We have examined the microstructural evolution of a two-phase composite (olivine + Fe-Ni-S) during large shear deformation, using a newly developed high-pressure X-ray tomography microscope. Two samples were examined: a load-bearing framework–type texture, where the alloy phase (Fe-Ni-S) was present as isolated spherical inclusions, and an interconnected network–type texture, where the alloy phase was concentrated along the silicate grain boundaries and tended to form an interconnected network. The samples, both containing ∼10 vol% alloy inclusions, were compressed to 6 GPa, followed by shear deformation at temperatures up to 800 K. Shear strains were introduced by twisting the samples at high pressure and high temperature. At each imposed shear strain, samples were cooled to ambient temperature and tomographic images collected. The three-dimensional tomographic images were analyzed for textural evolution. We found that in both samples, Fe-Ni-S, which is the weaker phase in the composite, underwent significant deformation. The resulting lens-shaped alloy phase is subparallel to the shear plane and has a laminated, highly anisotropic interconnected weak layer texture. Scanning electron microscopy showed that many alloy inclusions became film-like, with thicknesses <1 μm, suggesting that Fe-Ni-S was highly mobile under nonhydrostatic stress, migrated into silicate grain boundaries, and propagated in a manner similar to melt inclusions in a deforming solid matrix. The grain size of the silicate matrix was significantly reduced under large strain deformation. The strong shape-preferred orientation thus developed can profoundly influence a composite's bulk elastic and rheological properties. High-pressure–high temperature tomography not only provides quantitative observations on textural evolution, but also can be compared with simulation results to derive more rigorous models of the mechanical properties of composite materials relevant to Earth's deep mantle.
The entire rocky interior of Earth is composed of multiphase composites. Volumetric fractions of the constituents and the spatial relation of one phase relative to another have profound effects on the physical properties of the bulk constituents. It is well known that for a composite undergoing large deformation, two types of preferred orientations may develop. In cases where the constituents are deformed within the dislocation creep regime, a lattice-preferred orientation (LPO) can develop (e.g., see Karato, 1998; Wenk, 2006). Since deforming a weaker phase is energetically more favorable than deforming a stronger one, a shape-preferred orientation (SPO) is also inevitable (Handy, 1994a, 1994b). Here we use the terms “strong” and “weak” to indicate relative rheological property contrast: stronger materials are more resistant to flow under nonhydrostatic stress, whereas weaker materials are more susceptible to flow. Although researchers have investigated the effects of LPO on flow properties and seismic anisotropy for several mantle minerals (e.g., Bascou et al., 2002; Mainprice et al., 2004; Bystricky et al., 2006; Long et al., 2006; Warren et al., 2008), the effects of SPO have received little attention, especially for deep Earth dynamic processes.
In studying the flow laws of multiphase composites, Handy (1994a) showed that two end-member texture types can be defined for the plastic regime: (1) a load-bearing framework (LBF) texture, where the stronger phase surrounds isolated pockets of the weaker phase, and (2) interconnected layers of the weaker phase (IWL) separating boudins and clasts of the stronger phase. Under large deformation, bulk composite materials can undergo a transition from the initial LBF texture to IWL by developing SPO (e.g., Handy, 1994a; Holyoke and Tullis, 2006; Takeda and Griera, 2006). The materials science, mechanical engineering, and structural geology literature provides a wealth of information on models of the mechanical behaviors of composite materials (e.g., Guoan and Castañeda, 1993; Lee and Paul, 2005; Tandon and Weng, 1986; Fletcher, 2004; Handy, 1994a; Kanagawa, 1993; Treagus, 2002). Experimental efforts have also yielded valuable information on the mechanical behavior of crustal rocks and rock analogs (e.g., Jordan, 1987; Shea and Kronenberg, 1993; Holyoke and Tullis, 2006), by relating stress-strain curves with textural information.
Because of the technical challenges, virtually no rheological data are available under deep‑mantle conditions for rock composites corresponding to the mineralogies in the transition zone and the lower mantle. Theoretical bounding analyses (e.g., Handy, 1994a; Takeda, 1998) provide limits on the composite flow stress. These studies indicate that the lower bound corresponding to a homogeneous strain rate approaches the strength of the composite with an ideal IWL texture, whereas the upper bound associated with homogeneous stress approaches that of an ideal LBF texture.
Quantitative analyses of the effects of texture on rheological properties are difficult, if not impossible, to determine using analytical solutions. One approach is to conduct numerical simulations on a mixture of phases with known physical properties and a prescribed spatial and shape distribution. So far, numerical models of large shear deformation have been limited to two dimensions (e.g., Takeda and Griera, 2006). The applicability of these results to more realistic three-dimensional (3D) situations may be limited because the effects of geometry and mechanical interactions cannot be accounted for in the third dimension. Madi et al. (2005) conducted a 3D finite-element study to model the behavior of the two-phase lower mantle mineralogical assemblage during deformation. These simulations were limited to strains of a few percent because modeling large deformation is time consuming and costly. Although their preliminary high strain calculations suggested a trend toward a transition from LBF-like texture to IWL, no quantitative results were given.
Another approach is to conduct large strain deformation experiments on analog composites to obtain a quantitative statistical description (SPO and LPO) of the microstructure. Effective rheological properties of the composite may be either measured directly or predicted based on the observed microstructural details and the known properties of the constituent phases in the composite. The latter approach is widely used in industrial engineering and rock physics (e.g., Garboczi et al., 1999; Arns et al., 2002; Keehm, 2003).
In an effort to better constrain the relationship between composite material rheology and textural evolution, we performed sample analyses using the high-pressure X-ray tomography microscope (HPXTM). With HPXTM, we can track the development of textures in three dimensions, detailing the transition from LBF to IWP texture at high pressure, high temperature, and large shear strains (Wang et al., 2005). We have studied selected analog composite materials to examine their textural evolution under simple shear, with a spatial resolution of 4–5 μm, up to 10 GPa and 1300 K. The recovered samples were examined using scanning electron microscopy, to examine microstructures beyond the current resolving power of the HPXTM. In this report we present results on composites consisting of Fe-Ni-S and silicates and discuss the potential implications for the rheology and dynamic processes of Earth's mantle. The current HPXTM setup does not allow us to measure stress and strain directly. Hence, we concentrated on characterizing texture during large strain deformation. In the future we plan to combine high-pressure tomography with diffraction analyses using a multielement detector so that we can relate textural evolution directly to stress-strain measurements.
Sample Preparation and Characterization
For this study we chose a mixture of olivine and Fe-Ni-S as the model composite for three reasons: (1) silicate and iron-nickel sulfide do not have a strong chemical interaction, so we can focus on the physical aspects of large deformation; (2) the two phases have a large X-ray absorption contrast, allowing us to readily separate domains within the tomographic images; and (3) the strength contrast between olivine and Fe-Ni-S, expressed as a ratio of shear stresses, ranges from 500:1 to 1000:1 (see Discussion herein), similar to that between the predicted strengths of silicate perovskite and ferropericlase (Yamazaki and Karato, 2001), two important components of Earth's mantle. Two specimens, similar to those reported by Roberts et al. (2007), were prepared in a piston cylinder apparatus at Lawrence Livermore National Laboratory. Both samples A and B were made by mixing San Carlos olivine powder with (Fe92.5Ni7.5)S (hereafter referred to as Fe-Ni-S alloy or the metallic phase). Samples A and B contained 12 vol% and 10 vol% metallic alloy, respectively. Both were sintered for 24 h at 1 GPa and 1573 K. At these conditions the Fe-Ni-S was molten (Gaetani and Grove, 1999).
The samples were analyzed using a JEOL JSR-1000 scanning electron microscope (SEM) at the Geodynamics Research Center, Ehime University, Japan, and a Zeiss Ultra 55 SEM at the Institut de Minéralogie et de Physique des Milieux Condensés, Paris. Electron probe microanalyses (EPMA) were conducted with a Cameca SX-50 microprobe at Centre Camparis, Université Pierre et Marie Curie, Paris.
Sample A, which was encapsulated in a boron-nitride (BN) container, possessed a complex texture for the silicates, indicative of partial melting. EPMA confirmed that the large grains in sample A (Fig. 1) were enstatite (En) with homogeneous composition. Complex density contrast was observed in the darker silicate regions in backscattered electron micrographs (labeled m in Fig. 1; also see inset). EPMA showed that the compositions in these areas varied from stoichiometric olivine to more Mg rich [i.e., with the (Mg + Fe)/Si ratio >2]. We interpret these regions as quenched melt. Many fine Fe-Ni-S inclusions were present in these regions (a few are indicated by the arrows). Most important, essentially all the Fe-Ni-S inclusions were spherical in shape, with no connection to the nearby neighbors (Fig. 1). The nature of this complex texture is still not well understood. It was probably due to an unexpected power surge during sample synthesis, causing the temperature to fluctuate and olivine to melt incongruently to enstatite and liquid, as has been reported at high pressure by Ohtani et al. (1998). An excursion into the melting region is further supported by the spherical shape of Fe-Ni-S inclusions dispersed throughout the sample. While melting was not intended, this serendipitous event created an LBF texture, the initial mechanical response of which should be dominated by the strong phase (in this case the silicate matrix).
Sample B was synthesized in a graphite capsule at a more stable temperature, where only the Fe-Ni-S alloy was molten. The resulting texture consisted of an olivine matrix separated by interconnected channels of quenched Fe-Ni-S melt (Fig. 2). This texture approaches the idealized IWL texture where the interconnected phase is the weak phase.
In both samples, the metallic inclusions were composed of quench crystals rich in FeNi or FeS (Figs. 1 and 2). Due to the small amount of Ni in the starting material, FeS-rich quench crystals dominate the alloy inclusions (volume fraction >95%). Thus, the mechanical behavior of the alloy inclusions is dominated by FeS.
High-Pressure–High-Temperature Shear Deformation and Tomography Data Collection
Experiments reported here were conducted at the bending magnet beamline (13-BM‑D) of Sector 13 (GSECARS, GeoSoilEnviroCARS) at the Advanced Photon Source, Argonne National Laboratory. Details of the experimental setup can be found in Wang et al. (2005) and Lesher et al. (2009). Figure 3 shows the sample cell assembly that was placed in a modified Drickamer anvil cell to generate high pressure and high temperature (Uchida et al., 2008). The tungsten carbide (WC) anvils (10 mm diameter) had a tapering angle of 20° and a truncation diameter of 4 mm. A mixture of amorphous boron and epoxy (BE, with a boron/epoxy weight ratio of 4:1) was used as the pressure medium. Two sintered MgO disks placed between the sample and the anvils served as both a pressure standard and a mechanical coupling for shear deformation. A containment ring made of Ultem-1000 (polyetherimide; http://k-mac-plastics.net/data%20sheets/ultem_1000_technical_property_data.htm) was placed outside the anvils and the cell assembly. The Ultem-1000 was chosen because its toughness and rigidity at high temperature and its low X-ray absorption. The cell was loaded such that its cylindrical axis was vertical. Each anvil was supported by a low-profile thrust bearing so that it could be rotated under the hydraulic load applied by the 250 t hydraulic press (Wang et al., 2005). The horizontal X-ray beam passed through the sample, which was constrained by the Ultem-1000 containment ring (for details of the setup, see Wang et al., 2005).
A cylindrical graphite furnace with the current passing through the upper and lower anvils provided resistive heating. No thermocouple was used; however, to maintain temperature within 15% of the desired value, we applied a temperature versus power consumption calibration at 2 t, using a C-type thermocouple inserted through the Ultem-1000 containment ring–pressure medium, with the junction located at the center of the graphite heater.
A conventional energy-dispersive X-ray diffraction (EDXD) technique was used to determine pressure during experiments. Two pairs of WC slits driven into the beam path collimated the white beam to dimensions of 0.1 mm × 0.1 mm, and EDXD signal was collected from the MgO pressure standard using a Ge solid-state detector (SSD) with necessary collimating optics on the diffraction side. Details of the diffraction and imaging setup were given in Lesher et al. (2009). Pressures were determined using the equation of state specified by Speziale et al. (2001).
Shear strain was imposed by rotating the upper and lower anvils in opposite directions at any given pressure and temperature. The sample was twisted at a step size of 60° (each step required ∼30 min) during heating and then cooled to room temperature (but still under pressure) for the microtomography data collection (see following). This procedure was repeated until the relative rotation between the two anvils reached 725°. We define the maximum shear strain as γ = (α r/h), where α is the true twist angle, and r and h are the radius and height of the sample, respectively. Note that some slippage occurs between the rotating anvils and the sample during tortional deformation. The apparent twist angle, i.e., the angle between the two rotating anvils, does not represent the true value of α. Careful analysis of the relative changes in the spatial distribution of metallic inclusions in the tomographic images (see following) was used to estimate α.
After reaching a target shear strain level at high pressure and high temperature, the sample was rapidly cooled to room temperature for tomography data collection. This process prevented sample creep during data collection and typically required ∼30–120 min for a complete data set. To collect the tomography data, we rotated the two Drickamer anvils in unison with radiographs collected every 0.5°, from 0° to 179.5°. The incident white radiation was monochromatized by a Si (111) double-crystal monochromator, with a photon energy of 35–40 keV for imaging, during which the incident beam was collimated to ∼2 mm × 3 mm. A CoolSNAP charge-coupled device (CCD) camera was used for image recording. Procedures for tomography data collection were similar to conventional ambient-condition microtomography (Rivers et al., 1999; Gualda and Rivers, 2006). Flat-field images were taken from a dummy Ultem-1000 ring, which had dimensions identical to those of the containment ring used in the high-pressure cell. Only two flat-field images were taken for each tomographic data set, at 0° and 179.5°. These flat-field images were collected by driving the entire apparatus horizontally, perpendicular to the incident beam. Images were binned by 2 × 2 pixels for sample A, corresponding to a pixel size of 3.67 μm, and each image required ∼2 s for data collection. For sample B, images were unbinned, corresponding to a pixel size of 2.4 μm, and each image required 8 s of acquisition time.
One unique feature of the 13-BM-D setup is the ability to quickly switch between the polychromatic and monochromatic modes for EDXD and tomography data collection, respectively. The two monochromator crystals are offset vertically by ∼14 mm. Lowering the entire monochromator assembly by ∼6 mm allowed the white beam to pass through the opening between the two crystals and enter the high-pressure tomography apparatus (Lesher et al., 2009). The offset between the white and monochromatic beams remained constant throughout the experiment, and both the sample vertical position and the beam collimating slits were adjusted accordingly by motorized stages. Although not implemented yet, this setup has the potential for in situ stress measurement by replacing the current single-element SSD with a multielement detector, using the technique developed for rotational deformation apparatus (Nishihara et al., 2008; Kawazoe et al., 2009).
Image Reconstruction and Processing
Three-dimensional tomographic reconstructions were performed using the GSECARS standard tomography software Tomo_display (Rivers et al., 1999). A Hahn filter was used during image processing, and a ring smoothing parameter of 20–25 was adopted to minimize ring artifacts.
Visual examination of individual slices indicated that small features with 4–5 pixels could be recognized. Quantitative evaluation of spatial resolution is difficult. We examined the 3D reconstructed images using the software package Blob3D (Ketcham and Carlson, 2001) and a displaying software vol_animate provided by Guilherme Gualda (Vanderbilt University, Nashville, Tennessee) (Gualda and Rivers, 2006).
To summarize the SVD measurements, we used a 3D version of a rose diagram (see Ketcham, 2005a, fig. 6 therein), created by projecting each analysis direction vertex from the unit sphere inward or outward from the origin inside an inclusion. Vertex positions and colors were normalized by dividing by the maximum measurement value. A normalized value of 1.0 is plotted in red at a distance from the origin equal to the coordinate axis length. Lower values are plotted in successively “cooler” rainbow colors and proportionally closer to the origin. This coloring convention allows the relative measurement values to be easily visualized. For example, dark blue indicates that the difference between the minimum and maximum measurements is roughly a factor of 10. Also plotted on these diagrams are the eigenvector directions, with axis lengths scaled by their associated eigenvalues. Details of the analysis technique were given in Ketcham (2005a, 2005b) and Ketcham and Carlson (2001).
Results are presented for two deformation experiments (samples A and B). Sample A (run R0875) was compressed to 5 t and heated to 700 K. The maximum pressure was 6 GPa. Sample B (R0912) was compressed to 3.5 t and heated to 800 K. The maximum pressure was 4 GPa. The difference in pressure and temperature conditions does not affect in any significant way the mechanical properties of the constituents in the samples. During simple shear deformation, both samples were twisted to an apparent shear angle of 725°. The rotational speeds of the anvils corresponded to a maximum apparent shear strain rate of ∼5 × 10−4 s−1 near the outer diameter of the sample. This rate is considered an upper bound, given slippage between the sample, the pressure media, and the anvils. Initially, significant slippage occurred between the anvils and the sample, so that anvil twisting had little effect on shear in the sample. However, with increasing anvil rotation, mechanical coupling between the sample and the anvils was gradually established, and shear strains of ∼15 were achieved by the end of the experiments.
Shear Strain Determination
After each tomographic reconstruction, Fe-Ni-S inclusions were identified by selecting the image contrast threshold according to the initial volume fraction of the metallic phase. The spatial distribution of the inclusions and changes in inclusion shape after compression, heating, and twisting were used to estimate the maximum shear strain applied to the sample. Figure 4 shows an example of the shear strain determined for sample A. We examined Fe-Ni-S inclusions at both ends of the sample and used them as strain markers (Fig. 4A). For a Drickamer-type opposing anvil assembly, the shear strain increases linearly from the center to the outer diameter. By locating strain markers at both ends of the sample and knowing the distance of the markers from the sample axis, we can thus calculate shear strain.
Figures 4B through 4H present a series of tomographic image pairs of the top (left) and bottom (right) ends, with the olivine matrix digitally removed. On each end, a marker is identified (tied by the red line to the sample axis) and tracked throughout the deformation process. The three-number index for each image pair designates, respectively, the relative rotation of the top and bottom anvils, the actual twist angle between the top and bottom ends, and the calculated shear strain. Thus 50°-2°-0.07 indicates that the top and bottom anvils were rotated by 50° relative to each other, whereas the sample was actually twisted by 2°, corresponding to a shear strain of 0.07.
Table 1 summarizes observations for sample A. Significant axial shortening (∼21%) also occurred during cold compression. As the sample was heated to 700 K and cooled to room temperature, axial strain increased to 54% (row under 5/640/0 in Table 1). Such large axial strain introduced significant flattening of the originally spherical inclusions (e.g., cf. A1 and B1 in Fig. 5). In later stages during shear deformation, axial strain continued to increase at a much slower rate.
Alloy inclusions in sample B were smaller and more complicated in shape than those in sample A, making quantitative analysis challenging. A 3D animation showing the spatial distribution of the large alloy inclusions in sample B before and after shear deformation is provided as supplemental information (see Animations 1 and 2, respectively). It was difficult to identify with confidence major inclusions for such an analysis; therefore, no statistical data are presented here. Nevertheless, SEM analysis indicates that sample B underwent a larger shear deformation than sample A.
Tomographic Microstructural Analysis
Fe-Ni-S inclusions were extracted using Blob3D with a prescribed matrix-alloy interface threshold based on the technique described in Lesher et al. (2009). The utilities in Blob3D treated each inclusion as an ellipsoid, with lengths of the three axes, volume, and surface all recorded. Figure 5 provides a few examples. As the samples were compressed, the original sphere-like and tube-like inclusions became flattened along the directions perpendicular to the loading axis. With increasing shear deformation, inclusions became increasingly mutually connected (e.g., B2, C2, D2 in Fig. 5). However, at larger deformations, some alloy inclusions were severely deformed, becoming smears with very thin, film-like features. SEM analyses indicated that the shortest dimension of these thin layers is often below the current resolution of the high-pressure tomography instrument. Imaging these features may be possible in recovered samples using higher resolution X-ray computed microtomography.
We applied Quant3D (Ketcham, 2005a; Ketcham and Ryan, 2004) to obtain statistics of the inclusions in response to axial and shear strains. Figure 6 shows a series of rose diagrams based on SVD analysis for sample A. Initially, the eigenvalues of the Fe-Ni-S fabric can be represented by an ellipsoid, and the average ratio between the maximum (red) and minimum (green to light blue) axis lengths is ∼2 (Fig. 6A). There appears to be some preferred orientation in the distribution of the inclusions: the long axes tend to align with the radial direction, probably indicating that an axial stress component was introduced when the sample was synthesized in the piston cylinder device. Loading to 6 GPa at room temperature (axial strain of 21%) significantly flattened the inclusions; the eigenvalue representation became disk-like rather than rod-like, and the elongation in the horizontal directions increased, with the ratio of maximum (red) to minimum (intermediate blue) axis lengths of ∼5. Large shear deformation appears to have mostly increased this ratio to ∼10. In the end, the statistical shape of the inclusions is an almost perfectly round disk. This shape, however, applies to only the inclusions that could be properly imaged with our current spatial resolution (see further discussion on the minor effects of imaging resolution in the following).
Virtual Serial Sections and SEM Analyses
We generated virtual thin sections from the tomographic reconstructions and visually examined the textural evolution. These observations were then compared with the final, postmortem analysis using SEM, the spatial resolution of which is well below 1 μm. Figure 7 shows selected virtual serial sections of sample A at various stages of the deformation process. All of these sections are oriented parallel to the rotation axis. Figure 7 shows that inclusions were flattened during the initial loading and heating and then smeared along planes nearly perpendicular to the rotational axis, forming very thin layers that are barely detectable with our tomography technique.
We confirmed that the bright thin features observed in the virtual sections are not imaging artifacts by directly comparing them with SEM images made of actual serial sections through the recovered samples (Fig. 8). The SEM image of sample A (Fig. 8A may be directly compared with the last virtual thin section in Fig. 7). Note that the BN sleeve (see Fig. 3) surrounding sample A created a weak coupling to the sample during deformation. As a result, the large inclusions near the sample's outer boundary did not undergo as much shear deformation as the inclusions well inside. Inclusions near the sample's outer surface tended to migrate outward and remained less deformed than those well inside the sample. This phenomenon, unique to sample A, can be more clearly seen in the virtual thin sections in Figure 7. For a higher resolution tomographic image (a 3D animation) of this sample, after it was recovered from the high-pressure deformation experiment, see Animation 3.
Figure 8B is a backscattered electron image of sample B, showing texture essentially identical to that in sample A at comparable scales. The slight differences are attributed to the greater axial deformation given the higher temperature.
Figure 9 provides higher magnification SEM images taken of sample A, showing Fe-Ni-S veins at scales of 10 μm (Fig. 9A) and 1 μm (Fig. 9B). These veins are preferentially aligned in directions approximately perpendicular to the loading axis and parallel to the shear direction (Fig. 9A). At a finer scale, extremely thin Fe-Ni-S films appear to penetrate the silicate grains and connect to the adjacent metallic inclusions (Fig. 9B). These fine veins were nearly invisible in the tomographic images because of the technique's resolution limitations. Sample A's microstructure resembles melt distribution fabrics in partially molten rocks and rock analogs (e.g., Rosenberg and Handy, 2000; Rosenberg and Berger, 2001; Hustoft and Kohlstedt, 2006). This finding indicates that the softer metallic phase behaved in an almost fluid-like manner during deformation and propagated along silicate grain boundaries in a manner analogous to deformation-assisted melt migration mechanisms (e.g., Phipps Morgan and Holtzman, 2005; Stevenson, 1989; Kohlstedt and Holtzman, 2009). The eutectic melting point in the Fe-S system is well above 1000 K under our experimental conditions (Fei et al., 1997). In sample B, such thin films are more pronounced (Fig. 10), most likely because sample A initially had an IWL-type texture.
The silicate matrix underwent dramatic grain-size reduction in both samples, from an original 30–40 μm to ∼1 μm (cf. Figs. 9 and 10 to Figs. 1 and 2). Some remnants of large olivine grains remain and often contain numerous straight grain boundaries (e.g., Fig. 10B), indicative of severe brittle deformation. The enstatite grains in sample A, however, show a lesser degree of grain-size reduction, perhaps due to its greater strength (e.g., Carter, 1976; Mackwell, 1991), and the presence of the surrounding finer-grained quench silicates.
These observations document the development of SPO in multiphase composites as a result of large shear deformation. We show that SPO caused the texture of sample A to change from LBF to IWL. Furthermore, although the initial microstructures differed in the two samples, their final textures were very similar after large deformation.
A comparison of the virtual tomographic serial sections collected at the final deformation stage (e.g., Fig. 7I) and the SEM images of the recovered sample (Figs. 8A and 9) shows that the current HPXTM setup captures general features of the true microstructure. Of course, the utility of any given imaging techniques is limited by the spatial resolution. Gualda and Rivers (2006) analyzed rock inclusions using X-ray tomography and concluded that 3D objects can be properly imaged when the linear dimensions are at least five times the voxel size. This conclusion is in general agreement with our analysis: inclusions with linear dimensions >15–20 μm could be imaged with sufficient confidence (recall that our voxel sizes were ∼2–4 μm). Some of the alloy films (e.g., Figs. 8–10) are well below these voxel dimensions and therefore are not resolved by this technique. Several improvements to spatial resolution are being implemented, including more accurate alignment of the rotational axis, software corrections for off-axis errors in the mechanical setup, as well as more sensitive detectors and more responsive phosphor screens.
One technical challenge is to maintain sample height during high-temperature deformation, which may be mitigated by adopting harder gasket materials. These improvements to imaging quality will be the focus of future technical development. However, in general, axial compression flattens weak phase inclusions in the directions perpendicular to loading axis and does not significantly affect the later shear-induced texture. Further quantification of microstructure based on tomographic images, however, will require more sophisticated image analysis software. For example, an ability to describe inclusions in complex shapes and to correlate inclusions at various deformation stages based on spatial distribution statistics will help researchers extract detailed information on deformation and strain partitioning from the images. Although the experimental technique is still being developed and the results are preliminary, several interesting observations are worthy of discussion.
Examining dominant deformation mechanisms in the constituent silicate phases and their effects on texture development provides a context for further analysis and discussion. The silicates in sample A appear to have deformed in a ductile or semibrittle regime, as suggested by the irregular and elongated enstatite grains (Fig. 9A). The quenched silicate melt behaves differently, showing significant particle-size reduction that may be partly due to the compositional inhomogeneity in the quench glass. Microprobe analyses showed a varied Mg/Si ratio across the quenched melt, for which the definition of “particle” is somewhat ambiguous. There may be numerous domains (quenched crystals) with varied composition and mechanical properties. Under large shear strain, these domains may be separated, resulting in an apparent particle-size reduction. For sample B, the silicate matrix is essentially homogeneous olivine, which was most likely deformed in the brittle regime (Fig. 10), given the low pressures and temperatures during deformation.
As the shape of alloy inclusions becomes more lens-like, stress concentration increases near the tips of the lenses, causing the silicates to fracture. The alloy material can then propagate through the fractured interface in a manner similar to that of fluid (Fig. 9B).
Previous experiments showed that the texture transition from LBF to IWL occurs in numerous polyphase rocks and rock analogs, including gneiss (quartz-plagioclase-biotite; Holyoke and Tullis, 2006), aplite (quartz-feldspar; Dell'Angelo and Tullis, 1996), mica-quartz-feldspar (Shea and Kronenberg, 1993; Tullis and Wenk, 1994), muscovite/kaolinite-halite (Bos and Spiers, 2001), halite-calcite (Jordan, 1987), and camphor-octachloropropane (Bons and Cox, 1994). These experiments also found that the LBF-IWL texture transition can occur when the stronger phase (matrix) is either brittle or ductile. When matrix deformation is predominantly brittle, the LBF-IWL transition occurs in localized shear zones, weakening the entire rock sample by concentrating deformation in these shear zones. When deformation is ductile, the IWL texture occurs more or less uniformly throughout the sample.
One of the most important factors in controlling the LBF-IWL texture transition is the phase strength contrast (PSC), i.e., the strength ratio between the strong and the weak constituents (e.g., Handy, 1994a, 1994b; Holyoke and Tullis, 2006). High PSC generally results in greater stress concentration in the strong phase adjacent to the weaker phase. In the gneiss samples studied by Holyoke and Tullis (2006), local semibrittle flow of quartz and plagioclase allowed biotite grains (13 vol%) to become interconnected by shearing at ∼1000 K. Holyoke and Tullis (2006) estimated the PSC ratio to be ∼30:1 for feldspar-biotite and ∼50:1 for quartz-biotite.
For our samples, the PSC ratio is difficult to determine precisely because we do not have strength data for the alloy. Near stoichiometric FeS has widely varying strengths depending on crystal structure and slip systems. At 673 K and atmospheric pressure, hexagonal pyrrhotite (Fe1–xS, with x = 0–0.2) single crystals slip along the basal plane with shear strengths as low as 5 MPa (Kübler, 1985). Assuming that the Fe-Ni-S phase in our samples has a similar strength, the ratio of shear strength contrast between olivine (e.g., Carter, 1976) and the alloy is ∼500:1 to 1000:1. Because of the weak strength of the Fe-Ni-S phase, the presence of quenched silicate melts in sample A is unlikely to have significant effect on the observed fabric evolution. Bruhn et al. (2000) deformed an olivine sample with 4 vol% gold at 0.3 GPa and ∼1500 K; i.e., under conditions where the strong phase (olivine) was deforming in the dislocation creep regime. In that experiment, PSC may be even higher given that gold was in the liquid state. Under such large PSC, IWL texture develops readily. The similarity between the shear-induced IWL morphology (i.e., shape and spatial distribution of the weaker phase) reported here and that reported by Bruhn et al. (2000) indicates that in the stronger phase, the specific attributes of the deformation mechanisms are less important. Therefore, the LBF-IWL transition predominantly depends on PSC and the amount of strain. Note, however, that in the work of Bruhn et al. (2000) and other studies dealing with deformation of partially molten systems by tortional shear (e.g., Kohlstedt and Holtzman, 2009), the weak phase is generally oriented at 25°–30° with respect to the shear plane. In our study, the weak Fe-Ni-S alloy is oriented almost parallel to the shear plane. This difference is most likely related to the substantial amount of axial compressive stress that the samples undergo before and during deformation in simple shear.
Let us consider effects of PSC and shear-induced texture development on the rheological properties of the lower mantle. For simplification, we assume the mantle consists of silicate perovskite (Pv) and ferropericlase (Fp) only. We estimate the volume fraction of Pv to range from ∼70‰ to 90%, depending on the mineralogical models preferred (e.g., Stixrude et al., 1992; Ringwood, 1991). A number of observations suggest that Fp is the weaker phase (Weaver, 1967; Hulse et al., 1963; Paterson and Weaver, 1970; Uchida et al., 2004; Chen et al., 2002). When discussing mantle dynamics, it is more convenient to use viscosity, which, for solids, is proportional to the ratio of strength to strain rate, than the strength alone. Using experimentally measured diffusion coefficients and homologous temperature scaling, Yamazaki and Karato (2001) calculated that the viscosity of Pv is about three orders of magnitude higher than that of Fp.
Figure 11 shows one attempt to estimate the rheological properties of the lower mantle and the effects of texture on bulk viscosity. Based on the rheological properties for Pv and Fp given by Yamazaki and Karato (2001, their Table 1), viscosities are estimated for depths of 1000 and 2000 km using the approach outlined by Takeda (1998). Here we adopt a lower mantle geotherm with a temperature gradient of 0.3 K/km, with homologous temperature scaling for the viscosities of the two constituents (Yamazaki and Karato, 2001). Across the currently accepted mineralogical models (70–100 vol% Pv; shaded area in Fig. 11), the viscosities of the two-phase mineralogical assemblage vary by roughly three orders in magnitude. For each depth, the upper line represents viscosities for the ideal LBF texture, whereas the lower curve corresponds to viscosities for the ideal IWL texture (Takeda, 1998; Yamazaki and Karato, 2001). Thus, once the transition from LBF to IWL occurs, bulk viscosity will suddenly decrease from the upper curve to the lower one.
To further explore this scenario, we consider a lower mantle dominated by upwelling and downwelling flows separated by relatively stationary regions (Karato  called these regions “stagnant cores” of convection cells; Fig. 12A). We examine a cross section from the edge of the subducting slab (point A) to the edge of the upwelling conduit (point B), at a constant depth of, e.g., 1000 km. Points A′ and B′ are the demarcation points of flow-induced shear zones; regions AA′ and BB′ are under pronounced shear deformation due to the drag of viscous flows. These shear zones are also thermal boundary layers: temperatures adjacent to the downwelling and upwelling conduits may be a few hundred Kelvin cooler and hotter, respectively, than the ambient mantle (Fig. 12B). Figure 12C gives the likely deformation mechanisms of different regions along the cross section. In zone AA′, where temperatures are lower and stresses higher than the surrounding mantle, the dominant deformation mechanism is likely dislocation creep. In the normal mantle (A′B′), both diffusion creep (Karato and Li, 1992; Yamazaki and Karato, 2001) and superplasticity (Karato et al., 1995) have been proposed. In the hotter zone (B′B), diffusion creep is likely to dominate. With these competing deformation mechanisms, Figure 12D summarizes the expected fabric of the lower mantle phase assemblage Pv + Fp. Large shear deformation is likely to occur in the boundary layer (AA′): for a slab motion speed of ∼10 mm/yr, shear strains of ∼5 will be produced in ∼5 m.y., for a thickness of the shear zone of ∼10 km. Our observations show that at such shear strains, a transition from LBF to IWL had already occurred (Fig. 12, inset d1). As a result, the viscosity along the flow direction is dominated by that of Fp (Fig. 12E). In the normal mantle, the viscosity may be controlled by that of Pv if this phase forms a LBF (Fig. 12, inset d2), or by superplasticity if both phases are fine grained and deform by grain-boundary sliding. Hence, dynamic processes are likely controlled by the rheological properties of Fp.
Texture-induced rheological weakening may have profound effects on the dynamics of a subducting slab. A slab penetrating into the lower mantle introduces large deformation in the surrounding mantle, especially around the tip of the slab. The mantle material undergoes a textural transition to adapt an IWL fabric, and the effective viscosity decreases. The magnitude of this decrease in effective viscosity may range from 100 to 1000, resulting in an avalanching enhancement for the downwelling process. The weakened zone (AA′) may be only a few tens of kilometers in thickness, but it could play a critical role in mantle dynamics. Measurements of the rheological properties of Pv and a full understanding of dominant deformation mechanisms under various pressure, temperature, grain-size, and strain-rate conditions are required to evaluate the effects quantitatively.
Development of an IWL fabric is also associated with seismic anisotropy. A simple estimate, based on an IWL-induced, weak, transversely anisotropic composite (e.g., Brittan and Warner, 1995), yields ∼0.5% shear-wave anisotropy, with S wave speed in the laminating direction faster than that parallel to the layers. LPO associated with the texture may further enhance the degree of anisotropy. Future high-resolution seismic studies may be able to resolve the contributions of anisotropy caused by this shear zone from that within the slab.
We have developed a new experimental technique, called HPXTM (high-pressure X-ray tomography microscope), to study the mechanical properties of multiphase materials. Stress measurements were not performed at this stage of the development; however, by implementing a multi-element detector and conical slits (e.g., as described in Nishihara et al., 2008; Kawazoe et al., 2009), we can conduct such measurements in future high-pressure tomography experiments. Further improvements in optical components (such as scintillator materials and cameras) and mechanical components will be sought to increase spatial resolution.
Using HPXTM, we examined the evolution of strain and texture in an analog two-phase rock composite (olivine + Fe-Ni-S). Two types of starting samples were studied: an LBF-type texture, where the alloy phase was present as isolated spherical inclusions, and a near-IWL-type texture, where the alloy phase was concentrated near grain boundaries and tended to form an interconnected network. The 3D tomographic image analyses (with a spatial resolution of 4–5 μm) allowed us to track individual alloy inclusions at various shear deformation stages. SEM images of the recovered samples, with a spatial resolution of <1 μm, provided supporting observations and confirmed that at the resolution level of the tomography setup, HPXTM adequately captures the general features of a composite's texture. Results indicate that regardless of the initial texture, large shear deformation causes a dramatic texture transition from LBF to IWL, the alloy phase forming laminated layers subparallel to the shear plane.
For such a laminated IWL texture, effective rheological properties should be dominated by the weak phase. Our results indicate that the deformation mechanisms in the strong matrix material (silicate in our study) play a less important role in the development of the IWL fabric than does the contrast in rheological properties between the constituent phases. In addition, the observed texture transition should be a common phenomenon in rock assemblies with high phase-strength contrast. The texture transition from LBF to IWL will influence the dynamic process in several important ways. A rheological weakening is likely to occur in regions of the lower mantle where the Pv + Fp assembly is undergoing large deformation. The regions most likely to be affected are within the thermal boundary layers adjacent to subducting slabs, where a strong IWL texture is expected to develop, thereby greatly reducing the bulk viscosity in these regions. This scenario should be considered in geodynamic models. Also, since lamination develops in planes subparallel to the flow direction, SPO-induced elastic anisotropy will also develop in the composite. A simple model indicates that in these highly deformed regions, SPO-induced anisotropy may be as much as 0.5% for the lower mantle. Seismic studies on anisotropy may provide the clues researchers need to infer the degree of deformation and, hence, the rheological weakening in the lower mantle.
We thank Frank Westferro for the excellent engineering support during the high-pressure tomography experiments at GSECARS (GeoSoilEnviroCARS, Argonne National Laboratory) and Anne-Line Auzende for assistance during transmission electron microscopy studies at IMPMC (Institut de Minéralogie et de Physique des Milieux Condensés). We are grateful to G. Gualda, who provided the software vol_animate, which was very helpful in examining three-dimensional tomography microstructure, and to S. Karato for his valuable comments on early versions of the manuscript. We also thank two anonymous reviewers, whose thorough and constructive reviews significantly improved the manuscript. This work was performed at GSECARS (Sector 13), Advanced Photon Source, Argonne National Laboratory. GSECARS is supported by the National Science Foundation (NSF)–Earth Sciences (EAR-0622171) 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. We gratefully acknowledge financial support from the NSF through grants EAR-0711057 (Wang) and EAR-0711599 (Lesher). Work by J. Roberts was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.