Diffusion: Obstacles and Opportunities in Petrochronology

Abstract

Many of the approaches in petrochronology are rooted in the assumption of equilibrium. Diffusion is an expression of disequilibrium: the movement of mass in response to chemical potential gradients, and isotopes in response to isotopic gradients. It is extremely important that we be aware of how the effects of diffusion can place obstacles across our path towards petrochronologic enlightenment. Conversely the effects of diffusion also provide opportunities for understanding rates, processes, and conditions experienced by rocks. The enormity of the field does not permit us to provide a comprehensive review of either the mathematics of diffusion or quantitative data that have been obtained relevant to the interpretation of diffusive processes in rocks and minerals. Many resources cover these topics, including RiMG volume 72 ( Diffusion in Minerals and Melts ; Zhang and Cherniak 2010) and several textbooks (Crank 1975; Glicksman 2000). Particularly relevant to the discussion of petrochronology are summaries of the theory and controls on diffusion (Brady and Cherniak 2010; Zhang 2010), as well as diffusion rates in feldspar (Cherniak 2010a), accessory minerals (Cherniak 2010b), garnet (Ganguly 2010), mica, pyroxene, and amphibole (Cherniak and Dimanov 2010), and melts (Zhang and Ni 2010; Zhang et al. 2010). Rather than duplicate that material, our goal is to explore the obstacles and opportunities presented by the effects of diffusion as they inform the rates of petrologic processes. To achieve this goal, we emphasize key principles and illustrative examples. Quantitative interpretation of the effects of diffusion assumes predictability of numerous factors that may affect chemical or isotopic transport, including temperature, initial and boundary conditions, water and oxygen fugacities, activities of other components, multiple mechanisms of diffusion, and crystal chemistry (‘coupling’ of the substitution of elements into different crystallographic sites). Additionally, the extraction of meaningful ages, durations of events, and temperatures requires …