Influence of oxygen pressure on defect concentrations in olivine with a fixed cationic ratio

The variation of the point-defect concentrations with oxygen partial pressure, P_O2, and temperature are derived for forsterite, Mg₂SiO₄, and Mg-rich olivine (Mg,Fe)₂SiO₄ assuming the cation/cation ratios are fixed. These dependencies differ from the open-system situation in which matter is easily transferable between forsterite or olivine and other solid phases. The details depend on whether the cation/cation ratio is exactly stoichiometric, or, if non-stoichiometric, the nature of the majority defects at precise oxygen stoichiometry. One generality which emerges is that regardless of the cation/cation stoichiometry the dominant defects in forsterite at low P_O2 are free electrons, Mg and Si interstitials; at high P_O2 the majority defects are holes, Mg and Si vacancies. In Mg-rich olivine the same defect species exist at the extremes of oxygen partial pressure with the exception of trivalent Fe on Mg sites replacing holes. At low P_O2, therefore, both behave as n-type conductors. The models also suggest that in the P_O2 range around precise oxygen stoichiometry the electrical conductivity in both materials can be a complex function of P_O2.