Seismic Wave Velocities in Earth's Mantle from Mineral Elasticity

Structure and compressibility of Fe-bearing Al-phase D

“…This strategy has the advantage that only one set of V 0 , K T0 , and K' T0 needs to be determined for the high-spin state, the low-spin state, and the mixed-spin region, while the electronic contribution to the spincrossover equation is calculated separately. Buchen (2021) further showed that a good fit to the experimentally measured P-V data can be obtained even when most of these parameters, such as Δ 0 , b, 2 and the fit to the experimental data points is shown in Figure 3a. The EOS curve interpolates well the data points in both the high-spin state region and across the spin crossover, while the population density of the high-spin and low-spin electronic states, shown in the inset of Figure 3a, confirms that the transition is broad and takes place over a pressure interval of more than 30 GPa, as was previously observed by Chang et al (2013).…”

“…The number of data points collected after the onset of the spin crossover (i.e., above 38 GPa) is limited and does not allow to refine separate EOS parameters for the Fe-bearing Al-phase D sample in the high-and low-spin states. However, a fit of all data points (i.e., before and across the spin crossover) can be obtained using a new semi-empirical formalism that has been recently proposed by Buchen (2021). In this formalism, the contribution of the spin crossover to the elastic energy (and thus to pressure) is obtained from the volume dependency of crystal-field parameters such as the crystal-field splitting Δ and the Racah parameters B and C: where the zero in the subscript denotes parameters at room pressure.…”

“…In this formalism, the contribution of the spin crossover to the elastic energy (and thus to pressure) is obtained from the volume dependency of crystal-field parameters such as the crystal-field splitting Δ and the Racah parameters B and C: where the zero in the subscript denotes parameters at room pressure. The total Helmholtz free energy (F) at a given volume is then calculated by summing the elastic energy obtained from the finite strain equation (i.e., BM3 EOS in this case), the energies associated with the three most populated electronic states (i.e., 6 A 1 , 2 T 2 , and 4 T 1 for Fe 3+ ) according to the equations proposed by Tanabe and Sugano (1954), and a term accounting for configurational entropy (Buchen 2021). Finally, pressure is calculated by differentiating the total Helmholtz free energy relative to volume as P = -(∂F/∂V) T .…”

“…and c, are fixed to values determined by previous studies for octahedrally coordinated Fe 2+ and Fe 3+ cations in other compounds, while only B 0 and δ are refined. Following the examples provided byBuchen (2021), we assumed C/B to be constant and equal to 4.73, which implies c = b, with b = -2 (as Fe 3+ in CF-type aluminous phase, Buchen 2021) and Δ 0 = 14750 cm -1 (as Fe 3+ in corundum,Lehmann and Harder 1970;Krebs and Maisch 1971), while B 0 and δ were refined. The resulting fit parameters are reported in Table…”

Mantle Phase Changes Detected From Stochastic Tomography

“…Success has been achieved in constraining chemistries that match observed seismic velocities over a broad region of depth. With increasing degrees of sophistication, thermodynamic models examining effects of compositions in the form of either mechanical mixtures or solid solutions have succeeded in matching average elastic velocities, their gradients with depth, and mineral phase changes in the transition zone (e.g., Buchen, 2021; Cammarano et al., 2005; Chust et al., 2017; Stixrude & Lithgow‐Bertelloni, 2011; Wang et al., 2018; Xu et al., 2008).…”