doi:10.1016/j.pepi.2007.06.012
Copyright © 2007 Elsevier B.V. All rights reserved.
Ab initio calculations of the elastic properties of ferropericlase Mg1−xFexO (x≤0.25)
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L. Kočia, 
, 
, , L. Vitosa, b, c and R. Ahujaa, b
aCondensed Matter Theory Group, Physics Department, Uppsala University, Box 530, S-751 21 Uppsala, Sweden
bApplied Materials Physics, Department of Materials Science and Engineering, The Royal Institute of Technology, SE-10044 Stockholm, Sweden
cResearch Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
Received 7 March 2007;
revised 6 June 2007;
accepted 29 June 2007.
Available online 20 July 2007.
Abstract
Ferropericlase Mg1−xFexO is believed to be the second most abundant mineral in the Earth’s mantle. Therefore, the electronic and elastic properties of ferropericlase are important for the understanding of the Earth’s interior. Ab initio total energy calculations have been performed for Fe concentrations x≤0.25. The equation of state (EOS) clearly shows a volume expansion as a function of Fe concentration, consistent with experimental data. Magnetic moment calculations as a function of pressure show a high-spin to low-spin transition of Fe2+, and the theoretical transition pressure increases with iron composition. At ambient pressure, we have found that the shear constant C44 reproduces well the experimental data as a function of Fe concentration. The MgO and Mg0.9Fe0.1O minerals show an increasing C44 with pressure, whereas the 
is slightly negative after 26 GPa for Mg0.8Fe0.2O. The C44 softening could be related to the transition from the cubic to a rhombohedrally distorted phase, recently found by experiment.
Keywords: Ferropericlase; Elasticity; Pressure
Fig. 2. Magnetic moment of (Mg,Fe)O as a function of composition and pressure. For the iron poor compounds (6.25 and 12.5% Fe), the magnetic moment vanishes at approximately 60 GPa. The somewhat wider spin transition range for Mg0.83Fe0.17O (Lin et al., 2005) is inserted as vertical lines in the figure, separating the high-spin (HS) from the low-spin (LS) region. For the richer Fe phases, 18.8% Fe shows a transition just below 90 GPa, whereas for 25% Fe, the transition occurs within a wide (
100 GPa) pressure window.
Fig. 3. EOS as a function of the Fe content in Mg1−xFexO. The effect of increasing the amount of iron into the ferropericlase yields a volume increase. This is consistent with the higher molar volume for FeO compared to MgO.
Fig. 5. Shear constant C44 as a function of pressure and (Mg,Fe)O composition. Consistent with the results in Fig. 4, the effect of iron is a softening of the elastic constant. MgO and Mg0.9Fe0.1O show increasing data as a function of pressure. A kink is found for the C44 for Mg0.8Fe0.2O at 26 GPa, which could be due to a phase transition.
Fig. 6. The elastic constants (C11−C12) as a function of pressure and Mg1−xFexO compound. For MgO, the results from this work in the low-pressure range is somewhat underestimated compared to experiment (Sinogeikin and Bass, 1999), as shown in Table 1. The results from Mg0.9Fe0.1O and Mg0.8Fe0.2O are consistent with earlier findings, implying a softening with iron content.
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