MODELING DIFFUSION PHENOMENA IN MINERALS: THE CASE OF HELIUM IN ZIRCON (U-TH)/HE THERMOCHRONOMETER

Although bulk diffusivity data for different elements in minerals are available from laboratory experiments, little is known about the mechanism(s) of diffusion in the host structures. Considering the fact that diffusion rates are the limiting step in many relevant geochemical processes, a better understanding of the atomistic nature of chemical transport is needed to evaluate, for example, the mechanisms of diffusional loss of daughter products in radiogenic isotope systems.

For the case of He diffusion in zircon, empirical potentials and quantum-mechanical simulations show that the activation energy is lower through the open channels parallel to the c-axis (ΔE^*_[001] = 13.4 kJ.mol^-1, activation energy for tracer diffusion of a He atom along [001]). The energy barriers are higher in other directions where narrower channels for He diffusion are identified, such as [100], [101], and [110] (ΔE^* of 44.8 kJ·mol^-1, 101.7 kJ·mol^-1, and 421.3 kJ·mol^-1, respectively). Molecular dynamics simulations are in agreement with these results and provide additional insight in the diffusion mechanisms along different crystallographic directions, as well as the temperature dependence. Below the closure temperature of He for this system (≈180 °C), diffusion is anisotropic. He moves preferentially along the [001] direction, and calculated tracer diffusivities along the two most favorable directions differ by approximately five orders of magnitude (D_[001]/D_[100]≈10⁵, at T=25 °C). Above this temperature, He atoms start to hop between adjacent [001] channels, along [100] and [010]. The diffusion along [100] and [010] is thermally activated, such that at higher temperatures, He diffusion in zircon becomes nearly isotropic (D_[001]/D_[100]≈10, at T=580 °C).

These results suggest that the strong anisotropic nature of He diffusion at low temperatures must be considered in future diffusivity experiments, as well as in bulk modeling of relevance to the (U-Th)/He zircon thermochronometer. Considering the limited data available for this system, our results provide a basis for further investigations on the behavior of radiogenic helium in zircon and other minerals such as apatite and monazite.