Viscous and elastic anisotropy in partially molten rocks I ...benh/papers/y071210_AGU.pdf · and epicentral dista nces of >80 !, and stacking over a wide range of distances and depths.

I. Consequences of viscous and elastic anisotropyCauses and a definition of “multi-scale” anisotropy

II. Experimental Observationsmelt alignment, melt segregation, melt migration

III. TheoryNew diffusion creep model

IV. Applications to a simple oceanic upper mantle structurepredictions for multi-scale effective viscosity structure

Viscous and elastic anisotropy in partially molten rocks I:Experimental, field, and seismic observations

Ben Holtzman (LDEO, Columbia University) Yasuko Takei (Earthquake Research Institute, U. Tokyo)

Geodynamic consequences of anisotropic viscosity(and reduced effective shear viscosity due to anisotropy)

1) Degree of lithosphere / asthenosphere (convectosphere) coupling ? 2) Influences convective patterns - tends to tighten streamlines at boundary layers... (Honda, 1986; Christensen, 1987- and renewed interest now)...

3) Plate boundary rheology (reduction in meso-scale effective viscosity) gives plate like behavior in self-consistent plate generation models, e.g. Tackley, 2000; Bercovici; Ogawa...

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uniform and moderate yield stress:

strain rate weakening, melt weakening + asthenosphere:

and epicentral distances of >80!, and stacking over a widerange of distances and depths. At HRV we can use an evenmore conservative depth cutoff of 150 km by virtue of thelarger volume of data recorded at the station. In addition, wedo not use data from epicentral distances <55! since theseevents are incident to the discontinuity at angles beyond thecritical angle for Sp transmission. After picking identifiableS phases, our deconvolved, migrated waveforms contain 56events at HRV and 28 events at LMN (Figures 3c and 3d).

The standard deviation error bars (grey lines in Figure 3) onour deconvolved waveforms are calculated with bootstraptests in which a random 20% of the events in the bin arerandomly replaced by another random 20%, and the decon-volved, migrated waveforms are recalculated 100 times.

2.2. Imaging

[12] To image the discontinuities responsible for the Spand Ps converted phases, the data is first transformed into itsP and SV components using a free-surface transfer matrix.

Figure 2. Three-dimensional view of the lithosphere-asthenosphere boundary and surface topography.Red box in the inset map highlights the location of the study region within North America. Shading onthe top surface indicates topography. Yellow arrow points in the direction of absolute plate motion; platevelocity is 2.5 cm/yr. Red inverted triangles denote station locations. The lower surface represents thelocation of the base of the lithosphere interpolated from migrated Ps waveforms and our new migrated Spwaveforms recorded at stations HRV and LMN (blue circles mark conversion points). The Sp HRV datafrom northern back azimuths and the Ps from LBNH (grey circles mark conversion points) are not used tocalculate the interpolated surface because of a discrepancy in the depth to which the phase migrates (seesection 6.2). This surface ranges from 89 km (orange) to 105 km (pink) depth. Each color band covers2 km in depth. Black lines connect Ps piercing points to the station at which the conversion is observed.Grey lines connect Sp piercing points to the station where the conversion is observed. All depths arecalculated assuming Vp/Vs = 1.8 in subcrustal mantle.

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Related seismic observables (seismic velocities influences by same physical properties that cause anisotropy)

3) Receiver functions (e.g. E. N. Am., Rychert et al., Nature, 2005;JGR, 2007)

Nature © Macmillan Publishers Ltd 1998

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170 NATURE | VOL 394 | 9 JULY 1998

assumption that anisotropic effects are small. Nishimura andForsyth17,18 studied the variations in anisotropic properties of thePacific upper mantle in detail—however, their analysis emphasizedan age dependence for both isotropic and anisotropic properties.The results presented here suggest that this emphasis may have beentoo limiting.

Our new model S20A was derived using a wide variety of seismicobservations and allowing for anisotropic heterogeneity in theupper mantle (see Methods for details). Figure 1 shows the per-turbations in VSVand VSH with respect to their values in the referencemodel PREM19 at 50, 100 and 150 km depth in the mantle. At 50 kmdepth, the VSV and VSH models have very similar patterns of highvelocities under the continents and low velocities under the mid-ocean ridges. A pronounced difference between the models is seenbeneath the older portions of the Pacific plate. Here, the perturba-tion in VSV is positive and large, while VSH remains close to thePREM value. In comparison, the difference map for the rest of theworld shows minor anomalies not associated with identifiabletectonic elements; such differences, smaller than about !1%, weconsider to represent an unresolved background level.

At 100 km, the differences between the VSH and VSV models aresmall. The implication is that the radial anisotropy built into PREM,with VSH !3% faster than VSV, is a good average for both continentsand oceans. However, at 150 km depth, the pattern is dramaticallydifferent. Whereas VSH shows the central Pacific as faster than the

global average, VSV is significantly slower. The anomaly associatedwith the EPR is much better defined in VSH, where it is clearlycentred on the ridge axis; the negative VSV anomalies are insteaddiffuse, extending to the centre of the Pacific. The maximumdifference between the VSV and VSH perturbations of !5% isobtained for an area just southwest of Hawaii. It is notable that inthe global model of Montagner and Tanimoto11, the largest aniso-tropic signal seen at this depth lies in the same area, though it has asmaller absolute amplitude. Below 150 km depth, the differencebetween VSH and VSV beneath the central Pacific becomes smaller(Fig. 2d), and we do not believe we can resolve a difference betweenthe two at depths greater than 250 km with our current data set.

Two main conclusions result from our analysis. First, Fig. 1 showsthat for most of the world, the anisotropy of PREM provides a goodaverage. The only large region where this does not hold true is thePacific plate. Figure 2a, b shows average VSV and VSH valuescalculated for the mantle beneath the Pacific plate and for the restof the world. The average anisotropy that we obtain, with VSH !2–4%faster than VSV between the Moho and 200 km, is similar to thatobtained in previous detailed studies of the Pacific uppermantle13,14,18. The Pacific plate is large and well sampled by the

PacificPlate

non-PacificPlates

Pre-Camb.Cratons

Central Pacific

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PREM SH

SVSH

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c d

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Figure 2 Velocity profiles of the shear-wave velocities VSVand VSH. a, The average

velocities beneath the entire Pacific plate. The maximum difference between VSV

andVSH occurs at around 125 kmdepth, in contrast to PREM, inwhich it occurs just

below the Moho. Note also that the model shows that the upper mantle beneath

the Pacific plate is !1% slow with respect to PREM down to at least 400 km depth.

b, The average velocities calculated for all plates except the Pacific. The average

structure is close to that of the starting model PREM. c, Average velocity profiles

calculated for all Precambrian cratons within the Eurasia and North America

plates. These regions are sampled very well by our data, and the deviations from

the PREMstructureare largeand well resolved.Note, however, that the difference

between VSV and VSH remains very close to that of the starting model PREM. d,

Average velocity profiles calculated for a cap with 10! radius centred on the

anisotropy anomaly identified in this study at 15! N,160! W. At 130 km depth, VSH is

7% faster than VSV, almost three times the value predicted by PREM. In contrast

with PREM, the radial anisotropy in the shallowest mantle is small. Note that the

velocity discontinuity at 220 km is part of the starting model PREM, and not a

feature that can be resolved in our inversion.

Anisotropic variations

Isotropic variations

150E 180E 150W 120W 90W 60W

60N

30N

0N

30S

60S

60N

30N

0N

30S

60S

150E 180E 150W 120W 90W 60W

–4.8% 7.2%–2.4% 0.0% 2.4% 4.8%

Figure 3Shear-wave velocity variationsbeneath the Pacific plate at 150 km depth.

The top panel shows the anisotropy dVSV " dVSH on the same scale as the Voigt-

averaged isotropic variation in S-wave velocity (bottom panel) calculated using

the approximate expression dV VoigtS ! 1

3"dVSH # 2dVSV$. The maps clearly illustrate

that anisotropic velocity variations are as large as the isotropic (thermal) varia-

tions. The isotropic S-wave variations correlate better with the age of the ocean

floor than either the dVSV or dVSH maps in Fig.1. The largest deviation from this age

correlation is very clearly associated with the location of the Pacific Superswell3.

Nature © Macmillan Publishers Ltd 1998

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letters to nature

170 NATURE | VOL 394 | 9 JULY 1998

assumption that anisotropic effects are small. Nishimura andForsyth17,18 studied the variations in anisotropic properties of thePacific upper mantle in detail—however, their analysis emphasizedan age dependence for both isotropic and anisotropic properties.The results presented here suggest that this emphasis may have beentoo limiting.

Our new model S20A was derived using a wide variety of seismicobservations and allowing for anisotropic heterogeneity in theupper mantle (see Methods for details). Figure 1 shows the per-turbations in VSVand VSH with respect to their values in the referencemodel PREM19 at 50, 100 and 150 km depth in the mantle. At 50 kmdepth, the VSV and VSH models have very similar patterns of highvelocities under the continents and low velocities under the mid-ocean ridges. A pronounced difference between the models is seenbeneath the older portions of the Pacific plate. Here, the perturba-tion in VSV is positive and large, while VSH remains close to thePREM value. In comparison, the difference map for the rest of theworld shows minor anomalies not associated with identifiabletectonic elements; such differences, smaller than about !1%, weconsider to represent an unresolved background level.

At 100 km, the differences between the VSH and VSV models aresmall. The implication is that the radial anisotropy built into PREM,with VSH !3% faster than VSV, is a good average for both continentsand oceans. However, at 150 km depth, the pattern is dramaticallydifferent. Whereas VSH shows the central Pacific as faster than the

global average, VSV is significantly slower. The anomaly associatedwith the EPR is much better defined in VSH, where it is clearlycentred on the ridge axis; the negative VSV anomalies are insteaddiffuse, extending to the centre of the Pacific. The maximumdifference between the VSV and VSH perturbations of !5% isobtained for an area just southwest of Hawaii. It is notable that inthe global model of Montagner and Tanimoto11, the largest aniso-tropic signal seen at this depth lies in the same area, though it has asmaller absolute amplitude. Below 150 km depth, the differencebetween VSH and VSV beneath the central Pacific becomes smaller(Fig. 2d), and we do not believe we can resolve a difference betweenthe two at depths greater than 250 km with our current data set.

Two main conclusions result from our analysis. First, Fig. 1 showsthat for most of the world, the anisotropy of PREM provides a goodaverage. The only large region where this does not hold true is thePacific plate. Figure 2a, b shows average VSV and VSH valuescalculated for the mantle beneath the Pacific plate and for the restof the world. The average anisotropy that we obtain, with VSH !2–4%faster than VSV between the Moho and 200 km, is similar to thatobtained in previous detailed studies of the Pacific uppermantle13,14,18. The Pacific plate is large and well sampled by the

PacificPlate

non-PacificPlates

Pre-Camb.Cratons

Central Pacific

PREM SV

PREM SH

SVSH

a b

c d

S-velocity (km s–1) S-velocity (km s–1)4.3 4.4 4.5 4.6 4.7 4.8

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De

pth

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)

De

pth

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Figure 2 Velocity profiles of the shear-wave velocities VSVand VSH. a, The average

velocities beneath the entire Pacific plate. The maximum difference between VSV

andVSH occurs at around 125 kmdepth, in contrast to PREM, inwhich it occurs just

below the Moho. Note also that the model shows that the upper mantle beneath

the Pacific plate is !1% slow with respect to PREM down to at least 400 km depth.

b, The average velocities calculated for all plates except the Pacific. The average

structure is close to that of the starting model PREM. c, Average velocity profiles

calculated for all Precambrian cratons within the Eurasia and North America

plates. These regions are sampled very well by our data, and the deviations from

the PREMstructureare largeand well resolved.Note, however, that the difference

between VSV and VSH remains very close to that of the starting model PREM. d,

Average velocity profiles calculated for a cap with 10! radius centred on the

anisotropy anomaly identified in this study at 15! N,160! W. At 130 km depth, VSH is

7% faster than VSV, almost three times the value predicted by PREM. In contrast

with PREM, the radial anisotropy in the shallowest mantle is small. Note that the

velocity discontinuity at 220 km is part of the starting model PREM, and not a

feature that can be resolved in our inversion.

Anisotropic variations

Isotropic variations

150E 180E 150W 120W 90W 60W

60N

30N

0N

30S

60S

60N

30N

0N

30S

60S

150E 180E 150W 120W 90W 60W

–4.8% 7.2%–2.4% 0.0% 2.4% 4.8%

Figure 3Shear-wave velocity variationsbeneath the Pacific plate at 150 km depth.

The top panel shows the anisotropy dVSV " dVSH on the same scale as the Voigt-

averaged isotropic variation in S-wave velocity (bottom panel) calculated using

the approximate expression dV VoigtS ! 1

3"dVSH # 2dVSV$. The maps clearly illustrate

that anisotropic velocity variations are as large as the isotropic (thermal) varia-

tions. The isotropic S-wave variations correlate better with the age of the ocean

floor than either the dVSV or dVSH maps in Fig.1. The largest deviation from this age

correlation is very clearly associated with the location of the Pacific Superswell3.

1) Transverse Isotropy(Love-Rayleigh discrepancy, Pacific V_sh > V_sv)e.g. Ekstrom and Dziewonski, Nature 1997; Ritzwoller

cooling model [Turcotte and Schubert, 2002] (calculatedusing a thermal diffusivity of 10!6 W/m2 and an adiabatcalculated with variable compressibility [Schmelling et al.,2003]) predicts a lithospheric thickness of 41 km at10 Ma.Thus the North American plate is much thinner thanexpected.[30] Beneath the lithosphere, we predict a "75!C thermal

anomaly over a broad region centered beneath the ridge.This value is similar to estimates of anomalous mantle

temperatures based on a geochemical study of rare earthelements in Reykjanes Ridge basaltic rocks (<100!C [Whiteet al., 1995]). Note that the temperature anomaly in Figure 9aexhibits a thermal inversion in the mantle, where highertemperatures overlie slightly cooler temperatures. On theother hand, the low-velocity region could instead be causedby lateral variations in melt fraction. Assuming relaxedmoduli and that melt is organized in tubules at fractionsless than 1% and in films and tubules above 1% [Hammond

Figure 7. Tomographic images of (left) shear wave velocity, VSV, and (right) percent anisotropy. Shearwave velocity and anisotropy are calculated together in a joint inversion of the Love and Rayleigh wavephase velocities (shown in Figure 4). The images are oriented in a vertical plane, normal to the ridge axis;the horizontal axis indicates the distance from the ridge axis; the vertical axis indicates depth below theseafloor. The magnitude of anisotropy is defined as 100(VSH ! VSV)/Vaverage, where VSH is the shearwave velocity of a horizontally polarized shear wave, VSV is for a vertically polarized shear wave, andVaverage is the average of the two. Ratio, h, of the penalty constraints on VSV versus x (the anisotropyparameter): (a) 1, (b) 1/2, and (c) 2. A smoothness constraint added below (d) 135 and (e) 100 km thatsqueezes lateral variations in velocity or anisotropy structure to shallower depths (h = 1 used in bothcases). See text for discussion.

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cooling model [Turcotte and Schubert, 2002] (calculatedusing a thermal diffusivity of 10!6 W/m2 and an adiabatcalculated with variable compressibility [Schmelling et al.,2003]) predicts a lithospheric thickness of 41 km at10 Ma.Thus the North American plate is much thinner thanexpected.[30] Beneath the lithosphere, we predict a "75!C thermal

anomaly over a broad region centered beneath the ridge.This value is similar to estimates of anomalous mantle

temperatures based on a geochemical study of rare earthelements in Reykjanes Ridge basaltic rocks (<100!C [Whiteet al., 1995]). Note that the temperature anomaly in Figure 9aexhibits a thermal inversion in the mantle, where highertemperatures overlie slightly cooler temperatures. On theother hand, the low-velocity region could instead be causedby lateral variations in melt fraction. Assuming relaxedmoduli and that melt is organized in tubules at fractionsless than 1% and in films and tubules above 1% [Hammond

Figure 7. Tomographic images of (left) shear wave velocity, VSV, and (right) percent anisotropy. Shearwave velocity and anisotropy are calculated together in a joint inversion of the Love and Rayleigh wavephase velocities (shown in Figure 4). The images are oriented in a vertical plane, normal to the ridge axis;the horizontal axis indicates the distance from the ridge axis; the vertical axis indicates depth below theseafloor. The magnitude of anisotropy is defined as 100(VSH ! VSV)/Vaverage, where VSH is the shearwave velocity of a horizontally polarized shear wave, VSV is for a vertically polarized shear wave, andVaverage is the average of the two. Ratio, h, of the penalty constraints on VSV versus x (the anisotropyparameter): (a) 1, (b) 1/2, and (c) 2. A smoothness constraint added below (d) 135 and (e) 100 km thatsqueezes lateral variations in velocity or anisotropy structure to shallower depths (h = 1 used in bothcases). See text for discussion.

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2) Anomalous vertical anisotropy (Love-Rayleigh discrepancy, V_sv > V_sh)(e.g. Reykjanes Ridge, Gaherty, Science, 2001, Delorey et al., JGR, 2007)

4) SKS splitting (e.g. East AfricanRift, Ethiopia, Kendall et al., 2005;Ayele et al., 2004;Keir et al., 2005;Bastow et al., 2005)

New type of olivine fabric from deformation experimentsat modest water content and low stressKatayama, Jung and Karato, Geology, 2004

ab

c

type A

ab

c

type E

type C

a

b c

a

b

c

type B

note:Bystricky et al: type A+ E, Holyoke& Tullis:type D and type A

Causes of anisotropy1) Lattice preferred orientation of anisotropic crystals (in experiments)

pressure and high-temperature torsion appa-ratus (17 ), in which any small element of thesample undergoes deformation at constantstrain rate by simple shear (18). The shearstress and shear strain rate at the outer surfaceof the cylindrical sample were derived fromthe measured torque and twist rate, respec-tively (19). The experiments were performedat 1200°C and 300 MPa confining pressure,with the oxygen fugacity near the Fe/FeObuffer (10!12 bars). Fourier transform infra-red (FTIR) spectroscopy analyses of de-formed samples indicated that they containedless than 30 molar parts per million (ppm)H/Si (20). Samples were deformed to differ-ent amounts of bulk shear strain, under twoconstant angular displacement rates corre-sponding to constant shear strain rates ofeither 6 " 10!5 s!1 or 1.2 " 10!4 s!1 at theouter surface of the sample. For both defor-mation series, a peak stress occurred at ashear strain # $ 0.1, followed by 15% weak-ening up to # $ 0.5 (Fig. 1). At higherstrains, the flow stress was nearly steady-state, leading to a total weakening of theaggregate of about 20% from the peak stressto the flow stress at # $ 5. Stress exponentsof n % 3.3 determined after the weakeningsuggest dislocation creep as the rate-limitingmechanism, even at high strains.

Microstructures were analyzed with opticaland electron microscopy. Thin sections werecut perpendicular to the cylinder radius andwithin 200 to 300 &m of the sample outer edge.In such planes, deformation is nearly simpleshear (18). With increasing strain, the averagegrain size reduced by dynamic recrystallization(Fig. 2). At shear strains # $ 0.5, a typicaldeformation microstructure displays evidenceof incipient recrystallization (Fig. 2, C and D).At # $ 2, core-and-mantle structures suggestrecrystallization by subgrain rotation (Fig. 2, Eand F). The matrix wraps around porphyro-clasts and resembles the mosaic texture de-scribed in natural peridotites (21). With furtherstrain, the porphyroclasts become more elon-gated, with an oblique shape fabric consistentwith the sense and amount of shear. At # $ 5,recrystallization is nearly complete and a flu-idal mosaic microstructure (21) with a strongfoliation sub-parallel to the shear plane hasdeveloped (Fig. 2, G and H). The $5% ofremaining porphyroclasts consist of ribbonswith highly stretched tails (blue grains) andasymmetric porphyroclasts showing sub-grains and deformation features (whitegrains). High-resolution orientation imagingmaps are consistent with the observed micro-structures (Fig. 3). The spatial distribution ofsmall-angle misorientations within the clastsconfirms the formation of subgrains with asize similar to the recrystallized grains, pro-viding further evidence for recrystallizationby subgrain rotation.

LPOs were measured using electron back-

scatter diffraction (EBSD). During deforma-tion, the texture evolved through a transientdeformation texture (# $ 0.5) into a recrys-tallization texture at high strain (Fig. 4). At# $ 0.5, the [010] crystallographic axes tendto align normal to the shear plane and the

[100] axes develop two maxima, one parallelto the shear direction and one oblique to theshear direction. This LPO fits with previouslow strain experimental results (13, 14 ) andwith numerical simulations (22, 23). At high-er strains, the texture is much stronger and

Fig. 1. Shear stress versus shear strainfor samples deformed at 1200°C and300 MPa at constant nominal shearstrain rates of 6 " 10!5 s!1 (graycurve) and 1.2 " 10!4 s!1 (blackcurve). Conversion from torque andtwist of torsion deformation into shearstress and strain was performed as in(19). The peak stresses agree well withdislocation creep flow laws for olivineaggregates determined in axial compression experiments (12). Stepping tests performed at highstrains yielded stress exponents n (n % 3.2 at # $ 1.2 and n % 3.3 at # $ 3.2) typical ofdeformation by dislocation creep. Shaded area (left) shows magnified view of the low strain intervalat right (# ! 0.2), up to equivalent strains ($10%) where rheological data are typically obtainedin compression experiments. At these low strains, deformation often appears to be steady-statebecause the onset of weakening is rarely reached.

Fig. 2. Optical micro-graphs in cross-polarizedlight [from thin sectionscut as in (18)] of olivineaggregates deformed at6 " 10!5 s!1 to differentshear strains. Shear senseis dextral. (A and B) Start-ing material. Olivine ag-gregate hot-pressed for12 hours, showing anequigranular fabric withan average grain size of20 &m. Most grains haveeuhedral shapes with lowaspect ratios. Grain bound-aries are straight to curved.Few deformation featuressuch as lamellae and sub-grains are visible withinthe grains. The micro-graph in (A) was taken us-ing a gypsum plate. (Cand D) Deformed proto-lith. Deformation micro-structure at shear strain# $ 0.5. Evidence of dis-location creep and recov-ery in the form of defor-mation lamellae and 3 to4 &m subgrains. Grainboundaries are curved tolobate, with bulges indi-cating the onset of recrys-tallization. A weak obliqueshape preferred orientationis consistent with the sense of shear. (E and F) Protomylonite. Partially recrystallized microstructureat # $ 2. Recrystallized grain size is 3 to 4 &m. Elongated porphyroclasts with deformation lamellaehave aspect ratios R from 2 to 6 (R % 5.8 for the finite strain ellipse at # % 2). Core-and-mantlestructures and a subgrain size similar to the recrystallized grain size provide evidence forrecrystallization by subgrain rotation. (G and H) Ultramylonite. Fluidal mosaic microstructure at# $ 5. The recrystallized matrix ($95% volume) is very homogeneous with $3 &m equant grains.Two types of porphyroclasts with distinct crystallographic orientations remain. Highly elongatedribbon grains (blue) are in an orientation for easy slip on (010)[100] and track the bulk strain. Theiraspect ratios (R% 25 to 40) are consistent with the finite strain ellipse at # % 5 (R% 27). A secondtype of porphyroclasts (white) with lower aspect ratios (R ' 10) are full of subgrains anddeformation features, are strongly asymmetric in shape, and have an oblique lattice orientation.Both types have average grain areas equal to those of the starting grains (equivalent diameter,$20&m), suggesting that their shapes are due entirely to strain without major coalescence.

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Acknowledgements We thank A. Moore and P. T. Atkins for field and laboratory assistance. Thisresearch was supported by grants from the A. W. Mellon Foundation to L.A.D. and O.A.C., andfrom the N.S.F. to L.A.D., O.A.C. and A.C.K.

Competing interests statement The authors declare that they have no competing financialinterests.

Correspondence and requests for materials should be addressed to L.A.D. ([email protected]).

..............................................................

Pressure sensitivity of olivine slipsystems and seismic anisotropyof Earth’s upper mantleDavid Mainprice1, Andrea Tommasi1, Helene Couvy2,3, Patrick Cordier2

& Daniel J. Frost3

1Laboratoire de Tectonophysique, CNRS/Universite de Montpellier II, F-34095Montpellier cedex 5, France2Laboratoire Structure et Proprietes de l’Etat Solide, CNRS/Universite de Lille I,F-59650 Villeneuve d’Ascq, France3Bayerisches Geoinstitut, Universitat Bayreuth, D-95440 Bayreuth, Germany.............................................................................................................................................................................

The mineral olivine dominates the composition of the Earth’supper mantle and hence controls its mechanical behaviour andseismic anisotropy. Experiments at high temperature and mod-erate pressure, and extensive data on naturally deformed mantlerocks, have led to the conclusion that olivine at upper-mantleconditions deforms essentially by dislocation creep with domi-nant [100] slip. The resulting crystal preferred orientation hasbeen used extensively to explain the strong seismic anisotropyobserved down to 250 km depth1–4. The rapid decrease of aniso-tropy below this depth has been interpreted as marking thetransition from dislocation to diffusion creep in the uppermantle5. But new high-pressure experiments suggest that dislo-cation creep also dominates in the lower part of the uppermantle,but with a different slip direction. Here we show that this high-pressure dislocation creep produces crystal preferred orien-tations resulting in extremely low seismic anisotropy, consistentwith seismological observations below 250 km depth. Theseresults raise new questions about the mechanical state of thelower part of the upper mantle and its coupling with layers bothabove and below.

Despite the considerable effort to characterize olivine’s defor-mation mechanisms over the past 30 yr, it is only recently thatdeformation experiments could be conducted at pressure–temperature conditions of the entire upper mantle6–8. Newsimple-shear experiments on olivine aggregates at 11 GPa and1,400 8C, conditions equivalent to those at depths of 330 km, haveshown that deformation takes place by dislocation creep, withdominant activation of [001]{hk0} slip systems9, suggested by theconcentration of [001] parallel to the shear direction and of [100]and [010] normal to the shear plane (Fig. 1). Transmissionelectron microscopy shows the exclusive presence of dislocationswith [001] Burgers vectors in a screw orientation, compatible with[001](hk0) slip. Dominant [001] slip in the deep upper mantlerequires re-evaluation of the interpretation of anisotropicphysical properties. For instance, the fastest P-wave velocity willno longer parallel the shear direction as in an upper mantledeforming by dominant [100](010) slip, which is the assumptiontraditionally used in relating flow and seismic anisotropy in themantle10,11.

Several lines of evidence point to seismic anisotropy decreasingwith depth in the upper mantle. Most global one-dimensionalmodels (PREM, IASP, AK135 and AK303) show horizontallypropagating P waves travelling (at velocity vPH) faster than verticalones (at vPV), but the difference in velocity reduces with depth,resulting in isotropic behaviour at 350 km depth4. Some models(AK135 and 303) even show vPV slightly faster than vPH below350 km. The S-wave polarization anisotropy also decreases mono-tonically from the surface to become isotropic at 250 km. Forhorizontally propagating S waves, horizontally polarized wavesshow a higher velocity (vSH) than vertically polarized waves (vSV)down to about 250 km depth. Between 300 km and 400 km depth,vSV is higher than vSH, but anisotropy is five times lower than in theuppermost mantle. High-resolution global tomographic modelsbased on S-wave data12 or on the inversion of three-componentsurface and body waveform data13 support these general findings,with strong anisotropy characterized by vSH . vSV above 250 kmdepth. At greater depth, these models require a strong decrease inanisotropy, with a minimum around 300 km depth. S-wave dataalso call for weak anisotropy, with vSV . vSH at the base of the uppermantle beneath the central Pacific and Pre-Cambrian cratons12.Regional surface wave studies in the Pacific and Indian ocean basinsalso suggest that anisotropy is present from the surface to ,250–300 km depth1–3,14, with vSH being greater than vSV. Analysis of two-station surface wave profiles in the Pacific and Philippine platesimply a still shallower anisotropy limited to the upper 160 km of themantle15. SKS studies cannot constrain the depth of the anisotropiclayer, but the strong correlation of the direction of polarization ofthe fast shear wave with the surface geology and the observed delaytimes #2 s (ref. 14) suggests that SKS splitting occurs in the upper200–250 km of the mantle.Finally, a regional seismic discontinuity, called the Lehmann

discontinuity, has been detected at about 220 km depth by variousseismicmethods (reflection, surface waves, ScS reverberations and Pto S conversions), mainly beneath continents. This discontinuityhas been interpreted as being due to either (1) a strong anisotropycaused by intense deformation of olivine in a zone of mechanicalcoupling between the lithosphere and the asthenosphere16, or (2)the transition between an anisotropic uppermost mantle deformingby dislocation creep (which produces a crystal preferred orien-tation, CPO, of olivine) and an isotropic deep mantle deforming bydiffusion creep (which does not produce CPO)5. However, recenthigh-pressure, high-temperature experiments show that even infine-grained aggregates (,20–30 mm), dislocation creep is thedominant deformation mechanism under conditions equivalentto those prevailing at 300 km depth9,17,18.The pressure, or pressure interval, at which the transition from

Figure 1 Preferred orientation of [100], [010] and [001] crystallographic axes in syntheticolivine polycrystal S2954 deformed at 1,400 8C and 11 GPa confining pressure in simple

shear9. Lower hemisphere equal-area projection, contours at intervals of 0.5 multiples of

a uniform distribution. 3,269 measured orientations. Dextral shear (top to the right) is

indicated by half-arrows; SD, shear direction; NSP, normal to shear plane; X, finite strain

extension direction. Shear strain ,0.3. Inclined black line marks the foliation (flattening

plane).

letters to nature

NATURE |VOL 433 | 17 FEBRUARY 2005 | www.nature.com/nature 731©!!""#!Nature Publishing Group!

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1) High T olivine: reference a-axis parallel to shear direction

2) Effects of dissolved water and elevated stress on LPO

(Jung and Karato, 2001;Jung, 2006; Katayama et al., 2004, 2006

which should occur at shear stresses higherthan 0.1 MPa (14), olivine CPOs in the man-tle will be affected by the presence of melt.

Second, we argue that the transition inCPOs in going from samples of olivine andMORB (Fig. 2A) to samples with melt seg-regated into networks of bands (Fig. 2B) isdue to changes in the flow pattern rather thana change in the deformation mechanism. Thelatter CPO is similar to type-B CPO definedin (5), which the authors of that paper at-tribute to a change in the behavior of dislo-cations at high water fugacity and high stressconditions. However, neither of these con-ditions applies to our experiments. Severallines of evidence disfavor a change in dis-location dynamics (e.g., a change fromdominant a slip to c slip on b planes) as anexplanation for the CPO observed in ourexperiments, discussed in (15). We proposea kinematic explanation for the a-c switch,on the basis of three points, as follows:

1) The total strain in the sample partitionsbetween the melt-rich bands and melt-depleted lenses. Although the bands compriseonly !20% of the total sample volume, thestrain rate, and thus the strain, is higher in theweaker bands than in the stronger lenses. Inthe bands, shear strain is oriented at !20° tothe sample shear plane and, therefore, in thelenses the shear plane must be back-rotatedrelative to the sample shear plane (Fig. 3C).This back-rotation is observed in the orienta-tion of b axes in the CPO.

2) The observed CPO predominantly re-flects deformation in the melt-depleted lens-es, implying that the deformation in the bandsis not contributing to or strongly modifyingthe CPO (16). Observations that the CPO isbarely modified in the vicinity of a band(SOM Text, section 3) support this point.

3) The deformation that produces the CPO

in the melt-depleted lenses is not simpleshear, but it involves substantial componentsof strain normal to the shear direction. Align-ment of a axes normal to the shear directionsuggests that a slip on the b plane occursnormal to the shear direction (17). Becausemuch of the shear strain is accommodated inthe bands, the components of strain normal tothe shear direction in the lenses have muchgreater expression in the CPO than theywould if the bands were absent. This expres-sion may be enhanced further by the MPO-CPO effect. Thus, the “mechanism” for a-ax-is orientation is the kinematic effect of strainpartitioning, not a change in the dominantslip system.

The influence of melt segregation andstrain partitioning on CPO development willbe even more effective in partially moltenregions of Earth where deformation is morethree-dimensional than in our experiments.The olivine a axes will rotate if the geometryof the overall flow in the region permits orrequires an elongation of the melt-depletedlenses normal to the shear direction. Ananisotropic network of melt-rich layers willaffect the seismic properties of regions largein comparison to a seismic wavelength (") ifthe separation between layers (#S) is muchless than a seismic wavelength (i.e., #S $100-3 m %% " $ 104 m). The configuration(comprising average thickness, spacing, an-gle, and topology) of the network depends onthe physical properties of the solid and fluid,the kinetics of the processes governing theirinteractions and transport, and the geometric(kinematic) boundary conditions of regionalflow. Some of these properties are encom-passed in the first-order compaction lengthscaling argument discussed in (7) (SOMText, section 2). Others remain to be studiedexperimentally and theoretically.

A literal extrapolation of the process dis-cussed here may help to explain the complexseismic anisotropy observed in many partial-ly molten regions of the upper mantle (18).Several potential examples include (i) ver-tical fast-direction measurements beneaththe Reykjanes Ridge south of Iceland (19),(ii) trench parallel fast axes measured in themantle wedge above subduction zones (20),or (iii) tangential patterns of anisotropyaround plume heads, e.g., Iceland (21).Each of these observations has produced arange of hypotheses, a discussion of whichis beyond the scope of this paper (22).However, the processes discussed here sug-gest detailed field-based (23) and seismo-logical predictions and tests, which mayinfluence our interpretations of the dynam-ics of partially molten regions of Earth.

References and Notes1. D. Mainprice, Tectonophysics 279, 161 (1997).2. A. Nicolas, N. I. Christensen, Formation of Anisotropyin Upper Mantle Peridotites—A Review, GeodynamicSeries (American Geophysical Union, Washington,DC, 1987), vol. 16.

3. S. Zhang, S. Karato, Nature 375, 774 (1995).4. M. Bystricky, K. Kunze, L. Burlini, J.-P. Burg, Science290, 1564 (2000).

5. H. Jung, S. Karato, Science 293, 1460 (2001).6. G. Hirth, D. L. Kohlstedt, Earth Planet. Sci. Lett. 144,93 (1996).

7. B. K. Holtzman, N. J. Groebner, M. E. Zimmerman,S. B. Ginsberg, D. L. Kohlstedt, Geochem. Geophys.Geosyst. 4, 8607 (2003).

8. Material and Methods are available as supportingmaterial on Science Online.

9. M. E. Zimmerman, S. Zhang, D. L. Kohlstedt, S. Karato,Geophys. Res. Lett. 26, 1505 (1999).

10. D. McKenzie, J. Petrol. 25, 713 (1984).11. B. L. Adams, S. I. Wright, K. Kunze, Metall. Trans. 24A,819 (1993).

12. W. B. Durham, C. Goetze, J. Geophys. Res.82, 5737 (1977).13. M. S. Paterson, in Physics of Strength and Plasticity, A. S.Argon, Ed. (MIT Press, Cambridge, MA, 1969), pp. 377–392.

14. M. J. Daines, D. L. Kohlstedt, J. Geophys. Res. B102,10257 (1997).

15. The fabric in Fig. 2B would normally be interpreted asslip on the (010)[001] system. Such a change indominant slip system could result from locally highstresses due to the strong chromite grains activatingthe (010)[001] slip system in olivine, which is muchstronger than (010)[100] (12). However, this possi-bility is negated by the fact that the same CPO existsin the olivine and MORB with FeS sample, whichforms bands with a weak melt phase (i.e., FeS) inplace of strong chromite inclusions. Furthermore,TEM images of the dislocation structures revealed noevidence for a preponderance of dislocations with[001] Burgers vectors or with high local stresses (i.e.,increased dislocation density). Because no evidenceexists for a change in the relative strength of the slipsystems, another explanation for the a-c switch mustbe invoked.

16. The absence of variation in the CPO around andwithin a band supports the conclusion that deforma-tion in the bands does not contribute to or stronglymodify the CPO (SOM Text, section 3). At least tworeasons argue against formation of the observed CPOin the melt-rich bands: (i) To maintain a stable ori-entation during simple shear, the melt within thebands must move relative to the solid (7). Thus, thestrain associated with a band at a given location willprobably not be high enough to modify the CPO. (ii)The deformation mechanisms may be different in thetwo regions because of increased melt fraction in themelt-rich bands. Granular flow or grain boundarysliding accommodated by diffusion with rigid rota-

Fig. 3. Representation of ob-served melt distribution and in-ternal strain partitioning in ex-perimentally deformed samples.(A) Synthesis of the configura-tion of melt bands. Bands formanastomising networks withlarger bands at higher angles rel-ative to the shear plane (flat redarrow) connected by smallerbands at lower angles. Smallerarrows indicate that the samplesflatten and widen with shear. Inthree dimensions, the melt-richlayers connect and surroundmelt-depleted lenses. (B) Strainpartitioning between bands(anastomosing layers) andlenses. The flat arrows indicatethe total shear and the compo-nent concentrated in thebands. The narrow arrows indi-cate alignment of olivine a axes normal to the shear direction in the lenses. The black linesmark the orientation of the shear plane in the lenses, “back-rotated” relative to the sampleshear plane due to strain partitioning.

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S1; table S1). The samples consisted of oli-vine and mid-ocean ridge basalt (MORB) andolivine and MORB with either an additionalmelt (FeS) or solid (chromite) phase. Theadditional phases lower the permeability rel-ative to that of olivine and MORB samples bypartially plugging the melt channels, withoutsubstantially changing the rheological prop-erties (7, 8). In sheared samples of olivineand MORB, melt pockets align at !20° to theshear plane and distribute uniformly acrossthe sample (9). During deformation of sam-ples with reduced permeability, melt segre-gates from an initially homogeneous distribu-tion into melt-rich layers or “bands” orientedat !20° to the shear plane, separated bymelt-depleted regions or “lenses.” (Fig. 1, Aand B). When melt segregates, strain concen-trates in the weak melt-rich bands. The inter-action of strain partitioning and melt segre-gation leads to self-organization of themelt-rich bands. These bands form anasto-mosing networks (Fig. 1), with larger bandsat higher angles connected by smallerbands at lower angles. Because the distri-bution of band angles remains independentof strain, the melt in the bands must bemoving relative to the solid. The spacingbetween bands is governed by the compac-tion length of the sample [supporting onlinematerial (SOM) Text, section 2], consistentwith theory for porous flow in a permeableviscous deforming medium (7, 10).

Crystallographic preferred orientations(CPOs) of olivine grains were measured for1 undeformed and 10 sheared samples withelectron backscatter diffraction (EBSD)analysis (8, 11). In samples of olivine andMORB deformed in shear, the CPOs devel-op an “axial” pattern in which the b axes

concentrate normal to the sample shearplane (the walls of the pistons) and the aand c axes form girdles in the shear plane(Fig. 2A). In samples with an added thirdphase (olivine and MORB with either chro-mite or FeS melt), all of which formednetworks of melt-rich bands, the CPO ischaracterized by (i) significant concentra-tions of a axes normal to the shear direc-tion; (ii) tight clusters of b axes oriented15° to 20° from the pole to the sample shearplane, back-rotated relative to the orienta-tion caused by simple shear; and (iii) sig-nificant concentrations of c axes rotated15° to 20° counterclockwise from the sam-ple shear plane (90° from the b axes) (Fig.2B). In six samples deformed to shearstrains of " # 1.1, 2.1, and 3.3 to 3.5, theintensity of CPOs increases with increasingstrain. In addition, all samples progressive-ly decrease in thickness by up to 20% withincreasing strain, accommodated by minorbut important lengthening of the samplenormal to the shear direction.

Observations from detailed studies ofCPOs and microstructures by scanning andtransmission electron microscopy (SEM andTEM) constrain the microstructural processesactive in the samples (Fig. 1B). A map ofCPOs in the vicinity of a similar melt-richband exhibits no significant spatial varia-tions, suggesting that deformation in thebands does not modify the CPO (SOM Text,section 3). TEM observations reveal that dis-locations with Burgers vectors parallel to thea axis outnumbered those with Burgers vec-tors parallel to the c axis (SOM Text, section4). The density of dislocations is not ele-vated in olivine grains adjacent to strongerchromite grains, suggesting that the pres-

ence of chromite does not influence dislo-cation dynamics.

A commonly observed CPO for olivinedeformed in simple shear at high temperatureis characterized by a axes parallel to the sheardirection, b axes normal to the shear direc-tion, and c axes normal to the shear directionin the shear plane (Fig. 2C) (3) (SOM Text,section 5). This pattern reflects the fact that indry olivine, a slip on b planes is significantlyweaker than a slip on c planes, which isweaker than c slip on b planes (12). In con-trast, in partially molten samples deformed atsimilar temperature and stress conditions asdescribed in (3), the more diffuse CPO pat-tern is distinguished by a and c axis girdles inthe shear plane with strong concentrations ofb axes normal to the shear plane. Further,when melt segregates into bands, the b axesrotate 20° antithetic to the sense of shear, andconcentrations of a and c axes appear 90°from their “normal” positions, referred tobelow as the “a-c switch” (Fig. 2C).

First, we must explain how the orientedmelt pockets weaken a and c axis concentra-tions relative to CPOs from melt-free sam-ples (Fig. 2B). Melt pockets provide a fast-diffusion path for olivine components,enhancing the importance of diffusion-accommodated creep and possibly grainboundary sliding in the direction of shear,whereas movement of dislocations accommo-dates the remainder of the interactions be-tween grains, providing a mechanism formodifying the von Mises criterion (13).Strong anisotropy in melt-pocket orientation(MPO) may randomize the orientations of aand c axes, while leaving orientations of slipplanes (b axes) intact (“the MPO-CPO ef-fect”). As long as melt pockets are oriented,

Fig. 1. Microstructures. (A) Reflected-light im-age of a sample of olivine and chromite and 4%MORB sheared between tungsten pistons. Themelt-rich bands are visible as the darker regionsoriented 10° to 20° to the sample walls, form-ing an anastomosing network. (B) SEM back-scattered electron image of one band. Thechromite grains (white) are smaller than theolivine grains (gray). Chromite tends to sit inmelt (black) tubules, reducing the permeability.

Fig. 2. Pole figures for a, b, caxes for sheared samples. Theshear plane is horizontal andshear sense is at top right. (A)Sheared sample of olivine and4% MORB. (B) Sheared sampleof olivine and chromite and 6%MORB, shown in Fig. 1. The CPOmeasured in a sample of olivineand MORB with FeS melt is iden-tical to this one. (C) Schematicdiagrams of three sets of threepole figures for a melt-free oli-vine aggregate (top) [after (3)],olivine and oriented melt (mid-dle), and olivine and segregatedmelt (bottom), all deformed athigh T (1473 to 1573 K) and P (300 MPa) to shearstrains larger than " # 1. The reference position forthe back-rotation of the CPO is indicated by theoutlined areas. A similar obliquity between theshear plane and the axis aligned in the shear direc-tion can develop due to recrystallization, discussedfurther in SOM Text, section 5, but is not the originof the back-rotation observed here. The relativeseismic velocities are Va $ Vc $ Vb. At right is aspatial representation of the third CPO.

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3) Effects of pressure and stress

2) Effects of dissolved water and elevated stress on LPO 2) Effects of dissolved water and elevated stress on LPO

4) Effects of dissolved water and elevated stress on LPO(Holtzman et al., 2003)


ab

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e.g. Zhang & Karato, 1995Bystricky et al. 2000

Couvy et al., 2005Mainprice et al., 2005

a) alignment

b) segregation

c) migration

3) Melt distributionMultiple scales of isotropic and anisotropic organization

a) alignment (~grain size)melt pockets aligned relative to stress orientation (e.g. Zimmerman, et al., 1999)

b) segregation (< compaction length)melt segregates into bands at lengscales much longer than the grain size (e.g. Holtzman et al., 2003)

c) up-stress migration (> compaction length)melt migrates UP stress gradients that exist on (seismically observable?) scales of plate boundaries (Takei and Holtzman, in prep. and next talk...)

Causes of anisotropy

such that the melt distribution is a function of time.We do not claim that any melt distribution reachesa steady state, though this question will beaddressed in much greater detail in future papers.Therefore, when melt distributions between sam-ples are compared, samples deformed to the samestrain were selected, wherever possible. In Table 2,the experimental conditions and average propertiesof the melt fraction distributions are listed for eachsample. In the following sections, the results fromeach group of experiments are described.

4.1. Olivine + MORB

[23] In sheared samples of olivine + 3 vol%MORB,melt is uniformly, but anisotropically, distributedacross the sample in grain-scale pockets oriented25! to the shear plane (20! from the maximumprincipal stress), as illustrated in Figure 2 (modifiedfrom Kohlstedt and Zimmerman [1996] and Zim-

merman et al. [1999]). The melt pockets, spacedapproximately a grain width apart, form parallelinterconnected volumes often several grains long,which more closely approximate sheets than tubes

in 3-D (see Appendix A). Sixteen samples weredeformed, at varying stresses and to varying strains,none of which formed bands. Five of these samplesare listed in Table 2.

4.2. Anorthite + Basaltic Melt

[24] During deformation, melt migrates into melt-rich bands !20 mm wide and !100 mm apart, asshown in Figure 3. The bands are oriented !10–20! to the shear plane. The bands appear to formanastomosing networks. A high-resolution SEMimage of a band reveals a very high melt fractionand euhedral grains, lying ‘‘piggyback’’ on eachother, providing a clear sense-of-shear indicator, asillustrated in Figure 3b. In addition, many of thesebands root from or feed into small regions oflocally high melt fraction on the low-pressure sideof the peaks in the tungsten pistons.

4.3. Olivine + Chromite + MORB

[25] Eight shear experiments are reported here onthis system, with varying melt fractions and finite

olivine + 3 vol % MORB

Figure 2. Reflected light optical micrograph of an olivine + MORB sample (PI-273). The melt pockets (dark)strongly align at about 20! to the shear plane (horizontal). The melt distribution is homogeneous across the sample.(Modified from Kohlstedt and Zimmerman [1996] and Zimmerman et al. [1999].)

GeochemistryGeophysicsGeosystems G3G3 holtzman et al.: melt segregation in molten rocks 10.1029/2001GC000258

8 of 26

Deformation experiments: 1) Melt segregation and the effect of increasing strain:

In Fig. 5c, a band at lower angle appears to connect twobands at higher angles. The observation that narrowbands occur at lower angles than wider bands appears inall samples.A higher magnification view of one band in Fig. 5d

reveals several interesting features. First, in some places,the edges of the band are very well defined, marked by adramatic change in melt fraction; in other regions, thetransition from band- to non-band regions are more grada-tional. Furthermore, inside the band, variations in meltfraction are large, with islands of low melt fraction sur-rounded by melt-rich channels. In other words, a largerband may be viewed as a cluster of smaller bands. InFig. 5d and e, it is clear that the melt fraction can be locallyvery high in a band. As annotated in the images, the oli-vine crystals in the bands appear to be both dissolvingand growing by precipitation, as suggested by the presenceof very small grains (51 mm), incised or corrugated grainboundaries of the large grains and the highly euhedralovergrowths on olivine grains, respectively.

Melt configuration statisticsThe frequency distributions of band angles, thicknesses,and spacings are presented here (Table 4). The band

angles in each sample have normal distributions, as shownin Fig. 6. As a function of strain, the band angles appearremarkably constant, at 20! 68 in the ft" 0#02 set and17!68 in the ft" 0#06 set. The angles increase slightlywith increasing strain in the ft" 0#02 set but not in theft" 0#06 set, as shown in the top right box of Fig. 6.Bands were not clearly visible in most of the sample withft" 0#06 deformed to g"1#1 (PI-885), so no data exist forlow strain at ft" 0#06 in Figs. 6^8.In contrast to the distribution of angles, the statistical

distributions of the band thicknesses are clearly notnormal distributions; in log^log space (upper right cornerof Fig. 7), the distribution appears to follow a power law,nth / !$m

th , where nth is the frequency of occurrence of agiven thickness of a band of thickness, dth, where themean value of m is 1#7 (values for each sample are listed inFig. 7). We cannot test the robustness of the apparentpower-law nature of this distribution because the thicknessdata only span up to one order of magnitude. In the imagesin Fig. 4, the thicknesses of the bands appears to increasebetween g"1 and g" 2 in both the ft" 0#02 andft" 0#06 series, but there does not appear to be a system-atic difference between the data from samples deformed tog% 2 and g% 3. These visual inferences appear in the

Fig. 4. Reflected-light optical images of samples in the ‘strain series’, deformed top-to-the-right, the x^z plane (where z is normal to the shearplane x^y, and x is parallel to the shear direction). In all images, the vertical black lines are cracks created during the quenching of the sample;the white lines are the Ni strain marker; the grey lines are the melt-rich bands. The groove spacing is 250 mm. (a) Samples with f" 0#02 weresheared to g"1, 2 and 3. (b) Samples with f" 0#06 were sheared to g"1, 2 and 3#5.

HOLTZMANAND KOHLSTEDT MELT SEGREGATION EVOLUTION

9

Ni-foil

strain marker

sample

thoriated

tungsten

pistons

simple shear

experiment

Nickel

jacket

gas-

medium

pressure

vessel

constant load

is applied by

actuator from

below

alumina

pistons

and

spacers

olivine

single-crystal

pistons

(010)

T = 1250 C

P = 300 MPa

olivine + c hromite + 6%MOR B

c hromite " plugs "

10 µm10 um

olivine + chromite + MORB

P = 300 MPaT = 1250 C

melt first aligns at the grain scale and then segregates into bands(important observation for ideas in next talk...)

Christensen (1987) presented a simplified form for the case when the principle directions of theanisotropy layers are parallel to the principle directions of the stress tensor,

!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)

where "N = !"i" (!"" is the “spatial average” of ", (Christensen, 1987), and "S = !("i)!1"!1. Theanisotropy factor s = !""!"!1". So, for our purposes,

"HB =%

ab

"b+

(1# ab)"n

&!1

(16)

The resultant curves are then incorporated into the viscosity profiles, as perturbations to thedi!usion creep contribution to the total viscosity (or to the total?)... ???

B.3 E!ects of water

This is not done yet. see discussion in paper 2.

mechanism A n m Q V* $GB di!usion(dry) 1.5e9 1 3 375e3 10e-6 25GBS dislocation(dry) 4.7e10 3.5 2 600e3 15e-6 35Dislocation(dry) 3.5 0GB di!usion(wet) 1 3GBS dislocation(wet) 3.5 2Dislocation(wet) 3.5 0

Table 1: Flow law parameters, from Hirth & Kohlstedt (2003).

As % => 0,Dmelt => Dg.b.

& = Ag!g contact

Asurface

' $ 1

' $ 2

' $ 3

500 µm

12


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)


"HB =%

ab

"b+

(1# ab)"n

&!1

(16)


B.3 E!ects of water





& = Ag!g contact

Asurface

' $ 1

' $ 2

' $ 3

500 µm

12


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)


"HB =%

ab

"b+

(1# ab)"n

&!1

(16)


B.3 E!ects of water





& = Ag!g contact

Asurface

' $ 1

' $ 2

' $ 3

500 µm

12


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)


"HB =%

ab

"b+

(1# ab)"n

&!1

(16)


B.3 E!ects of water





& = Ag!g contact

Asurface

' $ 1

' $ 2

' $ 3

500 µm

12

nature of the melt-rich networks. As indicated in the sche-matic drawing of 3D networks from Holtzman et al.(2003b), the average length of lenses is greater in theplane normal to the shear direction than it is in the flowplane (the usual view). Also, some sample material hasbeen extruded laterally (in the shear plane, normal to theshear direction) beyond the edges of the piston. It alsoappears that the melt fraction is higher in and near thisextruded material, indicating that there may be some fluxof melt from the middle of the sample towards the edges.The visual and statistical signature of the anastomosing

networks is a bimodal distribution of band angles, as illus-trated in Fig. 13. In this image, and in all of the samples,there are indications of some scale-invariant properties of

the distribution of melt. The first-order structure is thelargest bands, which are oriented at a !15^258 to thesample shear plane (that is, the grooved piston surface) inFig. 13c.The population of smaller bands, the second-orderstructures, is oriented at a! 5^158 to the sample shearplane. However, if one views these structures in a localreference frame of the lenses, such that the shear plane inthe lenses is back-rotated by!108 to the sample shearplane (the piston surface), then the secondary bands areoriented at a!15^258 with respect to this secondary shearplane, illustrated in Fig. 13c. In other words, the secondarynarrow bands that cut across lenses are controlled by thelocal stress field in the lenses. This local rotation of thestress field in the lenses is suggested by the back-rotationof olivine b-planes (Holtzman et al., 2003b) and by the ana-lysis of strain partitioning (Holtzman et al., 2005).Extending this point of view one order downward inscale, the melt pockets most visible in the large bands arealso oriented! 208 to the wall of the band, the third-ordershear plane defined by the surfaces of the melt bands.Thus,from the sample scale to the grain scale, there are threelevels of scale-invariance to the orientation of melt align-ment relative to the local and applied stress tensors.Istherea lower limit tothemelt fractionrequired for segre-

gation to occur? The sample with f" 0#005 was deformedat moderate stresses (tf" 122MPa). Well-defined bandsformed, as shown in detail in Fig. 14.The bands are narrowand the lenses between them have almost no visible melt.Furthermore, the chromite grains in the lenses appear to bestretched and aligned, forming an apparent foliation.However, where a band is present, the chromite grains arelarger, fewer and less elongated, as shown in Fig.14.This pat-tern suggests that chromite grain growth (anOstwald ripen-ing process) is much more efficient in the presence of meltthan in its absence.These variations inchromitemorphologyare not present (or nearly as clearly) in samples with moremelt, suggesting that the presence of melt significantlyenhances chromite grain growth.

Fig. 10. Reflected light images samples (a) PI-1027, (b) PI-1025,and (b) PI-1020, in the stress series, sheared at constant load, top-to-the-right, decreasing in applied load from (a) to (c). As with theprevious strain series, the vertical black cracks are caused by quench-ing the sample at the end of an experimental run and should beignored. The groove spacing is 250 mm and the melt-rich bands arethe darker grey channels aligned at about 158 to the shear plane.

Fig. 11. Reflected light images of samples sheared under constant displacement rate conditions (that approximate constant strain rate) of(a) 3$10^4 s^1 and (b) 1$10^3 s^1.


13

constant load








13

constant strain rate








13

occurring simultaneously in a deforming sample, as illu-strated in Fig. 22.

NucleationWhy do bands nucleate and at what angle? Our observa-tions from the lowest shear strain experiments in thestrain series suggest that bands begin to form at 5^258,with a mean and standard deviation of 18!68. In shearedsamples of olivine"MORB, Zimmerman et al. (1999)found that melt pockets were elongated and oriented at

approximately the same angle, suggesting that this angleis ubiquitous and is stress controlled (not controlled bythe physical properties of the matrix). These observationssuggest that bands form at the same distribution of anglesat which they are observed when mature, by the collectionand accumulation of individual elongated pockets.Hier-Majumder et al. (2004) adopted a micromechanicalapproach to this question, looking at how shear stresscaused the growth of some pockets at the expense ofothers, and speculated that pockets at 0^458 to s1 openpreferentially by stress corrosion, causing an averageangle of# 208. Nucleation of small bands within the well-developed lenses occurs at lower angle (5^108 relative tothe shear plane), reflecting the local back-rotation of thestress field as a result of strain partitioning between lensesand bands. This local modification of stress fields was dis-cussed extensively in an earlier study (Holtzman et al.,2005). Once elongated pockets are nucleated, the stress-driven segregation instability is initiated.

Rotation and growthAs discussed by Holtzman et al. (2003a, 2005), Spiegelman(2003) and Katz et al. (2006), bands should rotate withshear if melt is not migrating relative to the solid. Theapparent rotation is caused by the simple shear, but it isactually the shear parallel advection of a material line(melt-rich band) at an angle to the shear plane, causingthe appearance of rotation. Spiegelman (2003) modifiedStevenson’s (1989) instability analysis from a pure shear to

Fig. 23. Band spacing, dsp, as a function of compaction length, dc.PI-1020 appears to be an outlier, as discussed in the text. The slope ofa linear fit to the rest of the data is m$ 0%4.

Fig. 22. The pumping mechanism. (a) A schematic illustration of lenses between two underformable plates.The light grey lines in the lenses arelocal shear planes and the melt-rich bands are transparent. (b) Inset in (a). The open arrows indicate stress orientations and the filled greyarrows indicate melt flow direction. We propose here and elsewhere (Holtzman et al., 2005) that the normal stress components on the bandsswitch sign above some critical angle (4308) from tensile or dilational to compressive or compactional, essentially because lenses have todeform more and more the closer a band is to 458, and the system will only tolerate a certain stress difference between bands and lenses.This flattening of the bands causes the melt pressure to rise and sets up a flow into lower angle bands. (c) Inset in (a). Bands can nucleateand propagate into a lens at a low angle, and can also close off, as shown in Fig. 13. (d) Inset in (c). A grain-scale view of the tip of apropagating band.


21








21

Deformation experiments: 2) Effects of boundary conditions on effective viscosity

higher stress

lower stress

102

Stress (MPa)

10-5

10-4

10-3

10-2

StrainRate(s-1)

time diffusion crp.

disloca

tion g.b.s.

crp.0 m

elt

0.04 m

elt

184 C.M. Gourlay, A.K. Dahle / Materials Science and Engineering A 413–414 (2005) 180–185

Fig. 5. Quantification of the porosity distributions. Area fraction porosity is

averaged within radius contours 1mm in thickness: (a) AZ91 and (b) A356.

the mush resistance to deformation and gives mushes with

fs > fCohs their yield point behaviour [5]. At stresses ! < !peak,

the dendrite network deforms whilst largely maintaining an

interconnected structure and the mush therefore behaves in a

solid-like manner where the shear stress increases near-linearly

with time. When ! = !peak (Fig. 1), the strength of the dendritic

network is reached. In the vane experiment, the maximum shear

stress is at the vane tips, but a plane of maximum shear stress

can be approximated as the cylindrical surface circumscribed by

the vane [19]. The mush strength is therefore first exceeded at

the vane path and the dendrite network collapses at this surface.

As the dendrites making up the network are highly branched

at 29% solid, they are entangled and interlocked. Collapsing

an entangled network requires some dendrites to be fragmented

(Fig. 2a and b). Collapse of the dendritic network destroys the

interconnected structure of the mush, allowing the collapsed

region to deform by the flow of discrete particles in suspen-

sion. The stress required to deform the suspension is much less

than for the interconnected structure which leads to the dra-

matic decrease in shear stress after peak shear stress observed in

Fig. 1b. The deformation rate induced by vane rotation can then

be achieved at lower stress and the peak shear stress is never

reached in the mush away from the cylindrical surface circum-

scribed by the vane. Deformation therefore becomes localised

at the vane path. This is typical of granular materials in which

failure does not occur homogeneously, instead being confined

to bands a number of particles wide [20].

Whilst the rheology andmany of themacrostructural features

of these alloys are similar, the distribution of porosity is dis-

tinctly different. In AZ91, an annulus of porosity was observed

in the region of localised deformation and fragmented dendrites

(Fig. 4a). It is unlikely that this porosity forms during deforma-

tion because, at 29%solid, the liquid is expected to be contiguous

throughout the sample, flow channels within and between den-

drites are expected to be broad and themush permeability is high

[21]. The large grain size increases the permeability further due

to the resulting low surface area to volume ratio of solid. It is

more likely that the porosity formed late during solidification

long after the deformation had stopped (Fig. 1a). This could be

explained if the localised deformation led to a region of higher

enriched liquid fraction than the surroundings during solidifica-

tion; in this case, the region would have taken longer to solidify

than the surroundings and thus would have been difficult to feed.

As AZ91 has a long non-equilibrium freezing range (!166 "C)and contains little eutectic (!16%) [1], the last regions to solid-ify are particularly prone to form porosity [22]. A356, however,

contains a significant eutectic fraction (!50%), and a shorternon-equilibrium freezing range (!60 "C) [23] making interden-dritc feeding easier. Other researchers have reported material

containing higher solute content than the surroundings (posi-

tive macrosegregation) at the deformation plane after shear at

low solid fraction [7], supporting the idea that enriched liq-

uid is drawn to the locally deforming region. Further work is

required to confirm the presence of positive macrosegregation

at the deformation region in the present study.

5. Conclusions

Shear deformation of aluminium alloy A356 and magne-

sium alloy AZ91 at 29% solid showed that, in the presence of a

loose dendrite network, both alloys exhibited distinct yield point

behaviour. The shear stress–time plots of the two alloys were

very similar. A short period of shear deformation at 29% solid

during solidification was observed to lead to distinct changes

in the as-cast microstructure. In both A356 and AZ91, post-

deformationmacrostructures revealed that deformation is highly

localised at the vane path, and that dendrite fragmentation occurs

at the region of maximum shear stress. In AZ91, there was also a

concentrated annulus of interdendritic porosity at the vane path

which was proposed to result from the presence of enriched liq-

uid at the deformation regionwhich becomes difficult to feed late

reached (Fig. 1c). Third, examination of post-deformation samplesreveals a band of concentrated porosity at the path circumscribed bythe vane (Fig. 1d–f, and Supplementary Fig. 14), suggesting that thestrain softening is associated with strain localization. In thisMg alloy,the shear band contains concentrated porosity at all cooling ratesstudied, and at cooling rates that result in large (>700 mm) highlybranched dendrites, crystal fragmentation was additionally observedin the band.

The shape of theM–h and sample height versus vane-rotation (h–h) responses in Fig. 1b, c and the localization of deformation intoshear bands in Fig. 1d–f are typical characteristics of compactedcohesionless granular materials, such as dense sand or glassbeads7,22–26. Compacted granular materials expand when shearedbecause particles must push one another apart and increase the spacebetween themselves in order to rearrange (Reynolds dilatancy)1,5. Thefact that partially solid alloys with fs. fs

Coh exhibit similar behaviourindicates that, after growth has caused impingement (fs. fs

Coh), thecrystals are sufficiently crowded that they cannot initially move pasteach other and that there is negligible intercrystal cohesion. TheM–hand h–h responses suggest that crystals push one another apart in

response to vane rotation, and that the dominant deformationmech-anism is Reynolds dilatancy-enabled crystal rearrangement. Thestrain localization in Fig. 1d–f and Supplementary Fig. 14 can beexplained by instabilities inherently caused by Reynolds dilatancyand fragmentation, because both decrease the local strength of theregion in which they occur, promoting further deformation in thatregion.

Shear bands also form in direct shear cell experiments. An exampleis given for Al-7Si-0.3Mg with globular morphology in Fig. 2 andSupplementary Fig. 16, where a band exists on the shear plane con-taining a higher volume fraction of eutectic than adjacent regions(positive macrosegregation). As the eutectic was liquid at fs5 0.5, theshear band had a higher liquid fraction than adjacent regions at theend of deformation, suggesting that liquid was drawn to the bandduring deformation.

We find that localized bands of porosity and positive macrosegre-gation form only when the material is deformed within a specificrange of fs: above those at which the material flows as a dilute sus-pension (when fs. fs

Coh) and below those at which the macroscopicshear response is crack propagation. This range of fs is dependent on

Torq

ue, M

(mN

m)

Torq

ue, M

(mN

m)

Vane rotation angle, ! (rad)

a

d e

f

b c

Vane rotation angle, ! (rad)

Tem

pera

ture

, T (º

C)

dT/d

t (K

s–1

)

Cha

nge

in h

eigh

t of s

ampl

e, !

h (m

m)

Time, t (s)

Nucleation ofMg17 Al12

160

120

80

40

00 "/2 3"/2"

160 0.5

0.4

0.3

0.2

0.1

0

120

80

40

00 "/2 3"/2"

1 mm Dilatant shear band

5 mm

–1

–2

0

Figure 1 | Vane rheometry of partially solidifiedMg-9Al-0.7Zn. a, Initially,liquid Mg-9Al-0.7Zn is cooled from 700 uC. Once nucleated, the decreasingtemperature leads to dendritic growth of equiaxed (Mg) crystals. At atemperature corresponding to a desired fs, the rotation of a four-bladed vaneis initiated at 5 rotations per minute. Deformation continues for one vanerotation (12 s) and is then stopped. As the temperature continues todecrease, solidification progresses by the growth and coarsening of (Mg). Atfs< 0.84, the eutectic reaction LR (Mg)1Mg17Al12 commences.b, Torque–vane-rotation responses for three typical experiments conductedat fs. fs

Coh. Experimental parameters (temperature T in uC, fs, and tpeak inkPa) as follows: top curve (580.7, 0.35, 9.1); middle curve (585.5, 0.29, 4.9);bottom curve (590.2, 0.22, 1.3). c, A sample expands as it is sheared, and

reaches a near-constant volume towards the end of deformation after globalvolumetric strain of eVol< 0.01 (T5 580.7 uC, fs5 0.35). d–f, Post-deformationmicrostructures of theMg alloy after complete solidification ina sample deformed at fs5 0.19. d, Macrograph of one-quarter of the cross-section through the centre of the vane. A localized band of porosity exists atthe path circumscribed by the vane. e, The equiaxed grain structurethroughout the same cross-section. f, A higher magnification image of theband shown in d and e, revealing that the porosity band is,11 grains wide.The shear strain rate within shear bands is _cc5 1–4 s21. A discussion of thechanges in grain size and shape between deformation and completesolidification is given in Supplementary Information sections 1.7 and 2.1.3.

NATURE |Vol 445 |4 January 2007 LETTERS

71Nature ©2007 Publishing Group

C.M. Gourlay, A.K. Dahle / Materials Science and Engineering A 413–414 (2005) 180–185 183

Fig. 3. The change in mean grain size with radial distance from the vane centre.

Grain size has been averaged within radius contours 1mm in thickness. The

vane edge is at 10mm: (a) AZ91 and (b) A356.

annulus of porosity is observed at the vane path whilst there

is little porosity in the remainder of the cross-section. The

width of the porosity-containing region is not constant but, is

always somewhat broader than the width of the microstructure

containing fragmented dendrites. The porosity distribution is

quantified with respect to radial distance from the vane centre in

Fig. 5a.

Fig. 4b shows a markedly different porosity distribution in

the A356 sample, where rounded pores are distributed fairly

evenly in the cross-section. These pores aremost likely hydrogen

related as the sample was not degassed. Comparing Fig. 5b with

Fig. 5a shows that the A356 alloy has a higher porosity content

than the AZ91 alloy, and confirms that there is no increase in

porosity at the vane path in A356.

Fig. 4. As-polishedmacrographs showing the porosity distribution in each alloy.

(a) A concentrated annulus of porosity exists at the vane path in AZ91. (b) Large

rounded pores are more evenly distributed in A356.

4. Discussion

In order to understand the mechanical behaviour of mush

at 29% solid, we must first consider the microstructure at this

point during solidification. Fig. 2 shows that the solid is equiaxed

dendritic. The dendrite coherency solid fraction is less than 29%

for both of these alloys cooled under these conditions [18] and

the mush therefore contains a loose network of entangled and

interlocked dendrites at 29% solid. At this solid fraction, den-

drite envelopes (the surface connecting both the primary and

secondary arms tips of a dendrite) are expected to contain a sig-

nificant liquid fraction. The remaining liquid exists between the

dendrite envelopes.

The shape of the shear stress–time curves in Fig. 1b can

be explained by considering how these microstructures deform.

The interconnected structure of the loose dendrite network gives

c) Migration up stress gradients: in two-phase metal composites, both solid state and partially molten, weak phasemigrates UP the stress gradient

poro

sity

solid state:partially molten state:

Materials Science and Engineering A 413–414 (2005) 180–185

Shear deformation at 29% solid during solidification of magnesiumalloy AZ91 and aluminium alloy A356

C.M. Gourlay !, A.K. DahleCAST CRC, School of Engineering, The University of Queensland, 4072 Qld, Australia

Received in revised form 1 July 2005

Abstract

Partially solid commercial Al–Si and Mg–Al alloys have been deformed in shear during solidification using vane rheometry. The dendritic mush

was deformed for a short period at 29% solid and allowed to cool naturally after deformation. Both alloys exhibited yield point behaviour and

deformation was highly localised at the surface of maximum shear stress. The short period of deformation was found to have a distinct impact on

the as-cast microstructure leading to fragmented dendrites in the deformation region of both alloys. In the case of the Mg–Al alloy, a concentrated

region of interdendritic porosity was also observed in the deformation region. Concentrated porosity was not observed in the Al–Si alloy.

© 2005 Elsevier B.V. All rights reserved.

Keywords: Mushy zone; Rheology; Shear; Vane; Semi-solid; Solidification

1. Introduction

Aluminium alloy A356 andmagnesium alloy AZ91 are com-

mon casting alloys often used in automotive applications. Both

are hypoeutectic alloys with relatively wide freezing ranges [1],

and they therefore contain relatively large mushy regions dur-

ing solidification. In most commercial casting processes these

alloys solidify with equiaxed dendrites and the dendrite–liquid

mixture is subjected to a range of stresses during the casting

process due to both the process itself and also solidification

related phenomena such as solidification shrinkage and ther-

mal contraction. Mush is deformed in processes where some

solidification occurs during filling such as in high-pressure die-

casting or squeeze casting and also in processes where pressure

is applied to assist the feeding of solidification shrinkage after

filling.

Our understanding of the shear rheology of dendritic mush

at low solid fraction has been obtained mainly from experi-

ments using Al–Si or Sn–Pb alloys [2–7]. Arnberg et al. [2]

found that distinct changes in shear response occur when the

growing dendrites impinge on one another at what is defined

the dendrite coherency solid fraction, fCohs . This point in the

solidification sequence marks the start of the development of an

! Corresponding author. Tel.: +61 7 3365 3639; fax: +61 7 3365 3888.E-mail address: [email protected] (C.M. Gourlay).

entangled skeleton of dendrites (the dendritic network). Metz

and Flemings [3] investigated the shear yield strength of solidi-

fying alloys and showed that dendritic alloys exhibit nomechan-

ical strength before dendrite coherency and that the shear yield

strength increases exponentially with solid fraction above den-

drite coherency. Spencer et al. [4] concluded that shear yield

strength is a strong function of morphology and that the yield

stress decreases dramatically at a given solid fraction as the solid

becomes more globular. More recently, the effect of solid size

and shape on mush yield strength has been examined by Dahle

andArnberg [5]who investigated a range of solidifyingAl alloys

with solid fractions in the range 0 < fs < 0.5. They were able toexplain the changes in rheological response brought about by

grain refiner additions and compositional changes by consider-

ing their effect on the solid shape and size. Larger and more

irregularly shaped dendrites were shown to begin to develop

strength at a lower solid fraction and highly branched den-

drites form more interconnected, stronger networks at a given

solid fraction. The importance of morphology has been further

emphasised by Nabulsi [6] and Sumitomo et al. [7] who showed

the role played by dendrite arms in providing interconnectiv-

ity to the dendritic network through interlocking. Deforming

a mush constituted of highly branched dendrites requires the

dendrites to be fragmented giving such microstructures greater

shear strength than those containing more rounded dendrites

which can deform by grain reorientation alone. Experimental

studies on the shear behaviour of magnesium alloy AZ91 have

0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2005.09.048

Materials Science and Engineering A 413–414 (2005) 180–185

Shear deformation at 29% solid during solidification of magnesiumalloy AZ91 and aluminium alloy A356

C.M. Gourlay !, A.K. DahleCAST CRC, School of Engineering, The University of Queensland, 4072 Qld, Australia

Received in revised form 1 July 2005

Abstract

Partially solid commercial Al–Si and Mg–Al alloys have been deformed in shear during solidification using vane rheometry. The dendritic mush

was deformed for a short period at 29% solid and allowed to cool naturally after deformation. Both alloys exhibited yield point behaviour and

deformation was highly localised at the surface of maximum shear stress. The short period of deformation was found to have a distinct impact on

the as-cast microstructure leading to fragmented dendrites in the deformation region of both alloys. In the case of the Mg–Al alloy, a concentrated

region of interdendritic porosity was also observed in the deformation region. Concentrated porosity was not observed in the Al–Si alloy.

© 2005 Elsevier B.V. All rights reserved.

Keywords: Mushy zone; Rheology; Shear; Vane; Semi-solid; Solidification

1. Introduction

Aluminium alloy A356 andmagnesium alloy AZ91 are com-

mon casting alloys often used in automotive applications. Both

are hypoeutectic alloys with relatively wide freezing ranges [1],

and they therefore contain relatively large mushy regions dur-

ing solidification. In most commercial casting processes these

alloys solidify with equiaxed dendrites and the dendrite–liquid

mixture is subjected to a range of stresses during the casting

process due to both the process itself and also solidification

related phenomena such as solidification shrinkage and ther-

mal contraction. Mush is deformed in processes where some

solidification occurs during filling such as in high-pressure die-

casting or squeeze casting and also in processes where pressure

is applied to assist the feeding of solidification shrinkage after

filling.

Our understanding of the shear rheology of dendritic mush

at low solid fraction has been obtained mainly from experi-

ments using Al–Si or Sn–Pb alloys [2–7]. Arnberg et al. [2]

found that distinct changes in shear response occur when the

growing dendrites impinge on one another at what is defined

the dendrite coherency solid fraction, fCohs . This point in the

solidification sequence marks the start of the development of an

! Corresponding author. Tel.: +61 7 3365 3639; fax: +61 7 3365 3888.E-mail address: [email protected] (C.M. Gourlay).

entangled skeleton of dendrites (the dendritic network). Metz

and Flemings [3] investigated the shear yield strength of solidi-

fying alloys and showed that dendritic alloys exhibit nomechan-

ical strength before dendrite coherency and that the shear yield

strength increases exponentially with solid fraction above den-

drite coherency. Spencer et al. [4] concluded that shear yield

strength is a strong function of morphology and that the yield

stress decreases dramatically at a given solid fraction as the solid

becomes more globular. More recently, the effect of solid size

and shape on mush yield strength has been examined by Dahle

andArnberg [5]who investigated a range of solidifyingAl alloys

with solid fractions in the range 0 < fs < 0.5. They were able toexplain the changes in rheological response brought about by

grain refiner additions and compositional changes by consider-

ing their effect on the solid shape and size. Larger and more

irregularly shaped dendrites were shown to begin to develop

strength at a lower solid fraction and highly branched den-

drites form more interconnected, stronger networks at a given

solid fraction. The importance of morphology has been further

emphasised by Nabulsi [6] and Sumitomo et al. [7] who showed

the role played by dendrite arms in providing interconnectiv-

ity to the dendritic network through interlocking. Deforming

a mush constituted of highly branched dendrites requires the

dendrites to be fragmented giving such microstructures greater

shear strength than those containing more rounded dendrites

which can deform by grain reorientation alone. Experimental

studies on the shear behaviour of magnesium alloy AZ91 have

0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2005.09.048

initial stress

0 +

0+

radial distance

melt/weak phaseflow direction

initi

al

stre

ss0

+

radial distance

in both experiments, weak phase migrates up the stress gradient

A new model for grain-boundary diffusion creep with meltElasticity: Takei, 1998; Viscosity: Takei and Holtzman, in prep.

contiguity, !

! =Acontact

Asurfacearea(1)

1 Overview

The The constitutive relation (elastic):

"ij = #

!$up

$xp%ij

"+ µ

!$ui

$xj+

$uj

$xi

"or "ij = #up,p%ij + µ(ui,j + uj,i) at r < R (2)

and # is the Lame constant and µ the shear modulus. The bulk modulus k = 3!+2µ3 and Poisson’s ratio

& = 3k!2µ6k+2µ .

2 Brief outline of theory

Here I very briefly outline the paths in Figure 1. from Strain to Stress, because this is parallel to the path weuse. I need to work to understand the di!erence between these paths, and how they di!er in their solutions,later. Note that this section has some di!erent notations, taken from YT98, describing the elastic formulation(such as the superscript f refers to ‘framework’ at the top, but later on, i think S refers to the same thing-standing for solid framework. f is ‘face number’ in all other sections). The viscous formulation will follow.

2.1 Path from Strain to Stress (A->B->C, clockwise in Fig. 1)

Path A. Macroscopic Strain to StressFirst, the definition of macroscopic framework strain:

'fij =

12

#$uS

i

$xj+

$uSj

$xi

$(3)

and the local displacement vector at each point on grain-grain contact surface:

ui(rR) = 'fijr

Rj at XC(rR) = 1 YT98 eqn(11) (4)

Path C. Grain-scale stress to macroscopic framework stress

(Sij =

1Vs

%

r<R"ij(r)dV (5)

where Vs is the volume of the spherical grain, dV = R2 sin )d)d*. fi(rR) is a traction applied on the grainsurface. "ijnj = fi at r = R. From the equilibrium condition (eqn. 6) and this definition of fi,

(Sij =

12Vs

%

r=R(fir

Rj + fir

Ri )dS (6)

Path B. Grain-scale governing equationsThe equilibrium condition:

$"ij

$xj= 0 at r < R i.e. "ij,j = 0 (7)

2

A third possibility is the “field boundary hypothesis”, which states that grain size evolves tothat which allows the aggregate to deform on the boundary between di!usion and dislocation creep(e.g. deBresser et al., 2001) . This model, at present, makes a rather di!erent prediction but Ihave not yet included it.

A somewhat less constrained, and very important question is the relationship between stressand depth. For now, I assume stress is a constant low value throughout the lithosphere. In thefuture, we can approximate a stress change at the base of the conductive layer (thermal boundarylayer) and then calculate a resultant grain size distribution. What would be the physical basis forthis stress change and how would we guess its magnitude? I need to consider this further, butfor this application, I think we should make the simplest assumptions, since the model is mostapplicable to partially molten asthenospheric parts of the temperature/viscosity profiles anyway.

B.2 Adding the e!ects of melt

Question:The model calculations are given as values normalized by the Coble creep viscosity. Can thesenormalized values be viewed as perturbations to the total viscosity (i.e. !! = !!!(!0)) or do wecalculate the perturbations as perturbations to the di!usion creep part, such as

!total =!(!disl)

"1 + (!!"di!)"1""1

(12)

where !!"di! = !!!"calc(!di!). In other words, the normalized shear viscosity calculated from the

model becomes a factor by which the flow-law value is reduced. Is this a reasonable first approxi-mation? If so, another question is, does the dislocation creep value remain una!ected, because wedo not know the direct e!ect of contiguity on dislocation creep.

The phenomenological relationship determined from experiments is:

!!

!0= exp(!"#) (13)

Hirth and Kohlstedt (2003) report di!erent values of " for di!usion and dislocation creep. However,I am not confident that these values are so discrete. So, I will plot this equation as a perturbationto the !total with several values of ".

B.3 E!ects of water

This is not done yet. see discussion in paper 2.As # => 0,Dmelt => Dg.b.

$ = Ag!g contact

Asurface

11

microscopic stress in a grain

microscopic deformation of a grain

ijS nj

AA

macroscopic stresses macroscopic strain rate of solid framework

macroscopic constitutive

relations

Pl ni

iu (r )

ijf

fr iRn (r )

governing equations for a grain deformation

C C(29)*

B8 & 13 & 14

21

Fig.1

22 or 23

in R(r )(P+p)l

(26 & 27 & 28)*

18

(30)*

- formulated in terms of grain boundary contiguity

- relationship between traction and velocity depends on rate of matter diffusion through grain boundary, solved at grain scale and homogenized upwards to give a macroscopic constitutive relation

traction

velocity

strain ratestress

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2

A=2

d 30, 12A=2.3

d 20, 14

,yti

ugit

noc

melt fraction,

d 30, 14

semi-empirical

theoretical

(b)

(a)

10-3

10-2

10-1

100

0 0.05 0.1 0.15 0.2 ,

ytisocsi

v r aehs

dez ilam r

on

cc

melt fraction,

d 30, 14

A=2d 30, 12

A=2.3

d 0, 14

R=5 m

=23

=18

Fig.9

Takei and Holtzman I and II, in prep.,

Viscosity as a function of melt fraction

A third possibility is the “field boundary hypothesis”, which states that grain size evolves tothat which allows the aggregate to deform on the boundary between di!usion and dislocation creep(e.g. deBresser et al., 2001) . This model, at present, makes a rather di!erent prediction but Ihave not yet included it.

A somewhat less constrained, and very important question is the relationship between stressand depth. For now, I assume stress is a constant low value throughout the lithosphere. In thefuture, we can approximate a stress change at the base of the conductive layer (thermal boundarylayer) and then calculate a resultant grain size distribution. What would be the physical basis forthis stress change and how would we guess its magnitude? I need to consider this further, butfor this application, I think we should make the simplest assumptions, since the model is mostapplicable to partially molten asthenospheric parts of the temperature/viscosity profiles anyway.

B.2 Adding the e!ects of melt

Question:The model calculations are given as values normalized by the Coble creep viscosity. Can thesenormalized values be viewed as perturbations to the total viscosity (i.e. !! = !!!(!0)) or do wecalculate the perturbations as perturbations to the di!usion creep part, such as

!total =!(!disl)

"1 + (!!"di!)"1""1

(12)

where !!"di! = !!!"calc(!di!). In other words, the normalized shear viscosity calculated from the

model becomes a factor by which the flow-law value is reduced. Is this a reasonable first approxi-mation? If so, another question is, does the dislocation creep value remain una!ected, because wedo not know the direct e!ect of contiguity on dislocation creep.

The phenomenological relationship determined from experiments is:

!!

!0= exp(!"#) (13)

Hirth and Kohlstedt (2003) report di!erent values of " for di!usion and dislocation creep. However,I am not confident that these values are so discrete. So, I will plot this equation as a perturbationto the !total with several values of ".

B.3 E!ects of water

This is not done yet. see discussion in paper 2.As # => 0,Dmelt => Dg.b.

11

This model helps resolve large discrepancy between melt-free olivine (Faul and Jackson, 2007) and San Carlos olivine + MORB.See David Kohlstedt’s talk, Weds. [MR33A-01]

the presence of a connected melt phase dramatically reduces diffusion path lengths through grain boundaries.

infinite melt diffusivity

finite melt diffusivity

temperature grain-scale melt

effect of homogeneous isotropic and anisotropic melt distribution for three melt fractions:

0 0.02 0.0460

70

80

90

100

110

120

!

dep

th, km

10!2

10!1

100

60

70

80

90

100

110

120

"!/"

solidus

L.-A. B.

anisotropicisotropic

exponential

Effect of segregation, calculated with Backus (1962) averaging of transverse isotropic medium with layers of differing viscosity (Honda, 1986).

comprised of 0.3 volume fraction bands, (same total melt fractions)


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)

where "N = !"i" (!"" is the spatial average of ". Does this mean that the viscosities are weightedby their volume or area fraction ? ), and "S = !("i)!1"!1. The anisotropy factor s = !""!"!1".

B.3 E!ects of water





& = Ag!g contact

Asurface

12


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)


B.3 E!ects of water





& = Ag!g contact

Asurface

12


!!xx

!xy

"

=#

"N 00 "S

$ !#xx

#xy

"

(15)


B.3 E!ects of water





& = Ag!g contact

Asurface

12

0 0.025 0.05 0.075 0.160

70

80

90

100

110

120

!

dep

th, km

10!2

10!1

100

60

70

80

90

100

110

120

"!/"

segregatedmelt

temperature grain-scale melt

solidus

L.-A. B.

bandslenses

total

Conclusions:

1. In experiments, melt aligns under stress at the grain scale, then segregates during deformation, and then can migrate up a stress gradient.

2. In the Earth, such multi-scale processes can cause a significant anisotropy in viscosity and a reduction in effective shear viscosity, easily up to two orders of magnitude.

3. Such viscosity reduction on boundary layers could have significant consequences for plate-mantle interactions, and have a distinct seismic signature.

Future work: We can now calculate elastic and viscous properties from the same melt distribution, and are developing predictive models for a range of hypothetical multi-scale melt distributions...

Fig. 8

10-4

10-3

10-2

10-1

100

10-2

10-1

100

(a)

10-4

10-3

10-2

10-1

100

10-2

10-1

100

14

12

8

8

12

81214

14

81214

(b)

cc

cc

viscosity

elasticity

!2

!1/2

contiguity,

No

rmal

ized

vis

cosi

ty a

nd

ela

stic

ity

µ µSsk

k kSsk

cc

cc

viscosity

elasticity

contiguity,

No

rmal

ized

vis

cosi

ty a

nd

ela

stic

ity

µ µSsk

k k Ssk

viscous and elastic properties as a function of grain boundary contiguity

No More

0 1 2 3 4

Strain

101

102

Stress(MPa)

0 1 2 3 4

Strain

1010

1011

1012

Viscosity(Pas)

in constant load samples, stress is always increasing, so samples cannot reach a steady state (stress and strain rate constant)








13

constant load








13

constant strain rate








13








21

0 1 2 3 4

Strain

1010

1011

1012

Viscosity(Pas)

102

Stress (MPa)

10-5

10-4

10-3

10-2

StrainRate(s-1)

Strain rates are limited by lenses in these spatially confined samples

speculation: the constant rate samples can reach steady state. the organization of strain partitioning (between low angle and high angle bands) is optimized to minimize dissipation (or viscosity) in steady state.

(current experiments in torsion, see King et al, [ref]

solidus

L.-A. B.

40 My

T: conductive+adiabatStress: constantgrain size: fcn of stressviscosity: combined mechanisms up to peak ?

J. Warren and G Hirth: 300 MPa stress in mylonites

max viscosity = 300 MPa1e-13 /s

= 3e21 Pa.s?

r

h

tangent section

radial section

Island Arc

(2006)

15,

2–3

© 2006 The AuthorsJournal compilation © 2006 Blackwell Publishing Asia Pty Ltd

doi:10.1111/j.1440-1738.2006.00517.x

Blackwell Publishing AsiaMelbourne, AustraliaIAR

Island Arc

1038-48712006 Blackwell Publishing Asia Pty LtdMarch 200615123Pictorial Article

Recycled crustal materials in the mantleT. Morishita

et al.

*Correspondence.

†

Present address: TK service, Hakusan 924-0820, Japan.Received 15 November 2005; accepted for publication 02 December 2005.

Pictorial Article

Corundum-bearing mafic granulites in the Horoman (Japan) and Ronda (Spain) Peridotite Massifs: Possible remnants of

recycled crustal materials in the mantle

T

OMOAKI

M

ORISHITA

,

1,

* E

IICHI

T

AKAZAWA

,

2

S

HOJI

A

RAI

,

1

M

ASAAKI

O

BATA

,

3

T

ADAHIRO

K

ODERA

1,†

AND

F

ERNANDO

G

ERVILLA

4

1

Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, Japan (email: [email protected]),

2

Department of Geology, Faculty of Science, Niigata University, Niigata 950-2181, Japan,

3

Division of Earth & Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto 606-8502,

Japan and

4

Instituto Andaluz de Ciencias de la Tierra, Universidad de Granada-CSIC, 18002 Granada, Spain

Corundum-bearing mafic granulites (i.e. rocks of high-Al maficcompositions) occur as a minor constituent in several orogenicperidotite massifs of upper mantle origin, for example, BeniBousera (Morocco; Kornprobst

et al.

1990), Ronda (Spain; Mori-shita

et al

. 2001) and Horoman (Japan; Morishita & Arai 2001).Corundum-bearing eclogite xenoliths are also rarely found in kim-berlite pipes (e.g. Sobolev

et al

. 1968). Thus, a minor but distinctivehigh-Al geochemical reservoir may exist in the upper mantle.These rocks generally show geochemical signatures similar to gab-broic rocks of lower crustal origin. From these lines of evidence,corundum-bearing mafic granulites/eclogites are interpreted tobe possible remnants of recycled crustal materials in the mantle.The present paper shows the occurrence of corundum-bearing(and associated corundum-free) mafic granulites in the Horoman(Figs 1,2) and Ronda (Figs 3,4) Massifs so as to provide goodexamples of heterogeneous mantle formed by mixing of recycledcrust materials.

ACKNOWLEDGEMENTS

We are grateful to the Board of Education of Samani Town forpermitting us to use the ‘Apoi-dake Shien Center’ (research

support center for young scientists), and to Akira Ishiwatari and

Atsushi Toramaru for their discussions. T. Morishita thanksTakashi Sawaguchi for his assistance in collecting samples. Con-structive reviews by Masaki Enami and Simon Wallis improvedthe manuscript.

REFERENCES

K

ORNPROBST

J., P

IBOULE

M., R

ODEN

M. & T

ABIT

A. 1990. Corundum-bearing garnet clinopyroxenites at Beni Bousera (Morocco): Originalplagioclase-rich gabbros recrystallized at depth within the mantle?

Journal of Petrology

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, 717–45.M

ORISHITA

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RAI

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F. 2001. High-pressure aluminousmafic rocks from the Ronda peridotite massif, southern Spain: Signifi-cance of sapphirine- and corundum-bearing mineral assemblages.

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REEN

D. H. 2003. Closed-systemgeochemical recycling of crustal materials in the upper mantle.

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N. V., K

UZNETSOVA

J. I. K. & Z

YUZIN

N. I. 1968. The petrologyof grospydite xenoliths from the Zagadochnaya kimberlite pipe inYakutia.


9

, 253–80.

Fig. 1

Occurrence of aluminous maficgranulites (M, corundum-free) associ-ated with peridotites (P) in the HoromanMassif. They usually occur as thin layers(1 cm

!

2 m thick) alternating with theperidotite layers (P, eroded part). In thisoutcrop, aluminous mafic granulite ismore abundant than peridotite. Alumi-nous mafic granulite layers occur parallelto the foliation of the peridotites in theupper and lower part of the outcrop.Some layers show isoclinal folding(middle part of the outcrop) as well asboudinage and slump-like structuresindicating strong deformation.

Island Arc

(2006)

15,

2–3


doi:10.1111/j.1440-1738.2006.00517.x


Island Arc



et al.

*Correspondence.

†


Pictorial Article



T

OMOAKI

M

ORISHITA

,

1,

* E

IICHI

T

AKAZAWA

,

2

S

HOJI

A

RAI

,

1

M

ASAAKI

O

BATA

,

3

T

ADAHIRO

K

ODERA

1,†

AND

F

ERNANDO

G

ERVILLA

4

1


2


3


Japan and

4



et al.


et al


et al


ACKNOWLEDGEMENTS




REFERENCES

K

ORNPROBST

J., P

IBOULE

M., R

ODEN

M. & T

ABIT



31

, 717–45.M

ORISHITA

T. & A

RAI



42

, 1279–99.M

ORISHITA

T., A

RAI

S. & G

ERVILLA


Lithos

57

, 143–61.M

ORISHITA

T., A

RAI

S., G

ERVILLA

F. & G

REEN



67

, 303–10.S

OBOLEV

N. V., K

UZNETSOVA

J. I. K. & Z

YUZIN



9

, 253–80.

Fig. 1


!


Island Arc

(2006)

15,

2–3


doi:10.1111/j.1440-1738.2006.00517.x


Island Arc



et al.

*Correspondence.

†


Pictorial Article



T

OMOAKI

M

ORISHITA

,

1,

* E

IICHI

T

AKAZAWA

,

2

S

HOJI

A

RAI

,

1

M

ASAAKI

O

BATA

,

3

T

ADAHIRO

K

ODERA

1,†

AND

F

ERNANDO

G

ERVILLA

4

1


2


3


Japan and

4



et al.


et al


et al


ACKNOWLEDGEMENTS




REFERENCES

K

ORNPROBST

J., P

IBOULE

M., R

ODEN

M. & T

ABIT



31

, 717–45.M

ORISHITA

T. & A

RAI



42

, 1279–99.M

ORISHITA

T., A

RAI

S. & G

ERVILLA


Lithos

57

, 143–61.M

ORISHITA

T., A

RAI

S., G

ERVILLA

F. & G

REEN



67

, 303–10.S

OBOLEV

N. V., K

UZNETSOVA

J. I. K. & Z

YUZIN



9

, 253–80.

Fig. 1


!


Island Arc

(2006)

15,

2–3


doi:10.1111/j.1440-1738.2006.00517.x


Island Arc



et al.

*Correspondence.

†


Pictorial Article



T

OMOAKI

M

ORISHITA

,

1,

* E

IICHI

T

AKAZAWA

,

2

S

HOJI

A

RAI

,

1

M

ASAAKI

O

BATA

,

3

T

ADAHIRO

K

ODERA

1,†

AND

F

ERNANDO

G

ERVILLA

4

1


2


3


Japan and

4



et al.


et al


et al


ACKNOWLEDGEMENTS




REFERENCES

K

ORNPROBST

J., P

IBOULE

M., R

ODEN

M. & T

ABIT



31

, 717–45.M

ORISHITA

T. & A

RAI



42

, 1279–99.M

ORISHITA

T., A

RAI

S. & G

ERVILLA


Lithos

57

, 143–61.M

ORISHITA

T., A

RAI

S., G

ERVILLA

F. & G

REEN



67

, 303–10.S

OBOLEV

N. V., K

UZNETSOVA

J. I. K. & Z

YUZIN



9

, 253–80.

Fig. 1


!


2) Layered distribution of solid phases of different isotropic or anisotropic propertiesCauses of anisotropy

!"!

3.3 Diffusion Creep at the Transition from Solute-rich to Melt-bearing Conditions

#$%$&'()*+)!'$,-$./'0.$(%.$$-($1-$.*,$&'2(3&(4*&$!+./*&$5(36*7*&$(2/,-6$2(4/8.*%/'$5(4.3,-395$.2( 2:&')$2*;$5( 8:( ')$( 236!+$6( ,$')35( <Faul and Jackson=( >??@A( Slotemaker=( >??BABeeman and Kohlstedt=(C""DE(:*$65$5(/(7*2%32*':(/(4/%'3.(34(FC??(6/.+$.(')/&(')/'(5$'$.,*&$54.3,( $1-$.*,$&'2( 3&( 2/,-6$2( )3'!-.$22$5( 4.3,( -395$.$5( G/&( H/.632( 36*7*&$( <Hirth andKohlstedt=(C""IA(Mei and Kohlstedt=(>???EJ((K)*2(-3*&'(*2(*6602'./'$5(*&(L*+0.$(MJ((N2(*&5*%/'$5(*&L*+0.$(M=('93(5$'/*62(%)/&+$(9)$&(/(,$6'(-)/2$(*2(/55$5('3(/()*+)!-0.*':(,/'$.*/6J((L*.2'=(3&$,02'(%3&2*5$.(')$(*&460$&%$(34(')$(,$6'(-)/2$(3&(O*&$'*%(-.3-$.'*$2J((G$%3&5=()39$7$.=(3&$(,02'/623( %3&2*5$.( ')$( $44$%'( 34( ')$( /223%*/'$5( %)/&+$( *&( +./*&( 830&5/.:( %)$,*2'.:( 3&( O*&$'*%8$)/7*3.=(/(-3*&'(&3'$5(8:(Slotemaker(<>??BE=(Faul and Jackson(<>??@E=(/&5(Kohlstedt(<>??@EJP3'$(')/'(*&(L*+0.$(M(')$(7*2%32*':(34(236!+$6(2/,-6$2(9*')(,$6'(*2(M1(')$(7*2%32*':(34(G/&(H/.632Q(RS#T(2/,-6$2=(-322*86$(')$($44$%'(34(5*44$.$&%$2(*&(+./*&(830&5/.:(%)$,*2'.:J((N623=(&3'$(')/'83')(':-$2(34(2/,-6$2(38$:(')$(.$6/'*3&2)*-(8$'9$$&(7*2%32*':(3&(,$6'(4./%'*3&(+*7$&(8:(UVJ(BJ

L*+0.$(DW(R36$(4./%'*3&(34(H3(7$.202(5*4402*3&5*2'/&%$('3(')$(BXIY2(-39$.(43.(H/!53-$5=G%!53-$5=(/&5(0&53-$5(2/,-6$2(34(H3(/&5R+(36*7*&$2J((N&/6:2*2(8/2$5(3&(UVJ(I*&5*%/'$2(')/'(*&($/%)(%/2$(+./*&(5*4402*3&3%%0..$5(*&(')$(.$+*,$(5$2%.*8$5(8:(':-$(TO*&$'*%2J((P3'$(')/'(')$(263-$(5$%.$/2$2<+./*&(830&5/.:(5*4402*7*':(*&%.$/2$2E(*&(')$3.5$.(H/!53-$5=(0&53-$5=(G%!53-$5

R+>G*SM(<Scott=(>??BA(Kohlstedt et al.=(>??@EJ

L*+0.$(MW(G$,*!63+(-63'(34(7*2%32*':(/2(/40&%'*3&(34(,$6'(4./%'*3&(43.(2/,-6$2(-.$-/.$54.3,(236!+$6(-395$.2(<Faul and Jackson=(>??@E/&5(2/,-6$2(4/8.*%/'$5(4.3,(-395$.$5(%.:2'/6234(G/&(H/.632(36*7*&$(<Hirth and Kohlstedt=C""IA(Hirth and Kohlstedt=(>??DEJ((P3'$(')$6/.+$(5$%.$/2$(*&(7*2%32*':(8$'9$$&(')$()*+)!-0.*':=(,$6'!4.$$(2/,-6$(/&5(')$(*,-0.$(2/,-6$9*')((?J>Z(2/,-6$J((N(O$:(V0$2'*3&W(“Is thislarge decrease in viscosity due entirely to theaddition of melt or does the associated changein grain boundary chemistry also play a role?”

Viscous and elastic anisotropy in partially molten rocks I ...benh/papers/y071210_AGU.pdf · and epicentral dista nces of >80 !, and stacking over a wide range of distances and depths.

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