1  

Phase Transformation and Nanometric Flow Cause Extreme Weakening During Faulting

SUPPLEMENTARY INFORMATION:

Post-Sliding Modifications of Sliding Surface of Dolomite High-Speed Experiment Surprisingly, in addition to the bare sliding surface exposed at the end of the experiment

on dolomite, a significant fraction of that surface was paved with small plates averaging about 100-200nm across (Figs. 1b; S1) that resemble paving stones in an old European city. The arrows in Fig. 1b point to places where the grooves in the sliding surface are either absent or muted in areas of plates, clearly showing that the plated surface was formed after sliding stopped.

White, approximately square areas in Fig. 1b (much larger in area than the bright pieces of dirt), represent places where EDS chemical analysis of the surface was performed. Fig. S1a shows the results of such analyses: The sliding surface has no carbon peak whereas the paved surface is carbonate. These observations show that the dolomite was broken down to oxides during sliding, that the reaction propagated into the interior away from the sliding surface, and that, after sliding stopped, CO2 escaped back to the sliding surface from continuing reaction beneath the surface and, possibly assisted by CO2 from the air, reacted with the oxides of the sliding surface to produce the undeformed magnesian calcite pavement (a similar paved surface was shown by Ref. 6). Figure S1b illustrates the “pores” through which CO2 that was generated below the surface accessed the surface (orange arrows, small pores; red arrows large pores), and also shows carbonate platelets forming at the expense of the nanocrystalline oxide sliding surface (yellow arrow). The larger pores are always at the perimeter of the paved surface hence their origin must in some way be connected to the surface reaction that creates the plates. The underlying process is not clear. The oxides in the sliding surface are much more dense than the carbonate plates so origin by tension does not appear likely unless it is an integrated effect of all of the surface tension in the grain boundaries of the paving “stones”. Conceivably, the crystals grow upward as they consume the oxide surface. Note also the grooved boundaries between the platelets; they are either deeply thermally etched or are the result of coalescence of individual calcite crystals growing with a rounded upper surface and only flattening out by surface tension when they impinge on other crystals. Even the areas of sliding surface without pavement appear to show some effects of this brief annealing after sliding stopped. The isolated, strongly rounded, almost spherical grains that stand out in relief in Fig. 1d (such as those with their diameters measured and many in the upper right corner) may have achieved their rounded shape when exposed to the warm surface immediately following termination of the experiment.

Foils for transmission electron microscopy were cut normal to the sliding surface in both pavement-free areas and paved areas by FIB44. The cross sections differed only by the upper 100nm that consists of larger carbonate plates (compare Fig. 2b, a cross section of unpaved surface, with Fig. S1c, a comparable cross section of a plated surface). As in the high-pressure fault, the sliding surface and the first ~200nm from the surface consist of a dense, equant, randomly oriented, nanocrystalline solid of the reaction products (in this case oxides).

The importance of the plated surface for this paper is that it demonstrates the highly unstable nature of the product oxides from this reaction. There are two important consequences for this. (1) This observation makes clear that preservation of some oxides in natural fault zones may be essentially impossible and (2) the recarbonation of the oxides (or rehydration of other oxides such as olivine in a serpentinite) can provide the necessary volatile-bearing phases for

S1b

Phase transformation and nanometric flow cause extreme weakening during fault slip

H. W. Green, II, F. Shi, K. Bozhilov, G. Xia, Z. Reches

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO2436

NATURE GEOSCIENCE | www.nature.com/naturegeoscience 1

  2  

transformation-induced weak gouge production in the next earthquake on a given fault. The minimum amount of volatile-bearing phases required to activate this process in a natural fault zone is not yet known but ~10% is sufficient to enable faulting in an experimental weakly-serpentinized harzburgite19.

High Pressure Faulting and Deep Earthquakes

Initiation of shear failure at high pressure in laboratory experiments requires generation of a small amount of low-viscosity material produced by a mineral reaction that both enables the instability that initiates faulting and lubricates sliding15,16. There are two types of such reaction that experimental and geophysical evidence strongly suggest are involved in earthquakes at depth: (i) A true fluid (eg. H2O, CO2, melt) released during devolatilization18,19,45or by melting21 is the leading candidate to explain “intermediate-depth” earthquakes (~50-350km)16,45. Production of this fluid leads to self-organization and failure of bulk material. (ii) Subducting slabs are essentially dry below 350km46,47 but another self-organizing mechanism is highly likely

Figure S1: Portion of sliding surface of dolomite specimen covered with pavement. (a) EDS analysis comparing paved and unpaved surfaces. (b) SEM image of edge of a paved region shows larger pores (larger orange arrows) between the “paving stones”, composed of carbonate, and the unpaved sliding surface composed of oxides, as well as smaller pores (smaller orange arrows) within and between paving stones as well as in unpaved surface. Yellow arrow points to a location where paving stones are replacing the original oxide surface. Note strong thermal etching of grain boundaries between paving stones. (c) FIB-cut cross section viewed in TEM showing larger carbonate “paving stones” overlying nanometric material. Compare with Fig. 2b.

S1c

 100nm

S1a S1b

  3  

in cold slabs in the Mantle Transition Zone (350-700km; P=12-23GPa) where olivine has been shown to be preserved in a metastable state in several subduction zones46,47 and where the deepest earthquakes occur46-48. The mechanism for this instability involves production of a nanocrystalline solid with a very low viscosity induced by runaway nucleation under growth-inhibited conditions when an exothermic polymorphic phase transformation with ∆V≠0 begins under stress15,16. This mechanism was discovered and explored during the transformation of olivine to spinel in Mg2GeO4

13-15,27,28,30 and further shown to operate in natural olivine during the olivine→wadsleyite transformation at 14GPa20 and in other exothermic polymorphic transformations17. The metastable olivine “wedge” required to enable this reaction has recently been imaged in the subducting slab beneath Japan47 and the deep earthquakes were shown to occur at the margin of or within the “wedge”. The experimental results involving the appropriate phase transformations, coupled with the seismically demonstrated metastable olivine in the MTZ (required for this mechanism) and the lack of any experimentally verified competing mechanism makes this transformation-induced faulting mechanism a primary candidate for the mechanism of these deepest earthquakes (350km-700km).

Figure S2 shows (a) conditions of faulting in Mg2GeO4; (b) a representative stress-strain curve accompanied by acoustic emissions; (c) lack of coherence of failure stress; (d) very low normal-stress dependence of sliding at 1µm/s on faults after their creation (µ = 0.1). Incoherence of failure stress is because the failure stress is not a property of the material but a competition between runaway nucleation within primary defects (anticracks and/or dislocation pileups) and their self-organization into a through-going fault.

Energy Budget for High-Pressure Fault Gouge

The average grain size in the gouge of high-pressure faults is ~10nm, hence, assuming quas-cubic shape, there are ~1024 grains per cubic meter and those grains will each have ~600nm2 of grain boundary. Each boundary is shared between two crystals, hence in bulk there is 3 x 1026 nm2 surface area per m3. Put in the context of our specimen, each square mm of the 70nm-thick gouge contains 7 x 1010 grains, with a total grain-boundary area of 2.1 x 1013nm2. The specific grain-boundary energy of Mg2GeO4 spinel (or olivine) is unknown. Therefore, for the purpose of rough approximation, we assume that the spinel phase has interfacial energy the same as natural silicate olivine (1.4J/m2 = 1.4x10-18J/nm2)47. We also assume that interfacial energy (a macroscopic parameter) does not change as grain size approaches the dimensions of a few unit cells). From these assumptions, we calculate that the grain-boundary energy per square mm of fault gouge is ~3 x 10-5J. The olivine→spinel phase transformation in Mg2GeO4 is exothermic. To calculate the heat released by the reaction under the conditions of our experiment (1.3GPa; 1200K), we use the thermodynamic data of Ross and Navrotsky50 and the procedure they provide on p. 478. These calculations yield a value of 7.5x104 kJ/m3 which corresponds to 5x10-6J per square mm of our fault gouge which is indistinguishable within uncertainty from the approximate value we calculate for the interfacial energy. This surprising result raises the tantalizing possibility that the grain size may be self-regulated by the amount of volume energy available for the transformation. At minimum, these results indicate that the surface energy generated consumes a large fraction of the energy provided by the transformation. This result is discussed in the main text.

  4  

 

a

Figure. S2: Mg2GeO4 faulting. (a) Phase diagram with conditions of faulting. Star represents conditions of deformation of specimen of Fig. 3 (Conf. Press.=1.3GPa). (b) Stress-strain curve (gold) showing typical yielding followed by strain softening, culminating in sudden failure and acoustic emission burst (blue). Note that AE initiation corresponds to initiation of stress drop but slightly precedes termination of stress drop showing that AE coincides with faulting but stress drop measurement is slightly delayed because stress is measured outside of high-pressure volume (see Supplemental text). (c) Stress at failure in faulting experiments (open symbols) and sliding resistance after faulting at sliding rate of ~1µm/s (filled symbols). Heavy line shows strength prediction assuming failure by overcoming static friction51; light line is least-squares fit to sliding resistance. (d) Sliding resistance data from (c) recast in terms of shear stress vs. normal stress on fault, hence slope of best-fit line is effective friction coefficient (µ = 0.1). a and b modified after ref. 52; c & d modified after ref. 14.

b

Confining Pressure (MPa)

Byerlee’s Law

c d

Normal Stress (MPa)

Stress Drop and Shear Heating of High Pressure Fault

Stress Drop: The extreme thinness of the fault zone in Figure 3 raises a question about whether the adiabatic approximation used in the text to estimate the friction coefficient is valid. None of the parameters necessary to calculate the exact answer to this question are known for Mg2GeO4. Moreover, the duration of the stress drop is below our ability to measure. The force on the piston in this apparatus is measured outside of the high-pressure volume by a load cell in series with the  

  5  

deformation piston. The signal of the stress drop is slowed down by the fact that inside the high-pressure volume, the Al2O3 piston that pushes on the high-P, high-T sample is surrounded by a soft salt, the tungsten carbide piston above it is surrounded by lead and there is a copper/brass sealing ring (lubricated by a thin film of MoS2) that stops the lead from squirting out the top of the pressure vessel. As a consequence, each of these parts is subject to at least the confining pressure (1.3 GPa in this experiment) on its surfaces and experiences frictional resistance as it moves in response to the specimen suddenly losing strength, at which time its elastic strain is converted to displacement on the fault as it forms. As a consequence, the measurement of the stress drop is abrupt and may be large but takes a couple of seconds to complete. Due to the foregoing, it is not possible to address the heat flow problem quantitatively. It is conceivable that in the future we can get a better measure of the speed of stress drop from the length of time occupied by major AE blooms in experiments in situ in the synchrotron28. Shear Heating: The temperature rise due to shear heating is given by: ∆T = µσnd/ρch (ref 29), where µ is the friction coefficient, σn is the normal stress, d is the slip distance, ρc is the specific heat capacity and h is the fault zone thickness. Thus, if ∆T is known, µ can be calculated from the observed geometry (Fig. 3). To put an upper bound on ∆T, we first use the experimental conditions under which this type of faulting occurs in Mg2GeO4 (Fig. S2a), the specific conditions of the specimen of Fig. 3, and a stress-strain curve that illustrates the correlation of acoustic emissions with stress drop (Fig. S2b). Second, we assume adiabatic shear heating because of the short duration of faulting and the poor thermal conductivity of Mg2GeO4. The conditions of faulting at 1.3 GPa confining pressure (star in Fig. S2a) are ~230K below the phase boundary, hence if ∆T in the fault zone were to exceed 230K, the spinel structure of the Mg2GeO4 would become unstable relative to its olivine structure, reaction would stop and sliding would be impossible at this high pressure because of loss of lubrication. We therefore make the conservative assumption that the temperature rise reached this maximum amount. The measured differential stress at failure was 1.5 GPa on top of a confining pressure of 1.3 GPa. We therefore conservatively set σn at 1.5 GPa. The observed fault offset, d, is 3 µm (Fig. 3a), the specific heat capacity, ρc, is 2-3 MPa/K (we use 3MPa/K) and the observed fault thickness is h = 70nm. Using these parameters and solving the shear heating equation for µ yields µ < 0.01.

This calculation restricts the temperature at the center of the fault zone to be no higher than that of the phase boundary. If we consider a less stringent constraint based upon the observation that the boundaries of the fault zone show no sign of olivine recrystallization, the upper bound on friction coefficient is doubled to µ < 0.02. Even this more conservative value is much lower than that displayed in high-speed friction studies, as shown in Fig. 1a and elsewhere2. Obviously, one could make even more conservative estimates, but no reasonable assumption is going to raise µ to the level of 0.1, which is the resistance we found when we allowed faults to slide at a rate of 1µm/s (Fig. S2d) and observed a significantly coarser grain size14. Thus, we conclude that the frictional resistance under this extreme normal stress is significantly lower than that measured in the high-speed friction experiment shown here and many others shown elsewhere2.

Additional Transformation-Induced Gouge Experiments Dehydration of Serpentinized Peridotite: Using transmission electron microscopy (TEM), we have also determined that high-pressure faulting as a result of devolatilization reactions such as dehydration of serpentinized peridotite (Fig. S3c) also yields a nanocrystalline gouge of the solid

  6  

 

 

 

 

 

 

 

 

 

 

 

 

 

  B

Figure S3: Additional Sliding Surface Types. (a) Melt-covered high-speed sliding surface of Sierra White Granite containing only small fraction of hydrous phases. Accordingly, during ELSE experiment analogous to the dolomite of Figs. 1 & 2, temperature rise due to shear heating continued to the melting point, resulting in a melt-covered sliding surface. (b) Detail of (a) showing tiny crystals in the upper left corner and the center of the image that grew on the surface at the end of the experiment. (c) Nanocrystalline fault gouge of serpentinite dehydration products. High-pressure experiment on serpentinized peridotite failed by dehydration embrittlement, producing a fault zone made up of breakdown products. Diffraction pattern (inset) shows diffraction rings from multiple phases with little or no preferred orientation. White lines along crystal grain boundaries reveal open boundaries. Whether or not they signify the presence of H2O on some boundaries at the end of the experiment, represent decompression cracking, or are TEM artifacts is not yet known (modified after ref . 19).

100nm

 

a b

c

30µm   5  µm  

  7  

reaction products18,19 that is similar to the higher-pressure fault zones resulting from solid-solid phase-transformation-induced failure (Figs. 3; S2) and the high-speed experiment on dolomite (Figs 1,2). The presence of this nanocrystalline, non-glassy, “gouge” within the fault zones of these laboratory dehydration experiments suggests that, in addition to release of fluid, such gouge may play a significant role in dynamic lubrication of crustal faults. This point was raised previously from results of certain high-speed friction experiments38. It is important to realize that such devolatilization reactions are another way that phase transformations can yield failure (and perhaps earthquakes in nature)42 when driven by bulk temperature conditions and can inhibit temperature rise to the melting point when driven by runaway shear heating – another reason why pseudotachylytes appear to be rare. Shear Melting of Granite: In materials that do not present a devolatilization reaction during shear heating, the temperature rise due to such heating has nothing to stop it from reaching the melting temperature, as observed in high-speed experiments on gabbro2 and shown also here in granite (Fig. S3a,b). Such shear melting experiments are experimental pseudotachylytes. There currently is a controversy in earthquake physics concerning whether pseudotachylytes are truly rare or only rarely observed. We believe that they are rare and that the mechanism proposed in this paper explains that rarity.

Grain Shape in Nanometric Gouge

In the characteristics of nanometric gouge, we make two comparisons in the text that may seem contradictory. We state that grains of the gouge are “rounded” and we also say that the gouge shows “no porosity”. Normally one would conclude that round grains would require interstices between them. However, the “rounded” shape we call attention to is largely a matter of scale. Figures 1c,d; 2b; 3b,c and S1c all show that the nanograins have a generally rounded shape when seen on a scale larger than an individual grain whereas Fig. 2d shows tight, approxi-mately planar, grain boundaries when the boundaries are examined directly (also shown in Fig. 2G of Ref. 11). Fig. S3c also shows that gouge grains are polygonal when imaged in detail.

Natural Fault Gouge (Punchbowl Fault, California)

See Figures S4 and S5 below.

                                   8  

 

 

A

A

A A

A A

Ti

Px

Q

Q Q

 c

4  µm  

Figure  S4:  Punchbowl  Fault.    (a,b)    Outcrop  showing   planar,   very   narrow,   fault   zone   and  gouge.     (c)   Back-­‐Scatter   SEM   image   of   gouge  showing   large,   porous,   post-­‐seismic   grain   of   K-­‐feldspar  (brown  outline)  that  has  engulfed  large  numbers   of   bright   nanometric   particles   of   the  original   gouge   and   protected   them   from  subsequent  hydrous  alteration.  Phases  identified  from   spectra   within   white   box   in   Fig.   S5.   (d)  Nearby   region;   post-­‐seismic   overgrowth   on   a  quartz   crystal  has  been   impeded  by  nanometric  original  gouge  grains  (arrows)  and  included  one  smaller   grain   (near   tail   of   left   arrow).   Q=qz;  A=albite;  Ti=sphene;  Px=  pyroxene.    

 d

b  a

  9  

 

Figure  S5:  X-­ray  maps  of  area  shown  in  white  box  in  Figure  S4.  Mineral  identifications  in  Figure  S4  are  derived  from  these  maps.  

Supplementary  References  –  Cited  only  in  Supplementary  Information  

45. Peacock, S.M. Are the lower planes of double seismic zones caused by serpentine dehydration in subducting oceanic mantle? Geology; 29, 299–302 (2001).

46. Green, H.W., Chen, W-P., Brudzinski, M. Seismic evidence of negligible water carried below 400-km depth in subducting lithosphere. Nature 467, 828-831 (2010).

47. Kawakatsu H., Yoshioka S. Metastable olivine wedge and deep dry cold slab beneath southwest Japan. EPSL 303:1-10 (2011).

48. Chen, W-P. & Brudzinski, M., Evidence for large-scale remnant of subducted lithosphere beneath Fiji. Science 292, 2475-2478 (2001).

49. Duyster, J., Stöckert, B. Grain boundary energies in olivine derived from natural microstructures. Contrib. Mineral. Petrol. 140, 567-576 (2001).

50. Ross, N. and Navrotsky, A. The Mg2GeO4 Olivine-Spinel Phase Transition, Phys. Chem. Minerals 14, 472-481 (1987).

51. Byerlee, J. Friction of rocks. PAGEOPH, 116, 615-626 (1978) 52. Green, H.W. Solving the paradox of deep earthquakes. Scientific American, Sept., 64-71 (1994).