### Abstract

We determined the forward rate constant (K^{+}) for the Fe^{2+}-Mg order-disorder between the M2 and M1 sites of orthopyroxene (OPx), which is described by the homogeneous reaction Fe^{2+} (M2) + Mg(M1) ↔ Mg(M2) + Fe^{2+} (M1), by both ordering and disordering experiments at isothermal condition and also by continuous cooling experiments. The rate constant was determined as a function of temperature in the range of 550-750°C, oxygen fugacity between quartz-fayalite-iron and Ni-NiO buffers, and at compositions of 16 and 50 mol% ferrosilite component. The K^{+} value derived from disordering experiment was found to be larger than that derived from ordering experiment at 550°C, while at T >580°C, these two values are essentially the same. The fO_{2} dependence of the rate constant can be described by the relation K^{+} α (fO_{2})^{n} with n=5.5-6.5, which is compatible with the theoretically expected relation. The Arrhenius relation at the WI buffer condition is given by ln (C_{o}K^{+}) = -41511 - 12600X_{Fe}/T(K) + 28:26 + 5:27 X_{Fe}, min^{-1} where C_{o} represents the total number of M2 + M1 sites occupied by Fe^{2+} and Mg per unit volume of the crystal. The above relation can be used to calculate the cooling rates of natural OPx crystals around the closure temperature (T_{c}) of Fe-Mg ordering, which are usually below 300°C for slowly cooled rocks. We determined the Fe-Mg ordering states of several OPx crystals (∼ Fs_{50}) from the Central Gneissic Complex (Khtada Lake), British Columbia, which yields T_{c} ∼290°C. Numerical simulation of the change of Fe^{2+}-Mg ordering in OPx as a function of temperature using the above expression of rate constant and a non-linear cooling model yields quenched values of ordering states that are in agreement with the observed values for cooling rates of 11-17°C/Myr below 300°C. The inferred cooling rate is in agreement with the available geochronological constraints.

Original language | English (US) |
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Pages (from-to) | 319-334 |

Number of pages | 16 |

Journal | Contributions to Mineralogy and Petrology |

Volume | 150 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1 2005 |

### ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology

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## Cite this

^{2+}-Mg order-disorder in orthopyroxene: Experimental studies and applications to cooling rates of rocks.

*Contributions to Mineralogy and Petrology*,

*150*(3), 319-334. https://doi.org/10.1007/s00410-005-0016-9