.

Figure 3.5 (a–c) Reanalysis of elastic moduli of ferropericlase (a), sound wave velocities of bridgmanite (b), and compression data on the CF phase (c) across spin transitions of ferrous (a) and ferric (b,c) iron. Respective data are from Yang et al. (2015) (a), Chantel et al. (2012), and Fu et al. (2018) (b), and Wu et al. (2017) (c). Bold black curves show the results of fitting a semi‐empirical crystal‐field model to the data as explained in the text with the respective crystal‐field parameters given in each panel. The values of crystal‐field parameters that were free to vary during fitting are marked with an asterisk (*). For bridgmanite, data of Chantel et al. (2012) and Fu et al. (2018) have been analyzed together to better constrain pressure derivatives of elastic moduli. The offset between both data sets arises from slightly different estimates for densities as reported in both studies. (d–f) Fractions of d electrons in multi‐electron states across spin transitions of Fe²⁺ in ferropericlase (d), Fe³⁺ in bridgmanite (on B site) (e), and Fe³⁺ in the CF phase (f) as predicted by the semi‐empirical crystal‐field model and along typical adiabatic compression paths (see Figure 3.8). Shading indicates differences in fractions that result from starting adiabatic compression at temperatures 500 K above and below 1900 K at 25 GPa. (g–i) P‐wave velocity reductions that result from spin transitions of Fe²⁺ in ferropericlase (g), Fe³⁺ in bridgmanite (on B site) (h), and Fe³⁺ in the CF phase (i) as predicted by the semi‐empirical crystal‐field model and along adiabatic compression paths starting at 1400 K, 1900 K, and 2400 K at 25 GPa (see Figure 3.8). The dashed curves show P‐wave velocity reductions along the central compression path (1900 K at 25 GPa) when the population of a third multi‐electron state with intermediate spin multiplicity is ignored.

3.8 EARTH’S LOWER MANTLE

      Seismic tomography shows lateral variations in P‐ and S‐wave velocities at all depths of the lower mantle and across length scales that are compatible with changes in temperature, chemical composition, and phase assemblage as well as combinations thereof (Durand et al., 2017; Hosseini et al., 2020; Koelemeijer et al., 2016). Scattering of seismic waves in the lower mantle, in contrast, points to changes in the elastic properties of the mantle over length scales that are commonly interpreted to be too short to arise from thermal gradients alone and require compositional heterogeneities or phase changes (Frost et al., 2017; Kaneshima & Helffrich, 2009; Waszek et al., 2018). Lateral and local variations are superimposed on the monotonous increase of seismic velocities that dominates global seismic reference models at depths between 800 km and 2400 km (Dziewonski & Anderson, 1981; Kennett et al., 1995; Kennett & Engdahl, 1991). The seismic structure of the upper mantle and transition zone can be compared with the results of mineral‐physical models (Cammarano et al., 2009; Cobden et al., 2008; Xu et al., 2008) that are based on internally consistent thermodynamic databases (Holland et al., 2013; Stixrude & Lithgow‐Bertelloni, 2011). For the lower mantle and depths in excess of 800 km, however, these databases are less reliable since both chemical compositions and elastic properties of relevant mantle minerals are less well constrained as discussed in Section 3.6 for bridgmanite. Moreover, existing thermodynamic databases do not include the effects of continuous phase transitions, such as the ferroelastic phase transition from stishovite to CaCl₂‐type SiO₂ and spin transitions, on elastic properties that are expected to affect seismic velocities in the lower mantle. This section focuses on seismic properties of relevant rock types in the depth interval from about 800 km to 2400 km. Chapter 8 of this volume addresses the lowermost mantle including the D" layer at depths in excess of 2400 km.

      Experiments on peridotitic rock compositions found bridgmanite (bm), ferropericlase (fp), and calcium silicate perovskite (cp) as major phases with approximately constant volume fractions of bm:fp:cp ~ 70:20:10 at pressures and temperatures of the lower mantle (Irifune et al., 2010; Kesson et al., 1998; Murakami et al., 2005). Depending on composition and temperature, bridgmanite transforms to the post‐perovskite phase at pressures in excess of 100 GPa corresponding to an approximate depth of 2400 km (Murakami et al., 2005, 2004; Shim et al., 2004; Sun et al., 2018). Since the composition of calcium silicate perovskite remains close to pure CaSiO₃ and bridgmanite incorporates virtually all available Al₂O₃, the main compositional variables are the Mg/(Fe+Mg) ratios of bridgmanite and ferropericlase that are coupled through Fe‐Mg exchange reactions. Fe‐Mg exchange between ferropericlase and bridgmanite is sensitive to a large number of thermodynamic parameters including pressure, temperature, composition, oxygen fugacity, and the spin states of Fe²⁺ and Fe³⁺ (Badro, 2014). Despite substantial progress in deciphering the effects of these parameters on the Fe‐Mg exchange between bridgmanite and ferropericlase, the variation of the Fe‐Mg exchange coefficient (Badro, 2014) through the lower mantle remains debated. While recent experimental studies found Fe‐Mg exchange coefficients of about 0.5 with no clear trend with increasing pressure between 40 GPa and 100 GPa (Piet et al., 2016; Prescher et al., 2014; Sinmyo & Hirose, 2013), DFT computations suggest generally smaller values that decrease with increasing pressure as a result of the progressing spin transition of Fe²⁺ in ferropericlase (Muir & Brodholt, 2016; Xu et al., 2017). The Fe‐Mg exchange coefficient for harzburgitic rocks seems to be closer to 0.2 and to decrease with increasing pressure (Auzende et al., 2008; Badro, 2014; Piet et al., 2016; Sakai et al., 2009; Sinmyo et al., 2008; Xu et al., 2017). Figure 3.6a summarizes experimental and computational findings on Fe‐Mg exchange between bridgmanite and ferropericlase.

For basaltic compositions that intend to represent recycled oceanic crust, experimental results suggest modal proportions of the major phases bridgmanite (bm), calcium silicate perovskite (cp), CF phase (cf), and stishovite (st) of bm:cp:cf:st ~ 45:30:15:10 throughout most of the lower mantle (Hirose et al., 2005, 1999; Ono et al., 2001; Perrillat et al., 2006; Ricolleau et al., 2010). At pressures between 25 GPa and 40 GPa, the NAL phase has been found to coexist with this assemblage but seems to become destabilized towards higher pressures (Perrillat et al., 2006; Ricolleau et al., 2010). Figure 3.6b shows exchange coefficients for Fe‐Mg and Al‐Mg exchange between bridgmanite and the CF phase as computed from experimentally observed mineral compositions for the assemblage bm‐cp‐cf‐st in basaltic bulk compositions. Although it appears difficult to assign robust trends of mineral compositions with changes in pressure or temperature, iron tends to be equally distributed between bridgmanite and the CF phase while aluminum seems to preferentially partition into the CF phase. The wide spread in experimentally observed mineral compositions is also reflected in the bridgmanite compositions shown in Figure 3.3. Clearly, more experiments are needed to better understand element partitioning and mineral compositions in peridotitic and metabasaltic rocks at conditions of the lower mantle.

Figure 3.6 Exchange coefficients for Fe‐Mg exchange between bridgmanite and ferropericlase in peridotitic bulk compositions (a) and for Fe‐Mg and Al‐Mg exchange between