resolved shear stresses (CRSS) and to constrain secondary slip systems (F. Lin et al., 2017).
In self‐consistent codes, each grain is treated as an inclusion in an anisotropic, homogeneous medium that has the average properties of the polycrystal. In VPSC and EVPSC, rate sensitivity of slip systems is included as a power law behavior. As deformation proceeds, crystals deform and rotate to generate texture. The resulting texture depends on the active slip systems and deformation geometry. Slip system activity depends on the stress resolved onto the slip systems and the critical resolved shear stress (CRSS) needed to activate the slip system. Applying different CRSS values favors one slip system over others. Different dominant slip systems result in different texture types and different lattice strain anisotropies. By determining which simulated texture and lattice strain evolution most closely resembles experiments, deformation mechanism can be inferred.
2.3.4 A Note on Scaling Experiments to the Lower Mantle
Caution should be exercised when extrapolating laboratory results to the deep Earth. First and foremost, laboratory strain rates are many orders of magnitude faster than natural strain rates. Laboratory strain rates for deformation of lower mantle phases are typically on the order of 10−4 s−1 to 10−7 s−1. In contrast, strain rates in the Earth are likely on the order of 10−12 s−1 to 10−16 s−1. Given the large difference in the human time scale and geologic time this discrepancy cannot be addressed directly by laboratory studies and systematic trends from laboratory experiments must be extrapolated to conditions of the Earth. One potential pitfall with this is the underlying assumption that no unknown deformation mechanism exists that operates at mantle conditions but is not operative in the laboratory (Boioli et al., 2017). Unlike the crust and upper mantle, natural samples that can provide evidence of operative deformation mechanisms do not exist and thus one is left to use the best data from the laboratory and from theory.
Total strain achieved in experiments can also be quite different than those in nature. While some devices can achieve large strains, for example the RDA has been used to achieve shear strains of ~2 (200%) (Y. Xu et al., 2005) and the rotational DAC has been used to deform samples to shear strains of ~4 (400%) (Nomura et al., 2017), compression studies typically attain strains of ~0.3 strain (30%) (e.g., Marquardt & Miyagi, 2015; Y. Wang et al., 2003). In contrast, slabs subducted into the lowermost mantle likely experience much larger shear strains on the order of 6–10 (e.g., Allègre & Turcotte, 1986; Tommasi et al., 2018; Wenk et al., 2011).
High pressures and temperatures of the full range of the lower mantle are also difficult to achieve in deformation experiments, and, thus, deformation experiments have been limited to lower pressures and high temperatures or high pressures and low temperatures. Unfortunately, deformation mechanisms in lower mantle phases can change with temperature (e.g., Immoor et al., 2018) and also with pressure (Marquardt & Miyagi, 2015), and thus direct extrapolation of lower‐pressure, high‐temperature studies or high‐pressure, low‐temperature studies may not represent the behavior in the deep Earth. However, with appropriate caution, some constraints on the deformation mechanisms and general rheology of the lower mantle can be obtained.
2.4 DEFORMATION STUDIES OF LOWER MANTLE PHASES
Most deformation experiments have focused on slip systems and texture development in lower mantle phase (Immoor et al., 2018; Merkel et al., 2007; Miyagi et al., 2010; Miyagi & Wenk, 2016), and only a few experiments have studied rheological properties (e.g., Girard et al., 2016). This is largely due to experimental difficulties related to measurement of rheological properties under controlled strain rate conditions and also due to intense interest in the relationship between texture and anisotropy in the lower mantle. Texture measurements have largely been performed at uncontrolled strain rates and in most cases at room temperature in the DAC. In contrast, measurements of rheological properties require precise control of strain rates and temperature in order to access and characterize stress–strain rate relationships for various deformation regimes. Most deformation experiments have been performed in the dislocation glide regime or in dislocation creep regime with no experimental studies on diffusion creep at lower mantle pressures and temperatures. Typically, diffusion creep rheology has been estimated based on measured or calculated diffusion coefficients and estimates of mantle grain size combined with the diffusion creep equation (e.g., Ammann et al., 2010; Deng & Lee, 2017; Van Orman et al., 2003; J. Xu et al., 2011; Yamazaki et al., 2000; Yamazaki & Karato, 2001b). A few diffusion creep studies have been performed on lower mantle analog materials (Karato et al., 1995).
The following discussion primarily focuses on experimental studies that achieve pressures in excess of ~20 GPa. These measurements were performed either in the dislocation glide or in dislocation creep regime. In the following sections, I will first discuss studies on mineral strengths and then will discuss texture measurements and slip system activities.
2.4.1 Differential Stress Measurements in Lower Mantle Phases
Radial diffraction experiments can provide information on flow stress of materials. Lattice strains measured during deformation experiments can be used to calculate differential stresses supported by each lattice plane sampled by diffraction. If plastic flow has been achieved, then these stresses represent the flow strength of the material. Note that particularly in DAC experiments, the measured differential stress value is unlikely to correspond to the yield strength/stress at pressure as the material undergoes strain hardening. Thus, if plasticity has occurred, these values are representative of the flow strength as opposed to the yield strength. In some studies, it is not clear that flow stress has been achieved, and thus these measurements can only provide a lower bounds for the flow stress. If significant texture evolution is observed, then one may be able to assume that the flow stress has been reached. However, more sophisticated modeling using, for example, EPSC (Clausen et al., 2008; Neil et al., 2010; Turner & Tomé, 1994) or EVPSC (H. Wang et al., 2010), methods can provide a more robust estimate of the flow strength (Burnley & Zhang, 2008; L. Li et al., 2004; F. Lin et al., 2017; Merkel et al., 2009; Raterron et al., 2013).
Methodologies used to calculate stresses in these types of experiments can result in discrepancies between measurements. Calculation of stresses not only requires knowledge of the elastic properties of the materials but also the assumption of an appropriate micromechanical model. Generally, some sort of Reuss‐Voigt‐Hill approximation is used to calculate stress from individual lattice strains using the method outlined in Singh (1993) and Singh et al. (1998). Alternately, some studies have used the moment pole stress model (Matthies & Humbert, 1993) and the bulk path geometric mean (Matthies et al., 2001) to calculate stress. Generally, elastic properties calculated with a Reuss‐Voigt‐Hill average and the geometric mean are quite close (Mainprice et al., 2000). However, differences can arise between these methodologies because the moment pole stress model typically assigns a single stress value based only on elastic anisotropy. As this does not account for plastic anisotropy, this may result in systematic deviations from the true stress. On the other hand, using the method of Singh (1993) and Singh et al. (1998) allows one to calculate a stress on each plane. This is particularly useful where large plastic anisotropy is observed. However, one is still left with the problem of deciding the appropriate way to average stresses measured on individual planes to get a “bulk stress”. The general practice is to take a simple arithmetic mean of the measured lattice planes on all planes and use the deviation in the values to calculate an error on the measurement. Because limited diffraction planes are sampled in experiments, sampling bias may result in systematically over‐ or underestimating the bulk stress. Again, more sophisticated modeling using the EPSC method (Clausen et al., 2008; Neil et al., 2010; Turner & Tomé, 1994) or EVPSC method (H. Wang et al., 2010) can alleviate issues with sampling bias (e.g., Burnley & Kaboli, 2019; Burnley & Zhang, 2008; Li et al., 2004; Li & Weidner, 2015; F. Lin et al., 2017; Merkel et al., 2009, 2012; Raterron et al., 2013). Another issue with flow strength measurement in the DAC, which is exacerbated at high temperatures is that strain rates are typically unconstrained, which is problematic for minerals that are generally rate sensitive. In the