texture development and slip systems in bridgmanite and...

1 3

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

ORIGINAL PAPER

Texture development and slip systems in bridgmanite and bridgmanite + ferropericlase aggregates

L. Miyagi1 · H.‑R. Wenk2

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

not result in a change in this texture type. However, at pres-sures >55 GPa a change in texture to a 100 maximum is observed, consistent with slip on the (100) plane. Ferroper-iclase, when deformed with bridgmanite, does not develop a coherent texture. This is likely due to strain heterogeneity within the softer ferropericlase grains. Thus, it is plausible that ferropericlase is not a significant source of anisotropy in the lower mantle.

Keywords Diamond anvil cell · Bridgmanite · Ferropericlase · Deformation · Slip systems · Seismic anisotropy

Introduction

The Earth’s lower mantle is believed to be predominantly of perovskite-structured (Mg,Fe)SiO3, bridgmanite and (Mg,Fe)O ferropericlase, with bridgmanite compris-ing ~80 % of the lower mantle by volume (Murakami et al. 2007; Komabayashi et al. 2010; Wang et al. 2015). At conditions similar to those of the D″ layer, the region just above the core mantle boundary, bridgmanite under-goes a transformation to the post-perovskite (pPv) struc-ture (Murakami et al. 2004; Oganov and Ono 2004; Shim et al. 2004). However, in localized regions of the D″ with higher temperature bridgmanite may be stable (Hernlund et al. 2005). In order to interpret seismic anisotropy in the lower mantle and D″, it is vital to understand texture devel-opment and slip system activity in bridgmanite and bridg-manite + ferropericlase aggregates.

Much of the lower mantle appears to be seismically iso-tropic (e.g., Chang et al. 2014), and it has been suggested that deformation processes that do not generate anisotropy dominate in the lower mantle (e.g., Karato et al. 1995;

Abstract Bridgmanite (Mg,Fe)SiO3 and ferropericlase (Mg,Fe)O are the most abundant phases in the lower man-tle and localized regions of the D″ layer just above the core mantle boundary. Seismic anisotropy is observed near sub-duction zones at the top of the lower mantle and in the D″ region. One source of anisotropy is dislocation glide and associated texture (crystallographic preferred orientation) development. Thus, in order to interpret seismic anisotropy, it is important to understand texture development and slip system activities in bridgmanite and bridgmanite + fer-ropericlase aggregates. Here we report on in situ texture development in bridgmanite and bridgmanite + ferroperi-clase aggregates deformed in the diamond anvil cell up to 61 GPa. When bridgmanite is synthesized from enstatite, it exhibits a strong (4.2 m.r.d.) 001 transformation texture due to a structural relationship with the precursor enstatite phase. When bridgmanite + ferropericlase are synthesized from olivine or ringwoodite, bridgmanite exhibits a rela-tively weak 100 transformation texture (1.2 and 1.6 m.r.d., respectively). This is likely due to minimization of elastic strain energy as a result of Young’s modulus anisotropy. In bridgmanite, 001 deformation textures are observed at pressures

598 Phys Chem Minerals (2016) 43:597–613

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Meade et al. 1995). Another study suggests that deforma-tion of bridgmanite + ferropericlase results in seismic ani-sotropies that are opposite for each phase, and average to a nearly isotropic aggregate (Wenk et al. 2006a). Anisotropy is observed in some regions at the top of the lower mantle and is attributed to deformation texturing of bridgmanite or ferropericlase (e.g., Wookey et al. 2002). Additionally, the D″ region is heterogeneous and exhibits strong seismic anisotropy (Vinnik et al. 1995; Cottaar and Romanowicz 2013; Chang et al. 2014; Lynner and Long 2014).

Dislocation glide and the associated crystal rotations are likely to be a major mechanism that generates anisotropy in the deep mantle. For bridgmanite, relatively little is known about its deformation properties. Quantitative rheology experiments are challenging to perform at conditions of the lower mantle (e.g., Girard et al. 2016), and bridgmanite is highly unstable upon quenching. Transmission electron microscopy (TEM) to image dislocations and deformation microstructures is difficult for bridgmanite, and only a few studies have been successful (Wang et al. 1990, 1992; Mar-tinez et al. 1997; Miyajima et al. 2009).

Since high-pressure experiments required to study bridg-manite are difficult, the study of analogs materials has been conducted, in hopes of establishing systematic deformation behavior for perovskites as a group (for reviews, see, e.g., Cordier 2002; Walte et al. 2007; Wang et al. 2013). Perovs-kites have a wide range of chemical compositions and struc-ture types (e.g., Navrotsky and Weidner 1989), and there is no clear systematic trend to creep behavior. Nonetheless, dislocations in many perovskites have been identified as having 〈100〉c and 〈110〉c (subscript used for the pseudo-cubic reference frame) Burgers vectors. The pseudo-cubic lattice is commonly used to describe perovskite structures in order to provide a unified reference frame to discuss perovs-kites of different symmetries. For slips system equivalencies between cubic and orthorhombic perovskite structures, the reader is directed to figure 10 of Wang et al. (2013). Based on ambient pressure deformation experiments on a range of cubic, tetragonal and orthorhombic perovskites, it appears that {110}c〈110〉c slip is active at lower temperatures and slip on (001)c〈100〉c is active at higher temperatures (e.g., Cordier 2002). Several recent studies have noted that defor-mation patterns of bridgmanite deviate from cubic symme-try (Wenk et al. 2004, 2006b; Ferré et al. 2007; Carrez et al. 2007). For the purpose of the following discussion, we use the orthorhombic reference with the Pbnm space group for bridgmanite. Bridgmanite is occasionally indexed using the Pnma space group, and to convert between Pbnm and Pnma the following transformation matrices can be used.

(a, b, c)Pnma

0 1 0

0 0 1

1 0 0

= (a, b, c)Pbnm

and

A few deformation studies exist on bridgmanite using the diamond anvil cell (DAC) (Meade and Jeanloz 1990; Meade et al. 1995; Merkel et al. 2003; Wenk et al. 2004, 2006b), a modified large volume press (LVP) assembly (Chen et al. 2002; Cordier et al. 2004; Miyajima et al. 2009), and the rotational Drickamer apparatus (RDA) (Girard et al. 2016). Early DAC deformation studies of bridgmanite found no evidence for texture development in decompressed samples (Meade et al. 1995) or in in situ measurements of samples deformed outside the bridg-manite stability field (Merkel et al. 2003). In contrast, Wenk et al. (2004) and Wenk et al. (2006b) reported sig-nificant texture development in bridgmanite and bridg-manite + ferropericlase aggregates synthesized in situ in the DAC from different starting materials. Different textures were observed, depending on starting material, and it was suggested that textures could be explained by slip on (010)[100], (100)[010] and (001)〈110〉. Twinning on (110) may be active as well (Wenk et al. 2004). Chen et al. (2002) performed in situ stress relaxation measure-ments at 20 GPa and 1073 K using the LVP and also found evidence for activity of (110) twinning. Additionally, TEM studies of recovered samples from high-pressure experi-ments have documented reflection twins on (110) and (112) (Wang et al. 1990, 1992; Martinez et al. 1997). Cordier et al. (2004) suggested (001)[100] and (001)[010] disloca-tions based on X-ray line broadening analysis of samples recovered from a LVP deformation experiment at 25 GPa and 1700 K. A TEM study by Miyajima et al. (2009) doc-umented 〈110〉 Burgers vectors. Girard et al. (2016) per-formed high-pressure and high-temperature shear defor-mation on aggregates of bridgmanite and ferropericlase at conditions equivalent to the top of the lower mantle. Deformation mechanisms were not reported; however, they found that ferropericlase is weaker than bridgmanite and that strain is preferentially partitioned into ferropericlase.

Slip systems in MgSiO3 perovskite have also been investigated numerically using the Peierls–Nabarro (PN) model and calculation of generalized stacking faults and the Peierls–Nabarro–Galerkin (PNG) model to evaluate Peierls stresses (Ferré et al. 2007; Gouriet et al. 2014). These studies find that (010)[100] and (100)[010] should be the easiest slip systems. On the other hand, Mainprice et al. (2008) combined Peierls stresses calculated from the PN model with the viscoplastic self-consistent (VPSC) code to model slip system activities. It was found that at pressures

599Phys Chem Minerals (2016) 43:597–613

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Core structure and mobility of (010)[100] and (100)[010] dislocation have been modeled with molecular dynam-ics, and (100)[010] slip was found to be more mobile than (010)[100] between 30 and 50 GPa, but less mobile above 50 GPa (Hirel et al. 2014). Recently, Kraych et al. (2016) used molecular dynamics simulations to study kink pair nucleation along (010)[100] screw dislocations, and calcu-lated a Peierls stress of 4.9 GPa at 30 GPa pressure.

Many studies have been dedicated to slip systems in ferropericlase and periclase. Room-temperature DAC experiments on periclase (Merkel et al. 2002) and fer-ropericlase (Tommaseo et al. 2006; Lin et al. 2009; Mar-quardt and Miyagi 2015) obtain textures best explained by slip on {110}

〈

110〉

. Experiments on ferropericlase using the Paterson and Griggs apparatuses find that at low pres-sures (300 MPa) and high temperature (up to 1400 K), {001}〈110〉 and possibly {111}〈110〉 may also become active (Stretton et al. 2001; Yamazaki and Karato 2002; Heidelbach et al. 2003). Single-crystal deformation experi-ments in the D-DIA up to 9 GPa and 1500 K recorded relative strengths of slip systems and found that at the conditions of the experiments {110}

〈

110〉

slip is domi-nant. However, based on the pressure dependence of slip system strengths a change to dominant {001}〈110〉 slip at ~23 GPa is expected (Girard et al. 2012). Theoretical cal-culations also predict an inversion in slip system activities between pressures of 40–60 GPa. At room temperature and pressures below 40 GPa, {110}

〈

110〉

is favored but above 60 GPa {001}〈110〉 becomes more active. At high tem-peratures, both slip systems may be active (Amodeo et al. 2012). Here we report on transformation and deformation textures and stress development during DAC deformation experiments performed on bridgmanite synthesized from enstatite and on two-phase mixtures of bridgmanite + fer-ropericlase synthesized from olivine and ringwoodite.

Experimental technique

Finely ground polycrystalline samples were loaded into two-stage boron kapton gaskets (Merkel and Yagi 2005) with an 80-μm-diameter sample chamber. Samples were compressed with 300-μm-flat culet diamonds. A small Pt flake ~10 µm in diameter and 4 µm thick (Alfa Aesar 99.95 % purity) was placed near the side of the sample chamber. This was used to locate the sample with X-ray absorption scans and for online pressure calibration using the third-order Birch–Murnaghan equation of state of Fei et al. (2007). After conversion bridgmanite or bridg-manite + ferropericlase, data were collected at the center of the sample (away from the Pt flake to minimize the Pt diffraction signal). Diffraction images were recorded on a MAR3450 image plate. Data were collected in radial

diffraction geometry where the sample is irradiated with X-rays perpendicular to the compression axis. Without a viscous pressure medium, the diamonds impose both pres-sure and axial differential stress, inducing elastic and plas-tic deformation. The radial diffraction geometry allows in situ measurement of texture and lattice strain develop-ment (Wenk et al. 2006b).

The first two experiment runs (Runs 1–2) were per-formed at beamline 16 ID-B of the HP-CAT sector of the Advanced Photon Source at Argonne National Labora-tory, Argonne IL. In both of these runs, sample to detec-tor distance and detector geometry were determined with a CeO2 standard. The X-ray wavelength was 0.3676 Å in Run 1 and 0.3680 Å in Run 2. Beam size in both runs was 10 × 10 μm. Diffraction images were collected using a 300 s exposure time. During data collection, samples were oscillated ±5° about an axis perpendicular to compression in order to improve grains statistics.

In Run 1, the starting material was Bamble enstatite ~(Mg0.86Fe0.14)SiO3, and in Run 2 it was San Carlos oli-vine ~(Mg0.87Fe0.13)2SiO4. Samples were compressed to ~29 (Run 1) and ~35 GPa (Run 2) and then converted to bridgmanite and bridgmanite + ferropericlase, respec-tively, using single-sided laser heating. In order to avoid grain growth which would result in a spotty diffraction pat-tern, heating was performed at the lowest temperature that the phase transformation could be induced. Laser heating temperatures were on the order of 1500–1600 K (ESM for Appendix A). After laser heating, a radial diffraction pat-tern was collected to confirm full conversion (Fig. 1a, d, g).

After conversion, pressure was manually increased at ambient temperature and in situ radial diffraction images were recorded at each pressure step. Once pressures of ~44 (Run 1) and ~55 GPa (Run 2) were reached, the sam-ples were annealed by laser heating to ~1500–1600 K to relax stresses and to see whether texture changes occurred at high temperature. Diffraction patterns were recorded to observe changes in textures and lattice strains. After heat-ing, pressure was increased again at room temperature to ~52 (Run 1) and ~65 GPa (Run 2) and diffraction images were collected.

The third experiment run (Run 3) was performed at beamline 12.2.2 of the Advanced Light Source at Law-rence Berkeley National Laboratory, Berkeley, CA. The X-ray beam with a wavelength of 0.4959 Å was collimated to 10 × 10 μm. Calibration was performed with a LaB6 standard. During data collection, X-ray exposure time was 300 s and the sample was oscillated ±5° around the com-pression axis.

Starting material in Run 3 was the same San Carlos olivine as in Run 2. The sample was compressed in the DAC using a gas membrane system specifically designed for radial diffraction (Miyagi et al. 2008). At ~19 GPa, the


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sample was converted to ringwoodite by single-sided laser heating. The sample was then deformed at room tempera-ture to ~35 GPa and subsequently laser-heated to convert to bridgmanite + ferropericlase. A laser heating procedure similar to the first two runs was used, and temperature dur-ing heating was on the order of 1500–1600 K. After con-version to bridgmanite + ferropericlase, pressure was incrementally increased at room temperature to ~52 GPa and then decompressed to ~40 GPa while recording in situ radial diffraction images.

Data analysis

Diffraction images were first processed using the program Fit2d (Hammersley et al. 1996). Images were integrated over 10° azimuthal arcs into 36 spectra (Fig. 1) and were analyzed using the Rietveld method as implemented in the software package MAUD (e.g., Lutterotti et al. 2014). For these analyses, we follow the general procedure for pro-cessing radial diffraction data as outlined in Wenk et al. (2014). A Q range of ~2.53–4.96 Å−1 was used for these analyses, where Q = 2π/d-spacing (Fig. 1, A1). Back-grounds were interpolated using fifteen points manually selected at positions between diffraction peaks. Diffraction patterns were refined for lattice parameters, crystallite size, lattice strains and preferred orientation. Crystallite size was refined using an isotropic size-strain model (Lutterotti and

Scardi 1990) that records the average size of coherently scattering domain within the sample. In general, crystal-lite size is poorly constrained from diffraction data (Toby 2006) and is particularly problematic for spotty diffraction images. As a result, crystallite sizes obtained in this study likely have true errors that are considerably larger than the standard deviations obtained from the Rietveld refinement.

Samples deformed in axial compression show varia-tions in lattice spacings with respect to the compression direction. These are due to elastic strains imposed by the deformation device and are apparent in synchrotron radial diffraction images as sinusoidal variations in peak posi-tions with azimuth (Fig. 1, A1). Azimuthal positions where peaks show high Q values (low d-spacings) correspond to the compression direction. Plastic deformation by disloca-tion glide and/or mechanical twinning causes crystal rota-tions which generate texture. Texture appears as systematic intensity variations along Debye rings (Fig. 1). By decon-voluting this information, the orientation distribution (OD) can be determined.

For refinement of elastic lattice strains and calculation of stresses, we use the moment pole stress model (Mat-thies and Humbert 1993) with the bulk path geometric mean micromechanical model (Matthies et al. 2001). The geometric mean lies between the Voigt and Reuss bounds. In DAC deformation experiments, the anvils impose both hydrostatic and deviatoric stresses on the sample. Accord-ing to the geometry of axial compression, the stress tensor

Fig. 1 Unrolled diffraction images from Runs 1 (a–c), 2 (d–f) and 3 (g–i). Images are shown in Q space vs azimuth (η). Compression direction is indicated by black arrows. The major bridgmanite peaks

are labeled as are all ferropericlase and platinum peaks. Pressures shown are calculated from the platinum unit cell volume


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σij can be separated into hydrostatic σp and deviatoric stress Dij components such that

where t is the axial stress component and provides a lower bound estimate for the flow strength of the material (e.g., Singh 1993). For refinement, stresses were fixed such that σ11 = σ22 and σ33 = −2σ11, where σ33 is the largest princi-pal stress and is negative for compression, according to the conventions in MAUD.

In order to calculate stresses from lattice strains, we use the equation of state for each phase (bridgmanite and ferropericlase) and use the calculated pressure to correct single-crystal elastic constants to experimental pressures. The presence of Fe in these samples and the effects of Fe partitioning between bridgmanite and ferropericlase com-plicates pressure calibration and the choice of elastic con-stants for these phases (ESM for Appendix A). For Run 1, we use the equation of state of bridgmanite with 15 % Fe substitution, and for Runs 2 and 3 we use the equation of state for iron free bridgmanite (Lundin et al. 2008). For all three runs, the ab initio single-crystal elastic constants of Wentzcovitch et al. (1998) for MgSiO3 were corrected to experimental pressures and used to calculate stress in bridgmanite. For pressure calibration and single-crystal elastic constants of ferropericlase, we use the high-spin equation of state and Cij for (Mg0.9,Fe0.1)O (Marquardt et al. 2009). It should be noted that the moment pole stress model is purely elastic and does not account for the effects of plasticity. In the implementation in MAUD, it is more heavily weighted to the lattice strains on the most intense diffraction peaks and thus may over- or underestimate the actual value of t.

We use the tomographic E-WIMV algorithm for texture refinement. E-WIMV is similar to the WIMV model (Mat-thies and Vinel 1982) but allows for incomplete and arbi-trary pole figure coverage. We use an orientation distribu-tion function (ODF) resolution of 15°. Textures were first refined without imposing symmetry. It was verified that textures exhibit approximate axial symmetry about com-pression and are well centered in the pole figure. Cylin-drical symmetry is then imposed about the compression axis, consistent with the geometry of axial compression, and the ODF was recalculated. The ODF from MAUD was exported to Beartex (Wenk et al. 1998) and smoothed with a 10° Gauss filter.

Textures generated during axial compression experi-ments can be compactly represented by an inverse pole fig-ure (IPF) which represents the orientation of the compres-sion axis relative to crystal coordinates. Pole densities are given in multiples of random distribution (m.r.d.), where

σij =

σP 0 0

0 σP 0

0 0 σP

+

−t�

3 0 0

0 −t�

3 0

0 0 2t�

3

= σP + Dij

1 m.r.d. corresponds to a random distribution. In the case of bridgmanite, the crystal symmetry is orthorhombic (Pbnm) and only one quadrant of the inverse pole figure is needed to represent the OD. For cubic ferropericlase, a smaller cubic sector is used.

Results

Pressure and differential stress

Pressure calculated from bridgmanite, ferropericlase and Pt is reasonably consistent throughout the experimental runs (Table 1). In Runs 1 and 3, pressure from Pt is gener-ally a few GPa higher than bridgmanite and ferropericlase (Table 1). Pressures calculated from bridgmanite and fer-ropericlase are typically within ~1 GPa. Discrepancies in pressures calculated from the various phases may be due to stress heterogeneity and pressure gradients within the cell or to incorrectly assumed Fe contents. Since the equation state of bridgmanite is only weakly dependent on Fe con-tent, pressures calculated from bridgmanite are likely more robust than those calculated from ferropericlase. Pressures calculated from Pt are likely affected by stress gradients due to the position of the Pt flake on the edge of the sample chamber.

After conversion to bridgmanite or bridgmanite + ferro-periclase, variations in Q values relative to the compres-sion direction are small, indicating that stresses are low (Fig. 1a, d, g). However, in the sample converted from oli-vine (Run 2) stresses immediately after conversion are rela-tively higher (Fig. 2d) than in the samples converted from enstatite (Run 1) (Fig. 2a) or from ringwoodite (Run 3) (Fig. 1g). Upon compression, stresses increase, and the dif-fraction patterns become slightly smoother due to effective crystallite size reduction (Fig. 1b, e, h). Laser annealing of samples in Runs 1 and 2 reduces stresses but does not result in spotty diffraction images, and thus grain growth and recrystallization are minimal (Fig. 1c, f). For Run 3 where decompression data were collected, stresses relax during unloading (Fig. 1i).

Stress levels in bridgmanite are quite similar in Runs 1 and 2 for similar pressures (Fig. 2; Table 1). In both runs, deviatoric stresses increase with increasing pressure, ranging from −2 to −12 GPa, and exhibit a similar slope (Fig. 2). Upon laser annealing at 1500–1600 K, stresses relax to similar levels in both runs, although pressure is significantly higher in Run 2 (Fig. 2). Further compression results in increased deviatoric stresses (Fig. 2; Table 1). In Run 2, stresses in ferropericlase also increase with increas-ing pressure. Prior to annealing, stresses in ferropericlase are ~20–30 % lower than those in bridgmanite (Fig. 2; Table 1). After annealing, stresses in bridgmanite and


1 3

Tabl

e 1

Exp

erim

enta

l con

ditio

ns, l

attic

e pa

ram

eter

s, m

icro

stru

ctur

e pa

ram

eter

s, s

tres

s an

d te

xtur

e in

form

atio

n fr

om R

ietv

eld

refin

emen

t for

Run

s 1–

3

Stan

dard

dev

iatio

ns f

rom

Rie

tvel

d re

finem

ent a

re g

iven

in p

aren

thes

is. N

ote

that

sta

ndar

d de

viat

ions

fro

m R

ietv

eld

refin

emen

t und

eres

timat

e ac

tual

unc

erta

intie

s, p

artic

ular

ly f

or c

ryst

allit

e si

ze.

Bri

dgm

anite

and

fer

rope

ricl

ase

are

abbr

evia

ted

Br

and

Fp, r

espe

ctiv

ely

a A

fter

lase

r an

neal

ing

to ~

1500

–160

0 K

b M

easu

red

duri

ng u

nloa

ding

Run

#Pr

essu

reU

nit c

ell p

aram

eter

sC

ryst

allit

e si

zeV

ol. f

ract

ion

tIP

F m

ax

Pt (

GPa

)B

r (G

Pa)

Fp (

GPa

)Pt

a (

Å)

Br

(Pbn

m)

a

(Å

)B

r (P

bnm

)

b (Å

)B

r (P

bnm

)

c (Å

)Fp

a (

Å)

Br

(Å)

Fp (

Å)

Br

(%)

Fp (

%)

Br

(G

Pa)

Fp (

GPa

)B

r (

m.r.

d.)

Fp (

m.r.

d.)

131

28–

3.80

84 (

3)4.

6372

(2)

4.80

52 (

3)6.

6929

(3)

–36

5 (1

)–

100

–−

1.91

(2)

–4.

2–

138

37–

3.78

84 (

6)4.

6041

(2)

4.77

38 (

2)6.

6401

(2)

–27

2 (1

)–

100

–−

5.80

(2)

–3.

5–

149

44–

3.75

96 (

1)4.

5774

(3)

4.74

63 (

3)6.

5964

(4)

–31

7 (2

)–

100

–−

9.85

(2)

–3.

5–

1a48

46–

3.76

15 (

3)4.

5579

(2)

4.74

54 (

2)6.

5871

(3)

–35

8 (2

)–

100

–−

2.27

(2)

–4.

0–

156

52–

3.74

26 (

5)4.

5366

(2)

4.72

55 (

2)6.

5585

(2)

–41

1 (3

)–

100

–−

5.0

(2)

–3.

4–

233

3335

3.80

12 (

20)

4.59

90 (

2)4.

7819

(3)

6.65

35 (

3)4.

0084

(1)

355

(2)

476

(5)

7327

−4.

41 (

3)−

3.35

(2)

1.2

1.1

236

3738

3.79

26 (

10)

4.58

57 (

2)4.

7692

(2)

6.63

42 (

3)3.

9952

(1)

352

(2)

501

(5)

7129

−6.

03 (

2)−

4.74

(2)

1.4

1.1

245

4546

3.76

93 (

14)

4.55

34 (

3)4.

7400

(4)

6.58

47 (

4)3.

9622

(1)

326

(2)

408

(4)

6733

−9.

53 (

4)−

7.25

(3)

1.7

1.1

252

5252

3.75

15 (

8)4.

5296

(4)

4.71

50 (

5)6.

5533

(6)

3.93

65 (

1)22

1 (1

)24

8 (2

)69

31−

11.8

9 (5

)−

8.67

(4)

1.7

1.1

2a53

5455

3.74

96 (

8)4.

5232

(2)

4.70

39 (

2)6.

5469

(3)

3.92

55 (

1)31

4 (1

)24

7 (1

)69

31−

2.45

(2)

−2.

09 (

3)2.

31.

4

261

6465

3.73

18 (

14)

4.48

04 (

2)4.

6872

(2)

6.49

63 (

2)3.

8906

(1)

377

(2)

340

(2)

6931

−6.

56 (

2)−

5.83

(2)

1.7

1.1

336

3536

3.79

43 (

1)4.

6023

(5)

4.77

28 (

6)6.

6389

(7)

4.00

56 (

1)26

9 (1

)35

1 (2

)80

20−

1.90

(4)

−1.

77 (

3)1.

61.

2

348

4645

3.76

09 (

1)4.

5577

8 (3

)4.

7353

(4)

6.57

94 (

5)3.

9645

(1)

240

(1)

442

(6)

8416

−6.

71 (

2)−

6.01

(3)

1.8

1.2

353

5049

3.74

85 (

1)4.

5483

(6)

4.71

92 (

6)6.

5618

(8)

3.94

97 (

2)25

2 (1

)59

8 (9

)85

15−

8.32

(5)

−7.

30 (

5)1.

71.

2

3b51

4847

3.75

34 (

1)4.

5492

(3)

4.72

74 (

3)6.

5715

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1)30

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)78

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3939

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5833

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4.75

79 (

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6212

(4)

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88 (

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7 (1

)49

1 (7

)81

19−

3.34

(2)

−3.

10 (

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61.

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3b39

3839

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46 (

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5849

(4)

4.76

00 (

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6244

(4)

3.99

11 (

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)35

0 (3

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88 (

3)1.

71.

1


1 3

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

Textures

Before conversion to bridgmanite, enstatite has a strong maximum at 100 with a minimum at 001 (Fig. 3a, 29 GPa). This texture is consistent with deformation on the (100)[001] slip system (e.g., Carter 1976). After trans-formation from enstatite, bridgmanite exhibits a texture with a sharp maximum at 001 (Fig. 3a, 31 GPa). Dur-ing compression, texture strength is reduced from 4.2. to 3.5 m.r.d.. During annealing, texture strength increases to

Fig. 2 Axial stress component (t) versus pressure for Runs 1–3. Pres-sures are calculated from the unit cell volumes of bridgmanite and ferropericlase. Dashed lines show points where the sample is laser-heated (~1500–1600 K) to allow relaxation of elastic stresses at high temperature. Dotted lines indicate decompression. Errors from Riet-veld refinement are smaller than the symbol size

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


1 3

4.0 m.r.d. (Fig. 3a, 48 GPa). Further compression results in a reduction in texture strength to 3.4 m.r.d. (Fig. 3a, 56 GPa, Table 1).

In Run 2, prior to transformation to bridgmanite + fer-ropericlase, olivine has a minimum at 001 maxima, with a girdle along the 100, 110, 010 periphery of the IPF (Fig. 3b). This pattern is similar to previous radial DAC measurements on olivine and is consistent with low tem-perature {0kl}[100] slip (Wenk et al. 2006b). For bridg-manite transformed from olivine, IPFs show an initially dif-fuse maximum spreading from 100 to 001, with minimum at 010 (Fig. 3b, 33 GPa). Upon compression, bridgmanite develops a maximum at 001 (1.7 m.r.d., Fig. 3b, 52 GPa). Annealing at ~1500–1600 K results in the texture maxi-mum near 001 becoming stronger (2.3 m.r.d.) and slightly offset toward 100 (Fig. 3b, 53 GPa). After laser annealing, further compression results in a change in texture type to a 100 maximum (1.7 m.r.d., Fig. 3b, 61 GPa). Textures in bridgmanite synthesized from olivine are only about half as strong as in Run 1 (2.3 vs. 4.2 m.r.d.) due to the strong enstatite to bridgmanite transformation texture (Table 1). IPFs for ferropericlase in Run 2 show that neither compres-sion nor laser heating induces significant texturing in fer-ropericlase (Fig. 3c).

Before the transformation to bridgmanite + ferroperi-clase, ringwoodite exhibits a maximum at 110 with a mini-mum at 111 (Fig. 5d). This is consistent with dominant {111}〈110〉 slip, as identified from previous texture meas-urements on ringwoodite (e.g., Wenk et al. 2006a; Miyagi et al. 2014). The ringwoodite IPF also exhibits a smaller maximum at 001 which could indicate some contribu-tion of {110}

〈

110〉

slip (Merkel et al. 2002). Bridgmanite transformed from ringwoodite exhibits a weak transforma-tion texture comparable to Run 2 (Fig. 3d, 36 GPa). With increased pressure, there is little texture change in bridg-manite (Fig. 5c, 53 GPa). During decompression, bridg-manite develops a maximum near 001 (1.7 m.r.d., Fig. 3d, 39 GPa, Table 1). Also in this experiment, ferropericlase remains essentially random (Fig. 3e) Textures in bridg-manite synthesized from ringwoodite, like in Run 2, are only about half as strong as in Run 1 (1.8 vs. 4.2 m.r.d.) (Table 1).

Discussion

Differential stress

In Runs 1 and 2, stresses in bridgmanite are considerably higher than in Run 3 (Fig. 2). It is likely that in Run 3 dif-ferential stress was not high enough to reach bulk plastic

yielding, consistent with the lack of significant texture evo-lution upon compression. Run 1 does not exhibit a change in texture type, only changes in texture strength. It is likely that bridgmanite reaches its flow strength in this run, but deformation textures are obscured by the strong (4.2 m.r.d.) transformation texture. In Run 2, bridgmanite exhibits clear texture evolution and we conclude that the highest stresses obtained in this run are reflective of the flow strength. Sev-eral authors have also measured stresses in bridgmanite, but results are difficult to compare. Compared to our result, these studies were either performed at lower pressures (Chen et al. 2002; Merkel et al. 2003), a different technique was used to measure differential stress (Meade and Jeanloz 1990), or experiments were performed at lower pressure, higher temperature and steady state (Girard et al. 2016). For Runs 1 and 2, differential stress measurements are lower than those of Chen et al. (2002) and Merkel et al. (2003), which is not surprising as these studies were performed on pre-synthesized samples and deformation occurred entirely or largely outside the stability field of bridgmanite. It is unclear how this may affect the strength of the material. In the current study, samples are synthesized at ~30 GPa, and thus, stresses are initially low due to stress relaxation during laser heating and the phase transformation. Meade and Jeanloz (1990) observed stresses in bridgmanite up to ~60 GPa confining pressure using the pressure gradient method. They found that deviatoric stresses reached a max-imum value of ~7 GPa at 40 GPa and did not increase with continued compression to 60 GPa. In Runs 1 and 2, stresses in bridgmanite are significantly higher (~10–12 GPa) prior to annealing (Fig. 2; Table 1). Stresses measured at the low-est pressures in our experiments (−1.9 to −4.4 GPa, Fig. 2. Table 1) are qualitatively similar to the work of Girard et al. (2016) which measured shear stresses up to ~6 GPa.

In Run 2, prior to annealing, the lower stresses in ferro-periclase indicate that ferropericlase is significantly weaker than bridgmanite under these conditions. During cold com-pression in Run 2, the strength contrast between bridgman-ite and ferropericlase ranges from 1.3 to 1.4, but decreases to 1.2 during annealing. This is a smaller strength contrast than the factor of 4 observed by Girard et al. (2016) and the factor of 2 observed by Wang et al. (2013) in CaGeO3 perovskite + MgO aggregates. Stresses in ferropericlase are similar to recent diamond anvil cell measurements of Marquardt and Miyagi (2015) and are larger than those measured by Lin et al. (2009). It is likely that ferropericlase in Run 2, at least prior to annealing, has reached its flow strength even though we do not observe significant texture evolution. In Run 3, stresses in ferropericlase are lower than in Run 2 and are considerably lower than those of Marquardt and Miyagi (2015).


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Textures in bridgmanite

Transformation textures

In Run 1, the IPFs before and after transformation show a strong correlation between the enstatite (100) and bridg-manite (001) poles. Other directions are less strongly cor-related. In both of these structures, these lattice planes are parallel to the layering of the Mg2+ cations (Fig. 4a, b). Oxygen anions are only slightly reshuffled as Si–O coor-dination changes from tetrahedral to octahedral during the phase transformation. This coordination change can be accomplished by chains of silicate tetrahedra bridging across the layering (along the c-axis) and also linking with adjacent chains (along the b-axis). Thus, interstitial posi-tions would only change slightly and Mg2+ cation layer-ing would be largely preserved between the two structures (Fig. 4c, d). In the Pbnm bridgmanite structure [100] and [010] directions are structurally quite similar (Fig. 4d) and it is to be expected that there would not be a strong cor-relation between enstatite [010] and [001] and bridgman-ite [100] or [010] directions. It is possible that akimotoite forms as a metastable phase during the transformation of enstatite to bridgmanite (Kuroda et al. 2000). We do not observe diffraction peaks consistent with the formation of akimotoite but cannot rule out that this may be an inter-mediate structure during the phase transformation. Simi-lar transformation textures are also observed in MgGeO3 post-perovskite synthesized from an enstatite phase (e.g., Merkel et al. 2006; Okada et al. 2010; Miyagi et al. 2011). Thus, it is not surprising that transformation textures would be generated during the transformation of enstatite to bridgmanite.

For synthesis from olivine and ringwoodite, a disso-ciation reaction occurs to form bridgmanite and ferro-periclase, and it is less likely that structural relationships control transformation textures. The Young’s modulus of bridgmanite is strongly anisotropic with [100] ~20 % softer than the [010] direction (Wentzcovitch et al. 1998). The low elastic strain configuration for bridgmanite is with the soft [100] direction in the direction of maximum stress (Wenk et al. 2004), similar to observed transformation tex-tures in Runs 1 and 3. Ferropericlase is random after the phase transformation, but is nearly elastically isotropic at ~30 GPa and 1500 K (Marquardt et al. 2009); thus, there would be no preferred low elastic strain energy orientation.

It is possible that bridgmanite grains nucleate preferen-tially during the phase transformation with the soft [100] in the direction of highest stress, i.e., oriented growth in a stress field. Alternately, {110} twinning may occur during the transformation relieving stress and resulting in a 100 texture (Wenk et al. 2004). {110} twins have been observed in recovered samples (Wang et al. 1990, 1992; Martinez et al. 1997), and their twin wall morphology suggests stress relief during formation (Wang et al. 1990). Our results can-not distinguish between these different mechanisms, and it is possible that a combination of the two processes occurs.

Polycrystal plasticity modeling

For simulations, we used the Los Alamos viscoplastic self-consistent code (VPSC) version 6 (Lebensohn and Tomé 1994). The development of textures depends on the starting texture, deformation geometry, the relative activities of var-ious deformation modes (slip and twinning) and total strain. Miyagi et al. (2011) showed that to interpret deformation

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


1 3

textures in terms of slip system activity one must account for transformation textures. We use the transformation tex-tures obtained just after synthesis of bridgmanite as start-ing points for our simulations. Transformation textures for Runs 2 and 3 are quite similar, and thus, we only show simulations where the transformation textures from Run 1 (Fig. 3a, 31 GPa) and Run 2 (Fig. 3b, 33 GPa) were used. Models were run for axial compression to 20 % strain as polycrystal plasticity models for 20 % strain compare well to DAC experiments (Wenk et al. 2006b).

As deformation proceeds, crystals deform and rotate to generate preferred orientation. Slip system and twin mode activities are determined by the orientation of slip planes and slip directions, their symmetric variants, and corre-sponding critical resolved shear stresses (CRSS) (Table 2 with starting texture transformed from enstatite and Table 3 with starting texture transformed from olivine). Applying different CRSS values will favor one deformation mode over another (Tables 2, 3) resulting in different textures (Figs. 5, 6). By determining which simulated texture most closely matches experimental textures, deformation mecha-nisms that are active under the experimental conditions can be inferred. In these models, we test (100)[010], (010)[100], (001)[100], (001) 〈110〉, (100)〈011〉 and (010) 〈101〉 slip systems. {111}〈101〉 slip is included to close the yield surface but is assigned a high CRSS and thus is minimally activated. We also include {110}

〈

110〉

and {112}〈

111〉

twinning (Tables 2, 3; Fig. 5, 6).

Models using the transformation texture in Run 1 at 20 % strain show little variation in texture type as all dis-play a maximum at 001 (Fig. 5, except j). The only excep-tion is {112} twinning where a maximum near 010 is observed (Fig. 5j). (100)[001] and (100)〈011〉 slip weaken texture strength (Fig. 5b, c) as does slip on (010) (Fig. 5d, e). In Run 1, a reduction in texture strength during cold compression (Fig. 3a, Table 1) may indicate activation of slip systems on planes other than (001). This sample has a strong 001 texture after conversion, and most grains are oriented with (001) at high angles to compression. As the angle between stress and the slip plane normal or the slip direction approaches 90°, the resolved shear stress on that slip system goes to 0, and thus, the slip system can-not be active. It would not be surprising that slip systems on planes other than (001) would be activated as the strong transformation texture will geometrically suppress slip on (001). The strong transformation texture in Run 1 also makes it ambiguous to interpret slip systems, as favoring different slip systems has little effect other than strength-ening and weakening the 001 maximum. We can, however, rule out significant activity of {112} twinning.

VPSC models starting with the transformation texture from Run 2 show significant variation depending on slip

systems (Fig. 6). This is due to the fact that the transfor-mation texture is weak; consequently, Run 2 provides robust indicators of active deformation modes. For bridg-manite, dominant slip on (100) results in a 100 maximum (Fig. 6a–c) and dominant slip on (001) produces a maxi-mum at 001 (Fig. 6f–h, k, l). Slip on (010) produces dif-fuse textures (Fig. 6c, d). Different slip directions in the same slip plane only have a minor effect on the resulting texture. Allowing slip in more directions within a given slip plane results in stronger textures with a more concentrated maximum (Fig. 6k, l). Twinning on {110}

〈

110〉

depletes 010 orientations and generates a maximum at 100 (Fig. 6i). {112}

〈

111〉

twinning results in the depletion of 001 orien-tations in IPFs and forms a maximum near 010 (Fig. 6j). Twinning textures are much stronger than experimental textures and stronger than textures induced by dislocation glide only. Thus, twinning is unlikely to be significant in these experiments.

The 001 maximum that develops during deformation in Run 2 (Fig. 3b, 52 GPa) is consistent with models for slip on (001) planes but allowing slip in several directions (Fig. 6k, l). After annealing in Run 2 (Fig. 5b, 53 GPa), the maximum at 001 becomes stronger and slightly offset toward 100 but is still consistent with slip on (001) (Fig. 6). The increase in texture strength after laser annealing is likely due to increased strain under high temperature. In Run 2, compression after laser heating results in the devel-opment of a 100 maximum. This is most similar to slip on (100) in the [010], [001] or 〈011〉 directions (Fig. 6a–c). {110} twinning can also produce a 100 maximum, but it is unlikely to produce this texture change. {110} twinning switches 010 orientations to 100, but once a 001 deforma-tion texture has developed (Fig. 5b, 53 GPa) and there are few orientations at 010 to twin to 100. Orientations at 001 are largely unaffected because they are unfavorably orien-tated. This is similar to the simulation shown in Fig. 5i.

The transformation texture in Run 3 is very similar to that of Run 2, and no reinterpretation of the conclusions based on the models using the transformation texture from Run 2 is needed. During compression, bridgman-ite synthesized from ringwoodite shows little change in texture. However, upon decompression development of a 001 maximum is observed. This would be consistent with slip on (001) as observed in Run 2. Although the sample is undergoing decompression, the deviatoric stress state is still that of axial compression; thus, it is possible to develop compression textures during decompression. This has also been observed in hcp Fe during decompression (Miyagi et al. 2008). Flow strength and associated texture devel-opment are likely time dependent. During decompression, there is a significant time lag (1–2 h) between reduction in gas membrane pressure and pressure decrease in the


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

Slip system Model

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

(100)[010]

CRSS 1 4 3 3 3 3 3 3 3 3 3 4

Start activity 27 % 9 % 7 % 1 % 3 % 7 % 8 % 9 % 8 % 5 % 0 % 6 %

End activity 23 % 10 % 7 % 1 % 4 % 7 % 8 % 8 % 8 % 23 % 7 % 6 %

(100)[001]

CRSS 4 1 2 2 3 1 3 3 3 3 3 3

Start activity 15 % 43 % 17 % 13 % 11 % 5 % 14 % 9 % 14 % 9 % 2 % 1 %

End activity 17 % 46 % 19 % 13 % 10 % 5 % 16 % 9 % 19 % 4 % 2 % 1 %

(100)〈011〉

CRSS 6 4 2 3 3 3 5 5 4 4 4 4

Start activity 5 % 6 % 35 % 17 % 16 % 4 % 6 % 4 % 10 % 6 % 3 % 4 %

End activity 6 % 7 % 37 % 16 % 15 % 4 % 6 % 4 % 13 % 8 % 3 % 4 %

(010)[100]

CRSS 3 5 5 1 3 3 3 3 3 3 3 4

Start activity 1 % 5 % 1 % 22 % 3 % 7 % 8 % 9 % 8 % 5 % 8 % 6 %

End activity 1 % 5 % 1 % 23 % 4 % 7 % 8 % 8 % 8 % 23 % 7 % 6 %

(010)〈101〉

CRSS 6 6 5 5 1.5 4 4 4 4 4 4 4

Start activity 10 % 12 % 14 % 12 % 35 % 10 % 2 % 6 % 10 % 6 % 3 % 3 %

End activity 9 % 10 % 12 % 12 % 37 % 10 % 2 % 6 % 8 % 15 % 3 % 3 %

(001)[100]

CRSS 4 3 3 3 3 0.5 3 3 3 3 1 1

Start activity 15 % 2 % 5 % 13 % 11 % 42 % 14 % 9 % 14 % 9 % 42 % 24 %

End activity 17 % 2 % 6 % 13 % 10 % 40 % 16 % 9 % 19 % 4 % 43 % 25 %

(001)[010]

CRSS 6 5 5 5 2 3 0.5 3 3 3 1 1

Start activity 8 % 12 % 10 % 10 % 7 % 12 % 38 % 6 % 14 % 8 % 33 % 15 %

End activity 8 % 10 % 9 % 10 % 7 % 14 % 31 % 6 % 9 % 14 % 33 % 14 %

(001)〈110〉

CRSS 6 6 6 6 3 3 3 2 4 4 5 1

Start activity 14 % 6 % 7 % 8 % 12 % 11 % 10 % 45 % 13 % 8 % 1 % 39 %

End activity 14 % 5 % 6 % 8 % 12 % 12 % 12 % 45 % 13 % 8 % 1 % 39 %

{111}〈

011〉

CRSS 30 30 30 30 30 30 30 30 30 30 30 30

Start activity 5 % 6 % 4 % 4 % 2 % 2 % 1 % 3 % 1 % 0 % 1 % 1 %

End activity 6 % 4 % 4 % 3 % 1 % 2 % 2 % 4 % 3 % 2 % 2 % 3 %

Twinning {110}〈

110〉

CRSS 25 25 25 25 25 25 25 25 1 25 25 25

Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 8 % 0 % 0 % 0 %

End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %

Twinning {112}〈

111〉

CRSS 25 25 25 25 25 25 25 25 25 2 25 25

Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 45 % 0 % 0 %

End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %

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


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

Slip system Model

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

(100)[010]

CRSS 1 4 3 3 3 3 3 3 3 3 3 4

Start activity 37 % 14 % 11 % 1 % 6 % 11 % 12 % 14 % 10 % 10 % 11 % 9 %

End activity 34 % 15 % 12 % 1 % 6 % 10 % 11 % 12 % 12 % 18 % 9 % 8 %

(100)[001]

CRSS 4 1 2 2 3 1 3 3 3 3 3 3

Start activity 12 % 36 % 12 % 11 % 9 % 5 % 11 % 7 % 10 % 10 % 1 % 1 %

End activity 14 % 35 % 13 % 10 % 8 % 5 % 13 % 7 % 17 % 6 % 1 % 1 %

(100)〈011〉

CRSS 6 4 2 3 3 3 5 5 4 4 4 4

Start activity 4 % 8 % 38 % 14 % 16 % 6 % 6 % 4 % 9 % 9 % 4 % 5 %

End activity 5 % 9 % 39 % 14 % 15 % 5 % 6 % 4 % 14 % 9 % 4 % 5 %

(010)[100]

CRSS 3 5 5 1 3 3 3 3 3 3 3 4

Start activity 1 % 7 % 2 % 33 % 6 % 11 % 12 % 14 % 10 % 10 % 11 % 9 %

End activity 1 % 8 % 3 % 33 % 6 % 10 % 11 % 12 % 12 % 18 % 10 % 8 %

(010)〈101〉

CRSS 6 6 5 5 1.5 4 4 4 4 4 4 4

Start activity 10 % 13 % 15 % 12 % 40 % 11 % 2 % 7 % 10 % 9 % 4 % 5 %

End activity 9 % 12 % 13 % 12 % 42 % 11 % 2 % 7 % 8 % 15 % 3 % 4 %

(001)[100]

CRSS 4 3 3 3 3 0.5 3 3 3 3 1 1

Start activity 12 % 1 % 4 % 11 % 9 % 36 % 11 % 7 % 10 % 10 % 35 % 20 %

End activity 14 % 1 % 4 % 10 % 8 % 36 % 13 % 7 % 17 % 6 % 38 % 22 %

(001)[010]

CRSS 6 5 5 5 2 3 0.5 3 3 3 1 1

Start activity 8 % 11 % 10 % 9 % 6 % 11 % 36 % 6 % 11 % 11 % 32 % 15 %

End activity 7 % 10 % 9 % 10 % 6 % 13 % 35 % 6 % 7 % 16 % 34 % 16 %

(001)〈110〉

CRSS 6 6 6 6 3 3 3 2 4 4 5 1

Start activity 13 % 6 % 6 % 7 % 10 % 10 % 8 % 40 % 10 % 10 % 1 % 35 %

End activity 13 % 5 % 5 % 8 % 9 % 11 % 9 % 42 % 11 % 9 % 1 % 37 %

{111}〈

011〉

CRSS 30 30 30 30 30 30 30 30 30 30 30 30

Start activity 3 % 3 % 3 % 2 % 1 % 1 % 1 % 2 % 0 % 0 % 1 % 1 %

End 4 % 4 % 3 % 2 % 1 % 1 % 1 % 2 % 2 % 3 % 1 % 1 %

Twinning {110}〈

110〉

CRSS 25 25 25 25 25 25 25 25 1 25 25 25

Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 20 % 0 % 0 % 0 %

End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 1 % 0 % 0 % 0 %

Twinning {112}〈

111〉

CRSS 25 25 25 25 25 25 25 25 25 2 25 25

Start activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 22 % 0 % 0 %

End activity 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 %

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


1 3

sample. This lag on decompression could allow the sample to creep and develop texture at lower stresses. It is likely that texture does not evolve during compression in Run 3 because stresses were too low to induce plastic flow on the timescale of the compression cycle. However, decompres-sion was slow enough to allow creep and texture evolution. Time-dependent texture development has been observed when bridgmanite was allowed to sit for 24 h under stress at ambient temperature, resulting in increased texture strength (Wenk et al. 2006b).

It is interesting that in contrast to more recent results (Cordier et al. 2004; Wenk et al. 2004; Wenk et al. 2006b; Miyajima et al. 2009 and this work), two early DAC meas-urements of bridgmanite found no evidence for texture development (Meade et al. 1995; Merkel et al. 2003). In these early measurements, the bulk of deformation was attained below the bridgmanite stability field, and it is pos-sible that it is difficult to induce texture outside the stability field of bridgmanite or that plasticity is reduced at lower pressures.

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

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


1 3

Textures in ferropericlase

During deformation with bridgmanite, ferropericlase does not develop a significant texture. This has been observed in previous experiments by Wenk et al. (2004). This is somewhat surprising since ferropericlase is expected to be the more ductile phase and should deform more easily (Marquardt and Miyagi 2015). In single-phase periclase as well as ferropericlase, strong texture development has been observed (e.g., Merkel et al. 2002; Lin et al. 2009). However, deviatoric stresses and texture evolution in poly-phase aggregates are likely to be influenced by the sample’s microstructure and strength contrast between the phases (Wang et al. 2013).

If bridgmanite forms a loadbearing framework around the softer ferropericlase, then the stronger bridgmanite will force the weaker ferropericlase to strain at the same rate as the bridgmanite phase (Handy 1994). Thus, the weaker phase should exhibit lower stress levels than the stronger phase, provided plastic flow has occurred in the strong phase. Lower stresses in the weaker phase are consistent with observations in Run 2. Alternately, if the softer ferropericlase forms an interconnected weak layer microstructure, it will control the deformation properties of the aggregate (Handy 1994). In this scenario, strain partitions into the soft phase and the weaker phase will modulate the stress levels in the harder bridgmanite phase. In either scenario, the weaker fer-ropericlase should experience as much or more strain than bridgmanite. Indeed in high shear strain deformation experi-ments on bridgmanite + ferropericlase aggregates, ferrop-ericlase deforms significantly more that bridgmanite (Girard et al. 2016). Since texture evolution is observed in bridgman-ite, the lack of texturing in ferropericlase is unlikely a result of low total strain. A more likely explanation is that the local deformation field in the ferropericlase grains is heterogene-ous. In D-DIA deformation experiments on NaMgF3 perovs-kite + halite (NaCl) aggregates, halite develops little texture, and polyphase plasticity modeling indicates that the lack of texture development in halite is due to strain heterogeneity (Kaercher et al. submitted).

VPSC models (Figs. 5, 6) assume that each crystal deforms homogeneously in a homogeneous medium, with-out information about orientation or strength of neighbor-ing grains. While this provides a good approximation for single-phase aggregates, understanding polyphase plastic-ity will require characterization of bulk textures as well as microstructure, preferably by 3D tomography, local orien-tation mapping and SEM and TEM microscopy. It is likely that portions of grains near phase boundaries behave differ-ently than regions in the interior. For plasticity modeling, finite element methods (e.g., Dawson 2002) or fast Fourier transform methods (Lebensohn et al. 2011) need to be con-sidered to account for microstructure.

Implications for the lower mantle

Here we observe that at pressures


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to indicate that at higher pressures (>23 GPa) {001}〈110〉 becomes more active. A recent room-temperature experi-mental study on ferropericlase may be consistent with a slip system change to {001}〈110〉 at pressures >60 GPa but was not conclusive (Marquardt and Miyagi 2015). If high pressure and temperature favor both {110}

〈

110〉

and {001}〈110〉, these may both be active in the lower mantle; however, if the geotherm is relatively cold, {001}〈110〉 may be favored (Amodeo et al. 2012). On the other hand, based on this study as well as D-DIA deformation of two-phase analogs (Kaercher et al. in prep), ferropericlase deformed with bridgmanite may not develop significant texture, and may be less important for seismic anisotropy in the lower mantle.

Conclusions

For the enstatite to bridgmanite transformation, a strong 001 transformation texture develops. This appears to be con-trolled by a structural relationship between enstatite (100) and bridgmanite (001). Bridgmanite synthesized from oli-vine and ringwoodite exhibits a weak 100 transformation texture. This texture is likely a result of deviatoric stresses and the Young’s modulus anisotropy of bridgmanite. Mini-mization of elastic strain energy in these cases may be accomplished through preferential nucleation of low strain energy orientations and/or by {110} twinning during the phase transformation. As far as slip systems during plastic deformation are concerned, it appears that at lower pressures (55 GPa, a change in domi-nant slip system appears to occur in bridgmanite from slip on (001) to slip (100), consistent with first principles cal-culations. We also conclude that at the conditions of these experiments deformation twining is not significant for tex-ture development. Slip on (001) in bridgmanite is consistent with high-temperature slip systems in other perovskites, and this may be the dominant slip system in the lower mantle. When bridgmanite and ferropericlase are deformed as a two-phase aggregate, ferropericlase does not develop significant texture. This is consistent with prior experimental work, and we hypothesize that is due to a heterogeneous strain field in the soft phase preventing formation of a coherent texture. If this applies to the deep Earth, ferropericlase would not be a significant source of anisotropy in the lower mantle.

Acknowledgments Portion of this work was performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT is supported by DOE-BES, DOE-NNSA, NSF, and the W.M. Keck Foundation. APS is supported by DOE-BES, under Contract No. DE-AC02-06CH11357. Remaining portions of

this work were performed at the Advanced Light Source (ALS). The ALS is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agree-ment EAR 01-35554 supported this project through funding crucial beamline equipment. LM acknowledges support from CDAC and NSF (EAR-0337006). HRW acknowledges support from NSF (EAR-1343908, CSEDI 1067513). We acknowledge help from beamline sci-entists, particularly Y. Meng at APS and M. Kunz at ALS.

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Texture development and slip systems in bridgmanite and bridgmanite + ferropericlase aggregatesAbstract IntroductionExperimental techniqueData analysisResultsPressure and differential stressTextures

DiscussionDifferential stressTextures in bridgmaniteTransformation texturesPolycrystal plasticity modeling

Textures in ferropericlaseImplications for the lower mantle

ConclusionsAcknowledgments References

texture development and slip systems in bridgmanite and...

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