Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth’s lower mantle

Physics of the Earth and Planetary Interiors 131 (2002) 251–267

Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth’s lower mantle Daisuke Yamazaki a,1 , Shun-ichiro Karato b,∗ b

a Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277, Japan Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA

Received 23 October 2001; accepted 10 May 2002

Abstract Large strain, shear deformation experiments were performed on (Mg1−x ,Fex )O (x = 0.25, 1.0), one of the important minerals in Earth’s lower mantle. Deformation experiments were made on coarse-grained (∼15–20 ␮m grain-size) hot-pressed aggregates at conditions of T /Tm ∼ 0.46–0.65 (T: temperature, Tm : melting temperature) and σ/µ ∼ 0.4 × 10−3 to 0.9 × 10−3 (σ : differential stress, µ: shear modulus) up to the shear strain of ∼7.8. Under these conditions, deformation occurs by dislocation creep. The microstructural development in (Mg,Fe)O is found to be sluggish and the complete dynamic recrystallization and nearly steady-state fabric (lattice preferred orientation) are achieved only after shear strains of γ ∼ 4. At nearly steady-state, (Mg,Fe)O shows strong fabrics characterized by the 1 1 0 axes being parallel to the shear direction and the poles of the {1 0 0} planes (and to a lesser extent the poles of the {1 1 1} planes) normal to the shear plane. The seismic anisotropy corresponding to the deformation fabrics in (Mg,Fe)O was calculated. The nature of anisotropy corresponding to a given flow geometry changes significantly with strain as a result of fabric evolution. Anisotropy changes also with depth (pressure) due to the large variation of elastic anisotropy of (Mg,Fe)O with depth. Seismic anisotropy caused by the deformation fabric of (Mg,Fe)O is very weak in the shallow lower mantle (<0.1%), but it becomes strong in the deeper portions due to the high elastic anisotropy of (Mg,Fe)O. Near the bottom of the mantle, the steady-state fabric of (Mg,Fe)O corresponding to the horizontal shear will result in ∼1–2% VSH > VSV anisotropy (assuming that (Mg,Fe)O occupies ∼20% volume fraction of the lower mantle) and little shear wave splitting of vertically travelling waves, a result that is consistent with the seismological observations in the D layer of the circum-Pacific regions. Thus, the deformation fabric of (Mg,Fe)O is a vital candidate of the cause of seismic anisotropy in these regions. Anisotropy caused by the lattice preferred orientation of (Mg,Fe)O has a distinct azimuthal anisotropy with a strong 4θ term (θ : azimuth): the direction of propagation of the fastest (slowest) SH (or P) wave is parallel (perpendicular) to the flow direction and the slowest (fastest) SH (or P) wave is at 45◦ from these two directions. © 2002 Elsevier Science B.V. All rights reserved. Keywords: (Mg,Fe)O; Seismic anisotropy; Slip system; Simple shear; D layer

1. Introduction ∗ Corresponding author. Tel.: +1-203-432-3114; fax: +1-203-432-3134. E-mail address: [email protected] (S.-i. Karato). 1 Present address: Department of Earth and Planetary Sciences, Ehime University, Matsuyama, Ehime, Japan.

Although (Mg,Fe)O is considered to be a relatively minor constituent of Earth’s lower mantle (less than ∼20–25%, e.g. Ringwood, 1991), its role in plastic flow and flow-induced microstructures could be

0031-9201/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 ( 0 2 ) 0 0 0 3 7 - 7

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of central importance to the geophysics of this region. This is due to its two unique properties. Firstly, creep strength of (Mg,Fe)O is likely to be considerably smaller than that of (Mg,Fe)SiO3 perovskite, and therefore, the viscosity of Earth’s lower mantle could be controlled largely by that of (Mg,Fe)O (e.g. Karato, 1989; Yamazaki and Karato, 2001). Secondly, despite its simple crystal structure (cubic symmetry), (Mg,Fe)O is likely to have large elastic anisotropy. According to first principles calculations, elastic anisotropy in (Mg,Fe)O is much stronger than that of (Mg,Fe)SiO3 perovskite particularly under deep lower mantle conditions (Karki et al., 1997; Wentzcovitch et al., 1998). Consequently, (Mg,Fe)O may contribute significantly to the development of seismic anisotropy in Earth’s lower mantle (e.g. Karato, 1998a,b). However, surprisingly little is known about the fabric (lattice preferred orientation (LPO)) development in MgO or (Mg,Fe)O. There are no systematic studies on the fabric development in MgO (or (Mg,Fe)O) under well-controlled conditions. To our knowledge, Rice (1970) is the only work on the fabric development in MgO where he found a fabric characterized by a strong maximum of 1 0 0 along the extrusion direction, but the physical conditions of deformation (e.g. strain rate or stress magnitude) are poorly controlled or characterized in this study (after this manuscript was prepared, Stretton et al., 2001 reported the results of tri-axial deformation experiments on (Mg,Fe)O in which fabric development was also investigated). (Mg,Fe)O assumes the NaCl (B1) structure and is stable throughout the whole conditions of Earth’s lower mantle. The slip systems in materials with the NaCl structure have been discussed in Nabarro (1967), Carter and Heard (1970), Skrotzki and Welch (1983) and Karato (1998b). The Burgers vector in materials with this crystal structure is always 1 1 0 whereas the slip planes can change among various materials (and presumably with physical conditions such as the temperatures and pressures). In highly ionic materials such as NaCl, the {1 1 0} planes dominate (i.e. the easiest plane for dislocation glide to occur) whereas in less ionic crystals, other planes such as the {1 0 0} and/or {1 1 1} could dominate (Nabarro, 1967; Skrotzki and Welch, 1983). (Mg,Fe)O is less ionic than NaCl, and therefore, the dominant slip systems might be different from that in NaCl (Karato, 1998b). Also, dynamic recrystallization that occurs at

high-temperatures and high strains may modify the fabrics. Therefore, a detailed study of fabric development in (Mg,Fe)O is needed to better understand the origin of seismic anisotropy in Earth’s lower mantle. In this paper, we report the results of large strain, shear deformation experiments on (Mg,Fe)O aggregates and discuss their implications for seismic anisotropy.

2. Experimental procedure 2.1. Sample preparation Deformation experiments were conducted on isostatically hot-pressed aggregates of (Mg0.75 Fe0.25 )O and FeO. The starting materials were prepared from the oxide reagents. To synthesize a (Mg0.75 Fe0.25 )O sample, an oxide mixture of MgO and Fe2 O3 with a molar ratio of 6:1 was mechanically mixed and ground to a grain-size of ∼1 ␮m. To synthesize an FeO sample, Fe2 O3 with a grain-size of ∼1 ␮m was used. These oxide powders were then put into a furnace at 1273–1473 K for 18 h with a CO2 /CO gas mixture yielding the oxygen fugacity within the stability field of final run products (f O2 = 10−10 to 10−6 Pa). These procedures were repeated at least twice to achieve nearly complete reaction. After the inspection by the powder X-ray patterns and by an optical microscope, the (Mg0.75 Fe0.25 )O and FeO powders were cold-pressed into an iron can with a uniaxial pressure of ∼200 MPa and dried in a vacuum oven at 393 K for ∼12 h. Using an internally heated gas-medium apparatus, the cold-pressed samples were then isostatically hot-pressed at 300 MPa and 1473 K for 220 min or at 220 MPa, and 1173–1273 K for ∼30 min for (Mg0.75 Fe0.25 )O and FeO samples, respectively. During hot-pressing, the oxygen fugacity was controlled by the sample itself and the reaction with an iron can. After hot-pressing, the recovered sample was observed by an optical microscope. The hot-pressed samples show near equilibrium textures (Fig. 1) and the average grain-size is ∼15 ␮m for (Mg0.75 Fe0.25 )O and ∼20 ␮m for FeO, respectively. 2.2. Deformation experiments A sample for shear deformation experiment was first cored from a hot-pressed cylindrical sample, and then

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Fig. 1. Optical microphotographs of (A) (Mg0.75 Fe0.25 )O and (B) FeO used as starting materials after hot-pressing. Refracted light with Nomarski contrast were used. Horizontal length of photographs is 150 ␮m.

cut at 45◦ to its long axis to a thickness of 0.3–0.5 mm. A slice of oblate specimen was then cut into two halves normal to it layer plane. The molybdenum foil (12.5 ␮m thickness) was inserted between the two cut surfaces as a strain marker. These two specimens and a molybdenum foil were sandwiched between two 45◦ -cut thoriated tungsten pistons. The surfaces of pistons in contact with a sample have grooves of 40 ␮m depth and 400 ␮m spacing to prevent sliding at the sample–piston interface. A sample and pistons were put into an iron jacket and deformed by the movement of alumina and zirconia pistons (Fig. 2).

The deformation experiments were made at temperatures of 1073–1473 K and confining pressure of 300 MPa with a constant axial displacement rates of ∼1 × 10−4 to 6 × 10−4 mm/s using a gas-medium deformation apparatus. The experimental conditions are shown in Table 1. For all experiments, we first raised the confining pressure to ∼100 MPa and then temperature was increased at a rate of 1 K per 2–4 s. When temperature reached to ∼873–973 K, the confining pressure was increased to 300 MPa. After temperature and pressure reached the desired values, the sample was annealed for about 1 h to minimize the

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Fig. 2. Specimen assembly for shear deformation experiments. Temperature was measured by a thermocouple located in the hole.

temperature gradients in the furnace and to make good contact between sample and pistons. After deformation, the load was kept until temperature dropped below ∼873–973 K to minimize the annealing of microstructures. 2.3. Microstructural observations Recovered samples were cut into two halves parallel to the shear direction and perpendicular to shear

plane and then a cut sample was polished finally with SytonTM to remove the damaged surface of the sample. Finally, sample was coated with ∼3 nm thick carbon to prevent charge-up during electron microscope observations. We used electron backscattered diffraction (EBSD) (Kikuchi pattern; Dingley and Randle, 1992) technique with SEM (JOEL 840) at University of Minnesota to observe microstructure such as lattice preferred orientation. Channel+ software package from HKL Technology was used for indexing the patterns. The orientations of crystals were determined by the automatic beam scanning. Typically, we measured orientation of ∼800–1200 points and the a step between points is 5–12 ␮m in most cases. This spacing is about the grain-size, and therefore, the statistics of orientation distribution does not reflect the internal structure of each grains. For sample PI805, we also measured the orientations using a 1 ␮m step (Fig. 3). In this case, we found cluster of orientations suggesting the presence of subgrains.

3. The results 3.1. Mechanical data Seven shear deformation experiments were conducted under a constant strain rate (constant displacement rate) mode. The results are summarized in Table 1. The mechanical data from shear deformation experiments are subject to large uncertainties due to

Table 1 Experimental conditions and results Run no.

Sample

Temperature (K)

Shear strain, γ

Final shear stressa , τ (MPa)

Shear strain rateb , γ˙ (s−1 )

PI796c PI873d PI784 PI793 PI867 PI805 PI854

FeO (Mg0.75 Fe0.25 )O (Mg0.75 Fe0.25 )O (Mg0.75 Fe0.25 )O (Mg0.75 Fe0.25 )O (Mg0.75 Fe0.25 )O (Mg0.75 Fe0.25 )O

1073 1273 1473 1473 1473 1473 1473

4.8 4.3 1.4 4.0 4.3 4.3 7.8

121 164 81 70 77 88 84

6.6 4.7 5.0 5.2 2.1 9.6 9.5

× × × × × × ×

10−4 10−4 10−4 10−4 10−3 10−4 10−4

All samples were deformed homogeneously, except for PI873. Initial grain-size for all samples is ∼15–20 ␮m. After deformation experiments, grain-size for all sample are ∼10–20 ␮m, except for PI796 and PI873. a Shear stress at the final stage for deformation experiments. b Shear strain rate at the final stage for deformation experiments. c This sample shows the porphyroclastic texture. Small- and large grain sizes are <1 ␮m and ∼20 ␮m, respectively. d This sample has a bimodal grain-size distribution, corresponding to heterogeneous strain; at smaller strain the grain-size is ∼20 ␮m, at larger strain grain-size is ∼3–4 ␮m.

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Fig. 3. Pole figures of 1 0 0, 1 1 0 and 1 1 1 for the sample PI805 using a 1 ␮m step. Equal area projection is used. The EW direction corresponds to the shear direction, the shear is dextral; 1088 points were measured. Many points show clustering indicating the presence of regions with similar orientations (i.e. subgrains).

the potentially large effects of heterogeneity in deformation, but we believe that the data provide enough information to infer the dominant mechanisms of deformation. We fitted the steady-state mechanical data to a flow law of the form γ˙ = Aτ n exp(−E ∗ /RT), where γ˙ is shear strain rate, n is the stress exponent, A is a constant, γ˙ is shear stress, E ∗ is activation energy, R is the gas constant and T is absolute temperature. The results are shown in Fig. 4, giving a stress exponent of n ∼ 3.8 suggesting that dislocation creep is the dominant deformation mechanism under the present experimental conditions. The activation energy was determined to be E ∗ ∼ 260 kJ/mol which is consistent with the previous results (Frost and Ashby, 1982). 3.2. Microstructural observation Fig. 5 shows optical micrographs of deformed samples. The geometry of strain markers shows that the majority of our samples deformed nearly homogeneously at the scale of a sample thickness (Fig. 5A). One exception, however, is a sample PI873 which was deformed at a lower temperature (T = 1273 K) than the rest of (Mg0.75 ,Fe0.25 )O. In this sample, the strain marker shows a large curvature, and the strains are much smaller in regions near the piston-sample boundary than in the central portions (Fig. 5B). At the scale of grains, most of the samples show rather homogeneous microstructure after deformation (Fig. 6). In five samples (PI784, PI793, PI867, PI805, PI864) grain-size is homogeneous and ∼15–20 ␮m (Fig. 6A) whereas PI873 shows heterogeneous grain-size (Fig. 6C): in regions near the piston,

Fig. 4. Stress versus strain rate relationship for (Mg0.75 Fe0.25 )O at 1273 and 1473 K. Dotted lines represent the tie-lines between the results in single runs. Solid lines are the flow law with n = 3.8 and E ∗ = 260 kJ/mol.

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Fig. 5. Optical microphotographs of deformed samples: (A) PI805, (B) PI873. Reflective light with the Nomarski contrast was used. Horizontal length of photographs is 1.2 mm. Shear sense is the top to left (sinistral). The bright lines at center of the sample are strain marker. For PI805 (A), strain marker is straight, in contrast, it is bent for PI873 (B).

grain-size remains the same as starting size, whereas in the central region, it becomes smaller (∼3–4 ␮m). Sample PI796 shows a bimodal grain-size, large elongated grains (∼20 ␮m maximum length, ∼3–6 ␮m minimum length) surrounded by small grains (∼1 ␮m) (Fig. 6B). The shape of large grains in PI796 is consistent with the value of the finite strain (γ ∼ 4.8), whereas in other samples grains are nearly equiaxed despite large shear strains. The pole figures of all the samples are shown in Fig. 7 and the inverse pole figures of selected samples are shown in Fig. 8. The deformation fabrics in

(Mg0.75 Fe0.25 )O do not change with stress magnitude within the range explored in this study (Fig. 7B, D and F). Both FeO and (Mg0.75 Fe0.25 )O show similar fabrics at a similar strain (Fig. 7B–D and F). However, the deformation fabrics change with increasing strain (in (Mg0.75 Fe0.25 )O) as shown in Fig. 7A, D–F. In the sample with small strain (PI784, Fig. 7A), the 1 0 0 axes concentrate on the direction of strain ellipsoid. However, with increasing strain, the position of concentration of 1 0 0 axes, e.g. change to the direction of shear plane normal. PI873 has two regions of different grain texture; one is fine-grain portion and the

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other is coarse grain portion. Fig. 7G shows the pole figures for whole sample measured for PI873. This pattern is similar to that for the other samples (e.g. PI805, Fig. 7D). Fig. 7H and I represent the pole figures from selected points for small strain (large grain) portion and large strain (small grain) portion in PI873, respectively. It is clear that the deformation fabrics for large strain (small grain) portion show stronger fabric than that for small strain (large grain) portion.

257

The evolution of deformation fabrics can also be seen in the inverse pole figures (Fig. 8). At a small strain (Fig. 8A, PI784), the 1 1 0 and, to a lesser extent, the 2 1 1 axes show concentration along the shear direction and the 1 1 1 and, to a lesser extent the 1 0 0 axes show concentration along the shear plane normal. At larger strains (Fig. 8B and C, PI805 and PI854), the concentration of 2 1 1 along the shear direction decreases and only the 1 1 0 axis show

Fig. 6. Optical microphotographs of deformed samples: (A) PI805, (B) PI796, (C) PI873. Reflective light with the Nomarski contrast was used. Homogeneous microstructure with equiaxed grains are seen in (A) (PI805) after large shear strains indicating dynamic recrystallization. The microstructure of FeO (B) is characterized by the presence of bimodal grain-size. Large elongated grains are surrounded by small “recrystallized” grains, indicating more sluggish kinetics of dynamic recrystallization in FeO than in (Mg,Fe)O. (C) shows microstructures near the boundary between small grain (central region (bottom half in this picture)) and large grain (near the sample–piston interface (top half in this picture)) regions. Horizontal length of photographs shows 150 ␮m. Shear sense is the top to left (sinistral).

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Fig. 6. (Continued ).

concentration along the shear direction. The concentration of the 1 1 1 axes along the shear plane normal also decreases with strain, and a broad concentration of the 1 0 0 axes develops. The concentration of the 1 1 0 axes normal to the shear plane is weak under all conditions, which is in marked contrast to the fabrics of NaCl (Franssen, 1993; Franssen and Spiers, 1990). 3.3. Seismic anisotropy Using the deformation fabrics (lattice preferred orientation) we measured in this study, we calculated the seismic wave velocities using the elastic constants and density of (Mg,Fe)O. The equation of state and elasticity of (Mg,Fe)O are less well known than those of MgO. We use the elastic constants of MgO that have been calculated to pressures equivalent to the bottom of the lower mantle (Karki et al., 1997). The effects of temperature are to slightly (less than ∼10% of total anisotropy) modify the anisotropy between 0 and 4000 K at 140 GPa, and therefore, ignored in this paper (e.g. Stixrude, 2000). The elastic constants of (Mg,Fe)O are only slightly different from those of MgO (Jacobsen et al., 2002), but the elastic constants of (Mg,Fe)O under deep mantle conditions are unknown. Results at pressures of 0, 25 and 125 GPa are presented here. We used the Voigt–Reuss–Hill average to calculate the elastic constants of aggregates. The results are summarized in Table 2. The results at

25 and 125 GPa can be considered to be representative of those at the shallow and deep lower mantle respectively. We calculated the velocities of (quasi-) compressional wave (VP ) and of two (quasi-) shear waves (VS1 and VS2 ). Also, the polarization of a faster shear waves is calculated by solving the Christoffel equation. We use B ≡ Max[|VS1 − VS2 |/VS2 ] × 100 as a measure of strength of (shear wave) anisotropy. Fig. 9 shows the change of strength of anisotropy, B, with increasing strain and shear stress at pressures of 0, 25 and 125 GPa. The strength of anisotropy (B) increases with strain, but it reaches nearly steady-state value at strain around γ ∼ 4 (Fig. 9A). The strength of anisotropy is insensitive to the stress magnitude in the range of stress explored in this study (Fig. 9B). More details of seismic anisotropy are shown in Figs. 10–12. Fig. 10 shows the orientation dependence of P-wave velocity, Fig. 11 the orientation dependence of the polarization of faster shear waves and Fig. 12 the azimuthal anisotropy of P- and S-waves in the shear plane (which is assumed to be horizontal). The method of Montagner and Nataf (1986) was used to calculate the azimuthal anisotropy. In all Figures, results for three samples (with different strains) corresponding to the elastic constants at three different pressures are shown (Fig. 13). It is seen that the difference in the lattice preferred orientation between a small strain sample (PI784) and

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Fig. 7. Pole figures for the 1 0 0, 1 1 0 and 1 1 1 orientation for all samples. Equal area projections (Schmid net) were used (a half-width of 15◦ and the cluster size of 3◦ are used in the plotting). A number below each set of pole figure shows a number of grains for which orientations are measured. The numbers in the legend represents the density of points relative to the random distribution (1 for the random distribution). The half-width of 15◦ and data clustering of 3◦ are used for contouring. Shear sense is the top to left (sinistral). The EW direction corresponds to the shear direction, and the north and the south poles correspond to the normal to the shear plane. (A) PI784; (B) PI793; (C) PI796; (D) PI80; (E) PI854; (F) PI867; (G) PI873, all grains; (H) PI873, large grains; (I) PI873, small grains.

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Fig. 7. (Continued ).

large strain samples (PI805, PI854) results in a significant difference in the anisotropy. The sign of VSH /VSV anisotropy changes with strain: for a wave propagating along the shear direction (at P = 125 GPa), VSV > VSH at small strains (PI784), whereas VSH > VSV at large strains (PI805, PI854) (Figs. 11 and 12). Anisotropy also changes with pressure due to the change in elastic anisotropy of (Mg,Fe)O. For example, at large strains, when transverse isotropy with a vertical symmetry axis is assumed, VSH > VSV corresponds to the deformation fabrics of (Mg,Fe)O caused by the horizontal flow at P = 125 GPa (D layer conditions) although VSV > VSH corresponds to the horizontal flow at P = 0 GPa (Figs. 11 and 12). Note also that for the anisotropic structure caused by the horizontal shear deformation of (Mg,Fe)O in the D layer, a vertically propagating shear wave has very small polarization anisotropy (Fig. 11). Fig. 12 shows that the azimuthal anisotropy contains a strong 4θ term. At P = 125 GPa, corresponding to a pressure near the D layer, the maximum polarization anisotropy of shear waves propagating along the shear

plane occurs along the shear direction. At this pressure, the fastest (slowest) SH (or P) wave velocity is parallel (or perpendicular) to the flow direction and the slowest (fastest) SH (or P) wave velocity is 45◦ from these two directions. Anisotropy of P-wave is in general weaker than that of S-waves.

4. Discussion The deformation fabrics (lattice preferred orientation) in (Mg,Fe)O found in this study are quite different from those in NaCl reported by Franssen (1993) and Franssen and Spiers (1990). In NaCl, strong maximum of {1 1 0} pole occurs along the shear plane normal, whereas the maxima of {1 0 0} and {1 1 1} are observed along the shear plane normal in (Mg,Fe)O. This difference in LPO results in a major difference in the nature of seismic anisotropy. With NaCl-type LPO, the horizontal shear would results in VSH < VSV anisotropy (Karato, 1998a,b), whereas for LPO of (Mg,Fe)O found in this work, the horizontal flow

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Table 2 Elastic constants (Cij in GPa) of MgO single crystal (Karki et al., 1997) and the calculated constants for the deformed polycrystal samples (except for PI796 and PI873) at 0, 15 and 125 GPa ij 11

12

0 Gpa Single PI784 PI793 PI867 PI805 PI854

291 340 338 339 341 343

91 72 78 78 77 76

25 Gpa Single PI784 PI793 PI867 PI805 PI854

464 481 482 481 480 479

123 145 142 142 143 143

13 91 75 71 71 70 69

14

15

16

22

0 0 1 −1 1 2 1 1 1 −1 1 0

0 −5 −4 −3 −3 −4

123 0 0 143 0 1 146 0 −1 146 0 0 146 0 0 147 −1 0

0 3 2 2 2 2

125 GPa Single 1302 276 276 0 0 PI784 988 440 426 −4 5 PI793 997 411 446 −3 −8 PI867 992 414 448 −4 −3 PI805 983 418 453 −2 3 PI854 975 422 456 −6 1

0 23 18 16 16 20

291 340 331 333 334 335

23

24

25

45

46

91 0 76 0 79 0 77 −1 77 0 77 −1

0 1 1 2 0 0

0 5 4 4 4 5

291 0 337 −1 338 0 340 1 341 −1 342 0

0 0 139 0 0 0 132 0 −3 0 135 0 −2 0 133 0 −1 −1 133 −1 0 −1 133 −1

0 1 1 2 0 0

0 0 0 0 0 0 1 −1 0 0 1 0

0 −3 −2 −2 −2 −3

464 482 482 481 480 480

0 1 0 0 0 0

0 0 1 1 −1 0

0 0 0 0 1 0

276 0 0 0 1302 0 425 −2 −3 −25 1003 6 410 2 −5 −20 998 2 415 7 −9 −18 990 −3 419 0 2 −21 982 3 417 6 1 −24 980 −1

0 −2 13 12 −5 −2

0 2 2 2 5 4

464 1231 481 43 486 142 485 142 484 143 484 142 1302 989 1034 1024 1017 1015

26

33

34

35

36

44

55 139 131 127 127 126 125

56

66

0 1 1 1 1 1

139 128 134 134 133 132

154 169 167 168 168 168

0 0 154 0 0 0 169 0 0 0 171 0 0 −1 172 0 1 0 172 0 0 1 173 −1

154 171 168 168 168 169

190 284 270 275 279 277

0 0 190 0 190 2 −3 286 −4 302 1 −4 307 −3 272 2 −8 309 −4 278 5 2 314 −3 279 3 0 318 −6 283

The reference axes for the elastic constants of polycrystal samples were defined as the direction “1”, “2” and “3” correspond to the shear direction, shear plane normal and perpendicular to both “1” and “2” directions, respectively.

would cause VSH > VSV anisotropy. Since there is no evidence of rapid grain-boundary migration under our experimental conditions, the difference in deformation fabrics must be due to the difference in the dominant slip systems. Karato (1998b) reviewed the slip systems in materials with B1 (NaCl) structure. In the B1 structure, the dominant slip direction (the Burgers vector) is always 1 1 0. However, the dominant glide plane could vary with materials and/or conditions of deformation. One parameter that might affect the choice of the glide plane is elastic anisotropy. However, elastic anisotropy is similar between NaCl and (Mg,Fe)O. Therefore, the different deformation fabrics in these two materials are likely due to other factors such as the difference in the nature of chemical bonding. In materials with strong ionic bonding, the dominant glide plane is {1 1 0} (i.e. the dominant slip system is 1 1 0{1 1¯ 0} although other glide planes are also active), whereas in materials with less ionic bonding, other planes such as the {1 0 0} and/or the {1 1 1}

planes play more important roles. The observed lattice preferred orientation in (Mg,Fe)O is consistent with the active glide planes of {1 0 0} and/or {1 1 1} and, therefore, we suggest that the deformation fabrics in (Mg,Fe)O found in this study reflects less ionic nature of chemical bonding in (Mg,Fe)O than in NaCl. The rate at which LPO develops in (Mg,Fe)O is significantly more sluggish than that in olivine (Zhang and Karato, 1995). This is in parallel with the slow development of dynamic recrystallization found in this study. Dynamic recrystallization completely modifies the microstructures at grain scale, and hence, causes changes in deformation fabrics (Karato, 1988; Lee et al., 2002). Therefore, we consider that the slow evolution of deformation fabrics in (Mg,Fe)O is due to the sluggish kinetics of dynamic recrystallization. Deformation in (Mg,Fe)O is heterogeneous particularly at relatively low temperatures. In a sample PI873, regions near the interface show less strain presumably due to the effects of grooves. However,

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Fig. 8. Representative inverse pole figures for the shear direction and the shear plane normal: (A) PI784; (B) PI805 and (C) PI854. Equal area projections (Schmid net) is used.

such heterogeneous deformation is not seen in other samples deformed at higher (homologous) temperatures. A major difference between samples deformed at high temperature and those at lower temperatures is the size of dynamically recrystallized grains. In high-temperature samples, the size of recrystallized grains is about the same as the starting grain-size. In contrast, in a sample deformed at a lower temperature, the size of dynamically recrystallized grains is considerably smaller than that of a starting material and is close to the size at which the dominant mechanism of deformation changes to diffusion creep (Frost and Ashby, 1982). Therefore, we interpret that the heterogeneous deformation seen in PI873 is caused by the grain-size reduction due to dynamic recrystallization: a small difference in strain between central regions and regions close to the boundary caused by grooving at the piston surfaces resulted in large difference in strength due to grain-size reduction, leading to the enhanced deformation in the central regions. The present experiments were conducted at T /Tm = 0.46–0.65, which are comparable to T/Tm in Earth’s lower mantle (e.g. Yamazaki and Karato, 2001). However, one important difference between the present experimental study and the conditions in Earth’s lower mantle is the nature of elastic anisotropy of (Mg,Fe)O. An elastic anisotropy factor defined by A ≡ 2C44 /(C11 − C12 ) for MgO changes from

Fig. 9. The change of degree of anisotropy with stress (A) and strain (B). The degree of anisotropy is defined as B ≡ Max[|VS1 − VS2 |/VS2 ] × 100 as a measure of strength of (shear wave) anisotropy where VS1,2 represents the two shear wave velocities along a given orientation. Elastic constants of (Mg,Fe)O at P = 0, 25 and 125 GPa are used. (A) The relation between B and stress magnitude, (B) relation between strain and B. The uncertainty of B is estimated to be ∼10% of B-value.

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Fig. 10. Dependence of P-wave velocity on the orientation of wave propagation. P-wave velocities at 0, 25 and 125 GPa are plotted as a function of wave propagation direction on the stereographic projection. Contour intervals are 0.1 km/s and the darker portions correspond to higher velocities. The EW direction corresponds to the shear direction and the top to the shear plane normal. Shear sense is the top to left (sinistral). (A) PI784, the iso-velocity lines correspond to 9.6, 9.7 and 9.8 km/s; (B) PI805, the iso-velocity line correspond to 11.1 km/s; (C) PI854, the iso-velocity lines correspond to 13.9, 14.0, 14.1, 14.2, 14.3 and 14.4 km/s.

A ∼ 1.4 (in our experimental conditions) to A ∼ 0.4 (in the D layer). A comparison of the results for (Mg,Fe)O (A ∼ 1.4) and FeO (A ∼ 1) (Jacobsen et al., 2002) indicates that a change in A has small effects on fabric within this range. However, more detailed study

is needed to justify the application of our data to deep lower mantle where A is significantly lower than the present experimental conditions. The VSH > VSV anisotropy can also be caused by the horizontal laminated structure (Kendall and

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Fig. 11. Dependence of shear wave splitting on the direction of wave propagation at 0, 25 and 125 GPa. Stereographic projection that preserves the orientation is used. At each orientation of wave propagation, the direction of the faster S-wave is shown, and the length of bar is proportional to the magnitude of shear wave splitting defined by (|VS1 − VS2 |/VS2 ) × 100. The EW direction corresponds to the shear direction and the top and the bottom to the shear plane normal. Shear sense is the top to left (sinistral). (A) PI784, (B) PI805 and (C) PI854.

Silver, 1996, 1998). However, unlike the case of laminated structure, anisotropy due to deformation fabrics (of (Mg,Fe)O) should have azimuthal anisotropy. At present, the presence and the details of azimuthal anisotropy are not well constrained (e.g. Lay et al., 1998b). Further studies in azimuthal anisotropy will be useful to constrain the causes for anisotropy and also to infer the flow geometry in or near the D layer.

Finally, contribution from deformation fabrics of (Mg,Fe)SiO3 perovskite must also be considered in a more thorough analysis of anisotropy. Virtually nothing is known about the deformation fabrics in (Mg,Fe)SiO3 perovskite, but for the following reasons, we consider that the contribution from (Mg,Fe)SiO3 perovskite is likely to be not very large in the D layer. First, (Mg,Fe)SiO3 perovskite is likely to be much stronger than (Mg,Fe)O (diffusion creep regime,

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Fig. 12. Azimuthal variation of seismic wave velocities in the shear plane (at 0, 25 and 125 GPa). Zero degree corresponds to the flow direction. Solid, dotted and dashed lines correspond to the shear wave polarization anisotropy ((VSH − VSV )/VSV ), shear wave velocities (VSH , VSV ) and compressional wave velocity (VP ), respectively. Zero degree corresponds to the shear direction. (A) PI784 (γ = 1.4), (B) PI805 (γ = 3.4) and (C) PI854 (γ = 7.8). The magnitude of anisotropy increases with strain (see also Fig. 9). The magnitude and nature of anisotropy also change with pressure as a result of large variation of elastic anisotropy with pressure.

Yamazaki and Karato, 2001; dislocation creep regime, Karato, 1989). In a two-phase aggregate with marked strength contrast, strain is largely partitioned into a weaker phase (e.g. Handy, 1994). Consequently, we expect stronger fabric development in (Mg,Fe)O than in (Mg,Fe)SiO3 perovskite. Second, the elastic anisotropy of (Mg,Fe)SiO3 perovskite is significantly weaker (∼1/4) than that of (Mg,Fe)O under the D layer conditions. Therefore, even if the strength of fabrics is the same for two materials, the strength of resul-

tant anisotropy would be similar (Fig. 13). Therefore, when a much higher strength and resultant smaller strain of (Mg,Fe)SiO3 perovskite is considered, it is likely that the contribution from deformation fabrics of (Mg,Fe)SiO3 perovskite is likely to be significantly smaller than that of (Mg,Fe)O in the D layer. Obviously, however, such a conclusion does not hold for the shallower lower mantle. In these regions, contribution from of (Mg,Fe)SiO3 perovskite cannot be ignored.

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Fig. 13. Polarization anisotropy ((VSH − VSV )/VSV ) corresponding to the horizontal flow of (Mg,Fe)O and (Mg,Fe)SiO3 perovskite. The magnitude of anisotropy corresponds to 100% of each material (in a mixture of the two phases with a certain volume fraction, an appropriate averaging scheme will be needed to calculate contributions from each component). The results for perovskite are from Karato (1998a) that are based on the results on lattice preferred orientation of an analog material, CaTiO3 and the elastic constants of MgSiO3 . Anisotropy due to lattice preferred orientation in the shallow lower mantle is dominated by that of perovskite, but in the deep lower mantle, (Mg,Fe)O has much larger anisotropy due primarily to the increase in elastic anisotropy in this material. Anisotropy in the D layer is likely due mainly to the lattice preferred orientation of (Mg,Fe)O.

5. Concluding remarks The present study has provided the first data set that provides a clue to interpret seismic anisotropy in the lower mantle in terms of flow geometry. The strong anisotropy caused by the deformation fabrics of (Mg,Fe)O in the dislocation creep regime suggests that this material may play an important role in controlling the anisotropy in the lower mantle particularly in the deep portions. We have also shown that strong anisotropy in this material develops only slowly. Therefore, not only the dominance of dislocation creep, but also a large strain is needed to cause significant anisotropy. Through mantle convection calculations assuming composite rheology, McNamara et al. (2001a) recently have shown that the deformation of subducting slabs in the lower mantle occurs mostly by dislocation creep, whereas deformation in other areas of the lower mantle likely occurs by diffusion creep. In addition, McNamara et al. (2001b) showed

that although the majority of the slab is likely to deform by dislocation creep, large strains are limited to the deeper portions. A combination of this convection modeling study with the present experimental study on deformation fabrics provides a plausible explanation for the observed regional variation of anisotropy in the lower mantle (e.g. Lay et al., 1998a,c): anisotropy in the D layer (in the circum-Pacific regions) is caused by high-stress and high strain deformation of (Mg,Fe)O caused by the collision of subducting materials with the core–mantle boundary. Wookey et al. (2001) recently found significant anisotropy in the shallow portions of the lower mantle. Anisotropy in that region cannot be attributed to the deformation fabrics of (Mg,Fe)O and is likely to be caused by the fabric of (Mg,Fe)SiO3 perovskite or by a laminated structure. Further studies on deformation fabrics in (Mg,Fe)SiO3 perovskite and other structures (such as laminated structures) are needed to interpret seismic anisotropy in the shallow lower mantle.

Acknowledgements The deformation experiments have been made using the facilities at Minnesota Mineral and Rock Physics Laboratory which is supported by NSF. We thank Kyung-Ho Lee and Haemyeong Jung for technical assistance in the EBSD measurements. We also thank Mark Zimmerman for the assistance in conducting deformation experiments and Zhenting Jiang for the help in preparing the pole figures. Daisuke Yamazaki was supported by the JSPS fellowship. This research is supported by grants by NSF to SK. References Carter, N.L., Heard, H.C., 1970. Temperature and rate dependent deformation on halite. Am. J. Sci. 269, 193–249. Dingley, D.J., Randle, V., 1992. Microstructural determination by electron backscattered diffraction. J. Mater. Sci. 27, 4545–4566. Franssen, R., 1993. Rheology of Synthetic Rocksalt. PhD. Thesis, University of Utrecht, pp. 221. Franssen, R.C.M.W., Spiers, C.J., 1990. Deformation of polycrystalline salt in compression in shear at 250–350 ◦ C. In: Knipe, R.J., Rutter, E.H. (Eds.), Deformation Mechanisms, Rheology and Tectonics. The Geological Society, London, pp. 201–213. Frost, H.J., Ashby, M.F., 1982. Deformation Mechanism Maps. Pergamon Press, Oxford, pp. 84–92 (Chapter 6).

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