High-pressure, high-temperature deformation of CaGeO3 (perovskite)±MgO aggregates: Implications for multiphase rheology of the lower mantle



[1] Sintered polycrystalline “rocks” of two-phase aggregate CaGeO3 perovskite (GePv) + MgO and single-phase GePv were deformed at pressure, temperature, and strain rates of 4–10 GPa, 600–1200 K, and ∼1–3 × 10−5 s−1, respectively, with maximum bulk strains up to ∼20%. The as-synthesized two-phase aggregate, produced from the reaction CaMgGeO4 (olivine) → GePv+MgO (MgO occupying ∼28% in volume), possessed a load-bearing framework (LBF) texture indistinguishable from that of (Mg,Fe)2SiO4 → (Mg,Fe)SiO3 perovskite + (Mg,Fe)O reported in previous studies. Stress states of the two phases in the deforming aggregate were evaluated based on systematic distortion of lattice spacings over the entire 360° diffraction azimuth angle. Compared with the single-phase GePv sample, stresses of GePv in the two-phase composite were about 10–20% higher at similar strain and strain rates. Stresses of MgO are about a factor of ∼2 lower than GePv in the same two-phased rock. Volumetrically averaged bulk stresses in the two samples were therefore virtually identical. Texture analyses showed that both samples deformed by dislocation glide, with the dominant slip systems {1 0 0}<1 1 0> (in cubic setting) for both GePv and MgO. These results show that, at low bulk strains up to ∼20%, the two-phase aggregate remains a LBF fabric, with rheological properties of GePv controlling those of the bulk. These experimental findings are in quantitative agreement with previous numerical simulations. Implications of the results to the silicate counterparts and dynamics of the lower mantle are discussed.

1. Introduction

[2] As the largest rocky layer in the Earth, the lower mantle occupies more than 60% of the total volume and plays a critical role in controlling convective currents in our planet [e.g., Turcotte and Schubert, 2002]. Petrological and mineralogical mantle models suggest that the lower mantle is dominated by (Mg,Fe)SiO3 perovskite (SiPv; about 70–90% in volume fraction) and (Mg,Fe)O ferropericlase (Fp), with a few volume percent of CaSiO3 perovskite and perhaps even lesser amounts of silica and the Al-rich phase [Irifune and Tsuchiya, 2007]. Knowledge of rheological properties of the major constituent minerals and stress/strain partitioning among the phases during deformation is crucial in understanding dynamic processes of the deep Earth.

[3] There is a wealth of information on rheological properties of periclase, the magnesium end member of Fp. Low-pressure, high-temperature experiments show that MgO crystals possess a highly anisotropic yield surface, with yield stress along the [1 1 1] direction about two orders of magnitude greater than that of [1 0 0] [Hulse et al., 1963; Huther and Reppich, 1973]. Earlier studies on polycrystalline MgO [Copley, 1963; Paterson and Weaver, 1970; Auten and Radcliffe, 1976] provided flow laws to temperatures (T) well above 1500 K, but pressures (P) below 1 GPa. Subsequent high-P diffraction studies on MgO determined yield stresses at ambient T in the diamond anvil cell (DAC) based on lattice distortion [Kinsland and Bassett, 1977; Meade and Jeanloz, 1988; Merkel et al., 2002a] and at simultaneous high P and T in the multianvil press (MAP) using peak width as a proxy for stress [e.g., Weidner et al., 1994]. With the development of deformation DIA (D-DIA) [Wang et al., 2000, 2003a], quantitative stress-strain data emerged at P-T conditions corresponding to the upper mantle [Uchida et al., 2004; Li et al., 2004; Mei et al., 2008].

[4] Despite numerous technical breakthroughs in the past years, quantitative stress-strain relations in SiPv remain a major experimental challenge. To date, deformation studies on SiPv only reported strength data in static compression using the DAC and MAP [e.g., Meade and Jeanloz, 1990; Merkel et al., 2003; Chen et al., 2002] and dislocation microstructure [Cordier et al., 2004; Miyajima et al., 2009], without information on strain. Quantitative creep experiments have been limited to analog perovkites at low P [e.g., Beauchesne and Poirier, 1989; Li et al., 1996; Poirier et al., 1983; Wang et al., 1993, 1999].

[5] Knowledge of rheological behavior of individual constituents alone is insufficient to understand the multiphase nature of the lower mantle. Fundamental issues of stress-strain interaction among the major phases must be properly addressed. Karato [1981] argues that rheology of the lower mantle is dominated by the weaker phase, Fp, “unless the framework effects is important.” Beauchesne and Poirier [1989] claim that the volumetrically dominant, interconnected SiPv phase controls the rheological behavior of the bulk. In both of these “end-member” arguments, effects of deformation on texture development have been largely ignored.

[6] It is well known in structural geology that large strains modify fabric of rocks that contain minerals with strong strength contrast, affecting rheological properties of the bulk [e.g., Handy, 1994]. Bercovici and Ricard [2012] analyzed effects of multiphase interaction as a mechanism for generating plate tectonics. For the lower mantle, strength contrast between SiPv and Fp has been estimated [Yamazaki and Karato, 2001, 2002], the former being much stronger than the latter. For a deforming lower-mantle mineral assemblage, two end-member texture types may be defined (1) a load-bearing framework (LBF) fabric, where the stronger phase (SiPv) surrounds isolated pockets of the weaker phase (Fp), and (2) interconnected layers of the weaker phase (IWL) separating boudins and clasts of the stronger phase. Due to the development of shape preferred orientation (SPO), rheology of the lower mantle may be strain and texture dependent.

[7] If all the major phases in the lower mantle adopt fine-grained texture, then diffusion creep is likely to be the dominant mechanism [Karato and Li, 1992; Karato et al., 1995]. The presence of multiple phases (SiPv, Fp, etc.) hinders grain growth [Morizet et al., 2007; Yamazaki et al., 2009], making grain boundary sliding and rotation an important agent for flow [Karato et al., 1995], similar to the phenomenon of superplasticity in fine-grained ceramics. Materials deformed via such a mechanism are thought to retain the original random crystalline orientation, without the development of lattice preferred orientation (LPO) [e.g., Karato, 1993]. The absence of seismic anisotropy in most part of the lower mantle has been used to support this mechanism [Karato et al., 1995]. However, recent studies in ceramics and rocks show that significant LPO and SPO may still develop during superplastic deformation [e.g., Murty, 1965; Wang et al., 2008; Sundberg and Cooper, 2008], leading to a fabric transition.

[8] Here we examine rheological properties of a two-phase assembly consisting of CaGeO3 perovskite (GePv) and MgO. The samples, prepared following the breakdown reaction CaMgGeO4 (in the olivine structure) →GePv+MgO, possess a microstructure virtually indistinguishable from that of (Mg, Fe)2SiO4 → SiPv+Fp [cf. Yamazaki et al., 2009]. In addition, Table 1 compares selected key properties of the two systems, demonstrating GePv+MgO to be an excellent analog to SiPv+MgO. We conducted controlled high P-T deformation experiments on a GePv+MgO composite and a pure GePv polycrystalline “rock,” with bulk axial strains up to ∼20% and strain rates between 1 and 3 × 10−5 s−1. By analyzing stress distributions of the two phases in the composite, textural development with the responsible slip systems, and comparing the results with observed slip systems in SiPv as well as previous numerical simulations, we discuss implications for rheological properties of the lower mantle.

Table 1. A Comparison of Properties for GePv and SiPv in the Context of Two-Phase Aggregates Pv+MgO
 CaGeO3 (GePv) + MgOMgSiO3 (SiPv) + MgO
  1. a

    Susaki et al. [1985].

  2. b

    Irifune, Nishiyama et al. [1998].

  3. c

    Volume fractions are given corresponding to ambient conditions.

  4. d

    Wang, Weidner et al. [1996].

  5. e

    Ito and Matsui [1978].

  6. f

    Sasaki et al. [1983].

  7. g

    Ratios of elastic moduli are from previous measurements under ambient conditions.

  8. h

    Liu et al. [2008].

  9. i

    Murakami, Sinogeikin et al. [2007].

  10. j

    Strength contrast experimentally determined at high pressure and temperatures.

  11. k

    This study (GePv) and Weidner et al. [1994] (MgO).

  12. l

    Chen, Weidner et al. [2002] (SiPv) and Weidner et al. [1994].

Stability pressure, GPa∼>7a∼>22b
MgO volume fraction, %c28d33e
Pv space groupPbnmfPbnme
Bulk modulus ratio, K(Pv)/K(MgO)g1.25h1.66i
Shear modulus ratio, G(Pv)/G(MgO)g1.22h1.42i
Strength contrast, Pv/MgOj2–3k3–4l

2. Materials and Methods

2.1. Synthesis of Starting Materials

[9] Mixtures of CaCO3+GeO2 and CaCO3+ MgO+GeO2 were prepared at 1423 K and ambient pressure overnight for decarbonation. The resulting powders of CaGeO3 and CaMgGeO4 were ground, pelletized, and heated at 1393 K overnight again. Heating and cooling rates were both ∼6 K/min. End products were pure CaGeO3 in the wollastonite structure and CaMgGeO4 in the monticellite structure, as confirmed by microprobe analysis and X-ray diffraction.

[10] Both materials were treated in a Kawai-type multianvil apparatus at Geodynamics Research Center, Ehime University, Japan. CaGeO3 wollastonite was subjected to 10 GPa and 1400 K for 2 h, resulting in fully sintered polycrystalline rods 0.8 mm in diameter and 1.0 mm in length, consisting of pure GePv. CaMgGeO4 was treated at 12 GPa and 1574 K for 3 h to complete the breakdown reaction, forming GePv + MgO, in the form of fully sintered polycrystalline rods.

[11] Samples were analyzed using a Zeiss ULTRA™ 55 scanning electron microscope (SEM) at Institut de Minéralogie et de Physique des Milieux Condensés (IMPMC), Paris. Electron probe microanalyses (EPMA) were conducted with a Cameca SX-50 microprobe at Centre Camparis, Université Pierre et Marie Curie, Paris. Both types of samples contained phases that were stoichiometric in composition within detection errors. Average grain size for the pure GePv samples was about 3 µm, and that of GePv+MgO ∼2 µm. Figure 1 is an SEM micrograph showing grain size and phase distribution in the GePv+MgO samples, displaying striking similarity to that of SiPv+Fp [e.g., Yamazaki et al., 2009].

Figure 1.

Secondary electron/secondary ion (SESI) image of the GePv+MgO starting material. Brighter phase is GePv, darker gray is MgO. Note equant grain geometry for GePv and MgO, indicative of an equilibrium texture.

2.2. Deformation Experiments

[12] Deformation experiments were carried out in the deformation DIA (D-DIA) apparatus [Wang et al., 2003a] at the GSECARS beamline 13-BM-D of the Advanced Photon Source, Argonne National Laboratory. Monochromatic diffraction (wavelength ∼0.225 Å) was conducted using a Si(111) double-bounce monochromator, with a SMART-1500 area detector (1024 × 1024 pixels; ∼90 µm/pixel). Radiographic sample images were collected using a MicroMAX CCD camera with a YAG scintillator and an objective lens. Details of the D-DIA setup are described elsewhere [Wang et al., 2003b; Uchida et al., 2004].

[13] Anvils with truncated edge length of 3 mm were used for pressure and stress generation. The cell assembly was similar to that used in Nishiyama et al. [2005] and Uchida et al. [2004]. The 5-mm edge-length cubic pressure medium was mullite with x-ray windows made of amorphous boron powder and epoxy (BE; B to epoxy ratio 5:1 by weight). Each sample was carefully polished on both ends, which were parallel, and inserted in a graphite tube furnace inside the BE cube, lined with a sleeve made of hexagonal boron nitride (hBN). Two alumina pistons, both ends also polished, were placed just above and below the sample, with gold foils in between, serving as strain markers. Preformed gaskets, made of soft-fired pyrophyllite, were attached to the anvil flanks prior to loading the cell assembly. The gaskets in the X-ray path had 1.5 mm diameter BE inserts, to avoid gasket diffraction contamination. No thermocouples were used during deformation experiments; temperature was estimated based on consumed power, calibrated in separate experiments using identical cell assemblies with thermocouples. Temperature uncertainties were estimated to be ∼10%.

[14] Two of the six anvils closest to the area detector were made of sintered polycrystalline cubic boron nitride (cBN), the rest being tungsten carbide (WC). The X-ray transparent cBN anvils permitted observation of diffraction Debye rings over the entire 360° detector azimuth range, essential for accurate stress measurements. Incident X-rays were collimated to 0.1 × 0.1 mm by WC slits (10 mm thick). Detector orientation relative to the incident beam was calibrated using a diffraction standard (CeO2) and the detector-sample distance was determined by matching the observed ambient d-values of the sample inside the D-DIA to those reported for MgO and GePv [Sasaki et al., 1983]. Sample length was measured by radiography using a wide X-ray beam (2 × 3 mm cross section), by driving the WC slits out of the beam path.

[15] Details of deformation experiment are given by Wang et al. [2003b], Uchida et al. [2004], Nishiyama et al. [2007], and Hilairet et al. [2012]. We performed two experiments, one on pure GePv (D0748) and the other on GePv+MgO (D0754). In each run, five shortening-and-lengthening cycles were carried out at fixed main ram load of 55 t, by advancing and retracting the differential rams at various temperatures, at ram speeds of 0.03 mm/s and 0.08 mm/s, respectively. The data collection system was automated with sample length and stress measured repeatedly by radiographic imaging (Figures 2a and 2b) and diffraction (Figures 2c and 2d), respectively, throughout the deformation cycles.

Figure 2.

Examples of radiographs and diffraction patterns collected during high P-T deformation. (a) Initial sample image in run D0754. Two horizontal thin dark lines are shadows of Au foils. The sample (1 mm in height and slightly darker gray in between the Au foils) is surrounded by a BN sleeve (lighter in contrast). The circular feature is the BE rods (X-ray windows) viewed end-on. (b) Sample image at 9 GPa and 800 K during deformation (∼9% axial train). The WC anvils on the upstream side of the cell have closed in due to compression, resulting in a much narrower view of the sample assembly. Two horizontal anvils on the down-stream side were made of sintered diamond, permitting complete diffraction Debye rings to be recorded (for details, see Uchida et al. [2005]). (c) 2-D diffraction pattern of D0754 at ambient conditions. The Debye rings have been transformed into straight lines to show that there is no lattice distortion. (d) Integrated intensity versus 2θ profile from (c). Peaks are labeled. Cubic indexing is used for GePv. MgO reflections 200 and 200 are weak but well resolved. (e) The same sample deformed at 9 GPa and 800 K to ∼11% bulk strain (image shown in Figure 2b). Lattice distortion (sinusoidal modulation in the diffraction lines) is apparent.

[16] Although known to have the orthorhombic symmetry (space group Pbnm) same as that of SiPv [Sasaki et al., 1983], powder diffraction patterns of GePv closely resemble that of a cubic perovskite (Figures 2c and 2d). No splitting of any diffraction peaks could be resolved (Figure 2d). Therefore, we treated GePv as pseudocubic throughout the paper. The relationship between the Pbnm (hereafter denoted by subscript orth) and Pm3m (either no subscript or pc in some cases to avoid ambiguity) crystal lattices can be found in Cordier et al. [2004], Sasaki et al. [1983], and Wang et al. [1990]. For MgO, due to its small volume fraction and low scattering power, diffraction intensities were much weaker than that of GePv (Figures 2c–2e). Figure 2d shows the integrated intensity versus 2θ plot for sample D0754, at ambient conditions (data from Figure 2c). A collection time of 300–400 s was required to ensure reliable diffraction intensities for MgO. Figure 2e is an unrolled “cake” pattern collected at ∼9 GPa, 800 K, and ∼11% bulk axial shortening (corresponding to sample image in Figure 2b). The modulation in the diffraction lines is apparent. This modulation, termed lattice distortion (or “lattice strain”), is a proxy for the differential stress in the polycrystalline sample, as described later.

[17] Figure 3a shows four of the heating and cooling cycles in D0754 (GePv+MgO). The P-T path for the pure GePv experiment (D0748) was similar, except for the fourth cycle, where temperature was ramped to 1000 K again to examine data reproducibility, instead of 1200 K as in D0754. About 250 diffraction-image pairs were collected in each experiment. There was notable pressure loss during temperature ramping, largely due to softening of the pressure media and diminishment of the differential stress (Figure 3a). The turn-over in P at room T (Figure 3a) was due to the reversal of differential rams from retraction (sample lengthening) to advancement (shortening). This procedure was adapted in order to restore the sample length, so that high-T deformation could be conducted repeatedly at compressive bulk strains between 0 and ∼15%, or until apparent steady state deformation was reached. This was also necessary to maintain sufficiently high confining pressures for GePv to be stable during most of the high-T deformation segments. Even with these precautions, the 1200 K segments still fell at pressure conditions outside of the GePv stability field [Susaki et al., 1985]. Nevertheless, GePv remained metastable because of the relatively low temperature, as indicated by refinement results from the diffraction patterns taken during and after the high-T deformation segment. In the fifth cycle (also at 1200 K, not shown in Figure 3), weak additional diffraction peaks appeared gradually, suggesting that GePv partially converted into the garnet structure. Because of this, data from the last cycle are not presented. The back transformation also altered microstructure of the samples, so that no final microstructure data were obtained.

Figure 3.

(a) Pressure (solid circles) and temperature (solid lines) history for D0854. Horizontal axis is file ID number of the stress and strain data collected at the corresponding P-T conditions, corresponding to an experimental duration of ∼50 h. All data were collected at a fixed main ram load of 55 t. Pressures increased (decreased) gradually as the differential rams were advanced (retracted). Also note significant pressure gain (loss) as temperature was decreased (increased) rapidly. Pressure errors are smaller than the size of the symbols. (b) Lattice distortion Q(h k l) for GePv and MgO, as defined in equation (1), as a function of data ID. Positive Q values correspond to differential stresses that shorten the sample.

2.3. Lattice Strain Analysis

[18] Method of lattice distortion analysis is similar to that described by Hilairet et al. [2012] and Nishiyama et al. [2005, 2007]. We used the software package Multifit, developed by S. Merkel, for data processing (http://merkel.zoneo.net/Multifit/). The lattice strain εL(h k l), representing the change of Bragg reflection h k l relative to its hydrostatic state, was determined based on Debye ring distortion in 2-D diffraction patterns [e.g., Wang and Hilairet, 2010; Hilairet et al., 2012]:

display math(1)

where ϕ is the true azimuth angle, relating to the diffraction angle θ and detector azimuth χ by inline image; inline image and inline image are d-spacings at azimuth angle ϕ under ambient and high P-T conditions, respectively. We divided the 360° azimuth angle into 72 equal segments and integrated intensities of diffraction peaks over each 5° interval, to obtain a series of intensity versus 2θ powder patterns. These patterns had sufficient signal-to-noise ratios for accurate lattice strain determination using equation (1).

2.4. Differential Stress Analysis

[19] The stress field generated by the D-DIA is well represented by three principle stress components σ1, σ2, and σ3, with σ1 parallel to the differential rams vertically and σ2 = σ3 horizontally. We calculated differential stresses (Δσ = σ1 − σ3) using the following equation [Singh, 1993] relating Δσ, (cubic) single-crystal elastic compliances (Sij), and differential lattice strain Q(h k l):

display math(2)


display math


display math

[20] Since Δσ(h k l) is linearly proportional to Q(h k l), it is often sufficient to examine the behavior of Q(h k l) in single-phase materials. For multiphase composites, it is necessary to convert lattice strain to stress using equation (2) for evaluation of stress partition.

[21] For MgO, elastic constants and their P and T dependence are available [Sinogeikin and Bass, 1999; Sinogeikin et al., 2004] (Table 2). There are no experimentally measured single-crystal elastic constants for GePv. We conducted first-principles calculations based on the density function theory (DFT) to obtain GePv elasticity at high P. Details of the calculations are given in supporting information1 . Results were converted to elastic compliances (Sij) and rotated with respect to the cubic setting to obtain cubic compliances and their pressure derivatives (Table 2). These first-principle calculations were limited to 0 K. Therefore, in converting lattice strain to stress, we ignored T dependence for both GePv and MgO. As our main goal is to examine the relative behavior of pure GePv versus the GePv+MgO composite, ignoring temperature effects on stress calculation only affects the absolute values of apparent stresses. It is unlikely that T dependences in GePv and MgO are drastically different. For each phase, the average differential stress Δσ is taken to be the mean of all available Δσ(h k l).

Table 2. Elastic Compliances (in 10−3 GPa−1) and Their Pressure Derivatives (in 10−5 GPa−2) of GePv (in the Cubic Setting, Fits to data in Table S1 up to 30 GPa) and MgO [From Sinogeikin and Bass, 1999].

2.5. Pressure Determination

[22] Hydrostatic components of the lattice strain correspond to the d-spacings dP(h k l) observed at the “magic” angle ϕ = 54.7° [Singh, 1993]. Unit cell volumes based on the hydrostatic d-spacing were refined based on four to six crystallographic planes for GePv and two planes for MgO. Pressures, P = (σ1+2σ3)/3, were then calculated following the thermal-pressure equations of state for GePv and MgO by Liu et al. [2008] and Speziale et al. [2001], respectively. Pressures determined from the two equations of state were in general agreement. In traditional gas medium “tri-axial” deformation, it is more customary to discuss “confining pressure,” Pc, versus differential stress Δσ. In this case, Pc = σ3 = P − Δσ.

2.6. Bulk Strain Measurement

[23] We determined total sample axial strains (i.e., bulk strains, ε) by measuring sample length from radiographs (e.g., Figures 2a and 2b), based on ε = (l0 − l)/l0, where l is the sample length measured during deformation and length l0 is a reference length. Average bulk strain rate inline image was calculated based on the bulk strain measurements as a function of time. The technique is described by Wang et al. [2010] and Hilairet et al. [2012].

2.7. Texture Analysis

[24] Selected diffraction patterns were analyzed for texture development. We used the software package MAUD [Lutterotti et al., 2007] and followed a procedure similar to that described by Miyagi et al. [2006]. Popa line broadening and isotropic crystallite functions were adopted for crystallite size (i.e., size of coherent crystal domains such as grains, subgrains, and dislocation cells) and microstrain refinement. Thermal vibrations were refined in all cases. The thermal parameters were stable over the refinement and improved goodness of fit, but did not change the overall characteristics of the texture. Texture was refined with the E-WIMV algorithm, a modification of WIMV [Matthies and Vinel, 1982]. In the case of axial symmetric compression, textures can be represented by an inverse pole figure (IPF) displaying crystallographic directions of crystallites within the sample relative to the compression direction (parallel to σ1). Pole densities are expressed in terms of multiples of random distribution (mrd). For a random polycrystal, all orientations have an equal density of 1 mrd. In a single crystal, m.r.d. is infinity for one orientation and 0 for all others. For cubic materials, only one eighth of the IPF is needed to fully represent the orientation distribution function (ODF). Again, we treated GePv as pseudocubic and used a 15° grid for the ODF. Initially, no ODF geometry was assumed in order to check whether a pseudoaxial symmetry was indeed observed on the experimental and reconstructed pole figures [e.g., Miyagi et al., 2006, 2009]. This having been confirmed, the ODF was reset and axial symmetric ODF geometry was imposed to the final fits [Miyagi et al., 2006].

3. Results

3.1. Stress-Strain Curves in the Two-Phase Composite (D0754)

[25] Figure 3b summarizes lattice distortion Q(h k l) for both GePv and MgO, respectively, using data file ID as a proxy for time (intervals between adjacent files ∼8 min). The four shortening segments (where Q ≥ 0), conducted at 1000, 800, 600, and 1200 K, are shown in areas labeled a, b, c, and d, respectively. The corresponding strain rates at greater than ∼6% bulk strain are 1.68(5), 1.26(5), 1.73(5), and 2.11(10) × 10−5 s−1, respectively.

[26] Figure 4 plots Q(h k l)'s for both GePv (4a) and MgO (4b) against sample bulk strain. These “stresses” [as represented by lattice distortions, Q(h k l)] versus strain hysteresis loops clearly show that even at room T (segments with Q values generally negative), the sample was deformed mainly by crystal plasticity, based on the following observations: (1) For GePv, room-T Q(1 0 0) and Q(2 0 0) values exhibit progressively deeper minima after the high-T deformation segments a, b, and c, while other Q(h k l)'s show progressively shallower minima (Figures 3b and 4a). (2) For MgO, the (2 0 0) plane yields much earlier during room-T elongation (lines without symbols in Figure 4b) and, as deformation is reverted to shortening, Q(2 0 0) increases much faster than Q(2 2 0), so that at some point Q(2 0 0) and Q(2 2 0) have opposite signs, indicating significant internal stress. This general behavior, known as the Bauschinger effect, is a strong indication that the sample deforms plastically, rather than by cataclasis. Note also that although P varies significantly during room-T deformation (Figure 3a), confining pressure remains more or less constant at about 8(1) GPa, roughly twice the magnitude of Δσ|. Under such high confinement, brittle fracture should be inhibited [Paterson and Wong, 2005]. At high T, intracrystalline plasticity should dominate the deformation process. Indeed, texture development with responses to reversible stress conditions (presented later) indicates that high-T deformation is dominated by dislocation plasticity.

Figure 4.

Hysteresis loops during deformation of GePv+MgO. Here, differential stresses are represented by lattice distortions Q(h k l) for (a) GePv and(b) MgO, which are plotted against bulk axial strain of the sample. Zero axial strain is referenced to the initial sample length. High-temperature data are shown with symbols [GePv: circles—1 0 0), triangles—(1 1 0), squares—(2 1 0); MgO: circles—(1 0 0), triangles—(1 1 0)]. Solid symbols correspond to 1000 and 800 K deformation, open symbols 600 K. All room temperature data are presented by lines without symbols. Note significant divergence between the MgO (1 0 0) and (1 1 0) lattice distortions as bulk strain changes, at room temperature, from decreasing (elongation) to increasing (shortening) between 2 and 5%. Also note the divergence with increasing strain at high temperatures.

[27] For GePv, all Q(h k l)'s increase monotonically during deformation at 1000 K (area a of Figure 3b), indicative of strain hardening, until about 10% strain. Q(1 1 0) and Q(2 1 0) exhibit similar variation with increasing bulk strain, both with magnitudes lower than Q(h 0 0) (h = 1, 2). At 800 K (area b), Q(1 1 0) and Q(2 1 0) also increase monotonically; at the end of the segment their magnitudes are comparable to, or slightly greater than, Q(h 0 0), which has reached saturation. The 600 K segment (area c) shows similar behavior to that at 800 K. At 1200 K (area d), all four reflections show virtually identical distortion and reach saturation at about 8% bulk strain.

[28] For MgO, only two reflections (2 0 0) and (2 2 0) are consistently resolved throughout the deformation history (Figure 3c). Both show lower magnitudes in lattice distortion than GePv. At 1000 and 1200 K, magnitudes of Q(2 0 0) and Q(2 2 0) are similar. At 800 and 600 K, Q(2 2 0) displays an unusual “weakening” behavior with increasing bulk strain.

[29] Figure 5 plots differential stresses of various crystallographic lattice planes in GePv and MgO as a function of bulk strain for the four shortening segments, based on equation (2), with compressive stress treated as positive. For bulk strain calculations, the reference sample length l0 is chosen at the point where the arithmetic average of the four GePv lattice strains [(1 0 0), (1 1 0), (2 0 0), and (2 1 0)] reach zero in each deformation segment. Average pressures for the 1000, 800, 600, and 1200 K curves are 5(1), 7(2), 9(2), and 3.9(1) GPa, respectively. The actual T dependence in stress should be greater than shown here, as in the conversion from lattice distortion to stress we did not take into account temperature derivatives of the elastic moduli.

Figure 5.

Differential stresses as a function of bulk strain (ε) for the GePv+MgO sample. (a) Deformation at 5(1) GPa and 1000 K. (b) At 7(2) GPa and 800 K. (c) At 9(2) GPa and 600 K. (d) At 4 (0.1) GPa and 1200 K. In all four figures, solid symbols represent stresses for GePv, and open symbols represent MgO. Solid red and black curves are smoothed arithmetic mean of the stresses based on the reflections indicated. Heavy gray curves are the volumetric average for the two phases and are considered to represent the “true” stress supported by the bulk sample. Note significant divergence of the 200 and 220 stresses in MgO at 800 and 600 K.

[30] Stress levels vary with different crystallographic orientations in both GePv and MgO. At 1000 K, the (h 0 0) planes of GePv show highest stress (Figure 5). At lower T, Δσ(h 0 0) reaches saturation at bulk axial strains ∼5 or 6%, whereas Δσ(h k 0) and Δσ(h k l) continue to rise. The room-T lengthening process introduced some stress heterogeneity in subsequent high-T deformation segments. This can be seen in the relatively low stresses at 800 and 600 K for the GePv (h k 0) and (h k l) lattices at bulk strains below ∼5%. For both GePv and MgO, the relationship between average stress and bulk strain can be satisfactorily described by an exponentially rising curve asymptotically approaching an “ultimate strength,” which is observed at bulk strains ∼5–8%, with average stress levels in GePv ∼2 to 2.5 times those in MgO.

[31] Clearly, stress states in the two phases are far from the Reuss-Sachs (iso-stress) bound. There is ample experimental evidence that under plastic deformation, stress states in a polycrystal are reasonably approximated by the Voigt-Taylor (iso-strain) bound [Uchida et al., 2004; Chen et al., 2006]. Texture analyses (presented later) show that both GePv and MgO deform by activation of the (cubic) {1 1 0}<1 1 0> systems, which provide sufficient symmetric variants to fulfill the von Mises criterion for plastic deformation, supporting the applicability of the Taylor approach in estimating stress.

[32] Taking the Taylor approximation, bulk differential stresses of the composite are represented by a volumetrically weighted average of the stresses calculated from the two phases, shown as the thick gray curve in each plot (Figure 5). Within the stress uncertainties (∼0.2 GPa at 1000, 800, and 600 K; ∼0.02 GPa at 1200 K), all shortening segments have essentially reached saturation in bulk stress. Judging by the constant strain rates above ∼6% strain, we consider these stresses to approximate the steady state flow stress. Table 3 summarizes average flow stresses Δσ and strain rates inline image for the deformation segments, along with effective viscosities ( inline image, in 10−14 Pa-s).

Table 3. Stress, Strain Rate, and Apparent Viscosity of the GePv+MgO and Pure GePv Samples at the Experimental Pressure and Temperature Conditions
P (GPa)T (K)Δσ (GPa) inline image, 10−5 (s−1) inline imagea
  1. a

    Apparent viscosities are given in 10−14 Pa-s.

GePv+MgO (D0754)    
GePv (D0748)    

3.2. Comparison with the Single-Phase Sample

[33] Figure 6 compares stresses in GePv in both the two-phase composite (D0754) and the single-phase GePv-aggregate (D0748). Orientation dependence of stresses is virtually identical in the two samples. However, mean stress levels in GePv grains of the two-phase composite are notably higher (by ∼10–25%) than that in the single phase sample. Bulk strain rates of the single-phase sample during the high temperature shortening segments at 1000, 800, and 600 K are 1.54(5), 1.55(5), and 2.11(5) × 10−5 s−1, respectively, comparable to the strain rates of the GePv+MgO sample. The quasi-steady state flow stresses and strain rates of the single-phase sample are also given in Table 3 for comparison. Effective viscosities of the single-phase sample are similar to those in the two-phase aggregate, with ∼30 vol % MgO.

Figure 6.

Differential stresses as a function of bulk strain in GePv for the two-phase composite (red solid symbols) and the single-phase aggregate (black open symbols). Solid red and black curves are smoothed mean stresses based on four reflections: 100, 110, 200, and 210. Heavy gray curves are the volumetrically averaged bulk stress for the two-phase composite (same as those in Figure 5). Mean stresses in GePv in the composite sample are systematically higher than those in the single-phase aggregate.

3.3. Texture Development During Deformation

[34] For the composite sample, GePv showed no detectable texture development at 1000 K (bulk strains to 13%) (Figures 7a and 7b). During subsequent deformation at 800 and 600 K, texture developed with the maximum compressive stress mostly oriented along <1 0 0>pc (Figures 7c–7f). At 1200 K, the initial sample texture was similar to those observed at 800 and 600 K, with one maximum along <1 0 0>pc (Figure 7g). With increasing deformation, however, another maximum developed with σ1 along <1 1 0> pc (Figure 7h). Texture development in the single-phase GePv sample (D0748), shown in Figure 8, displays remarkable similarity to GePv in the composite sample (Figure 7), save two differences: (1) While GePv in the composite showed no texture in the first cycle (Figure 7a versus 7b), a weak maximum already appears around <1 0 0>pc in the single-phase sample under identical conditions (Figure 8a versus 8b). (2) After returning from elongation to zero differential stress at room T (after the last 1000 K deformation segment shown in Figure 9), a second, significantly weaker, maximum at [1 1 0]pc, similar to that observed in Figure 7H (two-phase at 1200 K), appears in the single-phase sample. Interestingly, this weak maximum disappears during subsequent deformation at 1000 K.

Figure 7.

Inversed pole figures (IPFs) showing texture development in GePv in the composite sample (D0754). (a–h) IPFs corresponding to points at the beginning and end of the four high-temperature deformation segments (see Figure 3b). Texture strength increases continuously throughout the deformation process, from total absence (=1) in Figure 7a to a maximum of about 2 in Figure 7h.

Figure 8.

Inversed pole figures (IPFs) showing texture development in GePv in the single-phase sample (D0748). (a–h) IPFs corresponding to points at the beginning and end of the four high-temperature deformation segments (similar Figure 3b). Notice that in this case the fourth deformation segment was conducted at 1000 K, rather than 1200 K as in the case of D0754). Texture strength increases continuously throughout the deformation process, from random (∼1) in Figure 8a to a maximum of about 2 in Figure 8h. The general behavior is identical to GePv in the two-phase sample (Figure 7).

Figure 9.

Inversed pole figures (IPFs) showing texture development in MgO in the composite sample (D0754). (a–h) IPFs corresponding to points at the beginning and end of the four high-temperature deformation segments (see Figure 3b). Texture strength increases continuously throughout the deformation process, from total absence (=1) in Figure 9a to a maximum of about 2 in Figure 9h.

[35] For MgO, most of the crystallites were aligned with <1 0 0> along σ1 during deformation (Figure 9). The fact that greater texture contrast was present in the inverse pole figures at the end of the 800 K segment (Figure 9d) than the beginning of the 600 K one (Figure 9e), suggests randomization in crystallite orientation upon retraction of the differential rams during sample elongation. Texture strength clearly increased during deformation in the last two cycles (Figures 9e–9h).

[36] Coherent domain (or crystallite) sizes and micron strains were also refined (Table 4). Although absolute values of the domain sizes from the texture refinement may be subject to errors due to instrumental peak broadening calibration choices, relative variations in different deformation segment are a useful metric for the assessment of sample stress state and deformation behavior. For GePv in the two-phase sample, coherent domain sizes increase slightly (∼10%) during the 1000 K segment, decrease at 800 and 600 K, and remain unchanged at 1200 K. A roughly four fold increase in microstrains in GePv during the 1000 K deformation segment is noticed, with another ∼20% further increase during the 800 and 600 K segments (Table 5). No microstrain variation is observed during deformation at 1200 K.

Table 4. Results of Crystallite Size Refinement From Texture Analysis for the Two-Phase Samplea
CycleT (K)GePv PhaseMgO Phase
  1. a

    Only relative crystallite sizes are given, with the values normalized to the initial crystallite size at the beginning of the first deformation segment. For each cycle, crystal sizes at the beginning (A) and ending (B) of the deformation segment are presented as a pair (A versus B, C versus D, etc.), with labels identical to IPFs shown in Figures 7-9.

Table 5. Results of Microstrain Refinement From Texture Analysis for the Two-Phase Samplea
Deformation SegmentT (K)GePv PhaseMgo Phase
  1. a

    Microstrains at the beginning and ending of the deformation segment are presented as a pair. For each deformation segment, microstrains increase with deformation, except for the 1200 K cycle, where annealing may have played a role in reducing microstrain.


[37] Crystallite sizes for MgO remain essentially unchanged throughout the entire deformation process (Table 4). Microstrains from the refinements also show no systematic variations (Table 5). Due to the weaker and fewer reflections in MgO, these results are not as reliable as those for GePv.

4. Discussion

4.1. Texture, Slip Systems, and Deformation Mechanisms in GePv and MgO

[38] In both composite and single-phase samples, Q(h k l)s of GePv fall in a tight range, suggesting that the yield surface of GePv is rather isotropic. Texture analyses show that the dominating slip system family (see summary in Figure 10) in GePv is {1 1 0}<1 1 0>pc with a <1 0 0>pc type texture in both samples, similar to results on single-phased CaSiO3 perovskite by Miyagi et al. [2009]. This family of slip systems consists of three orthogonal sets of slip planes, each containing one slip direction, so that each slip plane and direction pair has an equivalent and opposite slip plane and direction pair, e.g., (1 1 0)[1 1 0]pc versus (1 1 0)[1 1 0]pc, with identical Schmidt factors. Therefore, lattice rotations caused by one (say, (1 1 0)[1 1 0]pc) tend to be canceled by the other. This, together with the fact that there are more than five independent slip systems for the family of {1 1 0}<1 1 0>pc alone, explains why GePv (and MgO as well—see below) has a relatively weak texture, and texture strengths change little during various high-T deformation segments, after reversing deformation directions at room T.

Figure 10.

Orientation relations between the Pbnm and pseudocubic settings for the perovskite structure and slip systems reported in the literature. The Pbnm perovskite unit cell is displayed, with the pseudocubic cell outlined as the smaller cube. The slip planes (shaded by blue) and slip directions (black arrows) are shown. Slip systems found by various high-pressure studies on MgSiO3, CaSiO3, CaGeO3, and ambient pressure creep experiments on other perovskites are shown. Single asterisk: Cubic—KTaO3, KNbO3, KZnO3, SrTiO3; tetragonal—BaTiO3; orthorhombic—CaTiO3, NaMgF3, YAlO3 [Beauchesne and Poirier, 1989, 1990; Besson et al., 1996; Poirier et al., 1983, 1989; Doukhan and Doukhan, 1986; Wright et al., 1992; Wang et al., 1999, etc.]. Double asterisk: Doukhan and Doukhan [1986]; Poirier et al. [1989].

[39] The 1200 K data reveal the development of another maximum with the maximum compressive stress along [1 1 0] pc in the two-phase sample (Figure 7h). In their texture simulation on ringwoodite (face-center cubic, subscript c), Wenk et al. [2005] examined various slip systems potentially responsible for the [1 1 0]c fabric. They concluded that both {1 1 1}<1 1 0>c and {0 0 1}<1 1 0>c may induce a [1 1 0]c texture. Based on these results, and previous observations in perovskites, we postulate that the [1 1 0]pc texture in GePv is due to activation of {0 0 1}<1 1 0>pc slip systems.

[40] Figure 10 summarizes the slip systems observed in a wide range of perovskites, using various deformation techniques, along with the relations between the pseudocubic and orthorhombic settings. Cordier et al. [2004], on a SiPv sample deformed at 25 GPa and 1673 K (T/TM ∼ 0.63, where the melting temperature TM is estimated from the melting curve of Kato and Kumazawa [1985], identified slip directions [1 0 0]orth and [0 1 0]orth, the same as in our study (i.e., <1 1 0>pc), but in the (0 0 1)orth plane (i.e., {0 0 1}pc). In a SiPv sample synthesized at 26 GPa and 2023 K (T/TM ∼ 0.74), Miyajima et al. [2009] observed a different Burgers vector <1 0 0>pc, and suggested that the difference in dislocations with the study of Cordier et al. [2004] is due to temperature: while at relatively low T the [1 0 0]orth and [0 1 0]orth slip dominate, at higher T [1 1 0]orth dislocations (belonging to {0 0 1}<1 0 0>pc) play a more important role. This is largely based on experimental data on analog perovskites at ambient pressure: high-T creep experiments show that dominant slip systems are generally {1 1 0}<1 1 0>pc [Beauchesne and Poirier, 1989, 1990; Besson et al., 1996; Poirier et al., 1983, 1989; Doukhan and Doukhan, 1986; Wright et al., 1992; Wang et al., 1999, etc.]. Dislocations with Burgers vectors <100>pc begin dominating with further increasing temperatures in some cases, suggesting a change in slip systems [e.g., Doukhan and Doukhan, 1986; Poirier et al., 1989].

[41] Earlier analyses on SiPv deformed in the DAC noted that texture in SiPv depends strongly on the starting materials used [e.g., Merkel et al., 2003; Wenk et al., 2004, 2006]. Miyagi [2009] discovered that for the SiPv+Fp sample transformed from olivine, the initial sample texture is more or less random and therefore provides most robust indicators of active slip systems, which are (1 0 0)[0 1 0]orth (that is, {1 1 0}<1 1 0>pc) and (0 0 1)<1 1 0>orth (that is, (0 0 1)<1 0 0>pc) [Miyagi, 2009]. Laser heating appears to enhance slip on the (0 0 1)orth plane [Miyagi, 2009].

[42] Our data on GePv±MgO fall into a temperature region with T/TM up to 0.65, where TM of GePv is ∼1850 K at 8.5 GPa [Wang et al., 1989]. The results at 600–1000 K are consistent with the general trend in perovskite structured compounds at relatively low T [Poirier et al., 1989]. The 1200 K results in the two-phase sample suggest activation of another slip system, (0 0 1)<1 1 0>orth, and are more consistent with Cordier et al. [2004] and some observations by Miyagi [2009]. However, there is no straightforward way to reconcile the appearance of the weak <1 1 0>pc pole at high T in the two-phase sample with that observed in the single-phase sample under conditions close to null differential stress at room T. Perhaps the activation of the (0 0 1)<1 1 0>orth slip system in the single-phase sample at room T is due to combined effects of low T, low stress, and the predominant <1 0 0>pc fabric. Ultimately, the activation of a specific slip system is determined by an energy threshold, a play-off between strain energy density and thermal energy density. Such information, unfortunately, is currently unavailable for SiPv.

[43] For MgO, the dominating slip system is also {1 1 0}<1 1 0> with a <1 0 0> type texture (e.g., simulation in Merkel et al. [2002b]). This is consistent with low-P deformation studies on MgO [Copley, 1963; Hulse et al., 1963; Paterson and Weaver, 1970] and high-P studies in the DAC on (Mg,Fe)O [Wenk et al., 2004; Merkel et al., 2002b; Tommaseo et al., 2006]. There are three known slip systems for MgO [Copley, 1963; Hulse et al., 1963; Paterson and Weaver, 1970], all involving with the same family of Burgers vectors <1 1 0>: {1 1 0}<1 1 0>, {1 1 1}<1 1 0>, and {1 0 0}<0 1 1>. High-precision creep studies show that it is the change in slip planes that affects yield stress [Hulse et al., 1963]. EPSC modeling by Li et al. [2004] shows that only when <1 1 0> dislocations slip in the {1 1 0} planes will Q(2 0 0) decrease significantly. Hulse et al. [1963] pointed out the interesting feature of the {1 1 0}<1 1 0> slip systems in MgO, similar to that of the {1 1 0}<1 1 0>pc in perovskites and categorized this family of slip systems into three subsets (I, II, and III), which occur when applied differential stress is preferentially aligned with <1 0 0>, <1 1 0>, and <h k 0> (but not too far from <1 1 0>), respectively, with increasing stress levels, to activate {1 1 0}<1 1 0>.

[44] No preferential softening as reported in Figures 3c and 4d was observed in the above studies. Nor has it been observed in any single-phase MgO aggregates at higher pressures in the D-DIA [e.g., Uchida et al., 2004; Li et al., 2004; Mei et al., 2008] or the DAC [Merkel et al., 2002b]. As the only difference between the current data on MgO and those reported before is the presence of GePv, we postulate that the increased activity of slip in {1 1 0} for MgO is due to interaction with the adjacent GePv grains. MgO crystallites bounded by GePv grains deform under changing local boundary conditions with increasing bulk strain. During initial deformation, slips on {1 0 0} and {1 1 1} may also be active. As strain increases, lattice planes rotate relative to the macroscopic differential stress field, slips on {1 1 0} become dominant, as indicated by the texture, thereby relaxing Q(2 0 0). This and similar observations of the “softening” of GePv Q(1 0 0) and Q(2 0 0) in the 800 and 600 K deformation segments (Figure 3b) provide further supporting evidence for creep behavior under our experimental conditions.

4.2. Effects of MgO Volume Fraction on Flow Stress on the Composite

[45] Volumetrically averaged stresses of the composite sample (Figure 5) are identical to those in the single-phase GePv deformed under similar P-T-strain conditions (Figure 6), indicating that with the MgO component up to 30 vol %, and at bulk strains up to ∼20% level, bulk strength of the composite is still controlled by the load-bearing framework formed by GePv. Furthermore, texture in GePv in the composite is essentially identical to that in the single-phase GePv sample, indicating that with MgO constituting up to 30% in volume and bulk strain up to 20%, deformation in the composite is dominated by the behavior of GePv.

[46] These observations are in discordance with the report by Li et al. [2007], who examined mechanical mixtures of MgO and MgAl2O4 (spinel), with MgO fractions from 0 to 100 vol %, and reported a marked decrease in bulk strength when the soft component MgO reached ∼25 vol %, at bulk strains as low as a few percent. In their study, loose powders were compressed to high P and then annealed at 1273 K, in an attempt to sinter the sample prior to deformation. The recovered samples showed large amounts of agglomerates of spinel, outlined by MgO grains (cf. their Figure 10). Although not possible to determine when such a texture was formed, we suspect that the connecting MgO grains (due either to poor mixing or to unmixing because of solubility of Al3+ into MgO) were the main cause of the weakening observed in their samples. This discrepancy highlights the importance of phase distribution on bulk properties. The agglomerated samples cannot be regarded as representative of the two-phase lower mantle with steady state texture. As long as the lower mantle assemblage maintains the “Voronoi mosaic” type of equilibrium architecture (Figure 1), our results suggest that the rheological properties are dominated by those of SiPv at relatively low strains (to ∼20%).

4.3. Comparison With Numerical Simulations Based on Power Law Rheology of SiPv+Fp

[47] In their numerical study, Madi et al. [2005] investigated creep behavior in two-phase aggregate with 70 vol % SiPv and 30 vol % Fp. They assumed power law creep for both phases, with stress exponents 3.5 and 4.0, for SiPv and Fp, respectively, under a shear stress of 10 MPa and bulk strain rate of 10−9 s−1. Although both stresses and strain rates are orders of magnitudes lower than in our experiments (our bulk shear stresses and strain rates are 800 and 200 MPa, and ∼1.7 × 10−5 and 2.1 × 10−5 s−1, at 1000 and 1200 K, respectively), the stress partition between the strong (SiPv versus GePv) and weak (Fp versus MgO) phases is remarkably similar (Table 6). Unfortunately, partition of strain and strain rates cannot be measured in our diffraction experiments for further comparison. Future experiments to higher strains with the aid of Elasto-Visco-Plastic Self-Consistent simulations [e.g., Wang et al., 2012] will improve our understanding of stress partitioning and slip systems involved in multiphase lower mantle aggregates. Future developments for modeling grain- and heterophase-boundary sliding are critical for complete treatment of large strain geological processes.

Table 6. Comparison of Deformation Partition in SiPv+Fpa and GePv+MgOb
RatiosSiPv/BulkcFp/BulkGePv/Bulk (1000 K)MgO/Bulk (1000 K)GePv/Bulk (1200 K)MgO/Bulk (1200 K)
  1. a

    Results from [Madi et al., 2005], after creep for 30,000 s.

  2. b

    Results from the present study, at the axial bulk strain of ∼12%.

  3. c

    “Bulk” stands for the composite properties for the two two-phase aggregates.

Strain rate0.4320    

[48] Nonetheless, the similarity in stress partition with the numerical creep analysis suggests that GePv+MgO may be deforming in the creep regime under high-T conditions. In the numerical simulation, both SiPv and Fp phases were considered rheologically isotropic. Since GePv has sufficient number of {1 1 0}<1 1 0>pc slip systems to fulfill the von Mises criterion, its deformation is close to isotropic, as indicated by the rather weak texture development. However, as pointed out by one of the reviewers (R. Cooper), the operation of this slip system may be due to the fact that our stress level is too high. Recent first-principles calculations on SiPv [Carrez et al., 2007; Ferré et al., 2007] show that throughout lower mantle pressures, Peierls stresses of (0 0 1)[1 0 0]orth dislocations are about twice that of (0 0 1)[0 1 0]orth dislocations. Hence, the latter slip system is energetically favored. These results, however, do not take into account effects of temperature. As the degree of orthorhombic distortion decreases at high temperature, the energetic difference between the two slip systems may diminish. The fact that {1 1 0}<1 1 0>pc system is observed in creep experiments for a large number of perovskites (e.g., Table 10) supports this view. In the following, therefore, we assume that, below certain temperature, SiPv deforms via the {1 1 0}<1 1 0>pc slip systems, similar to the GePv, and discuss potential implications for the lower mantle, with the caveat that this slip system may only operate at differential stress higher than realistic in the lower mantle.

4.4. Implications for the Lower Mantle

[49] Our deformation experiments show that the {1 1 0}<1 1 0>pc slip system dominates at homologous temperatures T/TM up to 0.65. Such low temperatures are expected near down-welling regions near the top of the lower mantle where cold down-welling materials sink into the lower mantle, cooling down the surrounding material [McNamara et al., 2003]. Numerical models show that while an entire down-welling region is under relatively high stress, the highest degree of shear deformation occurs at the sides of the down-welling conduit [McNamara et al., 2003]. Madi et al. [2005] show that with increasing bulk strain (to 15%), “the soft grains tend to deform into pancakes” in the SiPv+Fp assembly (see also Table 6), suggesting significantly increased strain partition into MgO and the development of SPO eventually leading to a fabric transition to IWL. Thus, under sufficiently large shear strains, an original LBF-type fabric transforms into interconnected weak layer (IWL) type [Handy, 1994] around the down-welling conduit.

[50] Yamazaki and Karato [2001] discussed certain implications of such a fabric transition in the lower mantle, in terms of viscosity changes from high shear strain areas (near up- and down-welling conduits). Here, we consider an extreme case where the “soft” Fp phase develops strong SPO, forming lamellar features subparallel to the shear plane [Wang et al., 2011]. A simple calculation based on the Thomsen model [Thomsen, 1986], with the approach by Brittan et al. [1995], shows that for a lower mantle containing ∼30 vol % Fp, seismic velocities would exhibit P wave anisotropy of 0.2–0.7% and S wave anisotropy of ∼0.4–1.0% (Figure 11). In addition to SPO-induced anisotropy, LPO-induced anisotropy is also expected in both Fp and SiPv [Karato, 1998; Merkel et al., 2002b; Wenk et al., 2004; Mainprice et al., 2008]. Based on the strong <1 0 0>pc texture for GePv and MgO (Figures 7 and 9), we postulate that the lower mantle will develop a similar fabric adjacent to down-welling conduits.

Figure 11.

Normalized quasi P wave (circles) quasi out-plane (“VSV”; diamonds), and quasi in-plane (“VSH”; squares) S wave velocities relative to wave propagation direction for 10 (brown), 20 (orange), and 30 vol % (light green) of Fp in possible lower-mantle assemblages. P wave anisotropy increases from ∼0.3% (Fp = 10 vol %) to 0.7% (Fp = 30 vol %), while S wave anisotropy increases from ∼0.4% (Fp = 10 vol %) to ∼1% (Fp = 30 vol %).

[51] The above-mentioned SPO-induced seismic anisotropy is rather large and may appear in contradiction with the absence of anisotropy in the lower mantle. This is however not the case. Shear deformation is localized near upwelling and down-welling conduits [e.g., McNamara et al., 2002]. With increasing distance from the conduits, the level of shear deformation decreases rapidly so that, in the “stagnant cores” of convection cells, effects of shear deformation (hence SPO-induced seismic anisotropy) are negligible. The geometry of these “shear zones,” the fact that lamination axes are generally subperpendicular to the radial direction of the Earth, makes it difficult for the “shear zones” to be detected by seismic ray crossing. Thin shear zones are also more difficult to resolve with long wave length seismic signals.

[52] The LFB-IWL fabric transition will also result in significant viscosity anisotropy. Along the lamellar planes, effective viscosity for the SiPv+Fp composite will be significantly reduced [Li and Weng, 1994] and dominated by that of Fp whose viscosity is about two orders of magnitude lower than SiPv [Yamazaki and Karato, 2001]. Recent simulations conducted by Lev and Hager [2008] show that anisotropic viscosity has profound effects on convection patterns for the lower mantle. For a down-going slab, once the down-welling process triggers the fabric transition in the surrounding lower mantle, the IWL fabric, along with its anisotropic viscosity, will act like a sink pipe, stabilizing the down-welling conduit from “whipping” for an extended time interval and restricting convection currents to narrow regions, leaving the bulk of the lower mantle relatively undeformed (and therefore isotropic) [Wang et al., 2011]. Future seismological development to detect thin anisotropic regions in the lower mantle is important to test this scenario.


[53] We thank M. Rivers for his continuing support throughout the years in the development of the D-DIA, S. Merkel for his data analysis software and suggestions during revision of the manuscript, and the National Science Foundation for continuing financial support (EAR-0652574 and 0968456). We are grateful to R. Cooper and an anonymous reviewer for their constructive comments, which significantly improved the manuscript. Work performed at GeoSoilEnviroCARS (Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation—Earth Sciences (EAR-1128799) and Department of Energy—Geosciences (DE-FG02–94ER14466). Use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02–06CH11357.