Species diffusion in clinopyroxene solid solution in the diopside-anorthite system

Matthias Bernhard Lierenfeld; Xin Zhong; Eric Reusser; Karsten Kunze; Benita Putlitz; Peter Ulmer

doi:10.1007/s00410-019-1571-9

Species diffusion in clinopyroxene solid solution in the diopside-anorthite system

Contrib Mineral Petrol. 2019;174(5):46. doi: 10.1007/s00410-019-1571-9. Epub 2019 May 13.

Authors

Matthias Bernhard Lierenfeld¹, Xin Zhong^{1

2}, Eric Reusser¹, Karsten Kunze³, Benita Putlitz⁴, Peter Ulmer¹

Affiliations

¹ 1Institute of Geochemistry and Petrology, Swiss Federal Institute of Technology (ETH Zürich), Clausiusstrasse 25, 8092 Zurich, Switzerland.
² 2Department of Geosciences, Physics of Geological Processes, The Njord Center, University of Oslo, PO Box 1048, Blindern, 0371 Oslo, Norway.
³ 3Scientific Center for Optical and Electron Microscopy, Swiss Federal Institute of Technology (ETH Zürich), Auguste-Piccard-Hof 1, 8093 Zurich, Switzerland.
⁴ 4Institut des Sciences de la Terre, Université de Lausanne, Mouline-Géopolis, 1015 Lausanne, Switzerland.

Abstract

The coupled multicomponent diffusion of the species Ca₂Si₂O₆, CaAl₂SiO₆ and Mg₂Si₂O₆ was determined in diopside crystals in the diopside/anorthite (Di/An) system at temperatures (T) of 1110-1260 °C and oxygen fugacities (fO ₂ ) between 1.0 log unit below and above the fayalite-magnetite-quartz equilibrium (FMQ ± 1). Diffusion couples were prepared by the seed overgrowth technique. Element concentration profiles were measured perpendicular to the rim/core interface by step-scanning profiling with a field emission gun scanning electron microscope (FEG-SEM). The multicomponent diffusion matrix was solved by fitting its eigenvalues (λ) and eigenvectors (v) to the measured concentration profiles. The full diffusion matrix D can be recovered by using the formula $D = P Λ P^{- 1}$ resulting in the following equation: $D_{Di/An} = (\begin{matrix} 1.00 & - 0.67 \\ - 0.38 & 1.00 \end{matrix}) (\begin{matrix} λ 1 (T) & 0 \\ 0 & λ 2 (T) \end{matrix}) {(\begin{matrix} 1.00 & - 0.67 \\ - 0.38 & 1.00 \end{matrix})}^{- 1} .$ The eigenvalues (λ1 and λ2) represent upper limit values and are described by the following Arrhenius-type equations: $λ 1 (Di/An) = 10^{- 15.98 \pm 1.17} \times exp (\frac{- 114.4 \pm 32.8 kJ/mol}{RT}),$ $λ 2 (Di/An) = 10^{- 16.23 \pm 1.17} \times exp (\frac{- 114.4 \pm 32.8 kJ/mol}{RT}),$ where λ1 and λ2 are the first and second eigenvalue of the diffusion matrix in m² s^-1 , R is the gas constant and T is the temperature in K. The dominant eigenvalue (λ1) is one quarter order of magnitude larger than the second eigenvalue (λ2). The eigenvectors are constant for all experiments inferring that the entire D matrix can be described with the eigenvalues as the only T-dependent parameter. Additionally, the derived diffusion data and modeling approach were applied to constrain the duration of magmatic processes recorded in zoned clinopyroxene (cpx) phenocrysts from a basaltic, post-plutonic dyke of the Tertiary Adamello batholiths (N-Italy). The results reveal residence times of the overgrown cpx prior to final emplacement in the range of 0.25-1.7 years (lower limit values) testifying that the data and method can be applied to model cpx diffusion profiles in complex natural cpx.

Keywords: Eigenvalues; Eigenvectors; Multicomponent coupled diffusion; Pyroxene diffusion; Seed overgrowth technique.