Preferred orientation of anorthite deformed experimentally...

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Earth and Planetary Science Le

Preferred orientation of anorthite deformed experimentallyin Newtonian creep

J. Gómez Barreiro a,⁎, I. Lonardelli a,b, H.R. Wenk a, G. Dresen c,E. Rybacki c, Y. Ren d, C.N. Tomé e

a Earth & Planetary Sciences, University of California at Berkeley, California 94720, USAb Ingegneria dei Materiali e Tecnologie Industriali, Universitá degli studi di Trento,Trento I-38050, Italy

c GeoForschungsZentrum Potsdam, Postdam, Germanyd Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA

e MST Division, Los Alamos National Laboratory, New Mexico 87545, USA

Received 21 September 2006; received in revised form 13 September 2007; accepted 20 September 2007

Editor: C.P. Jaupart

Available online 29 September 2007

Abstract

Synthetic anorthite aggregates were deformed in a Paterson gas deformation apparatus at confining pressures up to 400 MPa intorsion and axial compression at temperatures between 950 °C and 1200 °C. Samples deformed in torsion under Newtonian creepdisplay development of texture (or crystallographic preferred orientation) as documented with synchrotron X-ray diffractionmeasurements. Complex diffraction patterns were deconvoluted with the Rietveld method to obtain quantitative textureinformation. Torsion samples deformed up to shear strains of 4 and samples deformed in compression at higher stresses to totalstrains of 0.3 develop clear textures. Texture and shape preferred orientation (SPO) of torsion samples display a monoclinic patternwith an asymmetry inclined against the sense of shear, consistent with polycrystal plasticity simulations that assume thedeformation is accomplished by dislocation glide. These results show that a material deforming in linear-viscous creep can developa strong texture, in striking contrast to the paradigm that the presence of a texture precludes low-stress Newtonian behavior. Ourobservations show that the presence or absence of crystallographic preferred orientation is not sufficient to uniquely infer thedominant rheological/mechanical regime, as sometimes applied for interpretation of seismic anisotropy in the Earth.© 2007 Elsevier B.V. All rights reserved.

Keywords: anorthite; crystallographic preferred orientation; texture; Newtonian creep; feldspar; torsion; anisotropy; rheology

1. Introduction

Ductile flow of rocks is complex and depends onmany parameters, including temperature, strain, strainrate, pressure, grain size, chemical environment, phase

⁎ Corresponding author. Tel.: +1 510 642 7431; fax: +1 510 643 9980.E-mail address: [email protected] (J. GómezBarreiro).

0012-821X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2007.09.018

transformations and strain history (e.g., Frost and Ashby,1982; Karato, 1996). In geological systems it is difficultto pinpoint the importance of each variable anddeformation experiments proved to be invaluable forunderstanding the rheology and evolution of microstruc-ture and preferred orientation of crystals. In this paper weuse the widely accepted term “texture” synonymous with“crystallographic preferred orientation”.

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http://dx.doi.org/10.1016/j.epsl.2007.09.018

189J. Gómez Barreiro et al. / Earth and Planetary Science Letters 264 (2007) 188–207

Deformation by creep refers to the non-recoverablestrain resulting when a rock is subjected to a constantstress during a long period of time. Creep strain isattained by the movement of three types of defects withinthe polycrystalline material: point defects (vacancies),linear defects (dislocations) and planar defects (grainboundaries). It is recognized that each type of defect hasa distinctive contribution to the mechanical response ofthe aggregate (Langdon, 2000). As a consequence creepmechanisms may be identified from microstructuralobservations in combination with the values of empiricalparameters (e.g. stress exponent n).

The mechanical behavior is described over a widerange of stresseswith a power law, relating strain rate ɛ̇ andstress σ (ɛ̇∼σn). For dislocation creep the stress exponentn is usually observed between 3 and 5. However at lowstresses there is a transition to values of n around 1 and 2.Under these conditions and moderately high temperaturesthree possible mechanisms dominate: diffusion creep,Harper–Dorn creep and grain boundary sliding.

Creep accommodated by dislocation activity results ina preferred orientation of crystals and thus anisotropy ofmacroscopic physical properties, most notably seismicwave propagation. Grain-size sensitive deformationmechanisms accommodated purely by diffusion havebeen associated with deformation that does not producepreferred orientation. This latter association is supportedby experiments on limestone (Schmid et al., 1977),olivine (Fliervoet et al., 1999) and fine-grained perovskite(Karato et al., 1995). Since a Newtonian (linear) viscousbehavior (i.e. n=1) is observed for diffusion creep, it haslead to the conclusion that the development of anisotropyin the Earth is a feature restricted to non-Newtonian flow,assuming an isotropic orientation distribution when thebehavior is linear-viscous (Karato and Wu, 1993). It alsopromoted the reverse conclusion that, if anisotropy isobserved in the Earth, the mechanical behavior must benon-Newtonian (Savage, 1999; McNamara et al., 2001).We demonstrate that the relationship between mechanicalbehavior and texture is not unequivocal.

In this paper we investigate fine-grained anorthiteaggregates, deformed experimentally in a regime of New-tonian creep, which develop distinct preferred orientationof crystallites, indicating that even in linear-viscous flowanisotropy may develop. Compared to minerals such asquartz, calcite and olivine, relatively little is known aboutpreferred orientation of plagioclase. In naturally deformedanorthosites and some amphibolites it has been attributedto dislocation glide (Jensen and Starkey, 1985; Olsen andKohlstedt, 1985; Kruhl, 1987; Olesen, 1987; Ji et al.,1988; Siegesmund et al., 1994; Prior and Wheeler, 1999;Jiang et al., 2000; Xie et al., 2003). Several slip systems

have been observed to be active in plagioclase (Tullis,2002). In natural mylonites (010)[001] is an important slipsystem at medium to high-grade metamorphic conditions(Kruhl, 1987; Ji et al., 1988, 1994; Zhao, 1997). Opticaland TEM investigations in experimentally deformedaggregates and single crystals have confirmed this slipsystem (Olsen and Kohlstedt, 1984; Montardi andMainprice, 1987; Ji and Mainprice, 1988; Kruse andStünitz, 1999; Stünitz et al., 2003). Other studies report(010)[100] slip, suggesting that there may be a transitionfrom [001] to [100] slip with increasing temperature(Heidelbach et al., 2000; Ji et al., 1997, 2000, 2004).Other processes for orientation changes are recrystalliza-tion (Ji and Mainprice, 1990) and reorientation of non-equiaxed crystals during straining (Shelley, 1979; Agueet al., 1990; Feinberg et al., 2006).

Various techniques have been used to measure textureof plagioclase. Most older reports relied on U-stagemethods (Shelley, 1979, 1989; Suwa, 1979; Jensen andStarkey, 1985; Kruhl, 1987; Olesen, 1987; Ji andMainprice, 1988; Ji et al., 1988, 1994; Siegesmundet al., 1994; Ague et al., 1990; Lafrance et al., 1998;Egydio-Silva and Mainprice, 1999). The resolution ofconventional X-ray pole figure measurements is notsufficient to deconvolute the many overlapping diffrac-tion peaks of plagioclase. Electron Back ScatterDiffraction (EBSD) is offering new opportunities fordetermining texture of plagioclase, both in naturallydeformed rocks (Prior and Wheeler, 1999; Jiang et al.,2000; Lapworth et al., 2002; Xie et al., 2003), as well asin experimentally deformed aggregates (Ji et al., 2000,2004). Synchrotron X-rays and neutron diffraction haverecently been applied to feldspars. Both have improvedstatistics compared to U-stage and EBSD, becausevolumes, rather than surfaces are analyzed (Siegesmundet al., 1994; Ullemeyer et al., 1994; Xie et al., 2003;Heidelbach et al., 2000; Leiss et al., 2002; Ullemeyeret al., 2006).

The objectives of this study are to explore crystallo-graphic preferred orientation development in experi-mentally deformed anorthite with synchrotron hard X-rays and time-of-flight (TOF) neutron diffraction.Aggregates were deformed under Newtonian creep intorsion. In addition the transition from Newtonian tonon-Newtonian creep was explored in triaxial compres-sion. The experimental data indicate that significanttexture develops in both cases.

2. Deformation experiments

A series of deformation experiments was performed ina Paterson-type gas apparatus equipped with an internal

190 J. Gómez Barreiro et al. / Earth and Planetary Science Letters 264 (2007) 188–207

load/torque cell, in axial compression and in torsion atGFZ Potsdam to characterize the mechanical behavior ofanorthite aggregates at different conditions (Rybacki andDresen, 2000, 2005). Of these experiments six sampleswere selected for texture analysis based on a qualitativeassessment of preferred orientationwith gypsumplate anda petrographic microscope. Experimental details aresummarized in Table 1.

2.1. Sample description

Samples were fabricated from crushed anorthite(An98.9 Or0.2 Ab0.9) glass-powder (Schott Glaswerke).The particle size of the glass was b60 μm. The powderused for axial deformation was dried at 800 °C in air for60 h and kept at 120 °C for several days before coldpressing. The powder was encapsulated in a steel jacketand cold pressed at an axial stress of 300 MPa. Tofabricate “dry” specimens (An42) the aggregate washeated at 800 °C to 900 °C formore than 120 h prior to hotpressing at P–T conditions of 300 MPa and 1100 °C.“Wet” specimens (An10 and Pl11-1, Pl11-2, Pl-9, Pl12-1)were not pre-heated (Rybacki and Dresen, 2000, 2005).

Cylindrical samples for torsion (10 mm diameter and6.5 mm length) and compression (10 mm diameter and20 mm length) were prepared from hot-pressed aggre-gates. The grain size was d0≈3 μm and the averageaspect ratio R0≈2. The water content of the startingspecimens was measured using a Fourier-transforminfrared spectrometer (FTIR, Bruker IFS-66v) usingBeer–Lambert's law with a molar extinction coefficientof 32 LH2O mol−1 cm−1 (Beran, 1987). It was 0.004 and0.07 wt.% H2O for “dry” and “wet” conditions incompression, and 0.17 wt.% H2O (wet) in torsion.Details concerning sample preparation and analysistechnique for determination of water content are givenin Rybacki and Dresen (2000). The absorbance spectraare characteristic of molecular water or hydroxyl groups.

Table 1Experimental data for torsion and compression experiments

T(°C)

Strain Strain rate(s−1)

Stres(MPa

Pl9-1 1125 3.8 1.5×10−5 7.2Pl11-1 1200 4.3 1.6×10−5 1.6Pl11-2 1050 3.9 1.4×10−5 12.1Pl12-1 950 4 1.7×10−5 54An10 1120 9.48 10−5–10−3 300.5An42 1120 4.34 10−5–10−3 453.6

Stress, strain, and strain rate refer to the conditions at the sample peripheryCompression data from (Rybacki and Dresen, 2000).

Measurements at liquid nitrogen temperature show aweak ice peak, indicating the presence of freezable waterin fluid inclusions. No difference in water content wasdetected between hot-pressed and deformed samples.The glass content estimated from transmission electronmicroscopy (TEM) observations is less than b0.2 vol.%for “dry” and b2 vol.% for “wet” specimens; it occurs atthe grain junctions but no glass was observed along grainboundaries. Only in the starting material, used for torsionexperiments, spherulites were identified by petrographicmicroscope inspection. The appearance of spherulites isstrongly correlated to the presence of water and to thehot-press conditions (P–T-path). The term ‘spherulite’itself defines the spatial orientation of the elongatedgrains (radially arranged). They are muchmore abundantin the wet torsion samples than in compression samples.The initial SPO and texture related to the spherulites isevident in small (grain) scale, but should be minor withrespect to the relatively large spot size of the synchrotrondiffraction measurements that should neutralize thesmall scale effects due to the spherically symmetricarrangement of grain. Previous studies, where texture ofundeformed hot-pressed samples was characterized byEBSD, document a random distribution, supporting ourassertion (Ji et al., 2004). The starting material also has avery low dislocation density (≈5×107 cm−2).

2.2. Torsion experiments

Torsion experiments are the most effective way toachieve large strains. The deformation conditions at anypoint in the sample correspond to simple shear, with theshear plane normal to the rotation axis (Paterson andOlgaard, 2000). The experiments were conducted onfour anorthite samples at temperatures ranging from950 °C to 1200 °C (0.61–0.77 Tm) and a confiningpressure of 400 MPa (Table 1). Maximum shear strainsrange from 3.8 to 4.3, and shear stresses (at the end of

s)

H2Owt.%

n

0.14 1.4±1.1 Torsion0.19 0.9±0.3 Torsion0.21 0.9±0.2 Torsion0.15 1.1±0.6 Torsion0.07 (wet) From 1 to 3 Compression0.004 (dry) From 1 to 3 Compression

(torsion) and the maximum attained (compression). n stress exponent.

Fig. 1. (a) Shear stress–shear strain curves for samples deformed intorsion. Samples were deformed at 2×10−5 s−1 and confining pressureof 400 MPa. Maximum shear strain interval γ=3.8–4.3, and shearstress, τ=1.6–54 MPa. Samples above 1050 °C display a steady-stateflow after γ=1.5. (b) Log (strain rate) versus log (stress) plot forsamples deformed in axial compression. Strain rate increases withincreasing stress and water content. The data define two regimes withstress exponents n=1 and n=3, indicating Newtonian creep and non-Newtonian creep, respectively.


the test) from 1.6 MPa to 54 MPa. All samples weretwisted at rates θ̇≈2×10−5 s− 1 (Rybacki et al.,submitted for publication, Superplasticity of FeldsparRocks: Implications for Cavitation and Ductile Failurein the Lower Crust, by Erik Rybacki, Richard Wirth, andGeorg Dresen, submitted to GRL, 2007). In torsionexperiments the shear strain rate and the strain increaselinearly along the radius from the center towards theouter surface (Paterson and Olgaard, 2000). From therelation

:g ¼ :h D=2Lð Þ

we find a maximum shear strain rate γ·≈1.6×10−5 s−1

at the outer border of the samples (Table 1). Anequivalent expression is used to describe the shear strain(γ) substituting θ· by twist (θ). The torque M and twist-rate θ̇ data measured from the experiments were used toderive the shear stress t and the shear strain rate γ·, underthe assumption that the material obeys a power lawconstitutive relationship that describes creep as athermally activated process (Poirier, 1985):g ¼ Asn exp �Q=RTð Þwhere A is a constant, τ is the applied shear stress, n thestress exponent, Q the apparent activation energy, R theuniversal gas constant, and T the absolute temperature.In steady-state behavior n, Q, and A, are constants andcan be derived from multilinear regression of theexperimental data to the power law. To calculate thestress and temperature sensitivity of the material(parameters n and Q), strain rate and temperature werevaried in several strain steps during the experiments(Fig. 1).

The stress exponent n was calculated by stepping thetwist-rate and determining the slope between log (strainrate) and log (stress) (Paterson and Olgaard, 2000;Rybacki et al., 2003). All the specimens show values ofn≈1, indicating a Newtonian behavior (Table 1). Thestress–strain curve for lower temperature (950 °C)sample shows a continuous hardening with increasingstrain (Fig. 1a). In experiments above 1050 °C a nearlysteady-state was reached after a shear strain of about 1.5.At high strain, significant cavitation occurs, leading tofinal failure of the low temperature (950 °C) sample(Rybacki and Dresen, 2005).

2.3. Compression experiments

Compression experiments were conducted at stepwiseincreased constant load, a confining pressure of 300MPa,and a constant temperature of 1120 °C (0.7 Tm). Axial

differential stress was increased from about 30 MPa toabout 450 MPa, resulting in strain rates of ≈10−5–10−3 s−1, respectively. Strain for each step was ≈3%,with about 30%maximum shortening for a single sample.At low stress, the mechanical data indicate a linearrelationship of stress and strain rate, indicatingNewtoniancreep (Fig. 1b). With increasing stress above ≈200 MPathe stress exponent changed to n=3 indicating non-Newtonian creep (Rybacki and Dresen, 2000). A vonMises stress–strain comparison shows that low-stresscompression and torsion tests are in good agreement,although the kinematic boundary conditions are quitedifferent. The preserved mean dislocation density is about3 times higher than in the starting material, however dueto technical reasons samples could not be quenched under


load so this value represents a lower bound. A completedescription of the experimental results and microstructurecan be found in Rybacki and Dresen (2000).

3. Texture analysis

3.1. Texture analysis of torsion samples with synchrotronX-rays

For synchrotron texture analysis, the studied sampleis a thin slab, 1 mm in thickness. It is a median sectioncut from the cylinder, though not exactly centered(Fig. 2). The sample was analyzed in transmission withhard monochromatic X-rays (wavelength 0.1078 Å) atbeamline ID11-C of the Advanced Photon Source atArgonne National Laboratory. The beam diameter is0.5 mm. Diffraction images were recorded with aMAR345 (3450×3450 pixels) image plate positioned175.8 cm behind the sample. Four spots on the sample,with different distance from the cylinder axis, weremeasured to explore texture variations at different shearstrain and strain rate for each temperature. For each spot3 images were recorded at different tilt angles of thesample relative to the incident beam (−30°, 0°, 30°) toobtain better pole figure coverage. Images wereanalyzed with the Rietveld method as implemented inMAUD (Lutterotti et al., 1999) and recently applied tosynchrotron data (Wenk et al., 2007). A typical image is

Fig. 2. Reference system for torsion experiments. (a) Central slice with locatiopposite on opposite sides of the rotation axis. (b) XZ pole figure with folia

shown in Fig. 3a on which texture is visible in intensityvariations along Debye rings. 2D-images were decom-posed into 36 azimuthal sectors of 10° over whichintensity was integrated, providing diffraction spectrasuch as those in Fig. 3b. From the combination of 36spectra on 3 images instrumental parameters, crystalstructure and preferred orientation were refined with theRietveld method. Anorthite was refined in space groupP. Because of the low triclinic symmetry and large unitcell there is a large number of reflections, many of themoverlapping. Some reflections with high intensity aremarked in Fig. 3b. The refined orientation distribution(OD) was exported from MAUD and then used inBeartex (Wenk et al., 1998) to calculate pole figures.

3.2. Texture analysis with neutron diffraction

Synchrotron X-rays on 0.5 mm spots were used tocharacterize local texture variations in the torsionsamples. Neutron diffraction is advantageous to obtainquantitative information of the bulk crystallographicpreferred orientation of large, homogeneous samples asproduced in compression. Sample cylinders, 10 mm inlength and 8 mm in diameter, were fully immersed in theneutron beam. The experiments were done in theneutron time-of-flight (TOF) diffractometer HIPPO(High-Pressure-Preferred Orientation) at LANSCE(Los Alamos Neutron Science Center) (Wenk et al.,

on of spots analyzed with synchrotron X-rays. The sense of shear is thetion (SPO) and principal stresses labeled.


2003). For each measurement the samples were rotatedaround the cylinder axis (perpendicular to the incidentneutron beam) into four positions (0°, 45°, 67.5°, 90°) toimprove pole figures coverage. At each position datawere collected for 30 min resulting in a total time of120 min for each sample. Also TOF diffraction spectrawere analyzed with MAUD. The OD resolution was 15°(Matthies et al., 2005).

3.3. Microstructures

Sections from the border of the low-stress sample at1200 °C (Pl11-1) and the high stress sample at 950 °C(Pl12-1) were used to analyze microstructural featuresand explore variations with temperature and stress(Fig. 4a–d). Shear direction is parallel to the section andnormal to the cylinder axis. Strain and strain rate areapproximately uniform within the section (Paterson andOlgaard, 2000). Sections from hot-pressed undeformedsamples were analyzed to obtain the starting grain size(d0) and aspect ratio (R0). SEM sections were thermallyetched to display grain boundaries (Fig. 4). Manuallydigitized micrographs were analyzed with ImageJ v1.38software (Rasband, W.S., ImageJ, U.S. National insti-tute of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/, 1997–2006) (Figs. 5 and 6). The grainsize (d) is defined as the diameter of the equivalent circlewith the same area (A) as the measured grain (d2 =4A /π)(Heilbronner and Bruhn, 1998). The best fit ellipsealgorithm was used to evaluate the shape preferredorientation (SPO) of more than 1000 grains. The best fitellipse has the same area, orientation and centroid as the

Fig. 3. Torsion sample deformed at 1125 °C (Pl 9-1): (a) Synchrotron diffraspectra in different radial directions (40° intervals) with Rietveld fit. Variatio

original grain (Fig. 6a inset). SPO refers to the preferredalignment of elongate grains (e.g., Panozzo, 1983). Inour case “grain orientation” (α) is the angle between themajor axis of each ellipse and the shear plane. Theaspect ratio is defined as R=(long/short) axis of the bestfit ellipse. Results were used to construct R/α graphs(Figs 5 and 6).

4. Polycrystal plasticity simulations

Polycrystal plasticity modeling can help us toevaluate the effect of dislocation glide on various slipsystems upon texture patterns. Positive comparison ofpredicted and measured textures will allow us to supportthe idea that, at least partially, deformation is accommo-dated by dislocation glide. High temperature experi-ments and preferred orientation in naturally deformedhigh-grade plagioclase rocks point to a predominance of(010)[100] slip accompanied by (010)[001] slip(Lafrance et al., 1998; Ji et al., 2000) and possibly(001)[100] slip (Kruhl, 1987; Siegesmund et al., 1994).We have applied a visco-plastic self-consistent (VPSC)model (Lebensohn and Tomé, 1993; Tomé and Canova,2000) assuming the slip systems listed in Table 3 with(010) slip dominating (low critical shear stress coeffi-cient) but that other systems are also active. The shearrate in a given slip system is proportional to the nthpower of the ratio between the resolved and the criticalshear. This is the first application of polycrystal plasticityto an aggregate of triclinic crystals. The VPSC modeldoes not require the activation of five independent slipsystems per grain rather it activates preferentially the

ction image; some Debye rings are labeled. (b) Stack of 5 diffractionns in peak intensities are related to texture.

http://rsb.info.nih.gov/ij/,

http://rsb.info.nih.gov/ij/,


‘soft’ systems, and accounts for the grain shape and itsevolution with deformation. All of these features arecrucial for simulating the large plastic response of a low-symmetry system such as anorthite. In order to achievenumerical convergence some arbitrary slip systems withhigh order indices had to be introduced, assigning themhigh critical shear stress coefficients. We verified thattheir activity is negligible, since they contribute less than1% of the total shear at any step in the simulationprocess. Here, 2000 orientations are deformed incre-mentally to 100% von Mises strain in the case of shear(shear strain γ=1.73) and to 30% von Mises strain in thecase of axial compression. Shear and axial compressionare simulated for two different stress exponents, n=1(Newtonian) and n=3 (power law). The classicalpolycrystal plasticity theory, which assumes no or littlestrain rate dependence of the stress (stress exponentinfinity or very large), is applicable to metals but not tominerals. Lowering the stress exponent in the self-

Fig. 4. SEM micrographs of tangential sections of samples deformed in torsiohigh stresses (54 MPa) ((b) and (d)). The surface was thermally etched to disrelated to the final ductile failure of the aggregate appear at 25° to the shear plathe thermal etching. Shear bands (SC’) are also indicated.

consistent simulation has the effect of distributing strainover more slip systems (in mathematical terms roundingthe corners and edges of the single crystal yield surface(Kocks, 2000)). Themodel, as applied here, assumes thatall deformation is accommodated by slip and does notconsider grain boundary sliding, diffusion assisteddeformation, or recrystallization. The latter can beincorporated if recrystallization mechanisms are known(Wenk et al., 1997). If mechanisms that do not producetexture were also active, texture patterns would beweaker.

5. Results

5.1. Torsion experiments

5.1.1. MicrostructuresObservations were done in tangential sections at the

border (γ≈4) of the cylinder in the two samples

n at 1200 °C and low stresses (1.6 MPa) ((a) and (c)), and 950 °C andplay grain boundaries and perform SPO analysis. Cavities and fissuresne in both. The appearance (opening) of cavity stringers is enhanced by

Fig. 5. Grain-size analysis of samples deformed in torsion: a) grain-size distribution for undeformed (hot-pressed) sample and samples deformed intorsion. The geometric mean and the (Geometric Standard Deviation) are indicated. b) and c) Manually digitized grain boundaries maps from cylindertangent sections (γ≈4). Grain-size modes are shown. Grain-size reduction is important in both samples (Mode 1), but clearly dominates at 1200 °C.Microstructural features of Mode 1 grain suggests that can be related to dynamic recrystallization. R/α plots (inset) for different modes indicate1200 °C sample develops a stable orientation mainly independent on size and elongation, while 950 °C sample shows a complex correlation ofelongation and orientation and a worst alignment of SPO with the imposed macroscopic shear.


(Figs. 4–6). All torsion samples show a microstructurewith distinctly inequant grain shapes and an asymmetricdistribution of long axes relative to the shear plane(Fig. 6). A pervasive foliation is defined by the SPO.Straight or gently curved grain boundaries are verycommon within the sample at 950 °C, while more lobateand locally sutured boundaries dominate at 1200 °C(Figs. 4–6). In both samples it is possible to see smallgrains bulging into or even isolated inside the largestones (Fig. 5b, c). Transmission electron microscopyobservations show varying dislocation densities that aremostly low and similar to the starting material.However, in a few cases dislocation densities can beas high as 109 cm−2. The mean dislocation density iscomparable to that of the starting material; areas withrelatively high dislocation density also show smallrecrystallized grains. As in the starting material twins

are abundant and dislocations are frequently limited bytwin domains.

The grain-size (d) distribution is close to lognormal(Fig. 5). For stereological correction we used a factor of1.8 with respect of mean aspect ratios (Rybacki andDresen, 2000). The geometric mean and its GeometricStandard Deviation (GSD), are d950 °C=2.8 (GSD=1.9)μm for the high stress sample at 950 °C, d1200 °C=2.0(1.9) μm for the sample deformed at low stress and1200 °C, and d0=2.6 (1.7) μm for the undeformedsample. There is no significant variation of the meangrain size after deformation (Fig. 5a). But the shape ofthe distribution is broad at 950 °C and more peaked at1200 °C. The presence of several d populations (Fig. 5b,c) correlates with the microstructural features, whererelatively large grains tend to be surrounded by smallerones, especially in the sample deformed at 1200 °C.

Fig. 6. Microstructural analysis of samples deformed in torsion: a–b) manually digitized grain boundary maps from cylinder tangent sections (γ≈4).Angular relationship between SPO and shear plane (α), and grain best fit ellipse concept are illustrated. c) Aspect ratio (R)/α at different T and stress.Initial aspect ratio (R0: 2.65 (1.7)) is indicated. Different grain-size classes (N7, 5.5, 4, 2.5, 1.5, b0.5) are plotted. d) αaverage per aspect ratio interval(Ri) graph to illustrate dependence variations with T and stresses of shape and orientation. Frequency (%) curves of Ri are indicated at the graphbottom illustrating that most of the grains has R lower than 4.


In a detailed analysis of grain-size distributions(Fig. 5) we compare final d distributions against thestarting one (d0), considering the upper and lowerboundaries of d0 (d0upper: d0× (GSD)=4.4; d0lower:d0÷ (GSD)=1.5). We define net grain-size growthwhen dNd0 upper, and net grain-size refinement whendbd0 lower. After deformation, in both samples, a 45% ofgrains change the grain size. However, within this 45%of grains, we observe that at 1200 °C and low stresses,grain-size reduction dominates (80% of grains) overgrain-growth (20%). On the other hand, at 950 °C andhigh stresses, a 50% of grains experience a sizereduction, while the other half shows a size growth.These data suggest that grain-size distribution evolves

by a competition between grain-size reduction andgrain-growth processes.

The average (±σ) angle between the grain long axisand the shear plane is α=21°±30 for the sampledeformed at high stress and 950 °C, and α=14°±29 forthe sample deformed at low stress and 1200 °C, bothsynthetic with the sense of shearing (Figs. 4 and 6). Forthe sample deformed at 1200 °C this angle represent astable orientation with respect to the kinematic frame,mostly independent of grain size and grain-elongation(Figs. 5b inset, 6d); we can consider it an oblique orsteady-state foliation (Means, 1981; Ree, 1991). How-ever in the sample deformed at 950 °C the grainorientation depends on, but not linearly, size and

Table 2Summary of texture information

ODFmax ODFmin (010) max (010) min

Pl9-1 5.26 0.03 3.26 0.3 TorsionPl11-1 5.32 0.05 1.78 0.6 TorsionPl11-2 6.61 0.02 2.75 0.53 TorsionPl12-1 4.21 0.01 2.65 0.54 TorsionAn10 2.95 0.38 1.41 0.72 CompressionAn42 1.89 0.54 1.22 0.89 Compression

ODFmax/min and (010)max/min are the range across the sample.


elongation (Figs. 5c inset, 6d) this feature suggest thatmechanisms involved in the formation and destructionof the SPO are not balanced. There is no significant

Fig. 7. Torsion samples: Anorthite (010) pole figures for the different sampleslines show the orientation of the foliation (SPO). Equal area projection, linearMaximum/minimum values (m.r.d.) indicated underneath each pole figure.

variation in the mean aspect ratio (R) between deformedand undeformed samples. The geometric mean fordeformed samples is Rdeformed=2.1 (1.6) while forundeformed material is R0=1.9 (1.4). If we evaluate thenet grain-shrinkage/elongation, by comparing Rdeformed

values with R0 (GSD) (R0 upper=2.7; R0 lower=1.3), weget a net grain-elongation when RNR0 upper, and a netgrain-shrinkage when RbR0 lower. There is no differencewith respect to temperature/stresses in the percentage ofgrains (40%) which modify their R during deformation.Also the ratio of grains that elongate to those that shrinkis similar at 950 °C (3:1), and 1200 °C (2.6:1.4). Bothdeformed samples show the same mean R for grains thatelongate, 3.4 (1.3), and for those that shrink, 1.2 (1.1).

deformed in torsion at four positions in the cylinder (c.f. Fig. 2). Dashedcontours. Contour scale in multiples of a random distribution (m.r.d.).


In broad terms R/α plots (Figs. 5b–c and 6c) arereasonably symmetric around the median α value,which suggests an initial random distribution (Ramsayand Huber, 1983), in agreement with the observations inundeformed samples. By α averages within differentaspect ratio ranges (Ri) an inverse dependency of αaverages with aspect ratio ranges (Ri) is observed forsamples deformed at high stress (Fig. 6d). At hightemperature and low stress the average α is constant. Ifwe now analyze R/α variation within grain-sizedistributions (Fig. 5b, c insets) appear that the smallestsizes (mode 1) have the lowest R and α, while increasinggrain-size results in a longer grains laying at higherangles to the shear plane. Deviation from this trend of

Fig. 8. Torsion samples: Pole figures for (010), [100] and [001] at the bordtemperature. Equal area projection, linear contours (m.r.d.). Maximum/minindicated as a dashed line.

the largest grains in sample deformed at 950 °C (mode4) is the result of a higher dispersion of the measure-ments and might reflect a less efficient refiningmechanism. A SC fabric (Berthé et al., 1979) has beenrecognized in both samples at different scales(Figs. 4 6), where S is defined by the oblique foliationand C is defined by a preferred alignment of grainsparallel to shear plane (Figs. 4b, 6b). SC microstructureshave been associated to inhomogeneous simple shearflows, where strain partitioning may occur. σ-typeporphyroclasts are present in the high temperaturesample (arrow; Fig. 6a). Part of these shear bandsprobably contributes to drive the development of latecavitation zones (Fig. 4–6).

er of the cylinder (γ=4) to illustrate the variation of the texture withimum values (m.r.d.) indicated underneath each pole figure. SPO is

Fig. 9. Compression samples: recalculated (010)[100] [001] polefigures from neutron diffraction analyses of samples deformed at1120 °C and strain rates 10−5–10−3 s−1. (a) wet, ɛ=9.48 (An10); (b)dry, ɛ=4.34 (An42). s1 parallel to the vertical axis Z. Equal areaprojection, linear contours (m.r.d.).


5.1.2. TexturePole figures have been calculated from the orientation

distribution for lattice plane (010) and lattice directions[100] and [001]. In triclinic anorthite [100] is close to the(201̄) pole, [010] close to the (010) pole and [001] close tothe (1̄02) pole and they were actually used in thecalculation. (010) pole figures document significanttexture with a maximum of up to 3.3 multiples of arandom distribution (m.r.d.) (Table 2). The maximum is athigh angles to the shear plane but disposed asymmetri-cally against the sense of shear (Fig. 7). This pattern issimilar for all four torsion samples and all spots on asample. There is a tendency for the peripheral high shearspots (γ=4) to have a stronger crystallographic preferredorientation than the internal spots (γ=2). The sense ofshear is reversed for one side (spots 1 and 2) relative to theother side (spots 3 and 4) (Fig. 2) and correspondingly theasymmetry of the pole figures. There is a weak secondarymaximum close to the shear direction.

Fig. 8 shows (010), [100] and [001] pole figures ofhigh strain spots for all samples. The patterns for [100]and [001] axes are less regular and weaker than for (010)poles. In general [100] defines a peripheral maximuminclined synthetically to the shear direction. Particularlyat higher temperature there is a secondary maximum athigher angles to the shear direction. The [001] polefigures at lower stresses/higher T show a broadconcentration in the center of the pole figure in theshear plane and perpendicular to the shear direction. Athigher stresses/lower T there is a maximum in the sheardirection. At higher temperature the [100] maximumsplits into two peripheral maxima, with the addition ofone in the center at 1200 °C (Fig. 8).

5.2. Compression experiments

Optical inspection suggests a weak development oftexture and shape preferred orientation.Neutron diffractionanalyses showaweak but consistent texture (Table 2), witha concentration of (010) poles parallel to the compressiondirection (Fig. 9). The texture strength is higher in the wetsample (1.4 m.r.d.), but well below the values obtained intorsion. The total strain in the compression samples doesnot exceed 30%, but final stresseswere significantly higherthan in torsion experiments.

While a direct comparison of texture in torsion andcompression is difficult because the experimentalconditions are different, it is clear that the strain attaineddetermines the development and strength of texture.

5.3. Polycrystal plasticity simulations of texture

Plasticity simulations produce texture patterns thatare remarkably similar to those observed in the experi-ments (Fig. 10 vs. Figs. 8, 9). The simple shearsimulations produce textures with an asymmetry relativeto the shear plane and shear direction (Fig. 10a, b) There isa pronounced asymmetric (010) maximum, a weakermaximum for [100] and a broad distribution for [001].The main difference compared with the experiment is themuch stronger texture in the simulations even thoughstrain is lower. This is not surprising since in theexperiments not all strain is accommodated by dislocationglide. Also compression pole figures compare well withexperiments (Fig. 10c, d). The (010) poles concentratearound the maximum stress (Fig. 10c, d). There is aslightly larger dispersion and weaker texture for stressexponent n=1. The system activity that leads to thetextures depicted in Fig. 10 is summarized in Table 3. Forconvenience we will refer to systems (010)[100], (010)[001], (001)[100] and (001)[010] as #1, #2, #3 and #4,respectively. The assumed (relative) CRSS's are 1, 1.5,2.5 and 4, respectively. As a rule, the contribution todeformation of a given system is inversely proportional toits critical stress, with #1 accommodating approximately40%, #2 30%, #3 20% and #4 10%. These numberschange (but not drastically) as deformation proceeds andgrains reorient. The extra slip systems required to obtainnumerical convergence in the numerical procedure areassigned a CRSS of 100 and contribute less than 1% in theworst case.

As was to be expected, the difference in activitybetween the Newtonian creep (n=1) and the power lawcreep case (n=3) is that higher n increases thecontribution to shear from soft systems #1 and #2,leaves the intermediate #3 about the same, decreases the

Fig. 10. Texture development simulatedwith the visco-plastic self-consistentmodel forNewtonian (n=1) andnon-Newtonian (n=3) behavior, in simple shear(a–b) and compression (c–d) deformation of plagioclase. 2000 orientations after 100% strain in simple shear and 30% strain in compression. Shear plane ishorizontal (a–b) and maximum compressive stress vertical (c–d). Pole densities in multiples of a random distribution, linear contours. Equal area projection.

Table 3Assumed active slip systems, assumed critical stress and predictedrelative activity (in %) for polycrystal simulations

Slipsystem

CRSS Shear(n=1)

Shear(n=3)

Compression(n=1)

Compression(n=3)

(010)[100] 1 40→37 48→34 39→35 46→42(010)[001] 1.5 28→25 32→33 28→34 33→42(001)[100] 2.5 20→25 17→30 20→15 18→12(001)[010] 4 11→10 3→3 11→15 3→4Others 100 b0.7

each0 b0.5

each0

Relative activity is the ratio of the crystallographic shear rate contributed bya given system and the shear rates summed over all systems.Herewe reportthe range of activities within the total deformation interval (0%→100% inshear; 0%→30% compression) for stress exponents n=1 and n=3.


activity of harder system #4, and eliminates completelythe contribution from the hard systems (see Table 3). Inprinciple, it is possible to vary the relative CRSS valuesin order to better reproduce the textures measured atdifferent stress or temperature shown in Figs. 8 and 9.However, the purpose of this calculation is to qualita-tively demonstrate, by comparing predicted and mea-sured textures, that dislocation glide is likely one of themechanisms contributing to deformation of anorthite inthe temperature and stress ranges considered here. Theorigin of the asymmetry in the simulated simple sheartextures is best understood if we follow (010) polerotation trajectories of individual orientations (Fig. 11).Grain rotations are quite irregular and depend greatly onthe orientation. Some grains rotate quickly, othersremain stable. As the shear plane normal is approached,rotations slow down and this gives rise to theasymmetry. Upon further deformation grains will rotate

rapidly in the sense of shear and deplete orientations.The pole figure maximum is a dynamic average over allorientations and emphasizes orientations where

Fig. 11. Pole to (010) rotation trajectories for 10 selected grains duringsimple shear up to 100% von Mises equivalent strain (γ=1.73),simulated with the visco-plastic self-consistent model. Shear plane ishorizontal, symbol size is proportional to strain, i.e. the startingorientation iswith the smallest symbol of each trail. 5% strain increments.Equal area projection.


rotations are slowest. For (010) poles a stable position isreached around 18.5° to the shear plane normal, againstthe sense of shear (Fig. 11).

6. Discussion

Our data clearly demonstrate a pervasive develop-ment of texture under conditions of Newtonian creep athigh strains (γ≈4). Samples deformed in simple sheardisplay an asymmetric pattern with a (010) polemaximum at high angles to the shear plane, inclinedagainst the sense of the shear (Figs. 7, 8). In com-pression, at lower strains but higher stresses, a (010)maximum parallel to the compression direction isobserved (Fig. 9). Thus linear-viscous or Newtonianflow is compatible with the development of texture for awide range of strain, stress and temperature values.

This result is significant since deformation at hightemperatures and low stresses in theEarthmaybe localizedin shear zones, take place in a linear-viscous regime butstill produce texture and potentially seismic anisotropy.The presence or absence of texture (anisotropy) is thus nota sufficient criterion to unequivocally infer the dominantrheological/mechanical regime, as suggested by somegeophysicists (e.g., Karato and Wu, 1993, p. 771; Savage,1999, p. 67; McNamara et al., 2001, p. 86).

Low-stress sensitivity of the strain rate, as in New-tonian flow, is generally associated with “diffusionalprocesses” which do not produce a texture (Paterson,1990). This conclusion is based on experiments onmetals (Cutler et al., 1974; McDarmaid et al., 1985;Bowen et al., 1991; Padmanabhan et al., 1991; Fan andChaturvedi, 2000; Engler et al., 2000; Pérez-Prado et al.,

2001), calcite (Schmid et al., 1977), olivine (Fliervoet etal., 1999) and perovskite (Karato et al., 1995). Rutter etal. (1994) cautioned against generalization of thisconcept based on experiments on calcite that produceda weak texture at low strain in a Newtonian regime(n=1.7). Also, compression experiments on fine-grainedanhydrite rocks with a linear-viscous behavior (n=1.5)produced a strong texture with [100] aligned parallel tothe shortening direction (Müller et al., 1981). Theseconflicting reports indicate the uncertainties wheninterpreting creep data from experiments performed atvery low stresses.

There is considerable evidence in materials science(Ruano et al., 1993; Langdon, 2000; Kassner and Pérez-Prado, 2000; Kumar et al., 2007; Mohamed, 2007;Ruano, et al., 2003) demonstrating that three processescontribute to the flow of polycrystalline aggregates atelevated temperature and low stresses: the movement ofdislocations, the stress-directed flow of atoms/vacanciesand the relative displacement of adjacent grains.Specific creep mechanisms arise when one processdominates over the others: diffusion creep, Harper–Dorn creep, and grain boundary sliding. These mechan-isms show distinct dependences on experimentalparameters such as temperature, grain size, strain rateand stress. In practice it is often difficult to identify therate controlling flow mechanism. A brief discussionfollows.

When some form of diffusion creep dominates, themovement of vacancies/atoms leads to an elongation ofgrains along the tensile axis (Langdon, 2000). Somemicrostructural features have been proposed as evidencefor diffusion creep in polyphase rocks and metals. Theyinclude strongly lobated grain boundaries, stress-controlled compositional zoning and denuded zones(Ozawa, 1989; Gower and Simpson, 1992; Langdon,2000). In practice grain boundary sliding can accom-modate large strain diffusion creep (Raj and Ashby,1971; Mori et al., 1998; Langdon, 2000; Kim andHiraga, 2000; Langdon, 2006). This accommodationmechanism does not modify the relative position ofgrains. The mechanical response is invariably New-tonian (n=1), but differences arise, in terms of grain-size sensitivity and activation energy, if diffusion occursthrough the grains (Nabarro–Herring creep) or on grainboundaries (Coble creep) (Langdon, 1985, 2000). Sincedislocation activity and grain rotation are negligibleduring pure diffusion creep, texture does not develop.

When flow takes place because of dislocationactivity within the low-stress region of the Newtonianregime, a genuine creep process occurs: Harper–Dorncreep (H–D) (Nabarro, 1989; Wang, 1996; Ginter et al.,


2001; Mohamed, 2007; Kumar et al., 2007). Importantrequirements for H–D creep are a low initial dislocationdensity, high homologous temperatures (0.5–0.95Tmelting), and high purity. Recent experiments thatinvolve large strains have verified that the stressdependence of H–D creep changes from n=1 at smallstrains to n≈2 at higher strains (Ginter et al., 2001). Nodependence on grain size has been identified for H–Dcreep (Kumar et al., 2007). However experiments inmetals show that grain-size sensitivity increases as grainsize decreases; below a critical grain size a transition todiffusion creep has been reported (Kloc and Fiala, 1999;Kassner and Pérez-Prado, 2000; Mohamed; 2007). Thiscritical value of the grain size depends on the grainmicrostructure, such as dislocation density and stackingfault energy (Ruano et al., 1993). Although not fullyunderstood it is also recognized that H–D creep dependson temperature, with differentmicroprocesses occurring athigh temperature (≈0.95 Tmelting) and at low temperature(≈0.5 Tmelting) (Kumar et al., 2007). In practice, it isexpected that grains become elongated, without anyaccommodation through grain boundary sliding (Langdon,2000). Since dislocation activity is able to account for thestrain occurringwithin the aggregate, texturemay develop.

Grain boundary sliding (GBS) is a creep mechanismin which grains become displaced with respect to eachother. A shape preferred orientation may develop alongthe tensile stress (Langdon, 2000). GBS creep is a grain-size dependent mechanism. When the grain size issmaller than the equilibrium subgrain size, the samplecan deform extensively without failure, producing asuperplastic behavior (Kashyap et al., 1985; Nieh et al.,1997; Kassner and Pérez-Prado, 2000). The stressexponent range between n=2 and 3 (Langdon, 2000;Xun and Mohamed, 2003; Langdon, 2006). Graindisplacements within the aggregate are accommodatedby concomitant processes as dislocation motion,diffusional flow, grain boundary migration, and grainrotation (Langdon, 2000; Xun and Mohamed, 2003;Langdon, 2006). Accommodation processes can lead tochanges in grain boundaries and grain shapes. Straightboundaries become curved and grains more equiaxed,and minor elongations may occur (Kashyap et al., 1985;del Valle and Ruano, 2007). It is generally accepted thatGBS creep involving grain rotation progressivelyremoves the texture of the aggregate (Cutler et al.,1974; McDarmaid et al., 1985; Bowen et al., 1991;Padmanabhan et al., 1991; Chokshi et al., 1993; Fan andChaturvedi, 2000; Engler et al., 2000; Pérez-Prado et al.,2001; del Valle and Ruano, 2007).

Our anorthite samples deformed in torsion show alinear-viscous behavior (Table 1). A pervasive texture

and shape fabric, related to the stress geometry, developsfrom an initial random distribution of non-equiaxedgrains. Independently on temperature and stress, at theexperimental conditions, the volume of crystals whichexperiences a net variation of grain size is the same(≈45%). Grain-size reduction dominates at 1200 °C,while grain-growth and refinement are balanced at950 °C. Besides most of the grains (60%) havestatistically the same aspect ratio (R) as the startingmaterial; within those that change (40%), a 30%becomes more elongated. The grain boundaries becomecurved and wavy, particularly at 1200 °C and low stress(1.6 MPa) (Figs. 4c, 5b). All these features indicate thatgrain boundaries are mobile, and suggest that dynamicrecrystallization is responsible of the grain refinement.

The SPO in rocks reflects a dynamic balance ofrotations, grains interaction and strain. Under the strainlevels here supported SPO average values may reflect adynamic maximum where the angular rate of grainsreaches a minimum. In this line, oblique foliationsrepresent a steady-state feature which has been linked tocycles of passive rotation and elongation of grains anddynamic recrystallization which tends to destroy theSPO. The angle to the kinematic frame may changedepending on mechanisms balance, but invariablyrepresent a stable orientation (Means, 1981; Ree,1991). Sample deformed at 1200 °C represents anexample of steady-state SPO, where the different modesand shapes tend to rotate to the average orientationα=14° (Fig. 5b inset); the smaller and less elongatedgrains, resulting from dynamic recrystallization, have anorientation slightly closer to the shear plane (Mode 1;Fig. 5b inset). Similarly in this sample, potential slipplane (010) tends to parallelize to the shear plane(Figs. 7, 8, 12b), what suggests a strong influence ofrecrystallization on texture.

In the case of sample deformed at 950 °C middle-sizegrains are more flattened and oriented at higher angles tothe shear plane (Modes 2, 3; Fig. 5c inset). Texturemimics the SPO and (010) remains almost parallel to theSPO, independently on strain (Fig. 12b). On the otherhand recrystallized grains (Mode 1; Fig. 5c inset)represent the closest orientation to the shear plane, whilethe largest grains show a large dispersion whichprobably reflects partially reabsorbed clasts (Mode 4;Fig. 5c inset). It is clear that at low temperature grain-size reduction mechanism (dynamic recrystallization) isless efficient than at high temperature, and SPO andtexture are controlled by deformative processes (dislo-cation glide). It may be inferred that sample deformed at1200 °C and low stresses reached a steady-statemicrostructure, while sample deformed at 950 °C not.


Mechanical behaviour partially reflects this point, wherehardening is more pronounced in the sample deformedat 950 °C (Fig. 1), probably due to the grain-growth.

It is likely that several processes have been activeduring torsion experiments of anorthite: dislocationmotion is consistent with the texture development; grainboundary sliding (GSB) is compatible with the devel-opment of the SPO without significant shape change;grain-size reduction is probably due to dynamicrecrystallization which, in turn, requires stored plasticenergy via dislocation increase in order to be activated.An argument against dislocation processes is the lowdislocation density. However, in fine-grained materialsdislocations may easily annihilate at grain boundaries(Kashyap et al., 1985), and at high temperaturedislocations constantly combine during recovery, sothat the preserved dislocation density after quenching ofsamples may be underestimated. In our case probablymore important than quenching rate effect (≈30 °C/min) is the observation that dislocation densities areinhomogeneous, with a low mean density, but locallyhigh density that probably induces bulging andrecrystallization.

Traditional models of GBS controlled by dislocationmovement (Kassner and Pérez-Prado, 2000) predict ann≈2 and suggest that dislocation glide does notcontribute to the total strain. However it is importantto note that a large number of studies based on textureanalysis support the idea that dislocation glide operatesas a direct response to the applied stress, as well as being

Fig. 12. Texture analysis of samples deformed in torsion. (a) Intensity variation[001] at different T and spots (see Figs 2 and 6 for spot location). (b) The asymplane, showing the effect of T, strain, stress, and strain rate as varying from cestrength in terms of texture index (F2) along the section. Notice that the she

an accommodation process for GBS (Cutler et al., 1974;Kassner and Pérez-Prado, 2000; Pérez-Prado et al.,2001). Our results are consistent with that conclusion,since texture strength expressed by the (010) maximum(Fig. 12a), or the texture index F2 (Bunge, 1982)(Fig. 12c), increases from the center to the edge of thesample as strain, strain rate, and stress increase. Ruanoet al. (2003) demonstrate that, when dislocation glidebecomes the rate-controlling mechanism in this kind ofmodel, a stress exponent n=1 results.

Other creep processes such as high temperatureHarper–Dorn creep fail to explain the stress sensitivitysince temperatures are well below the requirements forthis mechanism, and grain size is very small (Kumaret al., 2007). Moreover, although not experimentallyproved for silicates, it has been demonstrated forHarper–Dorn creep of aluminum that nN1 whendeformed at high strains (Ginter et al., 2001); thereforeat the strains attained in our experiments, we mightexpect a higher stress sensitivity (n) if the Harper–Dornflow mechanism was active.

Compression experiments have been used to explorethe transition from Newtonian to non-Newtonian flow(Rybacki and Dresen, 2000). Reported features includerecrystallized grains, sutured grain boundaries, defor-mation twins and tabular grains, indicating restorativeprocesses like grain boundary migration and recrystal-lization (Rybacki and Dresen, 2000). Grain-size sensi-tivity was assumed to be around 3, based on previousstudies that explored a transition from grain boundary

(multiples of a random distribution, m.r.d.) for pole to (010), [100] andmetry of the texture evaluated as a function of the angle (010) to shear

nter to border. Gray bands are SPO intervals. (c) Variation of the texturear stress increases linearly to the border.


diffusion controlled creep to dislocation creep (Wanget al., 1996; Dinamov et al., 1999; Rybacki and Dresen,2004). The texture pattern can be satisfactorilyexplained by slip but the texture strength is muchlower in experiments than in simulations for comparablestrains (Fig. 9 vs. Fig. 10c, d; all corresponding to 30%compressive strain). This discrepancy is probablyrelated to the heterogeneous dislocation density ob-served in the compression experiments. In the texturesimulation a (spatially) homogeneous dislocation activ-ity is assumed, so that the average texture intensity maybe overestimated in comparison to experimental results.Also, diffusion processes may have been active in theexperimental samples to a small extent.

If we assume that flow was achieved by the coope-ration of GBS and dislocation glide, we could try toevaluate the contribution to the total strain of eachprocess, by analyses of SPO and texture features. Thegrain shape distribution is consistent with a simple shearexperiment. In homogeneous deformation, there is aregular relationship between shear strain γ, aspect ratio Rand α (tan 2α=2/γ; γ={(R2−1) tan α} /{1+R2tan2 α},R ¼ 1

2 g2 þ 2þ gffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffig2 þ 4ð Þp� �

; (Means, 1981). If we consid-er angles between the long axes of the grains and the shearplane of α950°C=21°, and α1200°C=14°, (Fig. 6a, b), theshear strains are γ950°C=2.3 and γ1200°C=3.79, represent-ing 57% and 95% of the total sample strain (Table 1).Since GBS modifies the relative position of each grain(Langdon, 2000), its main contribution to the total strainwould be recorded in the shape preferred orientation.However, other mechanisms, like dislocation glide,produce changes in the orientation of grains then wecannot only attribute to GBS the strain recorded by theSPO. In conclusion shear strains obtained from SPOrepresent upper bounds for GBS. Besides strain anal-ysis partially correlate with the texture index, whereF2

1200°CbF2950°C (Fig. 12c) which suggests that disloca-

tion glide is less active at the highest temperature. Thepredominance of GBS at higher temperatures and lowstresses, as might be inferred from results is alsocompatible with the model (Ruano et al., 2003) andprevious microstructural results. The interpretation of theaspect ratio (R) (Figs. 6c, d) is also complex since severalprocesses may contribute to it. Grains with a netelongation in both samples are the same (30%) andhave the equal meanR=3.4. If we assume that diffusionalmechanisms act as an accommodation process, and netelongations of grains are mainly due to the glide ofdislocations we get a γ950°C=γ1200°C=1.5×0.3=0.45.Total strain could be written now as γtotal= (γGBS+γglide),resulting in γ950°C=2.75 (69% γtotal) and γ1200°C=4.24(99% γtotal). Differences in total strain could be partially

explained by strain partitioning phenomena duringdeformation, but also to the extent microstructure hasreached a steady-state configuration.

Texture develops with a similar pattern and somedependence on strain; however variations in observedtexture with position in the sample must be interpretedwith care because of the complex interrelationshipsbetween strain, strain rate, and stress and more work isneeded to separate the contribution of those parameters(Fig. 12). Compared to samples deformed in axialcompression, samples deformed in torsion show muchstronger texture related to a much higher finite strain.

A common feature of the texture in all torsion samplesis the asymmetric (010) maximum at high angles to theshear plane, disposed against the sense of shear. It doesnot change greatly with strain or experimental condi-tions. As the polycrystal plasticity simulations suggest, itis compatible with dominant (010) slip. There are minorvariations within each sample and between the samples.Based on only three samples deformed at differentconditions it is highly speculative to interpret them, yetwe can suggest possibilities.

At higher stress and lower temperature, texture andSPO display a similar pattern with (010) parallel to thefoliation (Figs. 6, 7, 12b). At lower stress and highertemperature (010) is located closer to the shear plane, atleast at higher strains (γ=4) (Fig. 12b). In addition newtextural components appear in the (010) and [100] polefigures (Fig. 8). At 950 °C the [001] maximum is closeto the shear direction and quite strong (2 m.r.d., Figs. 8,12a), which is consistent with a transition in slipdirection with increasing temperature from [001] to[100] (Ji et al. 1997, 2000, 2004).

There appear to be some systematic textural changeswith strain and temperature, mainly in the degree ofasymmetry and strength (Figs. 7–8). As strain increasesthe (010) and [001] maxima increase, while the [100]maximum decreases at low stress. This tendencyreverses at the highest temperature (Fig. 12). Moreover,the angle of the (010) maximum to the shear planenormal slightly decreases at higher strains, highertemperatures, and lower stress, causing the texture tobecome more symmetric (Fig. 12b). However at highstress this angle shows a stable position around 23° tothe shear plane. The texture strength, in terms of thetexture index F2 (Bunge, 1982), decreases withincreasing temperature (F2

min=1.16), and the highestproportions of randomly oriented crystals appear at1200 °C (0.78 m.r.d.) (Fig. 12a, c). All these features areconsistent with a reduction of dislocation glide andincreasing of dynamic recrystallization with increasingtemperature and decreasing stress.


7. Conclusions

Anorthite aggregates, experimentally deformed athigh temperature under Newtonian creep, developsignificant texture as documented with synchrotron X-ray measurements and TOF neutron diffraction. Com-plex diffraction patterns were deconvoluted with theRietveld method to obtain quantitative texture informa-tion. In torsion (simple shear) texture and shapepreferred orientation display a monoclinic pattern withthe dominant (010) maximum inclined against the shearsense and at high angles to the shear plane. This patternis consistent with dominant (010)[100] slip andsubsidiary (010)[001] and (001)[100] slip, as indicatedby comparison with polycrystal plasticity simulations.

The results indicate that Newtonian creep does notpreclude texture. It follows that the presence or absenceof texture in a rock does not conclusively predict amechanical behavior or a distinct deformation mecha-nism. Similarly mechanical parameters alone do notallow one to unambiguously infer active deformationmechanisms nor texture development.

It is proposed that cooperative processes grainboundary sliding and dislocation glide have been active,accompanied by dynamic recrystallization.

Acknowledgements

We acknowledge support from DOE-BES (DE-FG02-05ER15637), NSF (EAR-0337006) and CDAC.Access to facilities at APS (beamline ID11-C) andLANSCE (HIPPO) to perform texture measurementswas invaluable. S. Vogel at Los Alamos helped uswith the neutron experiments. HRW is appreciativefor hospitality while on sabbatical leave at GfZ Pots-dam. JGB was supported by a Postdoctoral Fellow-ship (M.E.C. #EX-2005-0490). We wish to thank C. P.Jaupart and three anonymous reviewers for insightfuland encouraging suggestions.

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