Analysis of experimental data on divalent cation diffusion kinetics in aluminosilicate garnets with application to timescales of peak Barrovian metamorphism, Scotland

  • Xu ChuEmail author
  • Jay J. Ague
Original Paper


We present a new statistical framework to analyze the diffusion data for divalent cations (Fe, Mg, Mn, and Ca) in aluminosilicate garnet using published experimental data and an Arrhenius relationship that accounts for dependence on temperature, pressure, garnet unit-cell dimension, and oxygen fugacity. The regression is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo approach. All reported experimental uncertainties are incorporated, and the data are weighted by the precision of the experimental conditions. We also include a new term, the inter-experiment bias, to compensate for possible inconsistencies among experiments and to represent any experimental variability not explicitly presented in the Arrhenius relationship (e.g., water content, defect density). At high temperatures where most experiments were conducted, the diffusion coefficients calculated with the new parameters agree well with previous diffusion models (e.g., Chakraborty and Ganguly in Contrib Mineral Petrol, 111:74–86, 1992; Carlson in Am Mineral, 91:1–11, 2006). However, the down-temperature extrapolation leads to notable differences at lower temperatures for common petrological applications. For example, at 600 °C, the diffusion coefficients of Fe and Mn are one half-to-one order of magnitude faster and the diffusion coefficient of Ca is about one order of magnitude slower than calculated with parameters in Carlson (2006). Our statistical analysis also provides well-defined uncertainty bounds for timescale estimates based on garnet diffusion profiles. Application of the newly derived coefficients indicates that the timescale of the thermal peak of Barrovian metamorphism (Dalradian belt of Scotland) is about four to seven times longer than that estimated using previously published diffusion coefficients. The peak is still geologically brief, however—of the order of 106 years (0.75 Myr +0.70/−0.36 Myr; ±1σ). This brevity requires pulsed advective heat input, as provided by syn-orogenic mafic magmatism in these rocks.


Garnet Diffusion coefficient Markov chain Monte Carlo Barrovian metamorphic belt 



We are grateful to J. Korenaga, S. Chakraborty, Y. Yu, and Y. Liang for helpful discussions and comments. The paper benefited from careful and constructive reviews by J. Ganguly and F.S. Spear. We thank T.L. Grove for editorial handling. Support from the National Science Foundation Directorate of Geosciences (NSF EAR-0948092 and EAR-1250269) and Yale University is gratefully acknowledged. This work was also supported in part by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center and by the National Science Foundation under Grant #CNS 08-21132 that partially funded acquisition of the facilities. MATLAB scripts developed in this study are available upon request.

Compliance with ethical standards

Conflicts of interest

This study was funded by National Science Foundation Directorate of Geosciences (NSF EAR-0948092 and EAR-1250269). The authors declare that they have no conflict of interest.

Supplementary material

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Supplementary material 1 (PDF 583 kb)


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Authors and Affiliations

  1. 1.Department of Geology and GeophysicsYale UniversityNew HavenUSA
  2. 2.Peabody Museum of Natural HistoryYale UniversityNew HavenUSA

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