Phonon dispersion throughout the iron spin crossover in ferropericlase

Abstract

Ferropericlase (Fp), (Mg1-xFex)O, is the second most abundant phase in the Earth's lower mantle.At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), S=2, to low spin (LS), S=0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermo-elastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasi-harmonic approximation (QHA). Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin-crossover using ab initio DFT+Usc calculations. We address vibrational modes associated with isolated and (2 nd ) nearest neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient while optical modes are the most affected. We show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

Thermodynamics of spin crossover in ferropericlase: an improved LDA+$U_{sc}$ calculation

“…No imaginary frequency is found in either HS or LS state up to 100 GPa. This is consistent with the recent phonon calculations in x F e =0.0625 fp with density functional perturbation theory [29]. Therefore, both HS and LS states of fp with iron concentrations lower than 0.1875 are dynamically stable.…”

“…Because fp is a solid solution of FeO and MgO, a uniform distribution is more relevant to the real situation. Moreover, it has been shown that different types of Fe configurations have only a small effect on the spin crossover [29]. With x F e =0.1875, one would expect the exchange interaction between Fe ions in the HS state to be sizable because of the small Fe-Fe distance.…”

“…This transition pressure in fp18 is in good agreement with the experimental measurement of ferropericlase with x F e =0.17 at room temperature [7], which is ∼60GPa. A change in the distribution of iron in the supercell of fp18 changes the transition pressure by a few GPa only [29], but it gives rise to a distribution of transition pressures.…”

Intermediate spin state and the B1-B2 transition in ferropericlase at tera-Pascal pressures

“…We further investigate the B1-LS → B2-IS transition in fp with larger iron concentrations in Fe 2 Mg 30 O 32 and Fe 4 Mg 28 O 32 (x F e = 0.0625 and 0.125, noted as fp6 and fp12 hereafter). It has been shown that the iron arrangement in the fp solid solution has a minor effect on the spin state change pressure in the B1 phase, at least for small x F e as investigated here [44]. Therefore, we distribute Fe uniformly in both B1 and B2 lattices and disregard Fe-Fe interaction effects in first-order (see Supplementary Fig.…”

Two-state model for critical points and the negative slope of the melting curve

“…The present model allows for an isostructural phase transition at low temperature, as well as a crossover: such a true phase transition, an associated critical point, would require a coupling J between sites which disfavoured mixing. This coupling may come from short ranged strain [41,42], magnetic spin coupling or from phonons [71], or be calculated directly from first principles [70], and may vary with pressure [72]. Magnetowüstite (Mg,Fe)O and perovskite (Mg,Fe)SiO 3 in the iron rich regime are prime candidates.…”