Mantle Convection and Surface Expressions. Группа авторов

can provide a more controlled compression than a membrane‐driven DAC (Evans et al., 2007; Jenei et al., 2019). The dynamic DAC has recently been combined with high‐resolution radiography to successfully measure small strains in an iron sample at high pressure (Hunt et al., 2018). Estimated total strains for compression in the DAC are ~0.3 (30%) and strain rates (albeit discontinuous) are on the order of 10⁻⁴s⁻¹ (Marquardt & Miyagi, 2015). Recently, rotational DACs have been developed that allow large shear strains to be imposed at pressures in excess of 100 GPa (Azuma et al., 2018; Nomura et al., 2017).

      Small sample sizes in the DAC further limit its capabilities as a deformation device. Sample sizes are quite small in the DAC, generally 0.03–0.05 mm thick at the start of an experiment and on the order of a few hundredths of a millimeter to a few tenths of a millimeter in diameter. This yields corresponding sample volumes of ~10⁻² mm³ to 10⁻⁵ mm³, but volumes become significantly reduced at high pressures. As a sufficient number of grains must be sampled to obtain statistically representative information, the upper limit of grain sizes feasible in the DAC is quite low. This makes studying the effect of changing grain size on rheology problematic in the DAC. One techniques that has been recently developed that somewhat alleviates this problem is the use of multigrain crystallography, which allows the use of coarse‐grained samples (Nisr et al., 2012). In spite of its many limitations, the DAC remains the only deformation device that can reach pressures covering the entire range of the lower mantle (Figure 2.1).

      2.3.2 Large‐Volume Deformation Devices

These devices cover a more limited pressure and temperature range than the DAC (Figure 2.1) but have the advantage of allowing larger volume samples (on the order of a few mm³), longer and more stable heating (via resistive heating), measurement of strain and strain rate, greater variation of grain size, and better control of the stress state (Karato & Weidner, 2008). The D−DIA is a six‐ram cubic type multianvil press. In this configuration, the top and bottom rams are differential, meaning that they can be moved independently of the other four rams (Y. Wang et al., 2003). This allows the user to advance all six rams simultaneously to increase pressure quasi‐hydrostatically. Additionally, by cycling the differential rams, the user can impose differential stress to shorten or lengthen the sample at a near fixed confining pressure. This allows better control of stress state and to some degree allows the user to decouple hydrostatic and deviatoric stresses. The D‐DIA generally operates up to ~10 GPa at 1600 K, but recent efforts using a D‐DIA with a multianvil 6‐6 assembly (a second stage of six anvils in a cubic geometry) has reached conditions as high as 20 GPa and 2000 K (Kawazoe et al., 2010). Tsujino et al. (2016) used a cubic press with a 6‐8 (a second stage of 8 anvils in octahedral geometry) assembly to deform a Brg sample to 25 GPa and 1873 K, by using pistons cut at 45° to induce shear strain. Another approach using the multianvil type apparatus that has proven successful is a 6–8 Kawai type multianvil assembly that has been modified with a pair of differential rams and is called the differential T‐CUP or DT‐CUP (Hunt et al., 2014). The 6‐8 multianvil design compresses an octahedral sample assembly and due to better support of the anvils can reach significantly higher pressures than a cubic (DIA) type press. Using a so‐called broken anvil design, the DT‐CUP has been used to successfully perform deformation experiments to 24 GPa and ~1800 K (Hunt & Dobson, 2017).

      The Rotational Drickamer Apparatus (RDA) is an opposed anvil device, where one anvil has the capability to rotate. Pressure and compressive stress are increased by advancing the anvils. When the desired pressure is reached, large shear strain can be induced by rotation of the anvil (Yamazaki & Karato, 2001a). The RDA can reach P‐T conditions of the upper lower mantle ~27 GPa at ~2100 K (Girard et al., 2016). The main advantages of the RDA are that it can reach higher pressures than other large‐volume techniques and can reach high shear strains. However, the RDA is limited to smaller samples than the above multianvil techniques and also has larger temperature and pressure gradients. Due to the fact that deformation is induced by rotation of the anvils, the RDA also has large strain gradients across the sample, though this is somewhat alleviated by using a doughnut‐shaped sample. Generally speaking, the large volume apparatuses are far superior to the DAC in terms of measuring rheological properties but lack the pressure range available in the DAC, and thus, currently these two types of techniques are complementary for understanding deformation of lower mantle phases.

      2.3.3 Texture and Strength Measurements in High‐Pressure Experiments

      For samples deformed in axial compression, lattice planes perpendicular to compression are more reduced in spacing relative to planes perpendicular to the radial direction (Singh, 1993; Singh et al., 1998). This is due to elastic strain imposed by the deformation device. If single crystal elastic properties are known, differential stress supported by the sample can be calculated from measured lattice strains (Singh, 1993; Singh et al., 1998). Stresses measured during these experiments can provide a lower bounds estimate for the flow strength of the material (Kavner & Duffy, 2001; Merkel et al., 2002). During plastic deformation, lattice strains may become systematically larger or smaller on various crystallographic planes, as stress is anisotropically relieved by dislocation motion. Frequently, in high‐pressure experiments, aggregate flow strength is taken to be an arithmetic mean of stresses calculated on the measured lattice plane. This method can be biased, depending on which lattices planes are measured. Lattice strain anisotropy does provide information on active deformation mechanisms and can be used to constrain slip system activities (Karato, 2009; Turner & Tomé, 1994). Texture development is an expression of plastic deformation and results from dislocation glide/creep and/or mechanical twinning. Texture is easily observed with radial x‐ray diffraction as systematic intensity variations along diffraction rings. By deconvoluting these intensity variations, textures can be measured in‐situ in DACs or large volume deformation devices (Wenk, Lonardelli, et al., 2006). For an example methodology of texture analysis from radial x‐ray diffraction the reader is referred to Wenk et al. (2014).

Deformation mechanisms can be inferred from high‐pressure experiments by forward modeling texture development and/or lattice strain evolution with polycrystal plasticity codes. Although full field methods such as finite elements (Castelnau et al., 2008) or Fast Fourier Transform methods (Kaercher et al., 2016) can be used to model deformation behavior, homogenization schemes such as the self‐consistent method are more common (Merkel et al., 2009; Wenk, Lonardelli, et al., 2006). This is due to the high degree of efficacy coupled with considerably reduced computational expense for self‐consistent methods. The most commonly used method is the Visco Plastic Self‐Consistent (VPSC) code (Lebensohn & Tomé, 1993), which simulates texture development as a function of slip system activities. The VPSC method has been further modified to account for the effects of recrystallization (e.g., Wenk et al., 1997). Although VPSC can account for large strains and rate sensitive deformation, it neglects elastic deformation. As such, it does not account for hydrostatic pressure and cannot be used to model lattice strains. On the other hand, the Elasto‐Plastic Self Consistent (EPSC) method (Turner & Tomé, 1994) can be used to model slip system activities as a function of lattice strain evolution. However, strictly speaking, the strain formulation used in EPSC is applicable to small strains and does not include rate‐sensitive deformation. Early implementations of EPSC did not account for texture development due to slip and twinning or grain shape evolution. The EPSC method has been extended to include grain reorientation and stress relaxation due to twinning (Clausen et al., 2008) and then further modified to approximately account for large strains, ridged body rotation, texture, and grain shape evolution (Neil et al., 2010). This version of EPSC has been used to model texture and lattice strain evolution in high‐pressure experiments (e.g., Li & Weidner, 2015; Merkel et al., 2012; Raterron et al., 2013). Most recently, a fully general, rate sensitive, large‐strain Elasto‐Visco Plastic Self‐Consistent (EVPSC) method was developed (H. Wang et al., 2010) and applied to high‐pressure deformation (F. Lin et al., 2017) to simultaneously model lattice strain and texture evolution. One advantage of EVPSC is that it can effectively simulate large strain texture and lattice strain development to provide