Abstract

The structures of four Fe,Mg olivine crystals Fa11.6, Fa22.3, Fa27.6 and Fa27.8 have been investigated by ex situ and in situ experiments using single-crystal X-ray diffractometry. For the ex situ experiments, the crystals were quenched after equilibration at temperatures between 500 °C and 900 °C. Resetting effects were only observed for samples quenched from 900 °C. The in situ experiments were performed at temperatures up to 750 °C. With increasing equilibration temperature, Fe2+ was found to progressively segregate into the octahedral M1 site, i.e. the degree of anti-order increases with rising temperature. Thus, contrary to the results of Rinaldi et al. (2000) and Redfern et al. (2000), no indication of an ordering reversal at high temperatures is found. Incorporation of the results of Heinemann et al. (2006) on olivine Fa47.9 into the present study allows for the first time to systematically investigate the compositional variation of the temperature dependence of the Fe2+,Mg site occupancies. The formulation of Thompson (1969, 1970) for solid solutions undergoing non-convergent disordering processes,

 
\[{-}\ RTln\ K_{D}\ =\ [{\Delta}H_{exch}^{0}\ {-}\ (L_{M1}^{H}\ {-}\ L_{M2}^{H})X]\ {-}\ T[{\Delta}S_{exch}^{0}\ {-}\ (L_{M1}^{S}\ {-}\ L_{M2}^{S})X],\]
(1)

yielded

 
\begin{eqnarray*}&&{\Delta}H_{exch}^{0}\ =\ 1153\ ({\pm}67)\ J/mol{\ }{\ }{\Delta}S_{exch}^{0}\ =\ 3.743({\pm}0.072)\ J/molK\\&&L_{M1}^{H}\ {-}\ L_{M2}^{H}\ =\ 973\ ({\pm}211)\ J/mol{\ }{\ }L_{M1}^{S}\ {-}\ L_{M2}^{S}\ =\ {-}\ 0.89\ ({\pm}0.24)\ J/molK.\end{eqnarray*}

ΔHexch0 and ΔSexch0 are the exchange enthalpy and entropy, respectively, related to the Fe2+,Mg site exchange, LM1,M2H and LM1,M2S denote enthalpic and entropic intrasite interaction parameters. The compositional parameter X varies between −1 for forsterite (Fa0) and +1 for fayalite (Fa100). The magnitudes and signs of the four refined quantities can be rationalized in terms of thermodynamic and crystal-chemical considerations. (LM1H − LM2H) > 0 indicates that the interactions between the M1 sites are stronger than those between the M2 sites, conforming with the M1-M1 distances being shorter than the M2-M2 distances. (LM1S − LM2S) < 0 relates to the electronic entropy which is proportional to the Fa-content. According to equation (1), ΔHexch0 increases towards the Mg endmember while ΔSexch0 decreases. Since ΔHexch0 > 0 stabilizes the ordered state whereas ΔSexch0 >0 stabilizes the anti-ordered state, it follows that the ordered state is progressively favoured with increasing Mg content. Consequently, ordered site distributions should occur only in slowly cooled Mg-rich olivines, whereas olivines with Fa > 25 mol% should be found in their anti-ordered states frozen during cooling. This conclusion is supported by structure refinements and ordering path simulations for a metamorphic olivine Fa12.4 as well as two volcanic olivines Fa25.6 and Fa27.8.

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