How Strong/Weak Is Epidote Relative to Plagioclase?

In natural lower crustal rocks, we observe that plagioclase breakdown is often partial as evidenced by the presence of epidote‐group minerals and the absence of the remaining reaction products for example, kyanite and quartz. Due to the lack of experimental data on epidote deformation, it is unclear if this partial reaction would affect the strength of the plagioclase‐rich lower continental crust. We experimentally investigated the relative strength of pure epidote and pure plagioclase aggregates at a confining pressure of 1 GPa, two different temperatures (550 and 650°C) and two different strain rates (5 × 10−5 and 5 × 10−6 s−1) using a Griggs apparatus. Furthermore, we investigated potential strength differences due to differences in grain size by deforming aggregates with grain‐size ranges of either ≈90–135 μm or <25 μm. Under identical conditions, epidote aggregates are either as strong as their plagioclase counterparts or moderately stronger, suggesting that the partial replacement of plagioclase by epidote‐group minerals would not have a permanent weakening effect on the strength of the lower continental crust.


Introduction
The seminal studies by Dimanov et al. (1999), Rybacki and Dresen (2000), Rybacki and Dresen (2004), and Rybacki et al. (2006) experimentally demonstrated that under a confining pressure of 300 MPa, which relates to a depth of ≈10-15 km, the presence of as little as >0.004 wt.% aqueous fluid has a reducing effect on the strength of plagioclase-rich aggregates.Yet, under conditions prevailing at lower crustal depths (>25 km, >800 MPa, and temperatures >600°C), free fluids will be consumed by the breakdown of the Ca-rich anorthite component in plagioclase to form hydrous epidote-group minerals, and the nominally anhydrous reaction products kyanite and quartz (Boettcher, 1970;Goldsmith, 1981Goldsmith, , 1982)).At high pressure conditions (>50 km), the Na-rich plagioclase endmember albite will also become unstable and form quartz and jadeite (Holland, 1980).
The most common epidote-group minerals are zoisite, clinozoisite, and epidote.Zoisite contains almost no Fe 3+ and there is a continuous solid solution series between the Fe-poor clinozoisite and Fe-rich epidote, in which Fe 3+ substitutes for Al 3+ .Wayte et al. (1989) investigated the kinetics of plagioclase breakdown in much detail using Allalin Gabbro samples of the Western Alps, which experienced high-pressure metamorphism (≈600°C, ≈2 GPa).They found that up to a reaction progress of ≈10% only epidote-group minerals replace plagioclase in the presence of fluid.The remaining reaction products, that is, kyanite, quartz, and jadeite, grow only at a reaction progress >10%.Stünitz and Tullis (2001) studied the influence of plagioclase breakdown under lower crustal conditions on strength and experimentally showed that samples undergoing reaction are up to 6 times weaker than their unreacted counterparts when deformed at 750°C and up to 3 times weaker when deformed at 900°C (see Figure 2 in Stünitz and Tullis (2001)).In the microstructures of the reacted samples, the authors find epidote-group minerals of a few tens of micrometer in size, which are dispersed within the plagioclase matrix with a grain size of ≈2-6 μm.These epidote-group minerals are often dissected and displaced by narrow shear zones that have widths of a few micrometer and contain the remaining reaction products, namely nanocrystalline albitic plagioclase, an epidote-group mineral, white mica, as well as kyanite and quartz.The authors conclude that weakening due to reaction is not only of transient nature, but could prevail as phase mixing in the narrow shear zones will inhibit grain growth, that is, a process akin to Zener pinning, and could therefore stabilize diffusion-accommodated deformation mechanisms.Since the micrometer-sized zoisite grains were dissected and displaced by narrow shear zones, it follows that they grew earlier than the remaining reaction products filling the shear zones.This microstructural observation, that is, epidote-group minerals that are much larger than the other reaction products, further supports the observed early nucleation and growth of epidote-group minerals proposed by Wayte et al. (1989).The inferences from the experimental observations by Stünitz and Tullis (2001) is supported by various field observations that demonstrate a strong correlation between weakening and reaction, involving the growth of epidote-group minerals, in rocks exhumed from upper to lower crustal depths (e.g., Ceccato et al., 2022;Goncalves et al., 2012;Jolivet et al., 2005;Peverelli et al., 2022).
Observations on natural rocks, exhumed from lower crustal depths, for example, granulite-facies anorthosites exposed on Holsnøy, SW Norway, regularly reveal the onset of plagioclase breakdown by the nucleation and growth of fine (commonly <1 μm width) needles of epidote-group minerals (Figure 1).The lack of the remaining reaction products highlights that these rocks are only partially reacted with a reaction progress <10%.In siliceous schists that experienced blueschist to amphibolite-facies conditions, microboudinage of epidote-group minerals in albite porphyroblasts, showing slight undulous extinction, indicate that epidote-group minerals are stronger than albite (Masuda et al., 1995).Furthermore, in greenschist-facies mylonites, epidote needles within a ductile albitic matrix show low dislocation densities and no fractures pointing toward a deformation behavior best described as rigid particles in a ductile matrix (Stünitz, 1993).
The research question we want to answer in the present study is: How does the exclusive growth of epidote-group minerals, that is, partial reaction of plagioclase, affect the strength of the lower continental crust?By experimentally quantifying the relative strength between epidote and plagioclase under high pressure and temperature conditions, realized at lower crustal depths, we aim to investigate if the partial reaction of plagioclase would permanently affect the strength of the lower continental crust.

Starting Material and Sample Preparation
We used natural epidote and plagioclase as starting materials.Their chemical compositions, identified using Xray fluorescence spectroscopy (XRF) and electron microprobe analysis (EPMA), are given in Table 1.To the best of our knowledge, there is only limited data on the deformation behavior of epidote-group minerals in general and no constraints on potential differences in deformation behavior between members of the epidote group as a function of their Fe-content.The epidote single crystal, which we selected for this study, originates from Kayes, Mali, and is ≈6 cm long and ≈1.5 cm wide.It thus provides enough material to run several deformation tests.It is not pure but contains some minor amphibole, identified as magnesiotaramite, which cannot be distinguished from epidote with the naked eye due to a similar greenish color.The presence of accessory magnesiotaramite explains the relatively high concentration of 0.12 wt.% MgO in the XRF data (Table 1) in comparison to the typical range of 0.03-0.06wt.% for pure epidote (Deer et al., 2013).Using the XRF data, the amount of magnesiotaramite was estimated to be ≈0.7 wt.%.The origin of the plagioclase grains is unknown.The plagioclase grains are transparent and ≈2-4 cm in size.Microprobe analyses of plagioclase revealed an intermediate plagioclase chemistry with the endmember formula An 64 Ab 35 Or 01 (Table 1), that is, a slightly higher Ca-endmember anorthite (An) than of the Na-endmember albite (Ab) and only very little of the K-endmember orthoclase (Or).
The single crystals were crushed and sieved to obtain pure epidote or plagioclase powders with a grain size of either ≈90-135 or <25 μm.The powder with a grain size <25 μm was washed in distilled water to skim the dust fraction and dried in an oven at 60°C afterward.Each powder type was then filled into gold capsules separately.Filled capsules were placed into a custom-made device one at a time and compressed at ≈3 MPa at ambient temperature for a few minutes using a manual pump.The final height of the compressed powder was ≈8 mm.With an outer capsule diameter of ≈4 mm and a capsule wall thickness of ≈0.25 mm, the hot-pressed powders are ≈3.5 mm in diameter.The capsules were then closed by placing a 0.25 mm thick gold lid and a ceramic piston with a diameter of ≈3.5 mm and a height of ≈1 mm on top without any further mechanical sealing or welding.Storing the finished capsules in an oven at 60°for at least 2 days prior to the experiment, was intended to keep the powders dry.
Using powders instead of intact drill-core samples has two main advantages.First, the absence of an initial texture in hot-pressed powders is necessary for a sample-to-sample comparison.Second, using hot-pressed aggregates, we were able to control the sample's grain size.
The recovered deformation samples were cut lengthwise using a diamond-wire saw.Selected sample halves were embedded in epoxy and used to make thick sections and in some cases additional thin sections.Both section types were polished and carbon coated for the microstructural and chemical analyses.

Stability of Plagioclase and Epidote-Determination of Experimental Conditions
A direct comparison of the two materials requires an identical experimental protocol.Because epidote-group minerals are a reaction product of plagioclase hydration at high-pressure and high-temperature conditions (Hp/ HT ), prevailing at depths of the lower continental crust, we needed to find a pressure (p) and temperature (T ) window, in which both phases are either stable or at least metastable throughout the duration of the experiment.Previous Hp-deformation tests conducted at 1.5-3 GPa confining pressure on plagioclase-rich rocks (e.g., Incel et al., 2019Incel et al., , 2020;;Stünitz & Tullis, 2001;J. Tullis & Yund, 1985, 1992), suggest that in the presence of only minor amounts of aqueous fluids, reaction kinetics in pure plagioclase aggregates are sluggish at temperatures <700°C and that partial melting of plagioclase occurs at temperatures >800°C.
Since epidote contains ferric iron, its stability highly depends on oxygen fugacity with an increase in stability with an increase in oxygen fugacity (Liou, 1973).Furthermore, Liou (1973) experimentally demonstrated that its stability also increases with pressure (see Figure 5 in Liou (1973)).The experimental setup neither allowed us to control the oxygen fugacity nor to monitor water activity throughout the experiment.We, however, expect the conditions to be rather oxidizing as the assembly materials-except for the graphite furnace-are not expected to create a reducing atmosphere.Liou (1973) found that synthetic epidote, showing a similar composition to our starting material, will react to form garnet, quartz, anorthite, and hematite or magnetite at 0.3-0.5 GPa and temperatures of ≈600-700°C after run durations >148 hr (see Table 7 in Liou (1973)).These experimental results match with our thermodynamic calculations, performed using the epidote XRF analysis (Table 1; Figures S1b and  S1c in Supporting Information S1).Pseudosections were calculated using the software Perple_X (Connolly, 1990) with the thermodynamic data set of Holland and Powell (2004).We applied the following solidsolution models: feldspar (Holland & Powell, 2003), melt (HP; White et al., 2001), Ep(HP; THERMOCALC), Grt (JH; Jennings & Holland, 2015), Cpx (HP; Holland & Powell, 1996).To the best of our knowledge, the kinetics of this epidote breakdown at high-temperature conditions have not been quantified, making it unclear if epidote breakdown would occur on time-scales relevant for the deformation tests, that is, during run durations <48 hr.Combining all the information on epidote and plagioclase stability, we decided to perform the deformation tests on pure plagioclase and pure epidote aggregates at 1 GPa and either 550 or 650°C (Table 2).

Experimental Methods-Solid-Medium Apparatus
We used a solid-medium deformation apparatus (Griggs apparatus) to generate Hp-HT conditions in the laboratory.As confining medium we used NaCl.Heating of the sample was realized through a graphite furnace surrounding the sample and the temperature was measured using two Ni-CrNi (K-type) thermocouples, placed slightly above and slightly below the sample's center.For further details on the experimental setup and the sample assembly, the reader is referred to Rybacki et al. (1998).

Experimental Procedure and Data Treatment
We started compression and heating of the sample simultaneously with 1 MPa min 1 and 10°C min 1 .Once we reached 1 GPa and the desired run temperature (550 or 650°C), we hot-pressed the powder at nominally hydrostatic conditions for 3 hr.After the hot-pressing stage, we started deformation by advancing the deformation Geochemistry, Geophysics, Geosystems piston with a speed of 1.44 mm hr 1 or 0.14 mm hr 1 , corresponding to strain rates of 5 × 10 5 s 1 and 5 × 10 6 s 1 , respectively.Throughout deformation, T and p were held constant.We stopped deformation at total axial strains ranging from ≈10% to ≈32% strain (Table 2) and started retraction of the deformation piston with 1.44 mm/hr while pressure and temperature were kept constant.Once the load on the sample equaled hydrostatic conditions, we started decompression and cooling with 0.5-1 MPa/min and 10°C/min, respectively.
We sampled the mechanical data with a sampling frequency of 1 Hz and observed that the raw load data often fluctuated by ±1 kN, which corresponds to ≈51 MPa.To smooth the load data, we used the movmean function in MATLAB (The MathWorks Inc, 2022) that averages the data over a window of neighboring points of a certain length.In general, we employed a window length of 500, which is equal to ≈8 min, except for the experiment, in which we deformed a plagioclase powder with a grain size of 90-135 μm at 550°C with 5 × 10 6 s 1 , for which we used a window length of 1,000 samples, because load fluctuations were with ±1.7 kN larger than for the other runs.The smoothed mechanical data was then corrected for machine stiffness and friction to obtain axial strain and stress (see Druiventak et al. (2011) for further explanations).
The uncertainty in pressure and stress are mainly caused by friction between different assembly pieces (e.g., between the miter ring and the deformation piston) as well as by the finite strength of the confining medium (Mirwald et al., 1975;Rybacki et al., 1998;T. E. Tullis & Tullis, 1986).The actual pressure is estimated to be lower by ≈10% than the nominal one corresponding to the load on the outer piston.The uncertainty in stress ranges between 100 MPa (Burnley et al., 1991;Tingle et al., 1993) and 200 MPa (Druiventak et al., 2011).

Analytical Methods
Chemical analyses of the starting material were conducted using a Rigaku ZSX Primus IV X-ray fluorescence spectroscope.For the microstructural observations and energy-dispersive X-ray spectroscopy (EDS), we used a scanning-electron microscope (SEM; Zeiss Merlin FE-SEM) and wavelength-dispersive X-ray spectroscopy (WDS) was performed at an electron microprobe (EPMA) of the type Cameca SX Five FE.For the microstructural observations and the EDS analyses, we used an acceleration voltage of 20 kV and a probe current of 400-900 pA.The EPMA measurements were conducted with column conditions of 15 keV and 10 nA and a beam focus of 5 μm.The Na Kα was measured using LTAP, Al Kα and Si Kα were both measured using TAP, K Kα was measured using LPET, Ca Kα using PET, and Fe Kα using LLIF.Internal standards were used for the microprobe measurements.

Results
Most samples underwent shear-buckling during deformation, that is, the top of the sample was sheared relative to its bottom.This buckling behavior is most probably the result of irregular sample shapes produced during hotpressing and the upper alumina piston having roughly the same diameter as the sample (Chernak et al., 2009).
Repetitions demonstrated that buckling has a significant influence on peak strength, with samples being consistently weaker when buckling occurred during deformation (Figure 2).Due to the influence of buckling on peak strength, we will focus on the mechanical data and the microstructures of four plagioclase and two epidote samples, which are devoid of buckling.

Mechanical Data
After a first linear increase in differential stress with strain, the aggregates reached their respective yield points, marking the transition from nominally elastic to inelastic deformation.Yielding of the aggregates starts at axial strains >5% (Figure 3a).After reaching peak stress, the aggregates reveal different stress-strain evolutions.
Throughout the presentation and discussion of the mechanical data, we will use the maximum or peak stress, the aggregate supported during deformation, as their strength.In the light of the conservative uncertainty in stress of 100-200 MPa, the epidote aggregate may be modestly stronger than the plagioclase counterpart deformed at 650°C with 5 × 10 5 s 1 (Figure 3b).When deformed with a slower strain rate of 5 × 10 6 s 1 , the strengths match within uncertainty.
The plagioclase aggregate with a grain size of 90-135 μm, which was deformed under 550°C with 5 × 10 5 s 1 , exhibits the largest peak stress of ≈2,000 MPa and is the strongest of all tested aggregates (Figure 3b).Within the uncertainty in stress, there is no significant difference in strength between the other three plagioclase aggregates that all show peak stresses of ≈1,400 MPa, but a variable extent in post-peak strain softening.Strain softening is most pronounced in the plagioclase aggregate with a grain size <25 μm deformed at 650°C with 5 × 10 6 s 1 and least remarkable in its counterpart, deformed with 5 × 10 5 s 1 (Figure 3b).
Successful tests on epidote aggregates were all conducted on samples prepared from powders with a grain size <25 μm at 650°C (Figure 3b).The epidote aggregate deformed with 5 × 10 5 s 1 shows deformation at a constant stress of ≈1,800 MPa until deformation was stopped at ≈32% axial strain.In the light of the stress uncertainty, both epidote aggregates show similar peak stress values.The epidote aggregate deformed with a strain rate of 5 × 10 6 s 1 exhibits a slight decrease in stress with strain (≈50 MPa/4%) before, at ≈14% axial strain, stress drops by ≈750 MPa over ≈2.5% strain.From 16% axial strain until the end of deformation at ≈30%, stress steadily increases to ≈800 MPa.

Microstructural Data
The microstructures of the recovered plagioclase samples exhibit no sign of reaction confirming the assumption of slow reaction kinetics (Figures 4-6; Figure S2 and Table S1 in Supporting Information S1).In contrast, both epidote aggregates reveal the nucleation and growth of new phases in BSE mode (Figures 7 and 8; Figures S3-S6 and Table S2 in Supporting Information S1).One phase occurs as lens-shaped patches of various sizes, that is, from less than a μm to a few μm in diameter, and appears darker than the epidote matrix in BSE mode, indicating a composition contrast (Figures 7 and 8).At high magnification, this dark phase seems to be composed of at least two different phases-a brighter phase forming nanometer-sized needles dispersed within a darker matrix (Figure 7; Figure S3b in Supporting Information S1).Chemical analyses of these reacted zones differ substantially (Figure S3 and Table S2 in Supporting Information S1).The determination of the chemical composition of these phases is hampered by the inter-growth of different phases and their heterogeneous distribution on such a small spatial scale (Figure S3 in Supporting Information S1).In addition to these two inter-grown phases, we observe another new phase that is much brighter in BSE mode than the epidote matrix and forms sub-micron grains in the epidote aggregate deformed with 5 × 10 5 s 1 (Figure 7).Such a bright phase is also present in the epidote aggregate deformed with the slower strain rate, but it exhibits grains of several micrometer in diameter, analyzed as garnet containing ≈60% of the Fe(III)-rich garnet andradite and ≈40% of grossular (Figure 8; Figure S3c and Table S2 in Supporting Information S1).Due to the similarity in brightness contrast, we assume that the sub-micron-sized phase in the aggregate deformed with 5 × 10 5 s 1 is garnet as well (Figure 7b).Further, in the microstructure of the epidote aggregate deformed with 5 × 10 6 s 1 at 650°C, minor amounts of a phase, appearing even brighter than garnet, have been found and this phase most probably magnetite or hematite.
Using the software ImageJ (Abràmoff et al., 2004), we estimated the reaction progress of both epidote aggregates.The aggregate deformed with a faster strain rate of 5 × 10 5 s 1 shows a reaction progress of ≈5%, which is almost exclusively evidenced by the growth of the dark-appearing patches, whose compositions we were not able to identify, and an accessory phase (<1%) assumed to be garnet (Figure 7b).When deformed with a slower strain rate of 5 × 10 6 s 1 , the epidote aggregate shows heterogeneous reaction with areas exhibiting a reaction progress ranging from ≈10 up to ≈20%, in which a network is formed by the reaction products garnet, most likely an Fe-oxide (hematite or magnetite), and the dark-appearing patches (Figure 8).In both samples, the dark-appearing patches seem to be stretched around epidote grains (Figures 7 and 8).
Epidote grains in the aggregate deformed at 650°C with 5 × 10 5 s 1 reveal microcracking, with cracks forming at least two different sets, intersecting at ≈90°, and are commonly oriented at ±45°relative to σ 1 (Figure 7).From these microstructural observations, we deduce that deformation was mainly accommodated by microcracking and slip along cleavage cracks as well as by straining of the dark-appearing patches.
The plagioclase aggregate with a grain size of 90-135 μm that was hotpressed at 550°C and deformed with 5 × 10 5 s 1 shows the highest microcrack density (Figure 4).The hot-pressed only aggregate and the plagioclase aggregate with a grain size of 90-135 μm, deformed with 5 × 10 6 s 1 , show a similar amount of microcracks.In crossed polarized light, we neither observe a difference in the amount of undulous extinction nor mechanical twinning in the deformed plagioclase aggregates relative to the reference sample, recovered after the hot-pressing stage (Figures 4b, 4d,  and 4f).Relative to the hot-pressed aggregate, the aggregate with a grain size of 90-135 μm, deformed at the slow strain rate of 5 × 10 6 s 1 , shows more plagioclase grains that seem to be aligned with their long axis normal to σ 1 (Figure 4e).Zones of extensive grain-size reduction down to the sub-micron size are present, regardless of the aggregates' grain size and the experimental conditions (Figures 5 and 6).These zones are most abundant in the plagioclase aggregate with a grain size of 90-135 μm deformed at 550°C, in which they form subparallel bands along zones of highest shear stress, that is, 45°t oward the direction of maximum compression (Figures 5a and 5c; Figure S2 in Supporting Information S1).Due to the absence of strain markers, we can, however, only suspect their genesis by shear and will thus describe these features as structures resembling shear zones in the following.These structures resembling shear zones appear slightly brighter in BSE mode, which, in general, indicates variations in chemical composition (Figures 5a, 5c, and 6a; Figure S2 in Supporting Information S1).However, using EDS, we did not find any significant change in chemical composition between these domains and the initial plagioclase chemistry (Figure S2 and Table S1 in Supporting Information S1).Some plagioclase grains survived extensive grain size reduction but show pronounced microcracking, with cracks that show some preferential orientation, but-unlike cleavage cracks-these cracks are tortuous (Figures 5b and 5d).Occasionally, some of these highly cracked grains exhibit subparallel bands, which formed within the grains and are strikingly similar to the structures resembling shear zones (white arrows in Figures 5c and 5d; Figure S2 and Table S1 in Supporting Information S1).Regardless of grain size and the experimental conditions, we propose that beyond the yield point, deformation was mainly accommodated by grain-scale cracking and extensive grain-size reduction leading to cataclastic flow.
The porosity of the hot-pressed and the deformed aggregates was estimated by image analysis of plane polarized light images of thin sections in combination with BSE images of polished rock and thin sections using ImageJ  (Abràmoff et al., 2004).The estimation of initial porosity as well as its amount after deformation is complicated by the presence of cracks, which opened during quenching and decompression of the aggregates.We therefore expect that the amount of porosity, present prior to and during deformation, is overestimated by the analysis of the recovered aggregates.For the plagioclase aggregate with a grain size of 90-135 μm hot-pressed at 550°C, we estimated a porosity of ≈25% (Figure 4a).Regardless of temperature and strain rate, the estimated porosities of the deformed plagioclase and epidote aggregates range between ≈1% and 5% for aggregates with an initial grain size of <25 μm powders and between ≈10% and 30% for aggregates with an initial grain size of 90-135 μm.Similar estimated porosities between the epidote and plagioclase aggregates of the same grain size show that compaction appears to be equally efficient in both materials.Further, compaction is higher in powders with a smaller grain size of <25 μm compared to powders with a coarser grain size of 90-135 μm.Plagioclase aggregate deformed at 550°C with 5 × 10 5 s 1 .(e and f) Plagioclase aggregate deformed at 550°C with 5 × 10 6 s 1 .For the deformation samples, the direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.

Discussion
Porosity and the onset of reaction are both factors, influencing the strength of an aggregate.To evaluate if strength contrasts between epidote and plagioclase are real or altered by variations in initial porosity and/or the observed yet undesired breakdown of epidote, we will separately discuss the potential impact of these two factors in more detail below.We will then continue discussing the overall deformation behavior of our samples and how our experimental results could be linked to nature.

Influence of Porosity on the Relative Strength Between Epidote and Plagioclase Aggregates
We observe that compaction or densification is primarily controlled by grain size and appears to be independent of the studied materials, that is, epidote and plagioclase aggregates with the same initial grain size show similar densification.This similarity in densification could highlight a similar deformation behavior, which is supported by the mechanical data, showing epidote aggregates being only modestly stronger compared to their plagioclase counterparts (Figure 3).It has been previously demonstrated that porosity plays an important role for the compressive strength of rocks deformed under Hp/HT conditions (e.g., Hirth & Tullis, 1991;Renner et al., 2007;Xiao & Evans, 2003) as well as on the distribution of deformation and thus for the brittle-ductile transition (Hirth & Tullis, 1989).In fact, buckling may have been facilitated in heterogeneously porous aggregates and likely applies to the variability in stress-strain evolution, too (Figure 3a).Renner et al. (2007) showed that strength hardly decreases with increasing porosity from <1 to up to 8% (see Figure 6 in Renner et al. (2007)).We are therefore confident that porosity had no to only minor influence on the strength of epidote and plagioclase aggregates with a grain size of <25 μm showing similar porosities of ≈1%-5%.However, with ≈10%-30% estimated porosity for the aggregates with an initial grain size of 90-135 μm, the strength of the coarse-grained samples are possibly underestimated (Renner et al., 2007;Xiao & Evans, 2003).We will therefore refrain from comparing strengths between samples with a different initial grain size.

Breakdown of Epidote and Its Potential Influence on Aggregate Strength
Against our a-priori considerations on phase stability, epidote was not stable during our deformation tests.In fact, microstructural observations of epidote aggregates, which underwent buckling, demonstrate that epidote already started to react to form dark-appearing patches when deformed at 550°C with 5 × 10 5 s 1 , that is, at the coldest experimental conditions and shortest run durations, demonstrating that reaction kinetics were faster than we expected.
The two epidote aggregates deformed at 650°C with either 5 × 10 5 s 1 or 5 × 10 6 s 1 show a different reaction progress that correlates with the respective time spent under conditions, that is, the reaction progress is with ≈20% larger in the epidote aggregate deformed with a slower strain rate (≈40 hr under conditions) than a reaction progress of ≈5% in that deformed faster with 5 × 10 5 s 1 (≈7 hr under conditions).These two experiments on epidote aggregates document that the breakdown of epidote transits through a metastable phase forming darkappearing patches (Figures 7 and 8; white arrows in Figure S6 in Supporting Information S1), showing an enrichment in Si and a depletion in Fe and Ca (Figure S3 and Table S2 in Supporting Information S1).The adjacent Ep appears brighter in BSE mode, indicating that the surrounding Ep grains most likely incorporated the released Fe and Ca (Figure S5 in Supporting Information S1).Furthermore, we observe cracks passing through the epidote matrix and continue through a dark-appearing patch, demonstrating that these patches must have formed during deformation (black arrow in Figure S6 of Supporting Information S1).An EDS analysis on a sufficiently large garnet gives: andradite 58 grossular 33 almandine 9 , matching with the expected garnet composition under oxidizing conditions (Figure 8; Figures S3c, S4b, and Table S2 in Supporting Information S1; see Figure 2 in Liou (1973)).The growth of andradite-rich garnet is expected for epidote breakdown at high temperatures and expressed by the reaction: epidote = garnet (grandite) + hematite/magnetite + anorthite + quartz + H 2 O (Liou, 1973).Our thermodynamic calculations demonstrate that garnet should only be stable if less than 2 wt.% aqueous fluid is present (Figure S1 in Supporting Information S1).The absence of anorthite and quartz is most likely the result of the relatively short run durations of only a few hours.We acquired several EDS analyses that plot close to the composition of anorthite and quartz (Table S2, Figures S3, and S4 in Supporting Information S1; Marshall (1996) indicating (a) that these analyses are mix analyses, (b) that the nucleation and growth of anorthite and quartz is slower than that of andradite-rich garnet, (c) or a combination of both.In contrast to Liou (1973), we observe grains that grew in the dark-appearing patches that reveal high contents and could therefore indicate the presence of corundum (Figure S3e in Supporting Information S1; analysis 18 in Table S2 in Supporting Information S1).Furthermore, the EDS analyses reveal elevated amounts of K in the dark-appearing patches (Figure S3 in Supporting Information S1).As neither the starting epidote nor the accessory magnesiotaramite contained significant amounts of K (Tables S1 and S2 in Supporting Information S1), it must have been introduced during sample preparation of the recovered deformation samples and most likely stems from the epoxy resin used (Table 1; Table S2 in Supporting Information S1).An EDS analysis of a structure appearing like a hole (analysis 16; Figure S3d and Table S2 in Supporting Information S1) shows the highest amount of K and thus further evidences that K has been introduced to the sample during sample preparation.
To significantly affect rock strength in a long-lasting manner, a reaction progress must be reached that allows the formation of a network build by the reaction product or products (e.g., Holyoke & Tullis, 2006;Jordan, 1987).Since the reaction progress is with ≈5% insufficient to create a network of reaction products in the epidote aggregate that only spent ≈7 hr under conditions, we suppose that the epidote-matrix remained the load-bearing framework and that reaction had therefore no significant impact on the strength of this aggregate (Figure 7).This assumption is further supported by the corresponding mechanical data of the epidote aggregate deformed at 650°C with 5 × 10 5 s 1 showing no pronounced softening that could be linked to reaction weakening taking place in the aggregate (Figure 3).In contrast, the mechanical data of the epidote aggregate, deformed with the slower strain rate and showing the formation of a reaction-product network (Figure 8), exhibits pronounced softening (Figure 3).It is possible that, by the time both epidote aggregates reached peak stress conditions, reaction had no influence on the deformation behavior of the bulk.Our recorded strength values would, therefore, reflect the deformation behavior of pure epidote aggregates.In case, the reaction progress was sufficient to influence bulk aggregate strength, we are underestimating aggregate strength due to epidote breakdown.Consequently, unreacted epidote aggregates would be even stronger than their plagioclase counterparts under otherwise identical conditions.

Deformation of Plagioclase and Epidote at High-Pressure, High-Temperature Conditions
All samples reveal differential stresses (σ d ) larger than the confining pressure (p c ) or minimum principal stress (σ 3 ) and thus plot above the Goetze criterion, that is, σ d = σ 3 (=p c ; thick horizontal line in Figure 2).Although only applicable as a rule of thumb, this criterion can be used to separate the semi-brittle regime from the plastic regime as it qualitatively marks the threshold between conditions under which deformation is dominated by microcracking (σ d > σ 3 = p c ) and conditions favoring crystal-plastic deformation (σ d < σ 3 = p c ;Evans & Kohlstedt, 1995).Except for the epidote aggregate that underwent extensive reaction (Figure 8), deformation was dominantly accommodated by brittle deformation such as grain-scale fracturing of plagioclase and epidote grains We observe the growth of a new phase, appearing darker than the epidote matrix.This dark phase is chemically very heterogeneous and seems to consist of several different phases, leading to mix analyses using EDS (Figure S3 and Table S2 in Supporting Information S1).We were therefore unable to identify these phases.The white rectangle marks the position of the high-magnification image shown in (b).(b) Some Ep-grains reveal bended cleavage planes and flexure is accommodated by cracking.The phase appearing brighter than the Ep-matrix and the unidentified phase, is most likely garnet.Ep, epidote; Gt, garnet.
as well as extensive grain comminution of plagioclase.We did not find any evidence for plastic deformation, but it may still play a subordinate role, for example, in the structures resembling shear zones in plagioclase aggregates (Figures 5c,6a,and 6b) or in the bent epidote grains (Figure 7b).Combining the information from the mechanical with the microstructural data, we state that deformation took place in the semi-brittle regime.This statement excludes the epidote aggregate, which shows a reaction progress of up to ≈20%.
Besides distributed microcracking, the plagioclase aggregates reveal cataclastic flow in zones of high shear stresses, that is, at 45°relative to σ 1 (Figures 5a, 5c, and 6a).Individual grains cannot be distinguished in these structures resembling shear zones, demonstrating that grain comminution was very effective.Showing an inclination of ≈45°toward σ 1 , the normal stress σ n acting on these structures resembling shear zones is ≈1,000 MPa (with σ 3 = confining pressure = 1,000 MPa and a differential stress of ≈2,000 MPa).We therefore expect that the high normal stress acting on these structures is likely to influence the amount of fracturing as it has been previously shown by for example, Mair and Abe (2011).In addition, the presence of two perfect cleavage planes in plagioclase-or feldspar in general-leads to easy fracturing along these crystallographic planes (Incel et al., 2020;Incel, Baïsset, et al., 2023;Marshall & McLaren, 1977;J. Tullis & Yund, 1992), which could further enhance grain comminution.In fact, amorphization in feldspar due to mechanical grinding is quite common and pointed out in several studies in the past (e.g., Pec & Al Nasser, 2021;Marti et al., 2020;Yund et al., 1990).Hence, it is possible that these structures resembling shear zones contain or even entirely consist of amorphous material.Evidence for easy fracturing along cleavage cracks can be found in the lense-matrix structure of the microstructures of the plagioclase aggregates (Figure 5).Grains that kept their initial shape all underwent extensive microcracking with cracks that are rather randomly oriented (Figures 5a, 5b, and 5d) whereas grains that were favorably oriented for cleavage cracking experienced grain comminution to various extents depending on their respective location in the shear-stress field of the sample (white arrows in Figures 5b and 5c).Another argument for high-stresses being the main cause for extensive grain-size reduction instead of displacement, is the occurrence of intra-crystalline bands filled with sub-micron-sized material, which cannot be the result of grain comminution, because (a) the outline of the plagioclase grain rules out any significant displacement along grain-scale fractures and (b) most bands do not cut through the entire grain (Figure 5d).
Plagioclase clasts of different sizes surrounded by a fine-grained plagioclase matrix, that is, a lens-matrix structure, is indicative for cataclastic flow (Passchier & Trouw, 2005).Our experimental results on the deformation behavior of plagioclase aggregates are in agreement with previous experimental studies on similar materials, revealing cataclasis to prevail over a broad range in pressure, temperature, and strain rate (Hadizadeh & Tullis, 1992;J. Tullis & Yund, 1992).Despite differences in grain size or starting material between previous and the present experiments (intact drill core vs. hot-pressed aggregate), previous studies report strength values similar to the plagioclase-aggregate strengths presented in this study.J. Tullis and Yund (1992) performed tests at 1 GPa and 500°C with a strain rate of 10 5 s 1 and report a strength value of ≈1,800 MPa (Figure 2c in J. Tullis and Yund (1992)), similar to the strength of ≈2,000 MPa, exhibited by the plagioclase aggregate deformed at 1 GPa and 550°C with 5 × 10 5 s 1 (Figure 3).The similarity in strength is also true for the tests conducted at 600°C by J. Tullis and Yund (1992) or at 650°C in this study.

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The applied laboratory strain rates, the aggregates experienced, are ≈8 to 9 orders of magnitude faster than assumed for natural deformation rates of ≈10 14 s 1 (Pfiffner & Ramsay, 1982).However, rock strength is supposedly insensitive to changes in strain rate in the semi-brittle regime (see Figure 9 in Kirby and Kronenberg (1984)), as the active deformation mechanisms such as cracking, dislocation glide, and mechanical twinning either show no or little rate sensitivity (e.g., Kollé & Blacic, 1983;Rowe & Rutter, 1990).For siliceous schists that experienced blueschist to amphibolite-facies conditions, that is, conditions that include the experimental pressure and temperature conditions, Masuda et al. (1995) document pull-apart (microboundinage) structures of albite porphyroblasts that show only slight undulous extinction and no evidence for dynamic recrystallization.These Figure 8. High-magnification image taken in BSE mode of the epidote aggregate, which was deformed at 650°C with 5 × 10 6 s 1 .The direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.We observe a similar amount of the dark, unidentified phase and much more of the phase, which appears much brighter than the Ep-matrix.Latter was identified as andradite-rich garnet (Figures S3, S4b, and Table S2 in Supporting Information S1).The reaction products form an interconnected structure.Gt, garnet; Ep, epidote.albite porphyroblasts contain epidote grains that underwent microboundinage to various extents.It therefore follows that deformation of both phases-albite and epidote-was dominated by brittle deformation mechanisms and that plastic deformation only played a minor role, pointing toward deformation in the semi-brittle regime.Our aggregates were deformed in the same regime and reflect a similar strength contrast between plagioclase and epidote with plagioclase being weaker than epidote.Furthermore, under green-to blueschist-facies conditions, epidote grains seem to mainly deform by cracking and only exhibit the onset of crystal plastic deformation in the surroundings of cracks, probably as a result of the high stresses associated with crack tips (personal communication with Anna Rogowitz).
Here, we only directly compare epidote and plagioclase aggregates with the same initial grain size, yet, during the first stages of plagioclase breakdown, epidote-group minerals will be initially much smaller than plagioclase.Thus, the newly formed epidote-group minerals may be weaker than the plagioclase-rich host rock, as diffusionaccommodated processes are likely to take place in the fine-grained epidote zones.Furthermore, epidote-group minerals may remain weaker than plagioclase if their grain growth is slow or even inhibited.Observations on deformed samples do not reveal any evidence for weakening associated with the growth of epidote-group minerals (Stünitz & Tullis, 2001).The microstructures of the deformation samples from Stünitz and Tullis (2001) show epidote-group minerals that are dissected and displaced along narrow shear zones filled with the remaining reaction products.These epidote-group minerals are significantly larger than the other reaction products located within the narrow shear zones as well as plagioclase.We suggest that due to the exclusive growth of epidote-group minerals at low reaction progress (Wayte et al. (1989), their growth is not inhibited by the other reaction products and, therefore, fast-at least in the laboratory.
Combining the present experimental results with natural observations, it seems that the partial breakdown of plagioclase cannot explain long-term weakening of the lower continental crust.Hence, other processes, probably requiring a pronounced reaction progress have to be evoked for weakening and strain localization.One previously discussed candidate could be the inhibition of grain growth, for example, as a result of Zener pinning in polyphase shear zones, which could stabilize diffusion-accommodated deformation mechanisms (e.g., Bercovici & Ricard, 2012;Herwegh et al., 2011;Mehl & Hirth, 2008;Ruh et al., 2022;Stünitz & Tullis, 2001;Warren & Hirth, 2006).

Conclusions
We experimentally demonstrated that, in the semi-brittle regime, epidote aggregates are either stronger than plagioclase aggregates with comparable grain size or show a similar strength.From our experimental data, which are in line with qualitative strength differences between natural epidote and plagioclase, we assume that a partial breakdown of plagioclase to epidote has no weakening effect on the plagioclase-rich lower continental crust.The postulated weakening and strain localization in reacting lower crustal rocks as a result of Zener pinning, requires an advanced breakdown of plagioclase, involving the nucleation and growth of reaction products other than epidote.

Figure 2 .
Figure 2. (a) Diagram showing the peak differential stress as a function of temperature, strain rate, and grain size for all conducted deformation tests.The hollow black and green circles indicate samples that underwent buckling during deformation; The solid black and green circles represent successful tests.p c = confining pressure.

Figure 3 .
Figure 3. Differential stress versus axial strain curves.(a) All six successful runs are displayed.(b) Only tests are exhibited that were conducted at p c = 1 GPa and 650°C on aggregates with a grain size <25 μm; Ep = epidote; Pl = plagioclase.

Figure 4 .
Figure 4. (a, c, and e) Micrographs taken in plane and (b, d, and f) crossed-polarized light of plagioclase aggregates with an initial grain size of 90-135 μm.(a and b) Plagioclase aggregate after 3 hr of hot-pressing at 550°C and 1 GPa.(c d)Plagioclase aggregate deformed at 550°C with 5 × 10 5 s 1 .(e and f) Plagioclase aggregate deformed at 550°C with 5 × 10 6 s 1 .For the deformation samples, the direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.

Figure 5 .
Figure 5. Images taken in BSE mode at the SEM of the plagioclase aggregate with an initial grain size of 90-135 μm, deformed at 550°C with 5 × 10 5 s 1 .The direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.(a) Low-magnification image showing on overview of an area showing the formation of structures resembling shear zones with remaining plagioclase lenses.White rectangle marks the position of the high-magnification image presented in (b).(b and c) Extensively fractured plagioclase around a fine grained plagioclase matrix.(d) Fine grained sub-parallel bands within a plagioclase host.

Figure 6 .
Figure 6.BSE images of recovered plagioclase aggregates.Regardless of grain size, temperature or strain rate, plagioclase dominantly deformed by grain-scale fracturing and extensive grain-size reduction.(a and b) High-magnification images of the recovered aggregate with initially <25 μm grain size, deformed at 550°C with 5 × 10 5 s 1 .(c) Plagioclase aggregate with a grain size of 90-135 μm, deformed at 650°C with 5 × 10 5 s 1 and (d) at 550°C with 5 × 10 6 s 1 .The direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.

Figure 7 .
Figure 7. BSE images of the epidote aggregate, deformed at 650°C with 5 × 10 5 s 1 .The direction of maximum compression (σ 1 ) is oriented perpendicular to the long edge to the images.(a) We observe the growth of a new phase, appearing darker than the epidote matrix.This dark phase is chemically very heterogeneous and seems to consist of several different phases, leading to mix analyses using EDS (FigureS3and TableS2in Supporting Information S1).We were therefore unable to identify these phases.The white rectangle marks the position of the high-magnification image shown in (b).(b) Some Ep-grains reveal bended cleavage planes and flexure is accommodated by cracking.The phase appearing brighter than the Ep-matrix and the unidentified phase, is most likely garnet.Ep, epidote; Gt, garnet.

Table 1
Chemical Composition of the Starting Material All tests were conducted at 1 GPa confining pressure.