Texture Development and Slip Systems in Bridgmanite and Bridgmanite +

Phys Chem Minerals (2016) 43:597–613 DOI 10.1007/s00269-016-0820-y

ORIGINAL PAPER

Texture development and slip systems in bridgmanite and bridgmanite ferropericlase aggregates + L. Miyagi1 · H.‑R. Wenk2

Received: 26 January 2016 / Accepted: 16 May 2016 / Published online: 4 June 2016 © Springer-Verlag Berlin Heidelberg 2016

Abstract Bridgmanite (Mg,Fe)SiO3 and ferropericlase not result in a change in this texture type. However, at pres- (Mg,Fe)O are the most abundant phases in the lower man- sures >55 GPa a change in texture to a 100 maximum is tle and localized regions of the D″ layer just above the core observed, consistent with slip on the (100) plane. Ferroper- mantle boundary. Seismic anisotropy is observed near sub- iclase, when deformed with bridgmanite, does not develop duction zones at the top of the lower mantle and in the D″ a coherent texture. This is likely due to strain heterogeneity region. One source of anisotropy is dislocation glide and within the softer ferropericlase grains. Thus, it is plausible associated texture (crystallographic preferred orientation) that ferropericlase is not a significant source of anisotropy development. Thus, in order to interpret seismic anisotropy, in the lower mantle. it is important to understand texture development and slip system activities in bridgmanite and bridgmanite fer- Keywords Diamond anvil cell · Bridgmanite · + ropericlase aggregates. Here we report on in situ texture Ferropericlase · Deformation · Slip systems · Seismic development in bridgmanite and bridgmanite ferroperi- anisotropy + clase aggregates deformed in the diamond anvil cell up to 61 GPa. When bridgmanite is synthesized from enstatite, it exhibits a strong (4.2 m.r.d.) 001 transformation texture Introduction due to a structural relationship with the precursor enstatite phase. When bridgmanite ferropericlase are synthesized The Earth’s lower mantle is believed to be predominantly + from olivine or ringwoodite, bridgmanite exhibits a rela- of perovskite-structured (Mg,Fe)SiO3, bridgmanite and tively weak 100 transformation texture (1.2 and 1.6 m.r.d., (Mg,Fe)O ferropericlase, with bridgmanite compris- respectively). This is likely due to minimization of elastic ing ~80 % of the lower mantle by volume (Murakami strain energy as a result of Young’s modulus anisotropy. et al. 2007; Komabayashi et al. 2010; Wang et al. 2015). In bridgmanite, 001 deformation textures are observed at At conditions similar to those of the D″ layer, the region pressures <55 GPa. The 001 texture is likely due to slip just above the core mantle boundary, bridgmanite under- on (001) planes in the [100], [010] and 110 directions. goes a transformation to the post-perovskite (pPv) struc- Stress relaxation by laser annealing to 1500–1600 K does ture (Murakami et al. 2004; Oganov and Ono 2004; Shim et al. 2004). However, in localized regions of the D″ with higher temperature bridgmanite may be stable (Hernlund Electronic supplementary material The online version of this et al. 2005). In order to interpret seismic anisotropy in the article (doi:10.1007/s00269-016-0820-y) contains supplementary lower mantle and D″, it is vital to understand texture devel- material, which is available to authorized users. opment and slip system activity in bridgmanite and bridgmanite ferropericlase aggregates. * L. Miyagi + [email protected] Much of the lower mantle appears to be seismically isotropic (e.g., Chang et al. 2014), and it has been suggested 1 University of Utah, Salt Lake City, UT 84108, USA that deformation processes that do not generate anisotropy 2 University of California Berkeley, Berkeley, CA 94720, USA dominate in the lower mantle (e.g., Karato et al. 1995;

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Meade et al. 1995). Another study suggests that deforma- and tion of bridgmanite ferropericlase results in seismic ani- + 001 sotropies that are opposite for each phase, and average to a (a, b, c)  100 = (a, b, c) nearly isotropic aggregate (Wenk et al. 2006a). Anisotropy Pbnm Pnma  010 is observed in some regions at the top of the lower mantle and is attributed to deformation texturing of bridgmanite A few deformation studies exist on bridgmanite using or ferropericlase (e.g., Wookey et al. 2002). Additionally, the diamond anvil cell (DAC) (Meade and Jeanloz 1990; the D″ region is heterogeneous and exhibits strong seismic Meade et al. 1995; Merkel et al. 2003; Wenk et al. 2004, anisotropy (Vinnik et al. 1995; Cottaar and Romanowicz 2006b), a modified large volume press (LVP) assembly 2013; Chang et al. 2014; Lynner and Long 2014). (Chen et al. 2002; Cordier et al. 2004; Miyajima et al. Dislocation glide and the associated crystal rotations are 2009), and the rotational Drickamer apparatus (RDA) likely to be a major mechanism that generates anisotropy in (Girard et al. 2016). Early DAC deformation studies of the deep mantle. For bridgmanite, relatively little is known bridgmanite found no evidence for texture development about its deformation properties. Quantitative rheology in decompressed samples (Meade et al. 1995) or in in situ experiments are challenging to perform at conditions of measurements of samples deformed outside the bridg- the lower mantle (e.g., Girard et al. 2016), and bridgmanite manite stability field (Merkel et al. 2003). In contrast, is highly unstable upon quenching. Transmission electron Wenk et al. (2004) and Wenk et al. (2006b) reported sig- microscopy (TEM) to image dislocations and deformation nificant texture development in bridgmanite and bridg- microstructures is difficult for bridgmanite, and only a few manite ferropericlase aggregates synthesized in situ + studies have been successful (Wang et al. 1990, 1992; Mar- in the DAC from different starting materials. Different tinez et al. 1997; Miyajima et al. 2009). textures were observed, depending on starting material, Since high-pressure experiments required to study bridg- and it was suggested that textures could be explained by manite are difficult, the study of analogs materials has been slip on (010)[100], (100)[010] and (001) 110. Twinning conducted, in hopes of establishing systematic deformation on (110) may be active as well (Wenk et al. 2004). Chen behavior for perovskites as a group (for reviews, see, e.g., et al. (2002) performed in situ stress relaxation measure- Cordier 2002; Walte et al. 2007; Wang et al. 2013). Perovs- ments at 20 GPa and 1073 K using the LVP and also found kites have a wide range of chemical compositions and struc- evidence for activity of (110) twinning. Additionally, TEM ture types (e.g., Navrotsky and Weidner 1989), and there is studies of recovered samples from high-pressure experi- no clear systematic trend to creep behavior. Nonetheless, ments have documented reflection twins on (110) and (112) dislocations in many perovskites have been identified as (Wang et al. 1990, 1992; Martinez et al. 1997). Cordier having 100c and 110c (subscript used for the pseudo- et al. (2004) suggested (001)[100] and (001)[010] disloca- cubic reference frame) Burgers vectors. The pseudo-cubic tions based on X-ray line broadening analysis of samples lattice is commonly used to describe perovskite structures in recovered from a LVP deformation experiment at 25 GPa order to provide a unified reference frame to discuss perovs- and 1700 K. A TEM study by Miyajima et al. (2009) doc- kites of different symmetries. For slips system equivalencies umented 110 Burgers vectors. Girard et al. (2016) per- between cubic and orthorhombic perovskite structures, the formed high-pressure and high-temperature shear defor- reader is directed to figure 10 of Wang et al. (2013). Based mation on aggregates of bridgmanite and ferropericlase on ambient pressure deformation experiments on a range of at conditions equivalent to the top of the lower mantle. cubic, tetragonal and orthorhombic perovskites, it appears Deformation mechanisms were not reported; however, they that {110}c 110c slip is active at lower temperatures and found that ferropericlase is weaker than bridgmanite and slip on (001)c 100c is active at higher temperatures (e.g., that strain is preferentially partitioned into ferropericlase. Cordier 2002). Several recent studies have noted that defor- Slip systems in MgSiO3 perovskite have also been mation patterns of bridgmanite deviate from cubic symme- investigated numerically using the Peierls–Nabarro (PN) try (Wenk et al. 2004, 2006b; Ferré et al. 2007; Carrez et al. model and calculation of generalized stacking faults and 2007). For the purpose of the following discussion, we use the Peierls–Nabarro–Galerkin (PNG) model to evaluate the orthorhombic reference with the Pbnm space group for Peierls stresses (Ferré et al. 2007; Gouriet et al. 2014). bridgmanite. Bridgmanite is occasionally indexed using the These studies find that (010)[100] and (100)[010] should Pnma space group, and to convert between Pbnm and Pnma be the easiest slip systems. On the other hand, Mainprice the following transformation matrices can be used. et al. (2008) combined Peierls stresses calculated from the PN model with the viscoplastic self-consistent (VPSC) 010 code to model slip system activities. It was found that at (a, b, c)  001 = (a, b, c) Pnma Pbnm pressures <30 GPa (001) 110 slip is most active but at  100 higher pressures (100)[010] becomes increasingly active.

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Core structure and mobility of (010)[100] and (100)[010] diffraction geometry where the sample is irradiated with dislocation have been modeled with molecular dynam- X-rays perpendicular to the compression axis. Without a ics, and (100)[010] slip was found to be more mobile than viscous pressure medium, the diamonds impose both pres- (010)[100] between 30 and 50 GPa, but less mobile above sure and axial differential stress, inducing elastic and plas- 50 GPa (Hirel et al. 2014). Recently, Kraych et al. (2016) tic deformation. The radial diffraction geometry allows used molecular dynamics simulations to study kink pair in situ measurement of texture and lattice strain develop- nucleation along (010)[100] screw dislocations, and calcu- ment (Wenk et al. 2006b). lated a Peierls stress of 4.9 GPa at 30 GPa pressure. The first two experiment runs (Runs 1–2) were per- Many studies have been dedicated to slip systems in formed at beamline 16 ID-B of the HP-CAT sector of the ferropericlase and periclase. Room-temperature DAC Advanced Photon Source at Argonne National Labora- experiments on periclase (Merkel et al. 2002) and fer- tory, Argonne IL. In both of these runs, sample to detec- ropericlase (Tommaseo et al. 2006; Lin et al. 2009; Mar- tor distance and detector geometry were determined with quardt and Miyagi 2015) obtain textures best explained by a CeO2 standard. The X-ray wavelength was 0.3676 Å in slip on {110} 110 . Experiments on ferropericlase using Run 1 and 0.3680 in Run 2. Beam size in both runs was Å the Paterson and Griggs apparatuses find that at low pres- 10 10 μm. Diffraction images were collected using a × sures (300 MPa) and high temperature (up to 1400 K), 300 s exposure time. During data collection, samples were {001} 110 and possibly {111} 110 may also become oscillated 5° about an axis perpendicular to compression ± active (Stretton et al. 2001; Yamazaki and Karato 2002; in order to improve grains statistics. Heidelbach et al. 2003). Single-crystal deformation experi- In Run 1, the starting material was Bamble enstatite ments in the D-DIA up to 9 GPa and 1500 K recorded ~(Mg0.86Fe0.14)SiO3, and in Run 2 it was San Carlos oli- relative strengths of slip systems and found that at the vine ~(Mg0.87Fe0.13)2SiO4. Samples were compressed to conditions of the experiments {110} 110 slip is domi- ~29 (Run 1) and ~35 GPa (Run 2) and then converted to nant. However, based on the pressure dependence of slip bridgmanite and bridgmanite ferropericlase, respec- + system strengths a change to dominant {001} 110 slip at tively, using single-sided laser heating. In order to avoid ~23 GPa is expected (Girard et al. 2012). Theoretical cal- grain growth which would result in a spotty diffraction pat- culations also predict an inversion in slip system activities tern, heating was performed at the lowest temperature that between pressures of 40–60 GPa. At room temperature and the phase transformation could be induced. Laser heating pressures below 40 GPa, {110} 110 is favored but above temperatures were on the order of 1500–1600 K (ESM for 60 GPa {001} 110 becomes more active. At high tem- Appendix A). After laser heating, a radial diffraction pat- peratures, both slip systems may be active (Amodeo et al. tern was collected to confirm full conversion (Fig. 1a, d, g). 2012). Here we report on transformation and deformation After conversion, pressure was manually increased at textures and stress development during DAC deformation ambient temperature and in situ radial diffraction images experiments performed on bridgmanite synthesized from were recorded at each pressure step. Once pressures of enstatite and on two-phase mixtures of bridgmanite fer- ~44 (Run 1) and ~55 GPa (Run 2) were reached, the sam- + ropericlase synthesized from olivine and ringwoodite. ples were annealed by laser heating to ~1500–1600 K to relax stresses and to see whether texture changes occurred at high temperature. Diffraction patterns were recorded to Experimental technique observe changes in textures and lattice strains. After heating, pressure was increased again at room temperature to Finely ground polycrystalline samples were loaded into ~52 (Run 1) and ~65 GPa (Run 2) and diffraction images two-stage boron kapton gaskets (Merkel and Yagi 2005) were collected. with an 80-μm-diameter sample chamber. Samples were The third experiment run (Run 3) was performed at compressed with 300-μm-flat culet diamonds. A small beamline 12.2.2 of the Advanced Light Source at Law- Pt flake ~10 µm in diameter and 4 µm thick (Alfa Aesar rence Berkeley National Laboratory, Berkeley, CA. The 99.95 % purity) was placed near the side of the sample X-ray beam with a wavelength of 0.4959 Å was collimated chamber. This was used to locate the sample with X-ray to 10 10 μm. Calibration was performed with a LaB × 6 absorption scans and for online pressure calibration using standard. During data collection, X-ray exposure time was the third-order Birch–Murnaghan equation of state of 300 s and the sample was oscillated 5° around the com- ± Fei et al. (2007). After conversion bridgmanite or bridg- pression axis. manite ferropericlase, data were collected at the center Starting material in Run 3 was the same San Carlos + of the sample (away from the Pt flake to minimize the Pt olivine as in Run 2. The sample was compressed in the diffraction signal). Diffraction images were recorded on DAC using a gas membrane system specifically designed a MAR3450 image plate. Data were collected in radial for radial diffraction (Miyagi et al. 2008). At ~19 GPa, the

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Fig. 1 Unrolled diffraction images from Runs 1 (a–c), 2 (d–f) and are labeled as are all ferropericlase and platinum peaks. Pressures 3 (g–i). Images are shown in Q space vs azimuth (η). Compression shown are calculated from the platinum unit cell volume direction is indicated by black arrows. The major bridgmanite peaks sample was converted to ringwoodite by single-sided laser Scardi 1990) that records the average size of coherently heating. The sample was then deformed at room tempera- scattering domain within the sample. In general, crystal- ture to ~35 GPa and subsequently laser-heated to convert lite size is poorly constrained from diffraction data (Toby to bridgmanite ferropericlase. A laser heating procedure 2006) and is particularly problematic for spotty diffraction + similar to the first two runs was used, and temperature dur- images. As a result, crystallite sizes obtained in this study ing heating was on the order of 1500–1600 K. After con- likely have true errors that are considerably larger than the version to bridgmanite ferropericlase, pressure was standard deviations obtained from the Rietveld refinement. + incrementally increased at room temperature to ~52 GPa Samples deformed in axial compression show varia- and then decompressed to ~40 GPa while recording in situ tions in lattice spacings with respect to the compression radial diffraction images. direction. These are due to elastic strains imposed by the deformation device and are apparent in synchrotron radial diffraction images as sinusoidal variations in peak posi- Data analysis tions with azimuth (Fig. 1, A1). Azimuthal positions where peaks show high Q values (low d-spacings) correspond to Diffraction images were first processed using the program the compression direction. Plastic deformation by disloca- Fit2d (Hammersley et al. 1996). Images were integrated tion glide and/or mechanical twinning causes crystal rota- over 10° azimuthal arcs into 36 spectra (Fig. 1) and were tions which generate texture. Texture appears as systematic analyzed using the Rietveld method as implemented in the intensity variations along Debye rings (Fig. 1). By decon- software package MAUD (e.g., Lutterotti et al. 2014). For voluting this information, the orientation distribution (OD) these analyses, we follow the general procedure for pro- can be determined. cessing radial diffraction data as outlined in Wenk et al. For refinement of elastic lattice strains and calculation 1 (2014). A Q range of ~2.53–4.96 Å− was used for these of stresses, we use the moment pole stress model (Mat- analyses, where Q 2π/d-spacing (Fig. 1, A1). Back- thies and Humbert 1993) with the bulk path geometric = grounds were interpolated using fifteen points manually mean micromechanical model (Matthies et al. 2001). The selected at positions between diffraction peaks. Diffraction geometric mean lies between the Voigt and Reuss bounds. patterns were refined for lattice parameters, crystallite size, In DAC deformation experiments, the anvils impose both lattice strains and preferred orientation. Crystallite size was hydrostatic and deviatoric stresses on the sample. Accord- refined using an isotropic size-strain model (Lutterotti and ing to the geometry of axial compression, the stress tensor

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σij can be separated into hydrostatic σp and deviatoric stress 1 m.r.d. corresponds to a random distribution. In the case of Dij components such that bridgmanite, the crystal symmetry is orthorhombic (Pbnm) and only one quadrant of the inverse pole figure is needed σP 00 −t 30 0    �  to represent the OD. For cubic ferropericlase, a smaller σij = 0 σP 0 + 0 −t 30 = σP + Dij � cubic sector is used.  00σP   0 02t 3  � where t is the axial stress component and provides a lower bound estimate for the flow strength of the material (e.g., Results Singh 1993). For refinement, stresses were fixed such that σ σ and σ 2σ , where σ is the largest princi- Pressure and differential stress 11 = 22 33 = − 11 33 pal stress and is negative for compression, according to the conventions in MAUD. Pressure calculated from bridgmanite, ferropericlase and In order to calculate stresses from lattice strains, we Pt is reasonably consistent throughout the experimental use the equation of state for each phase (bridgmanite and runs (Table 1). In Runs 1 and 3, pressure from Pt is gener- ferropericlase) and use the calculated pressure to correct ally a few GPa higher than bridgmanite and ferropericlase single-crystal elastic constants to experimental pressures. (Table 1). Pressures calculated from bridgmanite and fer- The presence of Fe in these samples and the effects of Fe ropericlase are typically within ~1 GPa. Discrepancies in partitioning between bridgmanite and ferropericlase com- pressures calculated from the various phases may be due to plicates pressure calibration and the choice of elastic con- stress heterogeneity and pressure gradients within the cell stants for these phases (ESM for Appendix A). For Run or to incorrectly assumed Fe contents. Since the equation 1, we use the equation of state of bridgmanite with 15 % state of bridgmanite is only weakly dependent on Fe con- Fe substitution, and for Runs 2 and 3 we use the equation tent, pressures calculated from bridgmanite are likely more of state for iron free bridgmanite (Lundin et al. 2008). For robust than those calculated from ferropericlase. Pressures all three runs, the ab initio single-crystal elastic constants calculated from Pt are likely affected by stress gradients

of Wentzcovitch et al. (1998) for MgSiO3 were corrected due to the position of the Pt flake on the edge of the sample to experimental pressures and used to calculate stress in chamber. bridgmanite. For pressure calibration and single-crystal After conversion to bridgmanite or bridgmanite ferro- + elastic constants of ferropericlase, we use the high-spin periclase, variations in Q values relative to the compres-

equation of state and Cij for (Mg0.9,Fe0.1)O (Marquardt sion direction are small, indicating that stresses are low et al. 2009). It should be noted that the moment pole stress (Fig. 1a, d, g). However, in the sample converted from oli- model is purely elastic and does not account for the effects vine (Run 2) stresses immediately after conversion are rela- of plasticity. In the implementation in MAUD, it is more tively higher (Fig. 2d) than in the samples converted from heavily weighted to the lattice strains on the most intense enstatite (Run 1) (Fig. 2a) or from ringwoodite (Run 3) diffraction peaks and thus may over- or underestimate the (Fig. 1g). Upon compression, stresses increase, and the dif- actual value of t. fraction patterns become slightly smoother due to effective We use the tomographic E-WIMV algorithm for texture crystallite size reduction (Fig. 1b, e, h). Laser annealing refinement. E-WIMV is similar to the WIMV model (Mat- of samples in Runs 1 and 2 reduces stresses but does not thies and Vinel 1982) but allows for incomplete and arbi- result in spotty diffraction images, and thus grain growth trary pole figure coverage. We use an orientation distribu- and recrystallization are minimal (Fig. 1c, f). For Run 3 tion function (ODF) resolution of 15°. Textures were first where decompression data were collected, stresses relax refined without imposing symmetry. It was verified that during unloading (Fig. 1i). textures exhibit approximate axial symmetry about com- Stress levels in bridgmanite are quite similar in Runs pression and are well centered in the pole figure. Cylin- 1 and 2 for similar pressures (Fig. 2; Table 1). In both drical symmetry is then imposed about the compression runs, deviatoric stresses increase with increasing pressure, axis, consistent with the geometry of axial compression, ranging from 2 to 12 GPa, and exhibit a similar slope − − and the ODF was recalculated. The ODF from MAUD was (Fig. 2). Upon laser annealing at 1500–1600 K, stresses exported to Beartex (Wenk et al. 1998) and smoothed with relax to similar levels in both runs, although pressure is a 10° Gauss filter. significantly higher in Run 2 (Fig. 2). Further compression Textures generated during axial compression experi- results in increased deviatoric stresses (Fig. 2; Table 1). In ments can be compactly represented by an inverse pole fig- Run 2, stresses in ferropericlase also increase with increas- ure (IPF) which represents the orientation of the compres- ing pressure. Prior to annealing, stresses in ferropericlase sion axis relative to crystal coordinates. Pole densities are are ~20–30 % lower than those in bridgmanite (Fig. 2; given in multiples of random distribution (m.r.d.), where Table 1). After annealing, stresses in bridgmanite and

1 3 602 Phys Chem Minerals (2016) 43:597–613 Fp (m.r.d.) 1.4 1.3 1.2 1.1 – – 1.1 – – – 1.2 1.1 1.2 1.1 1.2 1.1 1.1 IPF max Br (m.r.d.) 2.3 1.6 1.6 1.7 4.0 4.2 1.7 3.4 3.5 3.5 1.6 1.2 1.8 1.4 1.7 1.7 1.7 Fp (GPa) − 2.09 (3) − 6.42 (3) − 3.10 (3) − 2.88 (3) – – − 5.83 (2) – – – − 1.77 (3) − 3.35 (2) − 6.01 (3) − 4.74 (2) − 7.30 (5) − 7.25 (3) − 8.67 (4) − 2.45 (2) − 7.40 (3) − 3.34 (2) − 3.12 (3) − 2.27 (2) − 1.91 (2) − 6.56 (2) − 5.0 (2) − 5.80 (2) − 9.85 (2) − 1.90 (4) − 4.41 (3) − 6.71 (2) − 6.03 (2) − 8.32 (5) − 9.53 (4) t Br (GPa) − 11.89 (5) Fp (%) 31 22 19 23 – – 31 – – – 20 27 16 29 15 33 31 69 78 81 77 69 80 73 84 71 85 67 69 Vol. fraction Vol. Br (%) 100 100 100 100 100 Fp (Å) – 247 (1) 434 (7) 491 (7) 350 (3) – 340 (2) – – – 351 (2) 476 (5) 442 (6) 501 (5) 598 (9) 408 (4) 248 (2) 358 (2) 314 (1) 303 (1) 307 (1) 313 (1) 365 (1) 377 (2) 411 (3) 272 (1) 317 (2) 269 (1) 355 (2) 240 (1) 352 (2) 252 (1) 326 (2) 221 (1) Crystallite size Br (Å) Fp a (Å) – 3.9255 (1) 3.9560 (1) 3.9888 (1) 3.9911 (1) – 3.8906 (1) – – – 4.0056 (1) 4.0084 (1) 3.9645 (1) 3.9952 (1) 3.9497 (2) 3.9622 (1) 3.9365 (1) Br (Pbnm) c (Å) 6.5871 (3) 6.5469 (3) 6.5715 (4) 6.6212 (4) 6.6244 (4) 6.6929 (3) 6.4963 (2) 6.5585 (2) 6.6401 (2) 6.5964 (4) 6.6389 (7) 6.6535 (3) 6.5794 (5) 6.6342 (3) 6.5618 (8) 6.5847 (4) 6.5533 (6) Br (Pbnm) b (Å) 4.7454 (2) 4.7039 (2) 4.7274 (3) 4.7579 (3) 4.7600 (4) 4.8052 (3) 4.6872 (2) 4.7255 (2) 4.7738 (2) 4.7463 (3) 4.7728 (6) 4.7819 (3) 4.7353 (4) 4.7692 (2) 4.7192 (6) 4.7400 (4) 4.7150 (5) Br (Pbnm) a (Å) 4.5579 (2) 4.5232 (2) 4.5492 (3) 4.5833 (3) 4.5849 (4) 4.6372 (2) 4.4804 (2) 4.5366 (2) 4.6041 (2) 4.5774 (3) 4.6023 (5) 4.5990 (2) 4.55778 (3) 4.5857 (2) 4.5483 (6) 4.5534 (3) 4.5296 (4) 3.7615 (3) 3.7496 (8) 3.7534 (1) 3.7825 (1) 3.7846 (1) 3.8084 (3) 3.7318 (14) 3.7426 (5) 3.7884 (6) 3.7596 (1) 3.7943 (1) 3.8012 (20) 3.7609 (1) 3.7926 (10) 3.7485 (1) 3.7693 (14) 3.7515 (8) Unit cell parameters Pt a (Å) – 55 47 39 39 Fp (GPa) – 65 – – 36 35 – 45 38 49 46 52 46 54 48 39 38 Br (GPa) 28 64 52 37 35 33 44 46 37 50 45 52 Experimental conditions, lattice parameters, microstructure parameters, stress and texture information from Rietveld refinement for Runs 1–3 information from Rietveld Experimental conditions, lattice parameters, microstructure stress and texture Pressure 48 53 51 40 39 Pt (GPa) 31 61 56 38 36 33 49 48 36 53 45 52 Measured during unloading After laser annealing to ~1500–1600 K a a b b b

1 Table refinement underestimate actual uncertainties, particularly for crystallite size. from Rietveld in parenthesis. Note that standard deviations refinement are given from Rietveld Standard deviations Br and Fp, respectively Bridgmanite and ferropericlase are abbreviated a b Run # 1 2 3 3 1 1 3 2 1 1 3 2 3 2 3 2 2

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ferropericlase are similar. Upon further compression, they increase at a comparable rate. At the highest pressures (~55 and ~65 GPa) of Run 2, it likely that the spin transition is occurring or has occurred in ferropericlase. As a result, we likely overestimate both pressures and stress in ferropericlase for these data points. For Run 3, stresses are lower than in Runs 1 or 2. Stresses in ferropericlase and bridgmanite are similar in magnitude, increasing during compression and decreasing during decompression (Fig. 2).

Textures

Before conversion to bridgmanite, enstatite has a strong maximum at 100 with a minimum at 001 (Fig. 3a, 29 GPa). This texture is consistent with deformation on Fig. 2 Axial stress component (t) versus pressure for Runs 1–3. Pres- sures are calculated from the unit cell volumes of bridgmanite and the (100)[001] slip system (e.g., Carter 1976). After trans- ferropericlase. Dashed lines show points where the sample is laser- formation from enstatite, bridgmanite exhibits a texture heated (~1500–1600 K) to allow relaxation of elastic stresses at high with a sharp maximum at 001 (Fig. 3a, 31 GPa). Dur- temperature. Dotted lines indicate decompression. Errors from Riet- ing compression, texture strength is reduced from 4.2. to veld refinement are smaller than the symbol size 3.5 m.r.d.. During annealing, texture strength increases to

Fig. 3 IPFs of starting materials, bridgmanite and ferropericlase for selected data points. Run 1 is shown in part a, and Run 2 is shown in part b (bridgmanite) and part c (ferropericlase). Run 3 is shown in part d (bridgmanite) and part e (ferropericlase). Pressures are calculated from the unit cell parameter of platinum. IPFs are shown in equal area upper hemisphere projections. Scale bar is given in m.r.d. where a value of 1 is random

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4.0 m.r.d. (Fig. 3a, 48 GPa). Further compression results yielding, consistent with the lack of significant texture evo- in a reduction in texture strength to 3.4 m.r.d. (Fig. 3a, lution upon compression. Run 1 does not exhibit a change 56 GPa, Table 1). in texture type, only changes in texture strength. It is likely In Run 2, prior to transformation to bridgmanite fer- that bridgmanite reaches its flow strength in this run, but + ropericlase, olivine has a minimum at 001 maxima, with deformation textures are obscured by the strong (4.2 m.r.d.) a girdle along the 100, 110, 010 periphery of the IPF transformation texture. In Run 2, bridgmanite exhibits clear (Fig. 3b). This pattern is similar to previous radial DAC texture evolution and we conclude that the highest stresses measurements on olivine and is consistent with low tem- obtained in this run are reflective of the flow strength. Sev- perature {0kl}[100] slip (Wenk et al. 2006b). For bridg- eral authors have also measured stresses in bridgmanite, manite transformed from olivine, IPFs show an initially dif- but results are difficult to compare. Compared to our result, fuse maximum spreading from 100 to 001, with minimum these studies were either performed at lower pressures at 010 (Fig. 3b, 33 GPa). Upon compression, bridgmanite (Chen et al. 2002; Merkel et al. 2003), a different technique develops a maximum at 001 (1.7 m.r.d., Fig. 3b, 52 GPa). was used to measure differential stress (Meade and Jeanloz Annealing at ~1500–1600 K results in the texture maxi- 1990), or experiments were performed at lower pressure, mum near 001 becoming stronger (2.3 m.r.d.) and slightly higher temperature and steady state (Girard et al. 2016). For offset toward 100 (Fig. 3b, 53 GPa). After laser annealing, Runs 1 and 2, differential stress measurements are lower further compression results in a change in texture type to than those of Chen et al. (2002) and Merkel et al. (2003), a 100 maximum (1.7 m.r.d., Fig. 3b, 61 GPa). Textures in which is not surprising as these studies were performed on bridgmanite synthesized from olivine are only about half pre-synthesized samples and deformation occurred entirely as strong as in Run 1 (2.3 vs. 4.2 m.r.d.) due to the strong or largely outside the stability field of bridgmanite. It is enstatite to bridgmanite transformation texture (Table 1). unclear how this may affect the strength of the material. IPFs for ferropericlase in Run 2 show that neither compres- In the current study, samples are synthesized at ~30 GPa, sion nor laser heating induces significant texturing in fer- and thus, stresses are initially low due to stress relaxation ropericlase (Fig. 3c). during laser heating and the phase transformation. Meade Before the transformation to bridgmanite ferroperi- and Jeanloz (1990) observed stresses in bridgmanite up to + clase, ringwoodite exhibits a maximum at 110 with a mini- ~60 GPa confining pressure using the pressure gradient mum at 111 (Fig. 5d). This is consistent with dominant method. They found that deviatoric stresses reached a max- {111} 110 slip, as identified from previous texture meas- imum value of ~7 GPa at 40 GPa and did not increase with urements on ringwoodite (e.g., Wenk et al. 2006a; Miyagi continued compression to 60 GPa. In Runs 1 and 2, stresses et al. 2014). The ringwoodite IPF also exhibits a smaller in bridgmanite are significantly higher (~10–12 GPa) prior maximum at 001 which could indicate some contribu- to annealing (Fig. 2; Table 1). Stresses measured at the low- tion of {110} 110 slip (Merkel et al. 2002). Bridgmanite est pressures in our experiments ( 1.9 to 4.4 GPa, Fig. 2. − − transformed from ringwoodite exhibits a weak transforma- Table 1) are qualitatively similar to the work of Girard et al. tion texture comparable to Run 2 (Fig. 3d, 36 GPa). With (2016) which measured shear stresses up to ~6 GPa. increased pressure, there is little texture change in bridg- In Run 2, prior to annealing, the lower stresses in ferro- manite (Fig. 5c, 53 GPa). During decompression, bridg- periclase indicate that ferropericlase is significantly weaker manite develops a maximum near 001 (1.7 m.r.d., Fig. 3d, than bridgmanite under these conditions. During cold com- 39 GPa, Table 1). Also in this experiment, ferropericlase pression in Run 2, the strength contrast between bridgman- remains essentially random (Fig. 3e) Textures in bridg- ite and ferropericlase ranges from 1.3 to 1.4, but decreases manite synthesized from ringwoodite, like in Run 2, are to 1.2 during annealing. This is a smaller strength contrast only about half as strong as in Run 1 (1.8 vs. 4.2 m.r.d.) than the factor of 4 observed by Girard et al. (2016) and

(Table 1). the factor of 2 observed by Wang et al. (2013) in CaGeO3 perovskite MgO aggregates. Stresses in ferropericlase + are similar to recent diamond anvil cell measurements of Discussion Marquardt and Miyagi (2015) and are larger than those measured by Lin et al. (2009). It is likely that ferropericlase Differential stress in Run 2, at least prior to annealing, has reached its flow strength even though we do not observe significant texture In Runs 1 and 2, stresses in bridgmanite are considerably evolution. In Run 3, stresses in ferropericlase are lower higher than in Run 3 (Fig. 2). It is likely that in Run 3 dif- than in Run 2 and are considerably lower than those of ferential stress was not high enough to reach bulk plastic Marquardt and Miyagi (2015).

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Textures in bridgmanite For synthesis from olivine and ringwoodite, a disso- ciation reaction occurs to form bridgmanite and ferro- Transformation textures periclase, and it is less likely that structural relationships control transformation textures. The Young’s modulus In Run 1, the IPFs before and after transformation show a of bridgmanite is strongly anisotropic with [100] ~20 % strong correlation between the enstatite (100) and bridg- softer than the [010] direction (Wentzcovitch et al. 1998). manite (001) poles. Other directions are less strongly cor- The low elastic strain configuration for bridgmanite is with related. In both of these structures, these lattice planes are the soft [100] direction in the direction of maximum stress 2 parallel to the layering of the Mg + cations (Fig. 4a, b). (Wenk et al. 2004), similar to observed transformation tex- Oxygen anions are only slightly reshuffled as Si–O coor- tures in Runs 1 and 3. Ferropericlase is random after the dination changes from tetrahedral to octahedral during phase transformation, but is nearly elastically isotropic at the phase transformation. This coordination change can ~30 GPa and 1500 K (Marquardt et al. 2009); thus, there be accomplished by chains of silicate tetrahedra bridging would be no preferred low elastic strain energy orientation. across the layering (along the c-axis) and also linking with It is possible that bridgmanite grains nucleate preferen- adjacent chains (along the b-axis). Thus, interstitial posi- tially during the phase transformation with the soft [100] 2 tions would only change slightly and Mg + cation layer- in the direction of highest stress, i.e., oriented growth in a ing would be largely preserved between the two structures stress field. Alternately, {110} twinning may occur during (Fig. 4c, d). In the Pbnm bridgmanite structure [100] and the transformation relieving stress and resulting in a 100 [010] directions are structurally quite similar (Fig. 4d) and texture (Wenk et al. 2004). {110} twins have been observed it is to be expected that there would not be a strong cor- in recovered samples (Wang et al. 1990, 1992; Martinez relation between enstatite [010] and [001] and bridgman- et al. 1997), and their twin wall morphology suggests stress ite [100] or [010] directions. It is possible that akimotoite relief during formation (Wang et al. 1990). Our results can- forms as a metastable phase during the transformation of not distinguish between these different mechanisms, and it enstatite to bridgmanite (Kuroda et al. 2000). We do not is possible that a combination of the two processes occurs. observe diffraction peaks consistent with the formation of akimotoite but cannot rule out that this may be an inter- Polycrystal plasticity modeling mediate structure during the phase transformation. Simi- lar transformation textures are also observed in MgGeO3 For simulations, we used the Los Alamos viscoplastic self- post-perovskite synthesized from an enstatite phase (e.g., consistent code (VPSC) version 6 (Lebensohn and Tomé Merkel et al. 2006; Okada et al. 2010; Miyagi et al. 2011). 1994). The development of textures depends on the starting Thus, it is not surprising that transformation textures would texture, deformation geometry, the relative activities of var- be generated during the transformation of enstatite to ious deformation modes (slip and twinning) and total strain. bridgmanite. Miyagi et al. (2011) showed that to interpret deformation

Fig. 4 Proposed structural relationship for the enstatite to bridgmanite transformation. Tetrahedra are SiO4 and octahedra are SiO6. The dark spheres are magnesium cations. a enstatite structure, b bridgmanite structure, c top view of the magnesium cations layers in the enstatite structure with the SiO4 tetrahedra hidden from view, d top view of the magnesium cation layering in the bridgmanite structure with SiO6 octahedra hidden from view

1 3 606 Phys Chem Minerals (2016) 43:597–613 textures in terms of slip system activity one must account systems (Fig. 6). This is due to the fact that the transfor- for transformation textures. We use the transformation tex- mation texture is weak; consequently, Run 2 provides tures obtained just after synthesis of bridgmanite as start- robust indicators of active deformation modes. For bridging points for our simulations. Transformation textures manite, dominant slip on (100) results in a 100 maximum for Runs 2 and 3 are quite similar, and thus, we only show (Fig. 6a–c) and dominant slip on (001) produces a maxi- simulations where the transformation textures from Run 1 mum at 001 (Fig. 6f–h, k, l). Slip on (010) produces dif- (Fig. 3a, 31 GPa) and Run 2 (Fig. 3b, 33 GPa) were used. fuse textures (Fig. 6c, d). Different slip directions in the Models were run for axial compression to 20 % strain as same slip plane only have a minor effect on the resulting polycrystal plasticity models for 20 % strain compare well texture. Allowing slip in more directions within a given slip to DAC experiments (Wenk et al. 2006b). plane results in stronger textures with a more concentrated As deformation proceeds, crystals deform and rotate to maximum (Fig. 6k, l). Twinning on {110} 110 depletes generate preferred orientation. Slip system and twin mode 010 orientations and generates a maximum at 100 (Fig. 6i). activities are determined by the orientation of slip planes {112} 111 twinning results in the depletion of 001 orien- and slip directions, their symmetric variants, and corre- tations in IPFs and forms a maximum near 010 (Fig. 6j). sponding critical resolved shear stresses (CRSS) (Table 2 Twinning textures are much stronger than experimental with starting texture transformed from enstatite and Table 3 textures and stronger than textures induced by dislocation with starting texture transformed from olivine). Applying glide only. Thus, twinning is unlikely to be significant in different CRSS values will favor one deformation mode these experiments. over another (Tables 2, 3) resulting in different textures The 001 maximum that develops during deformation (Figs. 5, 6). By determining which simulated texture most in Run 2 (Fig. 3b, 52 GPa) is consistent with models for closely matches experimental textures, deformation mecha- slip on (001) planes but allowing slip in several directions nisms that are active under the experimental conditions (Fig. 6k, l). After annealing in Run 2 (Fig. 5b, 53 GPa), can be inferred. In these models, we test (100)[010], (010) the maximum at 001 becomes stronger and slightly offset [100], (001)[100], (001) 110, (100) 011 and (010) 101 toward 100 but is still consistent with slip on (001) (Fig. 6). slip systems. {111} 101 slip is included to close the yield The increase in texture strength after laser annealing is surface but is assigned a high CRSS and thus is minimally likely due to increased strain under high temperature. In activated. We also include {110} 110 and {112} 111 Run 2, compression after laser heating results in the devel- twinning (Tables 2, 3; Fig. 5, 6). opment of a 100 maximum. This is most similar to slip on Models using the transformation texture in Run 1 at (100) in the [010], [001] or 011 directions (Fig. 6a–c). 20 % strain show little variation in texture type as all dis- {110} twinning can also produce a 100 maximum, but it play a maximum at 001 (Fig. 5, except j). The only excep- is unlikely to produce this texture change. {110} twinning tion is {112} twinning where a maximum near 010 is switches 010 orientations to 100, but once a 001 deforma- observed (Fig. 5j). (100)[001] and (100) 011 slip weaken tion texture has developed (Fig. 5b, 53 GPa) and there are texture strength (Fig. 5b, c) as does slip on (010) (Fig. 5d, few orientations at 010 to twin to 100. Orientations at 001 e). In Run 1, a reduction in texture strength during cold are largely unaffected because they are unfavorably orien- compression (Fig. 3a, Table 1) may indicate activation of tated. This is similar to the simulation shown in Fig. 5i. slip systems on planes other than (001). This sample has The transformation texture in Run 3 is very similar to a strong 001 texture after conversion, and most grains that of Run 2, and no reinterpretation of the conclusions are oriented with (001) at high angles to compression. As based on the models using the transformation texture the angle between stress and the slip plane normal or the from Run 2 is needed. During compression, bridgman- slip direction approaches 90°, the resolved shear stress on ite synthesized from ringwoodite shows little change in that slip system goes to 0, and thus, the slip system can- texture. However, upon decompression development of a not be active. It would not be surprising that slip systems 001 maximum is observed. This would be consistent with on planes other than (001) would be activated as the strong slip on (001) as observed in Run 2. Although the sample transformation texture will geometrically suppress slip is undergoing decompression, the deviatoric stress state is on (001). The strong transformation texture in Run 1 also still that of axial compression; thus, it is possible to develop makes it ambiguous to interpret slip systems, as favoring compression textures during decompression. This has also different slip systems has little effect other than strength- been observed in hcp Fe during decompression (Miyagi ening and weakening the 001 maximum. We can, however, et al. 2008). Flow strength and associated texture devel- rule out significant activity of {112} twinning. opment are likely time dependent. During decompression, VPSC models starting with the transformation texture there is a significant time lag (1–2 h) between reduction from Run 2 show significant variation depending on slip in gas membrane pressure and pressure decrease in the

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Table 2 CRSS and activities of slip systems and twin modes for VPSC models shown in Fig. 5a–l

Slip system Model a b c d e f g h i j k l

(100)[010] CRSS 1 4 3 3 3 3 3 3 3 3 3 4 Start activity 27 % 9 % 7 % 1 % 3 % 7 % 8 % 9 % 8 % 5 % 0 % 6 % End activity 23 % 10 % 7 % 1 % 4 % 7 % 8 % 8 % 8 % 23 % 7 % 6 % (100)[001] CRSS 4 1 2 2 3 1 3 3 3 3 3 3 Start activity 15 % 43 % 17 % 13 % 11 % 5 % 14 % 9 % 14 % 9 % 2 % 1 % End activity 17 % 46 % 19 % 13 % 10 % 5 % 16 % 9 % 19 % 4 % 2 % 1 % (100) 011 CRSS 6 4 2 3 3 3 5 5 4 4 4 4 Start activity 5 % 6 % 35 % 17 % 16 % 4 % 6 % 4 % 10 % 6 % 3 % 4 % End activity 6 % 7 % 37 % 16 % 15 % 4 % 6 % 4 % 13 % 8 % 3 % 4 % (010)[100] CRSS 3 5 5 1 3 3 3 3 3 3 3 4 Start activity 1 % 5 % 1 % 22 % 3 % 7 % 8 % 9 % 8 % 5 % 8 % 6 % End activity 1 % 5 % 1 % 23 % 4 % 7 % 8 % 8 % 8 % 23 % 7 % 6 % (010) 101 CRSS 6 6 5 5 1.5 4 4 4 4 4 4 4 Start activity 10 % 12 % 14 % 12 % 35 % 10 % 2 % 6 % 10 % 6 % 3 % 3 % End activity 9 % 10 % 12 % 12 % 37 % 10 % 2 % 6 % 8 % 15 % 3 % 3 % (001)[100] CRSS 4 3 3 3 3 0.5 3 3 3 3 1 1 Start activity 15 % 2 % 5 % 13 % 11 % 42 % 14 % 9 % 14 % 9 % 42 % 24 % End activity 17 % 2 % 6 % 13 % 10 % 40 % 16 % 9 % 19 % 4 % 43 % 25 % (001)[010] CRSS 6 5 5 5 2 3 0.5 3 3 3 1 1 Start activity 8 % 12 % 10 % 10 % 7 % 12 % 38 % 6 % 14 % 8 % 33 % 15 % End activity 8 % 10 % 9 % 10 % 7 % 14 % 31 % 6 % 9 % 14 % 33 % 14 % (001) 110 CRSS 6 6 6 6 3 3 3 2 4 4 5 1 Start activity 14 % 6 % 7 % 8 % 12 % 11 % 10 % 45 % 13 % 8 % 1 % 39 % End activity 14 % 5 % 6 % 8 % 12 % 12 % 12 % 45 % 13 % 8 % 1 % 39 % {111} 011 CRSS 30 30 30 30 30 30 30 30 30 30 30 30 Start activity 5 % 6 % 4 % 4 % 2 % 2 % 1 % 3 % 1 % 0 % 1 % 1 % End activity 6 % 4 % 4 % 3 % 1 % 2 % 2 % 4 % 3 % 2 % 2 % 3 % Twinning {110} 110 CRSS 25 25 25 25 25 25 25 25 1 25 25 25 Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 8 % 0 % 0 % 0 % End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % Twinning {112} 111 CRSS 25 25 25 25 25 25 25 25 25 2 25 25 Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 45 % 0 % 0 % End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %

The bridgmanite texture obtained after transformation from enstatite (Fig. 5a) is used as the starting point for these simulations. Activities are given for the start and end of the simulation

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Table 3 CRSS and activities of slip systems and twin modes for VPSC models shown in Fig. 6a–l

Slip system Model a b c d e f g h i j k l

(100)[010] CRSS 1 4 3 3 3 3 3 3 3 3 3 4 Start activity 37 % 14 % 11 % 1 % 6 % 11 % 12 % 14 % 10 % 10 % 11 % 9 % End activity 34 % 15 % 12 % 1 % 6 % 10 % 11 % 12 % 12 % 18 % 9 % 8 % (100)[001] CRSS 4 1 2 2 3 1 3 3 3 3 3 3 Start activity 12 % 36 % 12 % 11 % 9 % 5 % 11 % 7 % 10 % 10 % 1 % 1 % End activity 14 % 35 % 13 % 10 % 8 % 5 % 13 % 7 % 17 % 6 % 1 % 1 % (100) 011 CRSS 6 4 2 3 3 3 5 5 4 4 4 4 Start activity 4 % 8 % 38 % 14 % 16 % 6 % 6 % 4 % 9 % 9 % 4 % 5 % End activity 5 % 9 % 39 % 14 % 15 % 5 % 6 % 4 % 14 % 9 % 4 % 5 % (010)[100] CRSS 3 5 5 1 3 3 3 3 3 3 3 4 Start activity 1 % 7 % 2 % 33 % 6 % 11 % 12 % 14 % 10 % 10 % 11 % 9 % End activity 1 % 8 % 3 % 33 % 6 % 10 % 11 % 12 % 12 % 18 % 10 % 8 % (010) 101 CRSS 6 6 5 5 1.5 4 4 4 4 4 4 4 Start activity 10 % 13 % 15 % 12 % 40 % 11 % 2 % 7 % 10 % 9 % 4 % 5 % End activity 9 % 12 % 13 % 12 % 42 % 11 % 2 % 7 % 8 % 15 % 3 % 4 % (001)[100] CRSS 4 3 3 3 3 0.5 3 3 3 3 1 1 Start activity 12 % 1 % 4 % 11 % 9 % 36 % 11 % 7 % 10 % 10 % 35 % 20 % End activity 14 % 1 % 4 % 10 % 8 % 36 % 13 % 7 % 17 % 6 % 38 % 22 % (001)[010] CRSS 6 5 5 5 2 3 0.5 3 3 3 1 1 Start activity 8 % 11 % 10 % 9 % 6 % 11 % 36 % 6 % 11 % 11 % 32 % 15 % End activity 7 % 10 % 9 % 10 % 6 % 13 % 35 % 6 % 7 % 16 % 34 % 16 % (001) 110 CRSS 6 6 6 6 3 3 3 2 4 4 5 1 Start activity 13 % 6 % 6 % 7 % 10 % 10 % 8 % 40 % 10 % 10 % 1 % 35 % End activity 13 % 5 % 5 % 8 % 9 % 11 % 9 % 42 % 11 % 9 % 1 % 37 % {111} 011 CRSS 30 30 30 30 30 30 30 30 30 30 30 30 Start activity 3 % 3 % 3 % 2 % 1 % 1 % 1 % 2 % 0 % 0 % 1 % 1 % End 4 % 4 % 3 % 2 % 1 % 1 % 1 % 2 % 2 % 3 % 1 % 1 % Twinning {110} 110 CRSS 25 25 25 25 25 25 25 25 1 25 25 25 Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 20 % 0 % 0 % 0 % End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 1 % 0 % 0 % 0 % Twinning {112} 111 CRSS 25 25 25 25 25 25 25 25 25 2 25 25 Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 22 % 0 % 0 % End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %

The bridgmanite texture obtained after transformation from olivine (Fig. 5b) is used as the starting point for these simulations. Activities are given for the start and end of the simulation

1 3 Phys Chem Minerals (2016) 43:597–613 609

Fig. 5 VPSC results for models starting with the transformation texture obtained after conversion to bridgmanite from enstatite (Fig. 3a). The most active slip system in the simulation is indicated below the corresponding IPF. CRSS and slip and twin activities for these models are given in Table 2

Fig. 6 VPSC results for models starting with the transformation texture obtained after conversion to bridgmanite from olivine (Fig. 3b). The most active slip system in the simulation is indicated below the corresponding IPF. CRSS and slip and twin activities for these models are given in Table 3

sample. This lag on decompression could allow the sample It is interesting that in contrast to more recent results to creep and develop texture at lower stresses. It is likely (Cordier et al. 2004; Wenk et al. 2004; Wenk et al. 2006b; that texture does not evolve during compression in Run 3 Miyajima et al. 2009 and this work), two early DAC meas- because stresses were too low to induce plastic flow on the urements of bridgmanite found no evidence for texture timescale of the compression cycle. However, decompres- development (Meade et al. 1995; Merkel et al. 2003). In sion was slow enough to allow creep and texture evolution. these early measurements, the bulk of deformation was Time-dependent texture development has been observed attained below the bridgmanite stability field, and it is pos- when bridgmanite was allowed to sit for 24 h under stress sible that it is difficult to induce texture outside the stability at ambient temperature, resulting in increased texture field of bridgmanite or that plasticity is reduced at lower strength (Wenk et al. 2006b). pressures.

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Textures in ferropericlase Implications for the lower mantle

During deformation with bridgmanite, ferropericlase does Here we observe that at pressures <55 GPa and room tem- not develop a significant texture. This has been observed perature, (001) slip likely in the [100], [010] and 110 in previous experiments by Wenk et al. (2004). This is directions dominates. This is consistent with previous tex- somewhat surprising since ferropericlase is expected to ture measurements by Wenk et al. (2004) and Wenk et al. be the more ductile phase and should deform more easily (2006a) and is consistent with evidence for (001)[100] and (Marquardt and Miyagi 2015). In single-phase periclase (001)[010] by Cordier et al. (2004) and TEM observations as well as ferropericlase, strong texture development has of 110 Burgers vectors (Miyajima et al. 2009). Above been observed (e.g., Merkel et al. 2002; Lin et al. 2009). 55 GPa, it appears that a change in slip plane to (100) However, deviatoric stresses and texture evolution in poly- occurs, but the slip direction is ambiguous. This change in phase aggregates are likely to be influenced by the sample’s slip system has not been observed in previous experiments; microstructure and strength contrast between the phases however, these did not reach pressures as high as those (Wang et al. 2013). obtained in Run 2. Numerical modeling using first princi- If bridgmanite forms a loadbearing framework around the ples and the Peierls–Nabarro model suggests that at pres- softer ferropericlase, then the stronger bridgmanite will force sures <30 GPa slip on (001) 110 is dominant, but at higher the weaker ferropericlase to strain at the same rate as the pressures (100)[010] slip is more active in bridgmanite bridgmanite phase (Handy 1994). Thus, the weaker phase (Mainprice et al. 2008; Kraych et al. 2016). The results should exhibit lower stress levels than the stronger phase, of Run 2 support a change in dominant slip system but at provided plastic flow has occurred in the strong phase. higher pressures than predicted by the models. Lower stresses in the weaker phase are consistent with In general, perovskites exhibit dominant slip on {11 observations in Run 2. Alternately, if the softer ferropericlase 0}c 110c at lower temperatures and {001}c 100c slip at forms an interconnected weak layer microstructure, it will high temperatures (e.g., Cordier 2002; Wang et al. 2013, control the deformation properties of the aggregate (Handy Fig. 10). (001) 110 slip in the orthorhombic setting corre-

1994). In this scenario, strain partitions into the soft phase sponds to {001}c 100c in the pseudo-cubic setting, while and the weaker phase will modulate the stress levels in the (100)[010] corresponds to {110}c 110c. Notably in our harder bridgmanite phase. In either scenario, the weaker fer- experiments, bridgmanite shows no significant change in ropericlase should experience as much or more strain than texture type upon laser annealing (stress relaxation at high bridgmanite. Indeed in high shear strain deformation experi- temperature) up to 1500–1600 K, consistent with Cordier ments on bridgmanite ferropericlase aggregates, ferrop- et al. (2004) and Miyajima et al. (2009). If (001) 110 slip + ericlase deforms significantly more that bridgmanite (Girard is active at high temperature as suggested by high-tempera- et al. 2016). Since texture evolution is observed in bridgman- ture activity of {001}c 100c in perovskites as a group, then ite, the lack of texturing in ferropericlase is unlikely a result this is most likely the relevant slip system for the lower of low total strain. A more likely explanation is that the local mantle. This would, however, depend on the geotherm deformation field in the ferropericlase grains is heterogene- and the pressure–temperature field for activity of (100) ous. In D-DIA deformation experiments on NaMgF3 perovs- slip. One should also note that composition and strain rate kite halite (NaCl) aggregates, halite develops little texture, will likely play important roles in determining slip system + and polyphase plasticity modeling indicates that the lack of activities. texture development in halite is due to strain heterogeneity For single-phase periclase and ferropericlase, room- (Kaercher et al. submitted). temperature DAC experiments are consistent with slip on VPSC models (Figs. 5, 6) assume that each crystal {110} 110 (Merkel et al. 2002; Tommaseo et al. 2006; deforms homogeneously in a homogeneous medium, with- Lin et al. 2009; Marquardt and Miyagi 2015). However, out information about orientation or strength of neighbor- lower-pressure (300 MPa) and high-temperature (up to ing grains. While this provides a good approximation for 1400 K) experiments on ferropericlase indicate activa- single-phase aggregates, understanding polyphase plastic- tion of {001} 110 and possibly {111} 110 (Stretton et al. ity will require characterization of bulk textures as well as 2001; Yamazaki and Karato 2002; Heidelbach et al. 2003). microstructure, preferably by 3D tomography, local orien- More recently, theoretical calculations by (Amodeo et al. tation mapping and SEM and TEM microscopy. It is likely 2012) predict that at pressures below 40 GPa, {110} 110 that portions of grains near phase boundaries behave differ- is favored. At pressures above 60 GPa, {001} 110 becomes ently than regions in the interior. For plasticity modeling, more active. However, at high temperatures both slip sys- finite element methods (e.g., Dawson 2002) or fast Fourier tems may be active as they are in isostructural halite transform methods (Lebensohn et al. 2011) need to be con- (e.g., Carter and Heard 1970). Single-crystal deformation sidered to account for microstructure. experiments on periclase to 9 GPa and 1500 K also seem

1 3 Phys Chem Minerals (2016) 43:597–613 611 to indicate that at higher pressures (>23 GPa) {001} 110 this work were performed at the Advanced Light Source (ALS). The becomes more active. A recent room-temperature experi- ALS is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. mental study on ferropericlase may be consistent with a DE-AC02-05CH11231. COMPRES, the Consortium for Materials slip system change to {001} 110 at pressures >60 GPa Properties Research in Earth Sciences under NSF Cooperative Agree- but was not conclusive (Marquardt and Miyagi 2015). If ment EAR 01-35554 supported this project through funding crucial high pressure and temperature favor both {110} 110 and beamline equipment. LM acknowledges support from CDAC and 110 NSF (EAR-0337006). HRW acknowledges support from NSF (EAR- {001} , these may both be active in the lower mantle; 1343908, CSEDI 1067513). We acknowledge help from beamline sci- however, if the geotherm is relatively cold, {001} 110 may entists, particularly Y. Meng at APS and M. Kunz at ALS. be favored (Amodeo et al. 2012). On the other hand, based on this study as well as D-DIA deformation of two-phase analogs (Kaercher et al. in prep), ferropericlase deformed References with bridgmanite may not develop significant texture, and may be less important for seismic anisotropy in the lower Amodeo J, Carrez P, Cordier P (2012) Modeling the effect of pressure mantle. on the critical shear stress of MgO single crystals. Philos Mag 92:1523–1541. doi:10.1080/14786435.2011.652689 Carrez P, Ferré D, Cordier P (2007) Peierls-Nabarro model for dislocations in MgSiO3 post-perovskite calculated at Conclusions 120 GPa from first principles. Philos Mag 87:3229–3247. doi:10.1080/14786430701268914 Carter NL (1976) Steady state flow of rocks. 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