Multipath diffusion in geochronology

Recent developments in microanalytical tools such as the ion and laser microprobe have revealed spatial distributions of radiogenic isotopes in minerals which cannot be explained by a simple volume diffusion mechanism. Although it is known that diffusion of a substance along extended defects (such as dislocations, exsolution lamellae, micropores, microfractures, fission tracks, etc.), which may serve as high-diffusivity pathways in a crystal, can significantly influence the bulk diffusivity of a mineral, this has largely been ignored in the field of geochronology. A general numerical model has been developed, which solves coupled multipath diffusion equations that describe the simultaneous diffusion of a solute species through both the crystal lattice (via volume diffusion) and high-diffusivity pathways (via short-circuit diffusion) under non-steady state conditions. Addition of a radioactive source term to the appropriate equations further allows for the modelling of integrated cooling ages and closure temperatures, and has direct pertinence to geochronological and thermochronologial studies. Three key criteria can be used to distinguish multipath diffusion mechanisms from volume diffusion mechanisms: (a) non-Fickian concentration profiles, (b) enhanced solute diffusivity with increasing mineral grain size, and (c) a lack of any correlation between closure temperatures (and cooling ages) and larger grain sizes. With multipath diffusion, the effective diffusion dimension a for certain minerals appears to remain on the order of the grain size, and the model can adequately explain observed increases in the bulk diffusion coefficient D_b with a in the hydrothermal bomb data of previous Ar diffusion studies. Arrhenius diagrams of a multipath diffusion D_b vs 1/T will consist of curves that have a kink in them, reflecting a continuous change in the relative importance of the different diffusion mechanisms with temperature. The most important consequence of multipath diffusion is that the overall bulk diffusion coefficient D_b of a diffusing species can be enhanced significantly above its volume diffusion coefficient D_v. As a result, integrated ages and effective closure temperatures (T_c) can be much lower than those predicted assuming only a volume diffusion mechanism, to the extent that minerals normally characterized by low volume-diffusion T_c may potentially have older integrated ages that minerals normally associated with higher volume-diffusion T_c.