Direct Visualization of Grain Boundaries in Quartzites using Atomic Force Microscopy: Application to Study of Fluid Percolation in Continental Crust

Hydrous uids play a vital role in the chemical and rheological evolution of ductile, quartz-bearing continental crust, where uid percolation pathways are controlled by grain boundary domains. In this study, widths of grain boundary domains in seven quartzite samples metamorphosed under varying crustal conditions were investigated using Atomic Force Microscopy (AFM) which allows comparatively easy, high magnication imaging and precise width measurements. It is observed that dynamic recrystallization at higher metamorphic grades is much more ecient at reducing grain boundary widths than at lower temperature conditions. The concept of force-distance spectroscopy, applied to geological samples for the rst time, allows qualitative estimation of variations in the strength of grain boundary domains. The strength of grain boundary domains is inferred to be higher in the high grade quartzites, which is supported by Kernel Average Misorientation (KAM) studies using Electron Backscatter Diffraction (EBSD). The results of the study show that quartzites deformed and metamorphosed at higher grades have narrower channels without pores and an abundance of periodically arranged bridges oriented at right angles to the length of the boundary. We conclude that grain boundary domains in quartz-rich rocks are more resistant to uid percolation in the granulite rather than the greenschist facies.


Introduction
A number of mechanisms have been proposed in material and geological sciences to explain how uids percolate through a medium under ductile and brittle conditions [1][2][3][4][5][6][7][8][9][10] . Most postulated mechanisms agree that in a 3-dimensional material framework, grain/phase boundaries play a major role in uid percolation 7,11,12 . In the metallurgical and material sciences, it is well known that uid percolation leads to corrosion or cracking; to circumvent these effects, attempts have been made to impart certain bene cial characteristics to the grain boundary network and make the material more resistant, a process referred to as 'Grain Boundary Engineering (GBE)' 13,14 . In general, resistance to corrosion is controlled by the presence of 'Coincident Site Lattice (CSL)' boundaries between grains, which are basically high angle grain boundaries with additional periodic matches on lattice sites determined by a particular axis and angle of mismatch 15 which impart certain 'special' properties to materials. In such cases, it has been suggested that small deformation followed by annealing (single step or iterative) may improve grain boundary properties, by increasing the proportion of CSL boundaries 16,17 .
In the geological sciences, uid percolation has been investigated in mono-mineralic rocks like quartzites, as the mineral quartz constitutes much of the continental crust. Kruhl et al. 2 estimated variations in the widths of grain boundary domains in quartzites metamorphosed at different metamorphic grades using a Transmitted Electron Microscope (TEM). While TEM is a very high resolution and high magni cation technique, it is destructive in nature and involves an elaborate sample (wafer) preparation technique using a Focussed Ion Beam (FIB), which limits both its accessibility and convenience. In this study, we suggest Atomic Force Microscopy (AFM) as an alternative non-destructive method to study grain boundary morphology in geological materials. AFM enables nano-scale imaging of a sample surface directly from a thin section and gives additional information about the depth pro le. While surface morphology imaging using AFM is routinely used in Materials Science and Nanotechnology 18,19 , it has only rarely been applied in geosciences, e.g. to study in-situ dissolution precipitation of minerals such as barite, celestite and calcite and for studying calcite surface structure 20,21 . It has also been used to study grooving and wetting along grain boundaries in quartz during hydrothermal annealing 4 . In this study, we demonstrate direct visualization of systematic changes in grain boundary morphology in quartzite samples metamorphosed at different metamorphic grades using AFM. We show that high resolution imagery of grain boundary domains using AFM permits determination of grain boundary features with precision, and suggest that this technique may be used for relating the width of grain boundaries to uid percolation. Finally, we argue that these changes have implications for uid ow in the middle and lower continental crust.

Sample description
To eliminate variations originating from differences in mineralogy, seven relatively pure quartzite samples metamorphosed at different grades have been chosen for the purpose of this study. A polishing regimen similar to one used for Electron Backscatter Diffraction (EBSD) analyses has been used wherein the samples have been polished initially to a thickness of 30 microns on a polishing plate followed by polishing using colloidal silica for 6 hours to remove sur cial imperfections. The samples have been collected from the vicinity of a major terrane boundary zone in the eastern part of the Indian shieldspeci cally, between the Singhbhum Craton, the Rengali Province and the Eastern Ghats Province 22 (see Supplementary Figure S1). The tectonothermal histories as well as the geochronological evolution of these terranes have been described in detail elsewhere [23][24][25][26][27][28][29] . Samples collected during eldwork have been studied using a Leica DM-LP-4500 microscope. The metamorphic conditions experienced by the quartzites used in this study range from greenschist to granulite facies. RD 47 is an originally sedimentary quartzite metamorphosed under greenschist facies conditions, collected from the southern margin of the Singhbhum Craton. The quartz grains are polygonal in shape and evidence of strain retention is limited to Bulging Recrystallization (BLG) 30,31 along with Grain Boundary Area Reduction (GBAR). Comparatively high strain zones within the quartzite are characterised by sub-grain rotation (SGR) and the development of core-mantle structures, with larger relict grains of quartz surrounded by smaller, recrystallized grains (Fig. 1A).
Quartzites of the Rengali Province are signi cantly different in character from those in the Singhbhum Craton. The intensity of deformation, as well as the metamorphic grade is higher than that experienced by the samples from the Singhbhum Craton 32 . High grade (amphibolite to granulite facies) metamorphism of Archean age accompanied pervasive fabric formation and annealing, which was followed by intense shearing along the terrane margins of the Rengali Province under greenschist facies conditions around ~ 500 Ma 24 . In samples from a sheared quartzite unit of the Rengali Province (RN 178, RN 192 and RN 201), quartz shows evidence of widespread dynamic recrystallization which accompanied dextral strikeslip shearing under greenschist facies conditions 18 . Mylonitization and accompanying grain size reduction is a characteristic feature of these sheared quartzites (Fig. 1B). Rotated kyanite porphyroclasts in RN 201 survive within the sheared matrix and serve as shear sense indicators. Away from the sheared domains, the effect of shear-related recrystallization gradually diminishes. Quartz grains in RN 36 from the Rengali Province are equant in shape, show undulose extinction 30 , and largely preserve the earlier, annealed granoblastic mosaic texture (Fig. 1C), although the marginal parts are modi ed by Bulging Recrystallization during later shearing. The texture is characteristic of static recrystallization followed by annealing at high temperatures. In the interior of the Rengali Province, the quartzites show evidence of high temperature recrystallization without any subsequent low temperature overprint. RN 235 contains amoeboid grains (Fig. 1D) indicative of Grain Boundary Migration (GBM) 31 . RN 235 also contains sillimanite needles oriented along the long axis of quartz ribbons. Quartz grains within ANG 1, a quartzite collected from the Eastern Ghats Mobile Belt south of the Rengali Province shows chess-board extinction patterns consisting of rectangular subgrains with relatively straight boundaries characteristic of deformation above 550°C 30,33 .

Atomic Force Microscopy
Width data estimated from a total of 441 grain boundary segments is presented in Supplementary table S2 with average widths mentioned in bold at the end of each column and calculated population standard deviation values mentioned in red. Grain boundary width has been computed as the distance along a straight line between successive in ection points on the AFM curve (see The large difference in standard deviation values between samples metamorphosed at different grades is due to the development of pore spaces at triple junctions and along individual segments of grain boundaries. If these pores connect and create an inter-connected network, this could substantially ease percolation through these rocks. On the other hand, triple junctions in high grade rocks do not develop such pores but often consist of a comparatively wider boundary terminating at the junction of two comparatively narrower boundaries. While the average width is computed to be higher in the case of the statically recrystallized quartzite (RN 36), the widest grain boundary segments are present in the sheared (greenschist facies) quartzites which contain a number of pores along the grain boundary network, some of which are as wide as 1700 nm (see Appendix 1).
High magni cation imagery of the grain boundary domains reveals periodic 'bridge'-type structures that are otherwise undetectable both in thin section and at lower magni cations under the AFM (Fig. 2A). conditions. For the purpose of this study, boundaries between grains have been correctly identi ed and there are substantial morphological differences between grain boundaries as viewed under an AFM and sur cial features such as polishing effects. Scratches due to polishing are typically limited in horizontal and vertical extent and individual scratches are straight and typically a few microns long and only a few nanometers deep (see Fig. 2, caption). Grain boundaries, on the other hand are arcuate, with locally short straight segments that extend vertically for several nanometers, showing only slight variations in width with depth. The boundaries exist entirely between grains and have been traced horizontally over several microns to ensure that they are not artefacts, such as healed fractures. Optical microscopy con rms the absence of any evidence of brittle deformation within the grains. Table 1 presents the calculated deformation data using force-distance (FD) spectroscopy for ANG 1 and RN 171. It is to be noted that all the FD curves were generated by the same AFM tip and on the same day to avoid any change in the material of the tip due to ambient conditions. The deformation of the sample surface is signi cantly greater in the case of RN 171 compared to ANG 1, and this has important implications for grain boundary character. A total of 16 points in ANG 1 and 12 points in RN 171 have been chosen for the purpose of force-distance spectroscopy (see Table 1), and these points are evenly distributed across the interior of the grains as well as along grain boundary domains. The overall deformation of the surface due to interaction with the tip, in case of ANG 1, is signi cantly less than RN 171, in addition to variations in deformation within a sample depending upon the location of the point being analysed. Within ANG 1, the difference in degree of deformation between points on the grain boundary (containing bridge structures) and the interior of the grain is small (e.g. 62.  Fig. 3B) preserve a high degree of remnant strain in their microstructure, but most of it is restricted to intra-granular domains, away from grain boundaries. The statically recrystallized quartzite sample (RN 36, Fig. 3C) has the least remnant strain, since it was initially metamorphosed at higher, amphibolite facies conditions, and was in a low strain zone of the later greenschist facies shearing; only marginal effects along the grain boundary were impressed during this later event 18 . The quartzite recrystallized at high temperature (RN 235, Fig. 3D) has a signi cant amount of remnant strain in its microstructure, evidenced by dislocation build up within grains as well as a signi cant number of dislocation walls crosscutting grain boundary domains. The results of the KAM analyses indicate that the proportion of remnant strain does not necessarily accentuate grain boundary widths during polishing and sample preparation. The sheared quartzites have wider grain boundaries, and have strain concentrated in the grain interiors away from boundary domains; in contrast, the high temperature quartzite has narrower grain boundaries but a signi cant dislocation density near grain boundary domains.

Discussion
It has been suggested that open grain boundaries, cavities, and depressions can form a network which allows uid circulation in rocks 2,7,11,36−38 . However, such cavities and pores in rocks are not uniformly distributed 8,11,36,39 . During metamorphism, it is known that textural equilibration signi cantly modi es grain boundary geometry 30,40,41 ; however, there has been no systematic investigation as yet to determine if there is any correlation between the grain boundary width and the grade of metamorphism, which is one of the primary controls on rock texture, along with other factors such as the orientation of the grain boundary relative to local kinematics, stretching direction, or cavitation along speci c boundaries, to name a few. Textural equilibration is accompanied by attainment of equilibrium dihedral angles at triple junctions of grains 41 with a concomitant change in crystallographic orientations across grain boundaries; these changes are commonly determined by Electron Backscatter Diffraction (EBSD). During metamorphism, crystallographic re-orientation may in some cases lead to the formation of 'special' boundaries between grains, known as Coincident Site Lattice or CSL boundaries. The mechanical process of migration of uids along a grain boundary is controlled by the width of the channel, with a greater width facilitating easier uid transport along the channel. If some of these boundaries are CSL boundaries, they offer enhanced resistance to uid percolation along the grain boundary network 17,34,42,43 . Thus, in metallurgical and material science studies, the width of the grain boundaries, in terms of wider general boundaries and narrower CSL boundaries, are taken into consideration to model percolation behaviour in metals and materials 42,44 .
In this study, we estimated the width of the grain boundary domain using Atomic Force Microscopy (AFM), which also reveals other interesting morphological features along the boundaries. Comparison of grain boundaries in quartzites metamorphosed under conditions varying from the greenschist to granulite facies shows distinct differences. Quartzites metamorphosed under greenschist facies conditions have wider grain boundaries compared to those metamorphosed under granulite facies conditions. For all the dynamically recrystallized samples, the reduction of grain boundary width is correlatable with increasing metamorphic grade. This implies that lower grade rocks generally have wider grain boundary domains, with abundant pores along the grain boundary network, than high grade rocks, and are therefore more amenable to uid ow. The wide grain boundary domains in one apparently discrepant sample in this study (RN 36) can be attributed to the effect of modi cation of statically recrystallized grain boundary domains during the later lower temperature shearing event in the Rengali Province. Apart from the grain boundary width, an important morphological feature observed across the grain boundaries are the bridgetype structures detected with the AFM under high magni cation, suggesting enhanced bonding across these boundaries. These bridge-structures are exclusively observed along narrower grain boundary segments, and have not been previously documented with any alternative technique. The results of forcedistance spectroscopy provide more insight into the signi cance of these bridges. On grain boundary segments that contain bridges, the bridge domains show signi cantly less deformation on interaction with the AFM tip compared to the domains between the bridges. This suggests that there is a spatial variation in bond strength along these grain boundaries, being signi cantly higher across the bridges than in inter-bridge segments. Additionally, force-distance spectroscopy on one low grade and one high grade sample also suggests that bonding across grain boundaries in high grade rocks are signi cantly stronger than in low grade rocks. The enhanced bonding strength, and the presence of bridges across grain boundaries in high grade rocks increase the bulk strength of the rock and improve resistance to uid percolation; they may also be regarded as evidence for the existence of special (CSL) boundaries in rocks, similar to those reported in metals.
Since the present study attempts to relate grain boundary domains in metamorphic rocks of different grades to uid ow, it is pertinent to discuss if the grain boundary widths measured under ambient pressure temperature conditions are representative of the in situ situation at depth. Studies on quartz [45][46][47][48] show that volume reduction associated with decompression is anisotropic. This implies that quartz grains would undergo volume reduction as they cool through the brittle-ductile transition during uplift, with associated widening of grain boundaries. However, the results of this study argue that for high grade and low grade rocks, the situation should be different. The enhanced degree of bonding (manifested as bridges under an AFM) in high grade rocks would imply that the constriction of grains on either side of the boundary is limited, and does not necessarily in uence the boundary width itself. Additionally, strong bonds across a grain boundary would prevent the boundary from widening or forming voids due to decompression, to a much larger extent than boundaries across which the bonds are weak. The width of boundaries that contain bridge structures are therefore inferred to preserve their original widths from depth to the surface, and are not an artefact of exhumation. Thus, it appears that in quartzites, grain boundary widths reduce signi cantly with increasing metamorphic grade, with enhanced bonding at higher grades forming 'bridge-type' structures across the grain boundaries. Ultimately, this implies an increased resistance of channels in quartz-rich high grade rocks to uid ow, consistent with the relatively anhydrous character of the granulite facies. Enhanced bonding across most grain boundaries in high grade rocks reduces the degree of opening of grain boundaries on cooling and decompression, whereas the more limited amount of bonding in lower grade rocks means these boundaries open more; therefore, difference in observed widths re ect the difference in bonding and its in uence on grain boundary opening.

Conclusions
Atomic Force Microscopy allows comparatively easy, high magni cation imaging and precise width measurements along grain boundary domains within a rock. Within quartzites deformed and metamorphosed at different metamorphic conditions, those that are deformed at lower grades have wider grain boundaries with voids along the channels and at triple junctions and a much lower proportion of bridges compared to those that are deformed at higher grades. The latter have narrower channels, no voids along these channels, and an abundance of periodically arranged bridges oriented at right angles to the length of the boundary. The width of a grain boundary is not constant laterally and shows signi cant variability along the length of the boundary. The effect of the dominant recrystallization mechanism (dynamic vs static) on grain boundary widths has not been studied previously, and this study suggests that dynamic recrystallization results in much narrower grain boundaries compared to static recrystallization. Thus, dynamic recrystallization at higher metamorphic grades is much more e cient at reducing grain boundary widths compared to static recrystallization under similar or slightly lower temperature-pressure conditions. The concept of force-distance (FD) spectroscopy has been applied to geological samples for the rst time, and the results allow for a qualitative estimate of variations in strength of grain boundary domains and grain interiors within quartzites deformed at different metamorphic conditions. The results of FD spectroscopy demonstrate that high grade rocks are in general signi cantly less deformable compared to low grade rocks. Additionally, grain boundary domains containing bridges across them are less deformable compared to segments along which bridges are absent, irrespective of metamorphic grade. We suggest that the strength of grain boundary domains is higher in high grade metamorphic rocks compared to lower metamorphic grade rocks, and together with the other grain boundary features, contribute to enhanced resistance to uid percolation in granulite facies quartzites compared to those metamorphosed under greenschist facies conditions.

Atomic Force Microscopy
Surface morphologies of the seven quartzite samples were studied using an Atomic Force Microscope (Model 5100, Agilent Technologies).An Atomic Force Microscope images the surface of a 'material' based on minute variations in elevations of the sample surface relative to the deepest point that the AFM tip can probe for a speci c sample. A n doped -Silicon Nitride (PPP-NCL, Nanosensors Inc., USA) four sided AFM tip attached to a silicon cantilever, having a tip radius of curvature of 8 ± 2 nm, cantilever resonating frequency in the range of 180-250 kHz and force constant of 48 N/m, records the variation in topography at the surface. All AFM scans are obtained in intermittent contact mode (widely known as tapping mode) to ensure there is no damage made to either the AFM tip or the surface of the sample.
Scans have been generated by Raster Scanning at a speed of 0.3 lines per second. Since pure quartzites (containing more than 90% quartz) have been used in this study, all grain boundary width data relate to boundaries between adjacent quartz grains. Additionally, the quartzites have been studied under an optical microscope to delineate domains free of accessory minerals, and these domains have been further imaged using the AFM. The darkest zones are the deep trenches in the image and are obviously grain boundaries (see Fig. 2); depth pro les were obtained across them using the AFM. Grain boundary widths are then computed from these depth pro les.

Force Distance Spectroscopy
Force-distance spectra have been obtained using the AFM selectively over grain boundary domains. Details with regard to this technique have been outlined in Cappella and Dietler (1999). Out of several extractable parameters, which describe the sample surface with the help of Force -Distance (FD) Spectroscopy, a property known as 'Plastic Deformation' has been calculated in this study, which can qualitatively explain variations in intermolecular forces within the grain boundary domains, as well as variations in intermolecular forces between grain boundary domains and the grain interior. This is actually deformation that occurs and recovers gradually over time depending upon the elasticity of the material, and indicates that there is ongoing deformation at that particular point within the observation time-scale or time window during which the FD curves are being generated. Lesser deformation implies stronger grain boundary structures.

EBSD Studies
Electron Backscatter Diffraction (EBSD) data have been generated using a Zeiss-Auriga Compact system with a Gemini column Schottky type eld emission lament. EBSD pattern detection is carried out using an Oxford Nordlys detector. The EBSD analyses have been carried out using a voltage of 20 kV and a step size of 0.5 microns. Grains within the EBSD map have been delineated using a threshold angle of 10° and from indexed grains only. Raw EBSD data have been de-noised using a half-quadratic lter and the KAM threshold has been set as 2.5° to document sensitive local misorientations, which provide an estimate of the dislocation density in a region.

Declarations
Acknowledgments: RD  Author contributions: The idea of the work presented here was conceived by Saibal Gupta and Rabibrata Mukerjee. Ritabrata Dobe wrote the primary draft of the manuscript and did the EBSD work. Anuja Das performed all the AFM study. All authors looked through and worked on the nal draft of the manuscript, and approve the submission of the same.
Additional Information (including a Competing Interests Statement): None of the authors have any competing nancial or other interest.