Broad Elastic Softening of (Mg,Fe)O Ferropericlase Across the Iron Spin Crossover and a Mixed‐Spin Lower Mantle

Abstract

Introduction(Mg,Fe)O ferropericlase is the second most abundant mineral in Earth's lower mantle (e.g., Irifune et al., 2015). At room pressure, ferrous iron (Fe 2+ ) in ferropericlase adopts the high-spin electronic configuration where the six 3d-electrons partially fill the t 2g and e g orbitals, maximizing the number of unpaired electrons. At a pressure of about 40 GPa, a distortion of the iron-containing octahedral sites in the crystal structure triggers a change in iron electronic configuration to the low-spin state, where electron pairing in the t 2g orbitals is favored (Badro et al., 2003). Several studies have shown that the properties of ferropericlase in mixed-spin state are markedly different from those in either high-or low-spin state. In particular, the spin crossover is accompanied by a reduction in the Fe 2+ ionic radius (Shannon, 1976) enhancing the compressibility of ferropericlase over the pressure range where the spin crossover occurs (

Compressibility of ferropericlase at high-temperature: evidence for the iron spin crossover in seismic tomography

“…Further studies have proposed alternative methods, which include a non-ideal mixing model, with and without the contribution of magnetic entropy (Sun et al, 2022). Building on this, we recently showed that good agreement is obtained with ambient-temperature experimental results if, rather than assuming ideal mixing of high-and low-spin states, one calculates the series of successive spin transitions between stable spin states, from high-to low-spin (Méndez et al, 2022). In this method Equation 1 is applied to each individual spin transition, ∆𝐺 𝐻𝑆−𝐿𝑆 (𝑃, 𝑇) is the difference between the static and vibrational components of the Gibbs free energy of the higher and lower spin states, XFe the fraction of iron weighted by the fraction of iron involved in the spin transition, and kB is the Boltzmann constant.…”

“…In order to describe the correlated d electrons of iron in ferropericlase, we utilized the LDA+U scheme of Dudarev et al (1998), in which only the difference between onsite Coulomb interaction parameter U and onsite exchange parameter J is meaningful. In the present work, we used U -J = 3.3 eV, which was found to lead to the best agreement with experimental values for the spin crossover pressure in ferropericlase at 300 K (Méndez et al, 2022), and is similar to the 3.0 eV used in other studies of the spin crossover (Muir & Brodholt, 2015). Since the LDA is known to underestimate pressure, we calculated a correction using the method outlined by Oganov et al (2001), including the thermal pressure term calculated from our lattice dynamics calculations.…”

“…We will refer to this approach as the single spin transition method (SSTM), since it only involves calculation of ∆𝐺 𝐻𝑆−𝐿𝑆 (𝑃, 𝑇) for a single transition (from full HS to full LS). This method tends to lead to a spin crossover that is narrower at ambient-temperature than experimental results (Méndez et al, 2022).…”

“…The error in KT is propagated from the uncertainty in V and the standard error of the slope of the linear fit. When choosing the pressure interval, there is a trade-off between the uncertainties in the derived bulk moduli and the effective pressure resolution (Méndez et al, 2022). An interval of 5 GPa was found to be the best compromise for the ramps measured in RH1, while a 10 GPa interval was used for the ramp measured in RH2.…”

“…This model is larger than those in our previous work (Méndez et al, 2022), allowing on-axis iron atom neighbour pairs, while avoiding infinite repeating sequences of Fe and O atoms, arising from finite-size effects associated with the use of periodic boundary conditions. The latter was shown to have a nonnegligible effect on the calculated spin crossover (Méndez et al, 2022). In accordance with the observations of Waychunas et al (1994), the positions of the iron atoms were chosen at random.…”