Spin states and hyperfine interactions of iron incorporated in MgSiO3 post-perovskite
Introduction
Iron, the most abundant transition-metal element in the Earth, is widely present in major mantle minerals, including olivine, pyroxene, garnet, ferropericlase, magnesium silicate (MgSiO3) perovskite (Pv), and the recently discovered MgSiO3 post-perovskite (Ppv) with the CaIrO3-type (Cmcm) structure (Murakami et al., 2004, Oganov and Ono, 2004, Tsuchiya et al., 2004). Owing to its incomplete 3d electron shell and comparable crystal field splitting energy and Hund's exchange energy, the total electron spin moment S of iron in minerals can vary with pressure and temperature. This phenomenon, known as spin-state crossover, has a great influence on physical and chemical properties of the host minerals. A well studied example is ferropericlase [(Mg,Fe)O], the second most abundant mineral in the lower mantle. In this mineral, ferrous iron (Fe2 +) undergoes a spin-state crossover from high-spin (HS), S = 2, to low-spin (LS), S = 0, at pressures near the mid mantle (45–55 GPa), which strongly affects the compressibility (Badro et al., 2003, Tsuchiya et al., 2006), elasticity, and sound velocity of this mineral (Crowhurst et al., 2008, Wentzcovitch et al., 2009, Wu et al., 2009). This HS–LS crossover also reduces the radiative thermal conductivity (Goncharov et al., 2006) and is expected to alter the partition of Fe and Mg between ferropericlase and MgSiO3 Pv. In MgSiO3 Pv, the dominant mineral phase in the lower mantle, recent studies have shown that the ferric iron (Fe3 +) substituting for silicon at the octahedral (B) site undergoes a spin-state crossover from HS (S = 5/2) to LS (S = 1/2) state at 50–60 GPa, while the Fe3 + substituting for magnesium at the dodecahedral (A) site remains HS (Catalli et al., 2010b, Hsu et al., 2011). This B-site spin-state crossover leads to an elastic anomaly in the Pv phase, which can be a possible source of seismic anomaly (Hsu et al., 2011). As to Fe2 + in Pv, which substitutes for magnesium at the A site, first-principles calculations have shown that no spin-state crossover occurs in the 0–150 GPa pressure range, namely, the A-site Fe2 + remains in the HS state (Hsu et al., 2010b). While a very large iron nuclear quadrupole splitting (QS) of 3.5–4.0 mm/s observed in Mössbauer spectra was suggested to be evidence for intermediate-spin (IS) Fe2 + (Lin et al., 2008, McCammon et al., 2008, McCammon et al., 2010), first-principles calculations have shown this high-QS state to be HS Fe2 + (Bengtson et al., 2009, Hsu et al., 2010b).
The remaining piece of the puzzle for iron spin states in the deep mantle lies in the MgSiO3 Ppv phase, possibly a main component of the Earth's D″ layer, which is a thermal boundary layer between the mantle and the core and may be crucial for mantle dynamics (Lay and Garnero, 2007). Despite its importance, the iron spin states in Ppv are still unclear. Several possible spin states have been proposed in the past few years based on Mössbauer spectra, including IS Fe2 + (Lin et al., 2008, Mao et al., 2010), as well as HS Fe3 + at the A site and LS Fe3 + at the B site (Catalli et al., 2010a). In addition, metallic iron was also reported to occur in the compressed Ppv sample (Jackson et al., 2009). It should be noted that iron spin states cannot be identified merely based on measured QS values, as QS is not directly affected by the electron spin moment S, but directly proportional to the electric field gradient (EFG) at iron nucleus (see Section 2). The EFG is determined by the electron density and orbital occupancy; its relation with iron spin may not necessarily be straightforward. Previous calculations of iron nuclear QS in Pv (Hsu et al., 2011) show that the IS and LS states of Fe3 + at the A site have very close QS values, ~ 2 mm/s, and both LS Fe2 + and HS Fe3 + possess low QS values, ~ 0.9 mm/s. Moreover, it has been shown that for 3d6 ions, such as Fe2 + in Pv (Hsu et al., 2010b) and Co3 + in LaCoO3 (Hsu et al., 2010a), IS state does possess a lower EFG than HS state, which clearly indicates that associating high QS (~ 4 mm/s) with IS Fe2 + in Pv (Lin et al., 2008, McCammon et al., 2008) can be inaccurate. In this sense, first-principle calculations, combined with experimental data, is a necessary tool to identify iron spin states in complex minerals.
Several first-principle calculations based on density functional theory (DFT) (Kohn and Sham, 1965), have been conducted to study the iron spin states in MgSiO3 Ppv (Caracas, 2010, Caracas and Cohen, 2008, Zhang and Oganov, 2006), with or without taking aluminum into consideration. In these calculations, however, the iron nuclear QS was not computed, and only standard DFT functionals, such as local density approximation (LDA) (Ceperley and Alder, 1980, Perdew and Zunger, 1981) and the Perdew–Burke–Ernzerhof (PBE) type GGA (Perdew et al., 1996), were adopted. It is well known that standard DFT functionals do not describe the on-site Coulomb interactions between 3d electrons properly, which can lead to difficulties in predicting correctly the electronic band gap as well as 3d orbital occupancy in iron-bearing minerals. The DFT + Hubbard U (DFT + U) method (Anisimov et al., 1991), on the other hand, provides more reliable predictions. An example is the HS Fe3 + at the B site in Pv, which was not found by GGA (Zhang and Oganov, 2006) but is identified in both experiment (Catalli et al., 2010b) and DFT + U calculations (Hsu et al., 2011). In addition, when the Hubbard U is determined self-consistently (Usc) from the first-principles (Cococcioni and de Gironcoli, 2005), the predicted transition pressures satisfactorily agree with experiments for iron-bearing Pv (Hsu et al., 2010b, Hsu et al., 2011). In this paper, we thus use the DFT + Usc method to investigate iron spin states, hyperfine interactions, and relevant equation of states of iron-bearing MgSiO3 Ppv.
Section snippets
Method
In our DFT + U calculations, both the LDA and the GGA functionals are adopted. The self-consistent Usc parameter is determined by a linear response method (Campo and Cococcioni, 2010, Cococcioni and de Gironcoli, 2005, Hsu et al., 2011, Kulik et al., 2006), which is implemented in the quantum espresso package (Giannozzi et al., 2009), a DFT code using the plane-wave pseudopotential method. Using the DFT + Usc method, one can obtain electronically convergent HS, IS, and LS states for ferrous and
Results and discussion
The MgSiO3 Ppv has a layered structure, characterized by corner-sharing and edge-sharing SiO6 octahedra extending on the ac plane (Fig. 1). Intercalated in between two adjacent SiO6 layers are magnesium atoms at the dodecahedral (8–12 coordination) sites. Two substitution mechanisms have been studied in a 40-atom supercell: one Fe2 + substituting for one Mg2 + at the A site forming (Mg0.875,Fe0.125)SiO3 [Fig. 1(a)] and two Fe3 + substituting for a pair of the nearest-neighbor Mg2 + (A-site) and Si4 +
Conclusions
We have investigated the spin states and quadrupole splittings of iron incorporated in MgSiO3 post-perovskite using DFT + U calculations. We found that Fe2 + remains in the HS state throughout the D″ pressure range. The computed QS of this state, 3.09–3.67 mm/s, is in good agreement with that extracted from Mössbauer spectra, 3.77 ± 0.25 mm/s. The IS and LS Fe2 + are energetically unfavorable, and their QSs are very different from those extracted from Mössbauer spectra. A pair of Fe3 + ions that
Acknowledgments
This work is supported by the NSF grants EAR-0810272, EAR-1047629, and partially by the MRSEC Program of NSF grants DMR-0212302 and DMR-0819885. We thank Peter Blaha for valuable discussions on the calculations of EFG via the WIEN2k code. All calculations were performed at the Minnesota Supercomputing Institute (MSI).
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