modulus due to the spin transition of Fe3+ on the B site of bridgmanite (Fu et al., 2018) significantly reduces P‐wave velocities for the respective harzburgite models at pressures between 40 and 100 GPa. The low overall Al2O3 content affects both P‐ and S‐wave velocities.
While dominated by the elastic softening due to the ferroelastic phase transition between stishovite and CaCl2‐type SiO2, modeled P‐ and S‐wave velocity profiles of metabasalt are sensitive to both the Fe3+/∑Fe ratio of bridgmanite and Fe‐Mg exchange between bridgmanite and the CF phase. In contrast to pyrolite and harzburgite, higher Fe3+/∑Fe ratios appear to reduce velocity gradients with depths. Varying the Fe‐Mg exchange coefficient between bridgmanite and the CF phase has the opposing effect and results in higher P‐ and S‐wave velocities for higher values of the Fe‐Mg exchange coefficient. For all three bulk rock compositions addressed here, the sensitivity of P‐ and S‐wave velocities to variations in Fe‐Mg exchange coefficients demonstrates the need for better constraining equilibrium mineral compositions at relevant pressures and temperatures. While Fe‐Mg exchange coefficients and Fe3+/∑Fe ratios were treated here as independent parameters, they are coupled through the preferred incorporation of ferric iron into bridgmanite (Frost et al., 2004; Irifune et al., 2010). As shown in Figure 3.6, however, available data on element partitioning cannot unambiguously constrain mineral compositions. More experiments and thermodynamic data are required to improve forward models of the petrology and elastic properties of lower‐mantle rocks.
To depict the effect of continuous phase transitions on modeled P‐ and S‐wave velocities, I computed additional velocity profiles by ignoring changes in spin states of iron cations and by suppressing the phase transition from stishovite to CaCl2‐type SiO2. The results are included in Figure 3.9 for each reference scenario and for selected combinations of compositional parameters that are expected to be particularly susceptible to the effects of spin transitions. All pyrolite models as well as the reference scenario for harzburgite are only affected by the spin transition of ferrous iron in ferropericlase as no ferric iron is expected to enter the B site of bridgmanite for the respective combinations of Fe‐Mg exchange coefficients and Fe3+/∑Fe ratios of bridgmanite. Along an adiabatic compression path, the spin transition of Fe2+ in ferropericlase broadens substantially for reasons discussed in Section 3.7 and mainly reduces P‐wave velocities. As mentioned earlier, Fe3+ is found to enter the crystallographic B site of bridgmanite only for harzburgite models with Fe3+/∑Fe > 0.5 or
The spin transition of ferric iron in the CF phase does not seem to strongly affect P‐ or S‐wave velocities of metabasalt. In contrast, suppressing the effect of the ferroelastic phase transition from stishovite to CaCl2‐type SiO2 results in very different velocity profiles for metabasalt. While the softening of the shear modulus was modeled here based on a Landau theory prediction (Buchen et al., 2018a; Carpenter et al., 2000), the full extent of elastic softening remained uncertain until the very recent determination of complete elastic stiffness tensors of SiO2 single crystals across the ferroelastic phase transition (Zhang et al., 2021). Zhang et al. (2021) combined Brillouin spectroscopy, ISS, and X‐ray diffraction to track the evolution of the elastic stiffness tensor with increasing pressure and across the stishovite–CaCl2‐type SiO2 phase transition. In terms of the magnitude of the S‐wave velocity reduction, the predictions of Landau theory analyses seem to be consistent with the experimental results by Zhang et al. (2021). The elastic properties of stishovite and CaCl2‐type SiO2 had previously been computed for relevant pressures and temperatures using DFT and DFPT (Karki et al., 1997a; Yang and Wu, 2014). While indicating substantial elastic softening in the vicinity of the phase transition, the computations addressed both polymorphs independently and suggested discontinuous changes in the elastic properties at the phase transition, contradicting recent experimental results (Zhang et al., 2021) and earlier predictions based on Landau theory (Buchen et al., 2018a; Carpenter, 2006; Carpenter et al., 2000). First measurements on stishovite single crystals have captured the incipient elastic softening to pressures up to 12 GPa (Jiang et al., 2009) that has further been found to reduce the velocities of sound waves that propagate along selected crystallographic directions in aluminous SiO2 single crystals at higher pressures (Lakshtanov et al., 2007). For basaltic bulk rock compositions, stishovite was found to incorporate several weight percent Al2O3 (Hirose et al., 1999; Kesson et al., 1994; Ricolleau et al., 2010). Aluminum incorporation into stishovite has been shown to reduce the transition pressure to the CaCl2‐type polymorph (Bolfan‐Casanova et al., 2009; Lakshtanov et al., 2007). While the effect of aluminum incorporation into SiO2 phases has not been addressed in the modeling presented here, I illustrate the effect of changing the Clapeyron slope of the stishovite–CaCl2‐type SiO2 phase transition on the velocity profiles for metabasalt by using dP/dT = 11.1 MPa K–1 as reported by Nomura et al. (2010) instead of 15.5 MPa K–1 (Fischer et al., 2018) in an additional scenario shown in Figure 3.9.
While the modeling presented here primarily aims at providing examples for how elastic properties of rocks in Earth’s lower mantle can be assessed using mineral‐physical information on the elastic properties of mineral phases at high pressures and high temperatures, including the effects of continuous phase transitions, there are several sources of uncertainties that are difficult to evaluate quantitatively. For example, I combined computational with experimental results and used data from studies that used different types of samples, i.e., single crystals or polycrystals, and different methods to determine sound wave velocities, including Brillouin spectroscopy and ultrasonic interferometry. For none of the mineral phases do the available data cover the entire range of relevant pressures and temperatures. To illustrate uncertainties that result from averaging over the elastic properties of different mineral phases and compositions, Figure 3.9 shows the differences in P‐ and S‐wave velocities for the reference scenario of each bulk rock composition that result from the differences between the Voigt and Reuss bounds on the elastic moduli calculated based on the volume fractions that each mineral composition of Table 3.1 contributes to each of the rocks in Figure 3.9. It is further important to note that some compositions contribute with high volume
