct average growth velocity for a particular grain or moat.
The net diffusion coefficient quoted in main text was calculated as follows. We assume that the growth rate is controlled by a combination of interface detachment from gypsum, attachment to bassanite and by diffusion leading to a simple quantitative model for rate 35 . We adapt eqns 9 and 10 from there but growth is 2D so there some convergence in chemical flux towards the bassanite. To allow for this we simplify grain and moat shapes to be cylinders. Then diffusive flux will scale with 1/r where r is radial distance from the center line of a bassanite grain. Concentration will be a linear function of ln(r) because its gradient gives the flux. Modifying and rearranging Lasaga (1986) eqns 9 and 10 (35) gives: So, D is derived from the slope s of a best fit line on a 1/u versus w graph:

Supp. eqn (2)
We applied this equation to 16 moats. For some moats the correlation coefficient was low so we excluded them; for others the y-axis intercept was negative which is not in accord with supplementary eqn (1) so we excluded these too. We were left with 6 moats with the data shown in supplementary figure 5. Each moat yields an estimate of D and the average is 1.23 x10 -10 m 2 /s, the apparent diffusion coefficient of CaSO 4 . Since the anion and cation have their own diffusion coefficients this is also the harmonic mean of the diffusion coefficients of Ca 2+ and SO4 2- (36) . For comparison at 1 atm and 25 °C the apparent diffusion coefficient of CaSO 4 is 9.11 x10 -10 m 2 /s (37) . We obtain a similar order of magnitude, but we expect the diffusion coefficients to be faster at higher T; the discrepancy may be due to a pressure effect and/or diffusion pathways which are longer than the moat width.