A new statistical analysis of rare earth element diffusion data in garnet

Abstract:

The incorporation of rare earth elements (REE) in garnet, Sm and Lu in particular, links garnet chemical zoning to absolute age determinations. The application of REE-based geochronology depends critically on the diffusion behaviors of the parent and daughter isotopes. Previous experimental studies on REE diffusion in garnet, however, exhibit significant discrepancies that impact interpretations of garnet Sm/Nd and Lu/Hf ages.

We present a new statistical framework to analyze diffusion data for REE using an Arrhenius relationship that accounts for oxygen fugacity, cation radius and garnet unit-cell dimensions [1]. Our approach is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo method. A similar approach has been recently applied to model diffusion of divalent cations in garnet [2].

The analysis incorporates recent data [3] in addition to the data compilation in ref. [1]. We also include the inter-run bias that helps reconcile the discrepancies among data sets. This additional term estimates the reproducibility and other experimental variabilities not explicitly incorporated in the Arrhenius relationship [2] (e.g., compositional dependence [3] and water content).

The fitted Arrhenius relationships are consistent with the models in ref. [3], as well as refs. [1]&[4] at high temperatures. Down-temperature extrapolation leads to >0.5 order of magnitude faster diffusion coefficients than in refs. [1]&[4] at <750 °C. The predicted diffusion coefficients are significantly slower than ref. [5]. The fast diffusion [5] was supported by a field test of the Pikwitonei Granulite—the garnet Sm/Nd age postdates the metamorphic peak (750 °C) by ~30 Myr [6], suggesting considerable resetting of the Sm/Nd system during cooling. However, the Pikwitonei Granulite is a recently recognized UHT terrane with peak temperature exceeding 900 °C [7]. The revised closure temperature (~730 °C) is consistent with our new diffusion model.

[1] Carlson (2012) Am Mineral 97 1598–1618. [2] Chu & Ague (2015) Contrib Mineral Petrol, in press. [3] Bloch et al. (2015) Contrib Mineral Petrol 169 1–18. [4] Van Orman et al. (2002) Contrib Mineral Petrol 142 416–424. [5] Tirone et al. (2005) GCA 69 2385–2398. [6] Mezger et al. (1992) EPSL 113 397–409. [7] Kooijman et al. (2012) J Metamorph Geol 30 397–412.