Mantle Convection and Surface Expressions. Группа авторов

by (100) planes at high angles to compression (Figure 2.5b, c). Polycrystal plasticity modeling showed that these texture could be explained by slip on {110}〈10〉 and (100) planes (Merkel et al., 2006, 2007). It is important to note that both Merkel et al. (2006) and Merkel et al. (2007) converted to the pPv phase directly from the enstatite phase, and no change in texture was observed upon further pressure increase. Subsequent studies on MgGeO₃ pPv in the DAC using axial diffraction geometry (Okada et al., 2010) and radial diffraction geometry (Miyagi et al., 2011) found that alignment of (100) planes at high angles to compression resulted from the phase transformation from an enstatite starting material (Figure 2.5d). Further compression showed that the initial (100) transformation texture shifted to (001) (Figure 2.5e) upon deformation consistent with dominant slip on (001)[100] (Table 1; Miyagi et al., 2011; Okada et al., 2010).

      Slip on (001) planes in the pPv structure is supported by several DAC experiments both at ambient conditions (Miyagi et al., 2010, 2011; Okada et al., 2010) and high temperature (Hirose et al., 2010; Wu et al., 2017). Miyagi et al. (2010) found in pPv synthesized from MgSiO₃ glass that an initial (001) texture was observed after conversion at 148 GPa. Upon compression to 185 GPa this texture doubled in strength, consistent with slip on the (001) plane (Table 2.1; Figure 2.5f). High‐temperature deformation experiments on MnGeO₃ pPv documented the development of a (001) texture during compression from 63 GPa to 105 GPa at 2000 K (Figure 2.5g; Hirose et al., 2010). Deformation textures consistent with (001) slip have also been documented in MgGeO₃ pPv (Figure 2.5e; Miyagi et al., 2011; Okada et al., 2010). More recently, Wu et al. (2017) observed in MgSiO₃ pPv a similar transformation texture to that of Merkel et al. (2007) (Figure 2.5h) followed by the development of a (001) texture during compression to 150 GPa at 2500 K (Figure 2.5i).

      Experimental deformation of MnGeO₃ pPv, MgGeO₃ pPv, and MgSiO₃ pPv are all consistent with slip on (001) (Table 2.1; Figure 2.5e, f, g, i). There is no clear experimental evidence to support deformation on (100) or {110}〈10〉. Textures previously attributed to slip on (100) and {110}〈10〉 have been shown to be due to the transformation from enstatite to pPv (Figure 2.5d, h). The evidence that slip on (010)[100] is the dominant system in CaIrO₃ is clearly robust based on the large number of independent and consistent experimental results (Hunt et al., 2016; Miyajima et al., 2006; Miyajima & Walte, 2009; Niwa et al., 2007; Walte et al., 2007, 2009; Yamazaki et al., 2006). CaIrO₃ pPv has very different structural parameters than MgSiO₃ pPv, in terms of bond lengths, bond angles, and octahedral distortions (Kubo et al., 2008). Raman spectroscopy measurements have also indicated that bonding in CaIrO₃ pPv is different from other pPv structured compounds (Hustoft et al., 2008). First‐principles computations find CaIrO₃ pPv to have elastic properties and an electronic structure that are inconsistent with MgSiO₃ pPv (Tsuchiya & Tsuchiya, 2007). Finally, first‐principles calculations based on the Peierls‐Nabarro model indicate that MgSiO₃, MgGeO₃, and CaIrO₃ exhibit considerable variations in dislocation mobilities (Metsue et al., 2009). Thus, it is perhaps unsurprising that CaIrO₃ pPv appears to be a poor analog for the deformation behavior of MgSiO₃ pPv. This is unfortunate, as CaIrO₃ pPv is the only pPv to be systematically studied at high temperature and varied strain rates.

2.5 POLYPHASE DEFORMATION

      Nearly all deformation experiments on lower mantle phases have been performed on single‐phase materials. Some notable exceptions are DAC texture measurements on Brg and Fp mixtures (Miyagi & Wenk, 2016; Wenk et al., 2004; Wenk, Lonardelli, et al., 2006), differential stress measurements on Brg and Fp mixtures using the DAC (Miyagi & Wenk, 2016), and high shear strain steady state deformation using the RDA (Girard et al., 2016).

      2.5.1 Stress and Strain Partitioning in Polyphase Aggregates

      Several challenges exist for studying deformation of polyphase aggregates. Of primary importance is understanding stress and strain or strain rate partitioning between phases. This can affect both the interpretation of stress levels measured in the individual phases as well as attempts to estimate the bulk mechanical properties of the aggregate. Based on observations of naturally deformed crustal rocks and analogs deformed in laboratory experiments, Handy (1990, 1994) outlined a method to place bounds on the mechanical properties of a two‐phase aggregate with non‐Newtonian rheology and a strength contrast. Others have also outlined methods to study two‐phase deformation either analytically (e.g., Takeda (1998) for Newtonian rheology) or numerically (e.g., Jessell et al., 2009; Takeda & Griera, 2006; Treagus, 2002; Tullis et al., 1991). However Handy’s phenomenological description remains a useful approach to addressing the problem of polyphase deformation. Handy’s description will be briefly summarized below.

In Handy’s formulation the strength of a two‐phase mixture depends not only on the rheological properties of the individual phases but also on the microstructure and phase proportions. In Handy’s formalism bounds can be place on the mechanical behavior of a two phase aggregate as the bulk properties lie between two end members. These end members are based on the degree of interconnectivity of the weaker or the stronger phase. If the weak phase is interconnected, the microstructure is termed an interconnected weak layer (IWL) (Figure 2.6a), and if the strong phase is connected, it is termed a load‐bearing framework (LBF) (Figure 2.6b).

In the case of an IWL microstructure, the aggregate approaches an iso‐stress state. That is to say that both phases experience similar stress levels but strain at very different rates. For a pure iso‐stress condition, the soft phase modulates the stress levels and strain is partitioned into the weak phase (Figure 2.6c). Thus, the bulk properties of the aggregate approach those of the softer phase. In cases where yield strength contrast is large, stress levels in the hard phase may be too low to result in yielding as stress levels in the strong phase are limited by yielding of the soft phase. Although IWL approaches that of an iso‐stress state, these are not identical and there are several important differences. For IWL deformation, if the aggregate is composed of small to moderate amounts of the weak phase and/or the strong phase has a significantly higher stress exponent than the weak phase, then the weak phase will deform at higher stresses and strain rates than the iso‐stress condition and the stronger phase will deform at lower stress and strain rate than the iso‐stress condition. However, if there are large proportions of the softer phase and/or the stress exponent of the harder phase is similar or smaller than the soft phase, then stress levels in the harder phase will exceed the soft phase.

Figure 2.6 Schematic of (a) interconnected