An experimental investigation of the interactions between reaction driven and stress driven melt segregation: 1. Application to mantle melt extraction

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1 Article Volume 12, Number December 2011 Q12019, doi: /2011gc ISSN: An experimental investigation of the interactions between reaction driven and stress driven melt segregation: 1. Application to mantle melt extraction D. S. H. King Department of Earth Sciences, University of Minnesota, 310 Pillsbury Drive SE, Minneapolis, Minnesota 55455, USA Now at Department of Geosciences, Pennsylvania State University, 510 Deike Building, University Park, Pennsylvania 16802, USA B. K. Holtzman Lamont Doherty Earth Observatory, Columbia University, 61 Route 9W, Palisades, New York , USA D. L. Kohlstedt Department of Earth Sciences, University of Minnesota, 310 Pillsbury Drive SE, Minneapolis, Minnesota 55455, USA [1] We present results from experiments designed to investigate the interactions between stress driven melt segregation and reaction enhanced melt infiltration, two mechanisms that have previously been studied independently of each other. A melt source (with a melt fraction below the rheologically critical melt fraction) in which the basaltic melt is either orthopyroxene saturated or orthopyroxene undersaturated was coupled with a nominally melt free olivine + orthopyroxene sink in two cylindrical configurations deformed in torsion. As melt migrates from the source to the sink in samples with an orthopyroxene undersaturated melt source, the basalt dissolves orthopyroxene and precipitates olivine. The local increase in melt fraction during this process increases permeability and enhances melt infiltration. As melt migrates from the source to the sink in samples with an orthopyroxene saturated melt source, the reaction described above does not occur. These samples display modest infiltration associated with combined surface tension driven flow and mechanical segregation. Our experiments demonstrate (1) that combined reaction and deformation leads to greater infiltration of melt than does either mechanism alone, and (2) that melt segregation associated with deformation is an effective way to create perturbations in melt fraction along the source sink interface, which act as nucleation points for reaction enhanced infiltration in the experiments. Components: 2900 words, 13 figures, 1 table. Keywords: melt segregation; melt rich bands; partially molten rocks; reactive flow; torsional deformation. Index Terms: 3035 Marine Geology and : Midocean ridge processes; 8145 Tectonophysics: Physics of magma and magma bodies; 8178 Tectonophysics: Tectonics and magmatism. Received 3 May 2011; Revised 3 November 2011; Accepted 7 November 2011; Published 29 December King, D. S. H., B. K. Holtzman, and D. L. Kohlstedt (2011), An experimental investigation of the interactions between reaction driven and stress driven melt segregation: 1. Application to mantle melt extraction, Geochem. Geophys. Geosyst., 12, Q12019, doi: /2011gc Copyright 2011 by the American Geophysical Union 1 of 16

2 Geochemistry Geosystems 3 G KING ET AL.: DEFORMATION AND MELT-ROCK REACTION /2011GC Introduction [2] Interactions among partial melting, deformation, and melt rock reaction influence the nature of melt generation and transport in many geological settings, including mid ocean ridges, subduction zones and arcs, hot spots, and the roots of continental collisions. In understanding the source regions for melt in all of these settings, depicted in Figures 1a and 1b, open questions concern the mechanisms by which small amounts of melt concentrate and migrate. In the regions of melt emplacement and freezing, depicted in Figure 1c, the questions concern the processes of migration through the near and subsolidus country rock and the mechanisms of space accommodation for the intruding magma. In this and the companion paper by King et al. [2011a], we explore the interactions between deformation and melt rock reaction. Our findings are relevant to these questions on the initial and final stages of melt formation, migration and emplacement processes. The first paper investigates the interactions between mechanisms of melt segregation involving melt rock reaction and viscous shearing that could facilitate melt coalescence within the region of partial melting, where melt fractions are low. The second paper investigates the interactions of deformation and melt rock reaction across an interface with a very large gradient in melt fraction; the observations suggest that melt assisted granular flow may be important in disaggregating the country rock during magma emplacement. [3] In understanding the composition and dynamics in the source regions of mantle derived melts, a fundamental question concerns the mechanisms by which a dispersed melt distribution that forms at grain boundaries evolves toward a network of channels of segregated melt. Based on a variety of geochemical evidence from mid ocean ridge basalt (MORB), consensus has emerged that, during much of its ascent to the surface, MORB must have traveled through the upper mantle in channels that inhibit the melt from equilibrating with the surrounding peridotite [Johnson et al., 1990; Johnson and Dick, 1992; Spiegelman and Kenyon, 1992; Kelemen et al., 1997]. Most notably, erupted MORB sampled from the ocean floor is undersaturated in orthopyroxene (opx) compared to the lherzolite and harzburgite rocks that make up the upper mantle. Geological observations from ophiolites provide additional evidence for channelized flow in the upper mantle. Tabular dunite bodies in ophiolites have been widely interpreted as relict melt channels [e.g., Kelemen and Dick, 1995; Suhr, 1999; Braun Figure 1. (a) An interpretive sketch of the segregation, ascent, and emplacement of melt. (b) A close up view of the region within the partially molten asthenosphere where small amounts of melt coalesce into melt rich pathways. The mechanically and chemically driven mechanisms that could facilitate this behavior are explored in this paper. (c) A close up view of the disaggregation of country rock during magma emplacement and freezing, the process explored in the companion paper [King et al., 2011a]. and Kelemen, 2002]. Melting is a relatively homogeneous process down to the grain scale, and observations of U/Th and Th/Ra isotopic ratios also indicate that a significant amount of melt migration in the mantle occurs by diffuse, porous, reactive flow [Lundstrom et al., 1995; Sims et al., 1995; Kelemen et al., 1997; Morgan et al., 2008]. In this study, we seek to investigate the mechanisms by which this initially uniform melt distribution evolves into a segregated melt distribution. [4] Several physical/chemical processes influencing the distribution of melt in a partially molten rock that might provide a mechanistic understanding of these observations have been explored including stress driven melt segregation bands, reactive infiltration instabilities, vug waves, hydrofractures, and porosity waves (for a review, see Kohlstedt and Holtzman [2009]). The focus in this study is on mechanisms of melt migration that apply to the ductile portion of the upper mantle and do not involve fracture. [5] The reactive infiltration instability (RII) is one mechanism capable of inducing melt segregation and channelized flow in the upper mantle [Ortoleva et al., 1987; Aharonov et al., 1995, 1997; Kelemen 2 of 16

3 et al., 1997; Spiegelman et al., 2001; Liang et al., 2010; Liang and Parmentier, 2010]. This mechanism is driven by the increasing solubility of pyroxene in basaltic melt with decreasing pressure. Preferential dissolution of opx increases the melt fraction and permeability locally, leading to increased melt flow into these regions, which leads to further dissolution of opx. As melt propagates upward in the melting column, the dissolution of opx and precipitation of olivine creates a dunite channel. As melt continually flows upward through the channel, the dunite region can propagate either upward or downward depending upon the nature of the feedbacks involved. Reactive infiltration has been demonstrated in experiments in which a pyroxene undersaturated basaltic melt is coupled with a pyroxene rich multiphase rock that acts as a melt sink [Daines and Kohlstedt, 1993, 1994; Morgan and Liang, 2003, 2005]. Daines and Kohlstedt [1994] reported the occurrence of reactive instabilities, while Morgan and Liang [2003, 2005] observed only uniform infiltration. [6] Stress driven melt segregation is a second mechanism capable of segregating melt and possibly inducing channelized flow. Theoretical analysis predicts [Stevenson, 1989; Katz et al., 2006; Takei and Holtzman, 2009] and experiments confirm [Holtzman et al., 2003; Holtzman and Kohlstedt, 2007; Kohlstedt and Holtzman, 2009; King et al., 2010; Kohlstedt et al., 2010] that an applied shear stress can cause melt to segregate into melt rich bands. This mechanism of melt segregation leads to an organized network of melt rich bands oriented 20 to the shear plane in an antithetic orientation to the shear direction. [7] Here, we present results from experiments designed to investigate the interactions between melt rock reactions and shear deformation in partially molten harzburgite. Experiments were performed in which a source and a sink for melt are coupled as concentric rings that can either be statically annealed or deformed in torsion. In the present study, the first of two companion papers, the melt fraction in the melt source is 0.2, which is below the rheologically critical melt fraction at which grains in the matrix become disaggregated [e.g., Scott and Kohlstedt, 2006]. Results from similar experiments in which the melt source has a melt fraction well above the rheologically critical melt fraction are presented in the companion study by King et al. [2011a]. The melt distributions produced by static anneals of source sink couples are compared with those from torsion experiments of source sink couples, some with opx saturated and others with opx undersaturated melt sources. The results indicate that perturbations in melt fraction and permeability along the interface between source and sink, with a greater amplitude and length scale than variations at the grain scale, greatly enhance, and may be necessary for, the initiation of reactionenhanced infiltration observed in the experiments. In experiments, we observe that stress driven melt segregation creates such perturbations in melt fraction. In this way, stress driven segregation promotes conditions that favor reaction enhanced infiltration. The experiments do not incorporate the effects of buoyancy, which is a central aspect of the RII as it applies to Earth s upper mantle. Determining the implications of the experiments for Earth is therefore not straightforward. However, we can infer from these results that, in melt source regions such as depicted in Figure 1b, segregation driven by deformation may help initiate the RII and promote more efficient extraction of melt than obtained from either mechanism alone. 2. Methods 2.1. Sample Preparation and Assembly [8] Samples were synthesized from fine grained powders of olivine from San Carlos in Arizona (6 mm), enstatite (opx) from Bamble, Norway (10 mm), and MORB from the Mid Atlantic Ridge with an olivine tholeiite composition [Cooper and Kohlstedt, 1984]. All starting material was prepared by mechanically mixing powders of different combinations of the phases with an agate mortar and pestle. Powders were then cold pressed into a nickel capsule and isostatically hot pressed for at least 2 h at 1200 C and 300 MPa in a gas medium pressure vessel [Paterson, 1990]. At the fine grain size used in these specimens, melt and solid phases rapidly reach chemical and textural equilibrium during hot pressing. A source with a melt fraction of 0.2 was coupled with a nominally melt free sink. The sink material was olivine + opx in a 1:1 volume ratio. The opx undersaturated melt source was composed of olivine + MORB in an 8:2 volume ratio, and the opx saturated melt source was olivine + opx + MORB in a 4:4:2 volume ratio. At the interface between the source and sink, a chemical disequilibrium exists such that the activity of SiO 2 in the melt within the sink is higher than that in the source. In the saturated case, the source and sink are in chemical equilibrium with one another. [9] After hot pressing separate rods of the source and sink material, 4 mm long cylinders were cut from 3of16

4 Figure 2. each. Samples were prepared with the melt source either as the core of the sample or as the outer ring. Cores were taken out of each cylinder with the inner diameter of the outer ring and outer diameter of the inner core of 6.2 mm, as depicted in Figure 2. The nesting surfaces were smoothed with a diamond file for a snug fit. Pistons of porous alumina with a porosity of 0.20 were placed adjacent to the samples. The porous alumina prevented the development of a melt layer along the sample piston interface, leading to reliable mechanical coupling at that interface. As a melt sink, the porous alumina also drew some melt out of the source and reduced the overall melt fraction of the sample, both in samples with opx saturated and in those with opx undersaturated sources Procedure Sketch of sample assemblies. [10] Samples were deformed in a gas medium apparatus equipped with a torsion actuator [Paterson and Olgaard, 2000]. The experiments were performed at a constant rate of angular displacement as measured by a rotational variable displacement transducer (RVDT) outside the pressure vessel. Torque was measured by a torque cell housed inside the pressure vessel. Temperature was monitored within 3 mm of the sample using a Pt Pt/Rh thermocouple. Furnace calibrations confirm variation of <1 C along the length of the sample. Methods for determining shear stress and shear strain rate from torque and angular displacement as a function of time are described by Paterson and Olgaard [2000]. [11] To compare the effects resulting from meltrock reaction with those due to deformation, some samples were statically annealed while others were deformed (see Table 1). One sample was statically annealed for a total of 19 h with an opxundersaturated melt source as the outer ring. Four samples were deformed to a shear strain of g R 2.5 (where g R is the shear strain at the outer radius of the sample) at a constant twist rate corresponding to a strain rate at the outer radius of the sample of s 1. Two samples were prepared with the melt source (opx saturated and opx undersaturated) as the outer ring and two with the melt source as the inner core. The motivation for the two geometries was to explore the scenarios in which the propagation direction of stress driven melt segregation is the same as or opposite to the direction of reaction enhancement. Because of the strain gradient in torsion samples from the center to the outer radius of the samples, melt rich bands initially form by stress driven melt segregation at the outer radius of the sample and propagate inward with increasing strain. Surface tension driven flow and reaction enhanced flow will propagate from the source to the sink in either geometry. Figure 3 summarizes the propagation directions of reaction enhanced flow and mechanical melt segregation in the two geometries with an opx undersaturated melt source. [12] After deformation, samples were polished on an axial section, a longitudinal tangential section, and a transverse section (perpendicular to the axial and tangential sections) using diamond lapping film to 0.5 mm followed by 10 min of polishing with Table 1. Experiment Details Sample Source Annealing Time (h) Deformation Time (h) g R _ R PT0462 US (ring) 10 (19) PT0472 US (ring) PT0491 SAT (core) PT0492 SAT (ring) PT0500 US (core) of16

5 Figure 3. Sketch depicting the propagation directions for reaction enhanced flow and mechanical melt segregation processes in samples with the opx undersaturated source (a) as an outer ring and (b) as the core of the sample. colloidal silica (30 nm). The geometries of the sections that were polished for observation are shown in Figure 4. To make the melt more visible, samples were then etched with a 50:50 mix of HF and HCl diluted 20:1 with water for s, which preferentially etches the quenched melt phase as well as grain and phase boundaries. 3. Results 3.1. Static Anneal With Opx Undersaturated Source Ring [13] Static annealing of an opx undersaturated source coupled with a melt free sink produced a flat reaction front with no perturbations larger than the grain scale. One sample with an opx undersaturated melt source as the outer ring was annealed for 10 h at 1200 C. The axial section is pictured in Figure 5e. After the anneal, the source sink interface remained sharp in the 2 D cross section of the axial section with only minor irregularities and no significant gradient in melt fraction at length scales greater than the grain size, as shown in the reflected light micrograph of Figure 6a. Half of the sample was then rejacketed and annealed for an additional 9 h at Figure 4. (a) Sketch of a cylindrical torsion sample with dashed lines indicating the location of the cuts made to polish faces for analysis. (b) The axial section (half of this section is referred to as the radial section). (c) The tangential section. (d) The transverse section. Figure 5. Portions of the radial section (center of sample to the right, outer radius to the left) of samples. Samples with the melt source as an outer ring are shown (a) for opx saturated and (b) opx undersaturated sources, respectively. Samples with the melt source as a central core are shown (c) opx saturated and (d) opx undersaturated sources, respectively. (e) A portion of the statically annealed sample is displayed. 5of16

6 melt loss to the porous alumina pistons. The bands penetrate into the sample to the radius at which g =1, which is a robust observation associated with stressdriven melt segregation in torsion samples [King et al., 2010]. No melt is observed in the center of the sample beyond this stress driven melt segregation band front. [15] The transverse section of the sample, displayed in Figure 8a, reveals similar features as the axial section with melt rich pathways penetrating well into the sink material, but not further than the radius at which g = 1. Most of the melt rich pathways are continuous bands of high melt fraction within the source and penetrating into the sink. Although some regions of high melt fraction in the sink appear to be disconnected from the source in the plane of this image. Figure 6. Higher resolution images of source sink interface in low f opx undersaturated source anneal (a) at 1200 C for 10 h and (b) at 1250 C for an additional 9 h C. The source sink interface of the sample annealed longer, pictured in Figure 6b, is slightly more irregular, but no significant fingers of melt infiltration were observed. This result differs from that of Daines and Kohlstedt [1994]; however, the melt fraction within the source is significantly different between the two studies (0.9 compared to 0.2 in this study). In the companion study by King et al. [2011a], we explore combined reaction and deformation in samples with melt fractions comparable to the study by Daines and Kohlstedt [1994] Deformation With Opx Saturated Source Ring [14] The sample deformed with an opx saturated melt source as an outer ring is expected to record melt redistribution associated with deformation and not with reactive flow. The section pictured in Figure 5a displays clear melt segregation features. As viewed on the axial section, the bands propagate inward from the outer radius of the sample. Uniformly spaced melt rich bands are also visible on the tangential section at a 20 angle to the overall shear plane in an antithetic orientation, as pictured in Figure 7. Some bands, especially close to mid way between the top and bottom pistons (which is the portion displayed in Figure 5a), propagate well into the initially melt free sink in the core of the sample. Closer to the sample piston interface the bands do not penetrate as far into the sink, presumably due to 3.3. Deformation With Opx Undersaturated Source Ring [16] The sample deformed with an opxundersaturated melt source as an outer ring not only contains similar evidence for stress driven melt segregation but also exhibits distinct features that may be attributed to melt rock reaction. Melt rich bands of a geometry consistent with those produced by stress driven segregation are visible on the tangential section and near the outer radius of the axial section, though they are less distinct than in the opx saturated melt source case. Many of the bands propagated well past the source sink interface and are more distinct within the sink material. Some of the bands terminate at the radius at which g =1. However, unlike the case with the opx saturated Figure 7. Optical reflected light image from the tangential section of the sample deformed with an opx saturated source as a ring. This image is from within the source material. 6of16

7 Figure 8. Portions of the transverse sections of the samples. Samples with the melt source as an outer ring are shown (a) for opx saturated and (b) for opx undersaturated sources. Samples with the melt source as a central core are shown (c) for opx saturated and (d) for opx undersaturated sources. melt source, a body of melt, not clearly connected to the melt source in this 2D image, penetrated farther toward the center of the sample as pictured in Figure 5b. Some of these regions are connected to bands penetrating from the outside, but some appear as regions of high melt fraction not clearly connected on this 2 D face to deformation associated bands closer to the outer radius. [17] While fewer melt rich pathways penetrate into the sink from the source than in the opx saturated melt source sample, the pathways are wider, higher in melt fraction, and penetrate into the sink well past the radius at which g = 1. This difference is particularly clear in the transverse section displayed in Figure 8b. Also visible on the transverse section is the more finger like nature of the melt pathways in the sample with an opx undersaturated source. The pathway visible in this image is continuous from the source sink interface well into the sink. However, on the axial face in Figure 5b, the high melt fraction regions in the sink near the center of the sample appear to be disconnected from the source. [18] Evidence for irregularities in mineral abundance occur along the source sink interface, confirming that melt rock reaction has occurred non uniformly from source into sink. An x ray map of Mg from a portion of the source sink interface is displayed in Figure 9. The lightest gray represents olivine, the darker gray opx, and the darkest shade melt. The boundary between the region of 100% olivine and the opx bearing region, which was originally planar, is traced with a dashed line. This boundary now contains protrusions 100 mm long of 100% olivine into the sink material. The melt rich band that extends several hundred microns into the sink appears to originate at one of these protrusions. However, toward the top of this image, a protrusion of olivine is present with only minor amounts of melt present beyond it Deformation With Opx Saturated Source Core [19] One sample was deformed with a cylinder of opx saturated source material as the core of the sample. In the axial section, pictured in Figure 5c, melt rich bands parallel to the top and bottom of the sample on the axial face are present within the Figure 9. Mg x ray map of the source sink interface in the sample deformed with an opx undersaturated source ring. (left) The opx undersaturated melt source and (right) the opx bearing sink. The dashed line indicates the boundary of the opx bearing region. Melt infiltration is associated with one finger of apparent dissolution/precipitation reaction, while another finger of 100% olivine without melt present at the time of quenching is visible above it. 7of16

8 Figure 10. Mg x ray maps of the source sink interface in the samples deformed with an (a) opx saturated and (b) opxundersaturated source core. (c) An SEM image (BSE) of the region indicated by a box in Figure 10b. Grain size measurements were obtained from inside (3.5 ± 1.7 mm) and outside (6.1 ± 2.8 mm) of the melt rich region in Figure 10c. source material, and they terminate at the radius at which g = 1. The melt rich bands have also propagated outward 100 mm into the sink material. Because no melt was present initially in the sink material and the bands only occur in conjunction with a melt rich band in the source, this propagation presumably did not occur until the g = 1 front passed the source sink interface. The transverse section displayed in Figure 8c provides another perspective on the distribution of melt across the source sink interface. Similar to the axial section, only minor melt rich pathways penetrate into the sink material, and they are associated with bands of stress driven segregation within the source material. [20] Maps of phase distribution can be obtained from a Mg x ray map displayed in Figure 10a. In the opx saturated source sample, pyroxene is present throughout the image and the phase distribution is uniform with no significant difference between the source material and the sink material. However, the Mg concentration within pyroxene appears to be slightly greater (darker gray scale) in the source material than in the sink Deformation With Opx Undersaturated Source Core [21] The distance the bands extend from the source into the sink is significantly greater in the sample with an opx undersaturated source than in the sample with an opx saturated source, as depicted in the comparison of the source sink boundaries in Figures 5c and 5d. Also, the sample with an opx undersaturated source exhibits some off axis shearing. That is, the sample did not remain a right circular cylinder, as indicated by the non vertical outer radius in Figure 5d, due to a component of 8of16

9 shearing within the shear plane but not in the direction of angular displacement. [22] In contrast with the sample with an opxsaturated melt source core sample, the transverse section of the sample with an opx undersaturated source, displayed in Figure 8d, reveals many instances of melt rich pathways penetrating into the sink material. In some cases, these pathways extend >500 mm into the sink. Their occurrence is not uniformly distributed around the sample, with many pathways clumped together in some places and a significant extent of finger free source sink interface elsewhere. [23] AMgx ray map of the source sink interface is displayed in Figure 10b. One relatively small ( 150 mm) melt rich band extending from the source initiates from a slight irregularity in phase distribution near the bottom of the image. The band near the center of the x ray map is associated with a significant ( 100 mm) long region of 100% olivine extending into the sink region. This melt infiltration feature is clearly the largest in Figure 5d and deviates significantly from the flat, planar bands expected from stress driven segregation. A higher magnification SEM image (BSE) is displayed in Figure 10c. The grain size was measured in two regions of this image (1) within the melt rich region, but outside of what was initially the source region (center left of image), and (2) within the nominally melt free region outside of the melt rich band (upper and lower left of image). Grain size was measured using a linear intercept method with a geometrical correction factor of 1.5 [Gifkins, 1970]. The grain size determined within the band is 3.5 ± 1.7 mm, while the grain size measured outside the band is 6.1 ± 2.8 mm. The grain size outside of the band is comparable to the starting grain size of the olivine and slightly smaller than the starting grain size for the opx. The grain size within the band is smaller than the starting grain size for either mineral, indicating that the grain size is reduced within the melt rich bands Mechanical Data [24] Shear stress is plotted as a function of shear strain at the outer radius of the sample in Figure 11 for four samples. Shear stress is calculated from the measured torque using the relationship for shear stress as a function of radius t r [Paterson and Olgaard, 2000] 43þ1=n r ¼ M ð Þ 2r 1=n D 3 ; ð1þ D where M is the measured torque, D is the diameter of the sample, n is the stress exponent, and r is the radius for which shear stress is calculated (D/2 in this case). This method of calculating shear stress as a function of radius assumes a constant stress exponent and constant phase distribution throughout the sample. Because these samples do have a gradient in melt fraction as a function of radius, the calculated stress is not expected to represent rigorously the true mechanical properties of the material and caution should be exercised when comparing these data with those of the same material in different geometries. The same stress exponent (n = 3.5) was used for all samples in order to compare relative magnitudes of stress supported by the samples while accounting for the slight variations in sample diameter from one sample to the next. [25] For both opx undersaturated and opx saturated sources, samples with the source as a ring are weaker than their counterparts with the source as a core (Figure 11). This observation can be explained by the distribution of melt within the sample. Because the volume of the sample increases at a given radius toward the outside of the sample, the outer portion of the sample has a greater influence on the strength of the sample [Paterson and Olgaard, 2000]. Since the samples with the source as a ring have the high melt fraction near the outer radius of the sample, this geometry is expected to be weaker. Within each geometry, the sample with an opx undersaturated melt source is weaker than the sample with an opxsaturated melt source during most of the experiment (Figure 11). The differences in peak stress and in the stress later in the experiment between samples with opx saturated and opx undersaturated melt sources within each sample geometry is discussed in Section Summary of Observations [26] The evolution of melt distribution in the two sample geometries with both opx saturated and opx undersaturated melt sources is summarized in Figure 12. When the melt source is the outer ring of the sample (Figures 12a and 12b), melt segregates into bands within the source region. These bands propagate into the sink material in both cases, but they extend farther into the sink in the sample with an opx undersaturated source. When the melt source is the core of the sample (Figures 12c and 12d), melt also segregates within the source region and extends in (within the source) to about the same radius, corresponding to g = 1, in both cases. However, in the sample with an opx undersaturated source, melt 9of16

10 Figure 11. Shear stress vs shear strain for samples with opx saturated source ring (dashed gray line, PT0492), opx undersaturated source ring (solid gray line, PT0472), opx saturated source core (dashed black line, PT0491), and opx undersaturated source core (solid black line, PT0500). propagates significantly farther into the sink material than in the sample with an opx saturated source. 4. Discussion [27] In this set of experiments, we explored the combined effects of two different mechanisms that influence the distribution of melt within a partially (a) molten peridotite. Figure 13 summarizes the feedback loops associated with each process that both lead to the amplification of a local perturbation in melt fraction. The reaction enhancement effect (upper loop in Figure 13) occurs through a feedback established when an increased flux of opxundersaturated melt is available to the reaction front, enabled by the increased permeability due to the locally elevated melt fraction. The increased flux of opx undersaturated melt then leads to increased dissolution of opx, which further increases the melt fraction. In Earth, the melt flux associated with the RII is gravity driven, while in the experiments the flux associated with reaction enhanced infiltration is driven by surface energy minimization. Stressdriven melt segregation (lower loop in Figure 13) occurs through a feedback established when the viscosity reduction due to local increased melt fraction leads to local decreased pressure and corresponding flow of melt into the low pressure region. In the following sections we explore how these two feedback mechanisms may interact in experiments and in Earth How Are the Two Feedback Mechanisms Linked? [28] Based on our experimental observations, we infer that these two feedback loops are connected (b) (c) (d) Figure 12. Summary of observations from deformed samples in the low f source series with interpretations of the various combinations of driving forces. 10 of 16

11 Figure 13. Schematic diagram of interconnected feedback loops that lead to melt segregation. A perturbation in melt fraction (central node) can grow via a reactive instability (upper left loop) as well as via stress driven melt segregation (lower right loop). These mechanisms can act independently and simultaneously, but the stress driven segregation mechanism may be amplified by grain size reduction associated with dissolution of opx and precipitation of olivine, as illustrated by the light gray node. through the perturbations in melt fraction initially created by stress driven melt segregation, which then act as preferred locations for reaction enhanced infiltration. Local elevations in melt fraction in the source along the source sink interface lead to an elevated driving force both for surface tensiondriven flow and for melt rock reaction. (1) The steeper gradient in melt fraction at these locations creates a relatively high rate of surface tension driven flow [King et al., 2011b]. (2) The greater volume of undersaturated melt is able to dissolve more opx before becoming saturated. Through these two effects, we infer that a reaction enhancement effect analogous to the RII develops in samples with an opx undersaturated melt source. [29] Evidence for the role of stress driven perturbations in melt fractions as favored sites for reaction enhancement is illustrated by a visual comparison of Figures 5a 5d for the two source sink geometries. In the sample with an opx saturated source as the outer ring, pictured in Figure 5a, the bands propagate from the outer edge inward to a shear strain of g =1, as illustrated in Figure 12a, consistent with the observations of King et al. [2010]. In the sample with an opx undersaturated source as the outer ring (Figure 5b), many bands terminate at the same radius, that is, g = 1; however, some bands penetrate farther into the sample (as illustrated in Figure 12b) suggesting that reaction enhanced infiltration initiated from the perturbations in melt fraction (and thus permeability) augmenting the propagation rate of melt rich bands. As discussed in Section 4.3, the rheological data suggest that reaction enhanced propagation of the segregation front into the sample also weakens the sample, implying that strain localization resulting from melt segregation occurs within a larger volume of the sample. Thus we would expect some influence of stress on the morphology, even fairly deep into the sample. The melt rich structures observed here have a predominantly planar structure, consistent with being controlled by stress. However, the region of melt within the sink that appears disconnected from the source on the axial face visible in Figure 5b suggests that the planar morphology within the higher stress regions near the outer radius may locally transition into a fingering morphology within the lower stress central portion of the sample. [30] In more detail, compositional variations at small scales reveal that many melt infiltration features in the opx undersaturated melt source samples initiate at irregularities along the source sink interface where a region of 100% olivine protrudes into the sink material. This observation is evidence for an instability in dissolution/precipitation reactions. However, melt infiltration goes far beyond the region of 100% olivine, some melt rich bands do not initiate at such a feature (Figure 10b), and some protrusions of 100% olivine are present without an associated melt rich band (Figure 9). These observations all indicate interactions between deformation and reaction. In order for melt rich bands associated with deformation to maintain a constant geometry relative to the shear plane, they must continually reorganize with respect to the deforming matrix [Holtzman et al., 2005; Katz et al., 2006]. The protrusions of olivine not associated with a melt rich band likely represent regions where a melt rich band existed at a lower strain before the melt within that band migrated elsewhere as the band network reorganized with increasing deformation. [31] Another link between the two feedback mechanisms, illustrated in Figure 13, could be through grain size reduction associated with dissolution of opx and precipitation of olivine. As discussed in Section 3.5, the grain size within the melt rich bands is observed to be smaller than the grain size within the nominally melt free sink material. We interpret this to indicate that as opx grains are dissolved into the melt they become smaller, and newly precipitated olivine grains start out small and grow larger. Through the effects of surface tension, the system evolves toward a constant radius of curvature at solid/liquid inter- 11 of 16

12 faces. A region with a smaller grain size has more melt pockets with constant curvature, so the smaller grain size can lead directly to amplification of the perturbation in melt fraction [Wark and Watson, 1998]. This elevated melt fraction leads to increased weakening. Also, if the sample is deforming by a grain size sensitive creep mechanism (or if grain size reduction changes the creep mechanism locally), grain size reduction will lead to a reduction in viscosity. Both effects would further decrease the pressure and amplify the stress driven melt segregation mechanism. The increased permeability associated with increased melt fraction leads to enhanced transport of unreacted melt within the band, which sustains chemical disequilibrium at the tip Comparison Between Different Sample Geometries [32] Observations, particularly from the transverse sections, of the two deformation geometries differ in the extent of melt infiltration in samples with both opx saturated and opx undersaturated melt sources. Much greater infiltration is observed in the samples with the melt source as the outer ring, as depicted schematically in the comparison between Figures 12c and 12d. This difference can be explained in terms of the difference in the time of the experiment at which the mechanical instability initiates. (1) In samples with the source as the outer ring, stress driven segregation is developed when the outer radius reaches a shear strain of g =1.As strain increases, these bands propagate into the sink as low viscosity, low pressure regions that draw melt out of the source (the process active in the sample with an opx saturated source, Figure 8a). In the sample with an opx undersaturated source, Figure 8b, melt rock reaction enhances the driving force for propagation from source into sink. (2) In contrast, in samples with the melt source as the core of the sample, because the outer ring is initially meltfree, stress driven melt segregation does not initiate until the source sink interface reaches a shear strain of g = 1. Therefore, less time has elapsed (and less strain has accumulated) between the formation of perturbations in melt fraction and the end of the experiment, allowing for less growth of the melt pathways through mechanical segregation or meltrock reaction. [33] However, we emphasize that, within each deformation geometry, samples deformed with an opx undersaturated melt source display infiltration of a greater volume of melt than do samples with an opx saturated melt source. Hence, we conclude that the presence of both mechanisms leads to greater segregation and infiltration than either alone Interpretation of Mechanical Data [34] The comparison of the mechanical data in Figure 11 reveals that, within each geometry, the sample with an opx undersaturated source is generally weaker than the sample with an opx saturated source. The peak stress early in the experiment is also significantly smaller in the samples with an opx undersaturated melt source. At least two factors contribute to this observed difference: [35] 1. The greater strength of samples with an opxsaturated source could be explained, at least in part, by the fact that material composed of olivine + opx + MORB has been observed to be stronger than material composed of olivine + MORB. Triaxial compressive creep experiments by Zimmerman and Kohlstedt [2004] demonstrate that, while nominally melt free olivine is stronger than nominally meltfree lherzolite (olivine + opx + cpx), olivine + 20% MORB is weaker than lherzolite + 20% MORB. At the strain rate ( s 1 ) and grain size (8 mm) used in this study, the flow law for partially molten lherzolite [Zimmerman and Kohlstedt, 2004] gives a stress 1.6 times greater than that given by the flow law for partially molten olivine [Hirth and Kohlstedt, 2003]. The peak stresses observed in the samples in this study with an opx saturated source are about 1.4 times greater than the opx undersaturated samples. [36] 2. The effects of melt rock reaction in samples with an opx undersaturated source may also play a role in the different peak stresses and evolution of stress with increasing strain by promoting greater shear localization than occurs in samples with an opx saturated melt source. Observations of off axis shearing and offsets in the source sink interface visible on the axial section indicate greater shear localization in samples with an opx undersaturated melt source. If such strain localization initiated early in the experiment, this could explain why the peak stress in the samples with an opx undersaturated source is so much lower (i.e., strain localization prevented the material from reaching the peak stress that it would have reached deforming homogeneously). The higher peak stress and the onset of strain weakening at higher strains in the samples with an opx saturated source suggest that strain localization does not occur until g > 1. Future experiments exploring the evolution of melt distribution at lower strains could determine if melt bands form at g < 1 in samples with an opx undersaturated source. 12 of 16

13 4.4. Does the Presence of Opx Help Facilitate Stress Driven Melt Segregation? [37] Stress driven segregation occurs when the compaction length is less than the height of the sample [Holtzman et al., 2003]. Estimates of the compaction length in olivine + MORB samples are on the order of a few millimeters, very close to the height of the samples in this study. In prior studies of stress driven melt segregation, chromite was used to reduce the permeability of the sample, which in turn reduces the compaction length to much less than the height of the sample. [38] The bands are much more clearly defined in source regions of olivine + opx + MORB than in source regions of just olivine + MORB. This result suggests that the mixture of olivine + opx + MORB has a shorter compaction length than olivine + MORB. The shorter compaction length could be due to the different interfacial energies and wetting properties at ol opx MORB or opx opx MORB triple junctions than at ol ol MORB triple junctions. Measurements of dihedral angles in statically annealed samples support this interpretation. In samples annealed at 1300 C and 1 GPa, ol opx melt and opx opx melt triple junctions have a dihedral angle of 75 [Toramaru and Fujii, 1986], which is significantly larger than ol ol melt dihedral angles of 30 [Waff and Bulau, 1979; Mei et al., 2002]. With higher dihedral angles, particularly greater than 60, the tortuosity of interconnected melt pathways within the sample is greatly increased. In this way, the increased average dihedral angle associated with the presence of 50% opx significantly reduces the permeability and thus compaction length of the source region in the opx saturated source case Implications for Melt Extraction From Earth s Mantle [39] Field relationships observed in peridotites record evidence for both deformation and melt rock reaction associated with dunite bodies, which are inferred to be relict melt channels. Reaction and deformation are typically inferred to have been acting simultaneously [e.g., Kelemen and Dick, 1995; Webber et al., 2010]. In describing dunites in the Josephine Peridotite, Kelemen and Dick [1995] point out that no dunites are observed to have formed in the absence of shear zones, although there are many shear zones formed in the absence of dunite. These observations raise questions about the nature of the interactions between deformation and melt rock reaction. Do the processes enhance one another? Does one or the other dominate? How are they coupled in space and time? [40] Reactive infiltration and stress driven segregation have both been observed experimentally, though only independently prior to this study [e.g., Daines and Kohlstedt, 1994; Holtzman et al., 2003]. In the experiments of Daines and Kohlstedt [1994] and in those presented here, surface tension acts as the driving force for infiltration from the meltrich source to the melt poor sink. The chemical disequilibrium that acts as the driving force for reaction enhancement was created by coupling a reservoir of opx undersaturated basaltic melt with an opx bearing sink. In Earth, the scenario is different. The driving force for the RII is the increasing solubility of opx in basaltic melt as pressure decreases coupled with buoyant ascent of melt, which is predicted to lead to coalescing of channels upward in the mantle (downstream in magma flow) [Spiegelman, 1996]. The effect of buoyancy, which is negligible at the laboratory sample scale, plays a significant role in Earth s mantle. Still, we interpret the enhanced melt infiltration observed in samples with an opx undersaturated source as evidence for a reactive instability arising from the coupling of a physical driving force (surface tension) with a chemical driving force (opx undersaturation of the melt). [41] Much of the focus of experiments exploring stress driven melt segregation thus far has been to determine the length scale of segregation. In experiments, the band spacing is observed to scale with the compaction length. The spacing between the largest bands is approximately 0.2 compaction lengths with narrower bands forming at shorter spacing [Holtzman and Kohlstedt, 2007; King et al., 2010]. Extrapolation of this length scale is consistent with geological observations of dunite features in ophiolites [Braun and Kelemen, 2002; Holtzman et al., 2003]. These similarities between experiments and field observations strongly support the interpretation that deformation influences the distribution of melt in the upper mantle. However, in order to understand the interaction with reaction driven mechanisms, we must better understand the kinetics of stress driven segregation, the rate at which segregation evolves in different thermodynamic conditions. [42] In the deformation experiments discussed here, the samples are closed systems with respect to mass flow. To explore the behavior of these coupled processes in fully open systems, such as occur in Earth, numerical models are critical. In simulations 13 of 16

14 of buoyancy driven melt flow within a horizontal simple shear flow field, Butler [2009] found that two sets of bands form, one at a low angle to the shear plane ( 20 ) similar to those observed in experiments, and another at a high angle to the shear plane ( 20 ), the latter stabilized by the vertically migrating melt. In another recent example, Katz [2010] developed models of mid ocean ridge dynamics with melting, compaction, and a porosityweakening viscosity, in which networks of bands by stress driven segregation did not develop. Two possible explanations for the lack of stress driven segregation are the choices of constitutive equations and the resolution of the model. While the constitutive equation used (which has a stress exponent of n = 1) does generate melt rich bands at 45 to the shear plane, Katz et al. [2006] show that it does not promote the stabilization of low angle melt rich bands ( 20 to the shear plane) and thus does not reduce the effective viscosity. The resolution relative to the compaction length is an important concern because stress driven melt segregation is a process that emerges from the grain scale upward. [43] We wish to emphasize that the smallest scale of melt rich bands, which are on the order of the grain size [e.g., Zimmerman et al., 1999; Hier Majumder et al., 2004; Holtzman and Kohlstedt, 2007; King et al., 2010], will likely influence the rheological and transport properties of the entire system as they begin to emerge. The anisotropic constitutive model of Takei and Holtzman [2009] approximates effects of grain scale alignment, and so may capture important dynamics when incorporated into numerical models. We also want to point out that the state or degree of segregation can evolve independently from the total melt fraction. Once a network of melt rich bands emerges, we speculate that it would be dynamic but persistent. Bands will persist because surface tension provides a memory; the time necessary for bands to relax or anneal is long compared to the time necessary for bands to form [Parsons et al., 2008; King et al., 2011b]. Small melt fractions will be retained in the networks, causing them to act as preferred channels for incoming melt. The networks will remain dynamic while deformation continues. If deformation stops, surface tension will anneal away the networks. The melt rock reactions explored in this paper may act to enhance the segregation rates and also to stabilize the meltrich networks. [44] The results from this study provide insight into the interactions between stress driven and reactiondriven melt segregation. At our experimental conditions, we observe stress driven melt segregation to proceed at a faster rate than reaction driven melt segregation, which then leads to coupling between the mechanisms in which reaction driven processes enhance melt infiltration. However, depending upon the strain rate, the degree of disequilibrium, and the strength of the physical driving force for infiltration (either surface tension or buoyancy), either mechanism could initiate the melt segregation that leads to the coupling of the two mechanisms. Perhaps more important is the observation that coupling does occur. Dunite channels are observed in an orientation that is consistent with the geometry of bands forming from stress driven melt segregation. This observation implies that in the mantle deformation could facilitate alignment favorable for focusing melt at a mid ocean ridge [Phipps Morgan, 1987; Daines and Kohlstedt, 1997; Katz et al., 2006], while reactive infiltration enhances the propagation and stabilizes the channels. Further analysis of the thermodynamics of deforming partially molten systems with chemical disequilibrium are important for studying the interactions among chemical and mechanical processes at varying degrees of disequilibrium. Further experiments designed according to these analyses will bring us closer to understanding how to extrapolate the behavior to conditions in Earth. 5. Conclusions [45] The results from this series of experiments indicate that the coupling of deformation and meltrock reaction leads to infiltration of a greater volume of melt than does either mechanism acting alone. In the experiments, melt infiltration from source to sink increases dramatically in deformed samples compared to a statically annealed sample. The greater infiltration in samples with an opx undersaturated melt source indicates coupling between deformation and melt rock reaction. In these experiments, we interpret that stress driven melt segregation creates perturbations in melt fraction from which reactionenhanced melt infiltration can initiate in a way analogous to the RII. These experiments provide insight for how the RII and stress driven melt segregation may be coupled in Earth s mantle. Acknowledgments [46] We are grateful to Mark Zimmerman for his input in designing the sample assembly. This work was supported by NSF OCE (to DLK), a Doctoral Dissertation Fellowship from the University of Minnesota (to DSHK), and NSF 14 of 16