Mantle Convection and Surface Expressions. Группа авторов

Becker, 2010; Nowacki et al., 2010, 2011; Tommasi et al., 2018; Walker et al., 2011, 2018).

      Although the exact mineralogy and chemistry of the lower mantle is still debated, seismic velocities and densities of the lower mantle are consistent with a mineralogy composed predominantly (65% to 85% by volume) of (Mg,Fe)(Si,Al,Fe)O₃ bridgmanite (Brg) with (Mg,Fe)O ferropericlase (Fp) as the second‐most abundant phase, and a few percent of CaSiO₃ perovskite (Ca‐Pv) (e.g., Kurnosov et al., 2017; Matas et al., 2007; Mattern et al., 2005). At conditions similar to those of the D” (~2700 km), Brg undergoes a solid‐solid phase transformation to a post‐perovskite structured phase (pPv) (Murakami et al., 2004; Oganov & Ono, 2004; Shim et al., 2004). The stability and depth of this phase transition varies considerably depending on chemical composition (Grocholski et al., 2012), but pPv is likely to be a major phase at least in localized regions above the CMB. Iron content in the lower mantle is likely to be in the 10 mole % range (Matas et al., 2007) but the partitioning of iron between Fp, Brg, and pPv is not fully constrained (e.g., Piet et al., 2016). This chapter will focus on reviewing the current state of deformation experiments on the major lower mantle phases (Brg, Ca‐Pv, pPv, and Fp) with a discussion of the current knowledge of deformation mechanisms in these phases and the potential for interactions between phases when deformed in a polyphase rock.

2.2 BACKGROUND

      In high‐pressure laboratory experiments, minerals deform by several mechanisms. At high temperatures and low stress, crystals deform by motion of point defects through grains and/or along grain boundaries. These types of diffusion creep are typically referred to as Nabbaro‐Herring Creep (Herring, 1950; Nabarro, 1948) and Coble Creep (Coble, 1963), respectively. While there are some subtle rheological differences between flow dominated by each of these mechanisms, generally speaking, diffusion creep leads to a Newtonian rheology – that is, a linear stress–strain rate relationship. Strain rate ( in the diffusion creep regime is generally written in the following form:

      where α is a parameter that describes the contribution of grain boundary sliding, D is the diffusion coefficient, σ is stress, Ω is atomic volume, h is grain size, m is 2–3, R is the gas constant (8.314510 J/mol∙K), and T is temperature. Grain size dependence comes about because efficiency of diffusion is strongly dependent on length scale (D ≈ l²/t) and thus diffusion creep is efficient only over short lengths, i.e., small grain sizes. Diffusion coefficients have an Arrhenius type relationship with temperature (Arrhenius, 1889; van’t Hoff, 1884). The effect of pressure can also be included, leading to a temperature and pressure dependence of the diffusion coefficient, which is given by

      where D₀ is termed the frequency factor, E_a is activation energy and V_a is the activation volume (e.g., Poirier, 1985). Thus, high temperature increases the efficiency of diffusion creep while pressure lowers efficacy. Thus, viscosity of a mineral will generally decrease with temperature and increase with pressure.

      On the other end of the spectrum, at high stress and low temperatures, plasticity occurs by dislocation glide. Dislocations accommodate strain through the propagation of linear defects through a crystal. Dislocations occur on a slip system that is characterized by a plane (hkl) and a direction <uvw>. Shearing along the slip plane in the slip direction results in an offset in the crystal lattice thus accommodating shear strain. Resistance to glide is controlled by the Peierls stress (Nabarro, 1947; Peierls, 1940). For a monoatomic lattice, the Peierls stress (σ_p) is given by

where G is the shear modulus, w is a term that depends on the dislocation character (screw vs. edge), d_hkl is the lattice spacing of the glide plane and is the Burgers vector. The Burgers vector gives the magnitude and direction of lattice distortion resulting from a dislocation. A few general trends can be seen from this formulation. If G is large, then σ_p∝ elastic properties. Since G in minerals is strongly dependent on pressure, the strength of minerals, likewise, is strongly dependent on pressure. The term is sometimes used to predict which glide plane should be favored as a large d_hkl and short should result in a lower Peierls stress. However, caution should be used when applying this to minerals, as the above formulation is derived for a monoatomic lattice. Minerals, in contrast, have mixed bond strength and often do not follow this rule. Recent developments have allowed calculation of lattice friction for minerals over a wide range of conditions using the Peierls‐Nabarro model (e.g., Carrez et al., 2007a; Cordier & Goryaeva, 2018). Of particular importance, to the following discussion is that dislocation activity leads to grain rotation, which results in texture. Texture frequently leads to anisotropic bulk physical properties of polycrystals.

      At stress conditions, intermediate to dislocation glide and diffusion creep, deformation is dominated by dislocation creep, i.e., glide accommodated by climb via diffusion. When dislocation glide alone is active, dislocations can interact and encounter obstacles to dislocation motion, which results in hardening. When stresses are low (typically due to high temperature and/or slow strain rates), dislocations can climb (diffuse) out of plane to bypass obstacles. Depending on ease of climb, various forms of constitutive laws can be written (Weertman, 1970; Weertman & Weertman, 1975). These lead to a nonlinear stress–strain rate relationship where ∝σⁿ and n = 3–5. Notably, there is no grain size dependence.

      Frequently a general constitutive equation is used that can capture both diffusion and dislocation creep (Hirth & Kohlstedt, 2003):

      where A is an empirically determined pre‐exponential factor. For diffusion creep, n is 1 and m is 2–3, and for dislocation creep n is typically 3–5 and m = 0.

      While it is relatively straightforward to determine deformation mechanisms in the laboratory, it is much harder to determine operative mechanisms in the deep Earth. For crustal and upper mantle rocks, microstructural signatures of deformation can be observed and provide constraints on active deformation mechanisms (e.g., Knipe, 1989; Park & Jung, 2017; Passchier & Trouw, 2005). However, for the lower mantle natural samples of sufficient size to study and determine deformation mechanisms are not available, and deformation mechanisms must be inferred indirectly. Seismic observations are one of the few methods to image the Earth’s deep interior, and seismic anisotropy can provide clues to deformation mechanisms in the deep Earth. Seismic anisotropy is generally attributed to texture development due to plastic deformation by dislocation creep. It is generally assumed that if there is no anisotropy, diffusion creep is operative, as in most case diffusion creep does not induce texture. Conversely, the general assumption is that if seismic anisotropy is observed, dislocation creep is likely (see Karato (2010) for a discussion of potential deformation mechanism in the mantle).

      Note that a few cases have been observed where texture does develop in minerals deformed in diffusion creep, as defined by Newtonian rheology (n = 1). These are generally samples that have been deformed near the transition between diffusion creep and dislocation creep (e.g., Barreiro et al., 2007), unusual cases in the presence of fluid/melt (Bons & den Brok, 2000), or due to strongly anisotropic grain shapes (Miyazaki et al., 2013; Yoshizawa et al., 2004). One should also recognize