Mantle Convection and Surface Expressions. Группа авторов

for realistic bulk rock compositions requires accurate descriptions of elastic properties across solid solutions of mantle minerals. In contrast to the elastic properties of mantle minerals with compositions spanned by binary solid solutions, i.e., olivine and ferropericlase, the change of elastic properties with chemical composition is not well constrained for mantle minerals that form complex solid solutions between several end member compositions, such as pyroxenes, garnets, bridgmanite, and the calcium ferrite‐type aluminous (CF) phase. High‐pressure experimental data on bridgmanite, for example, barely span bridgmanite compositions observed in experiments on peridotitic bulk rock compositions. While DFT computations have addressed wider compositional ranges (Shukla et al., 2016, 2015; Zhang et al., 2016), the results are not always consistent with those of direct measurements or are limited to specific combinations of pressure and temperature, making it difficult to derive finite‐strain parameters. Inter‐ and extrapolations of elastic properties between different mineral compositions and beyond compositional limits imposed by available elasticity data are subject to uncertainties that arise from averaging over elastic properties of different mineral compositions and from assumptions about how elastic properties vary across solid solutions. Experiments on peridotitic and basaltic bulk rock compositions at pressures and temperatures of the lower mantle show substantial spread in observed mineral compositions and, as a consequence, in derived element exchange or partition coefficients. Despite progress in deriving trends for element partitioning with pressure, temperature, and compositional parameters for specific bulk compositions (Hyung et al., 2016; Irifune et al., 2010; Nakajima et al., 2012; Piet et al., 2016; Xu et al., 2017), it remains difficult to assess to which extent experimentally observed mineral compositions are representative of chemical equilibrium. While capable of reproducing pressures and temperatures of the lower mantle, laser‐heating experiments in diamond anvil cells often give rise to strong thermal gradients across the sample that can drive disparate diffusion of chemical elements and bias mineral compositions (Andrault and Fiquet, 2001; Sinmyo and Hirose, 2010). In comparison to typical sample sizes, thermal gradients tend to be less pronounced for experiments in multi‐anvil presses. Recent progress in multi‐anvil press technology has extended achievable pressures to those of the lowermost mantle (Ishii et al., 2019; Yamazaki et al., 2019) and promises to facilitate experiments that better constrain equilibrium mineral compositions at pressures and temperatures of the lower mantle. When modeling seismic properties for a given bulk rock composition, uncertainties on element partitioning and on other compositional variables translate into uncertainties on the chemical compositions of individual mineral phases and hence on computed elastic properties and wave speeds.

      Several major mantle minerals go through continuous phase transitions at pressures and temperatures relevant to Earth’s lower mantle. Continuous phase transitions include ferroelastic phase transitions between polymorphs of calcium silicate perovskite (Shim et al., 2002; Stixrude et al., 2007) and between stishovite and CaCl₂‐type SiO₂ (Andrault et al., 1998; Carpenter et al., 2000; Karki et al., 1997b; Lakshtanov et al., 2007) as well as continuous changes in the electronic configurations of ferrous and ferric iron, i.e., spin transitions (Badro, 2014; Lin et al., 2013). Both ferroelastic phase transitions and spin transitions are associated with substantial softening of elastic moduli that is not commonly accounted for in mineral‐physical models. Anomalies in elastic properties that arise from ferroelastic phase transitions can be described in terms of excess properties using Landau theory (Carpenter and Salje, 1998) and integrated into finite‐strain formalisms (Buchen et al., 2018a; Tröster et al., 2014, 2002). To model elastic softening due to spin transitions, a similar approach can be adopted by formulating excess properties that arise from compression‐ and temperature‐induced changes in the distribution of d electrons of iron cations over multi‐electron states. Crystal‐field theory provides the basis for a semi‐empirical formalism that can be used to describe elastic anomalies associated with spin transitions of Fe²⁺ in ferropericlase and of Fe³⁺ in bridgmanite and in the CF phase at ambient temperature. In the absence of direct measurements of elastic softening at combined high pressures and high temperatures, predictions and extrapolations of elastic properties to realistic mantle temperatures based on Landau theory, crystal‐field theory, or DFT computations need to be made with caution.

      Integrating elastic anomalies caused by continuous phase transitions into forward models for elastic properties of rocks in Earth’s lower mantle leads to discernible perturbations of P‐ and S‐wave velocities. While the broad spin transition of Fe²⁺ in ferropericlase reduces the computed P‐wave velocities of peridotitic rocks throughout the entire lower mantle, the spin transition of ferric iron in very Fe³⁺‐rich bridgmanite would mostly affect P‐wave velocities in the upper half of the lower mantle. In addition to their direct impact on P‐wave velocities, spin transitions are expected to alter the Fe‐Mg exchange between ferropericlase and bridgmanite (Badro, 2014; Xu et al., 2017) that appears to exert a strong leverage especially on S‐wave velocities. The potential compositional effect of spin transitions on seismic properties could have implications for the interpretations of large low‐velocity provinces (LLVP). A comparison of the overall seismic signature of peridotitic rocks with the preliminary reference Earth model (PREM; Dziewonski & Anderson, 1981) reveals trade‐offs between feasible interpretations in terms of the chemical and thermal structure of the lower mantle. Despite the low volume fraction of free silica phases found in experiments on basaltic bulk rock compositions, the softening of the shear modulus across the ferroelastic phase transition between stishovite and CaCl₂‐type SiO₂ might be strong enough to dominate elastic wave speeds of metabasaltic rocks in the lower mantle. The resulting low elastic wave speeds could give rise to scattering of seismic waves by fragments of recycled oceanic crust and contribute to low elastic wave speeds within LLVPs.

      

ACKNOWLEDGMENTS

      The author would like to thank J. M. Jackson and W. Sturhahn for discussions about spin transitions and G. Steinle‐Neumann for providing valuable feedback on parts of the manuscript. The constructive feedback of three anonymous reviewers is highly appreciated and helped to improve the manuscript. National Science Foundation’s Collaborative Study of Earth’s Deep Interior (EAR‐1161046, awarded to J. M. Jackson) supported a portion of this work.

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