Journal of Geophysical Research: Solid Earth

Quartz grain boundaries as fluid pathways in metamorphic rocks


Corresponding author: J. H. Kruhl, Technical University Munich, Tectonics and Material Fabrics Section, 80333 Munich, Germany. (


[1] TEM and SEM/FIB sequential imaging of quartz grain boundaries from contact and regional metamorphic rocks show that most of the grain boundaries are open on the nanometer scale. Three types of voids occur. (i) Roughly 40–500 nm wide open zones parallel to the grain boundaries. They are suggested to be caused by general volume reduction as a result of anisotropic cooling contraction at temperatures decreasing below ca. 300°C, the threshold temperature of diffusion in quartz and of decompression expansion at pressures decreasing below several hundred MPa. (ii) Cavities of variable shape and up to micrometer size along the open grain boundaries and (iii) cone-shaped, nanometer-sized depressions at sites where dislocation lines meet the open grain boundaries. The latter two types are generated by dissolution–precipitation processes. Open grain boundaries, cavities, and depressions form a connected network of porosity, which allows fluid circulation and may affect physical properties of the rocks. The same process is suggested to occur along grain and phase boundaries in other rocks as exemplified in this study, and it should be expected along intracrystalline cracks or cleavage planes.

1 Introduction

[2] Grain and phase boundaries are one of the most important features of crystalline material. They affect rheological and petrophysical properties of rocks, such as strength, resistance to cracking and corrosion, and fluid permeability [Aust et al., 1994; Mainprice et al., 1993] and provide information about the tectonometamorphic history of rocks [Vernon, 2004]. In metamorphic rocks, quartz grain boundaries are formed and changed by different processes. As an example, grain boundary migration as a result of dynamic and static recrystallization leads to straight grain boundary segments [Kruhl, 2001; Kruhl and Peternell, 2002], which occupy noncoherent but crystallographically controlled stable orientations [Kuntcheva et al., 2006; Liebl et al., 2007]. Noncoherent straight grain boundary segments are also reported from metals [Wolf and Merkle, 1992]. In general, the crystallographic control implies that the grain boundaries are compact structures that do not allow migration of fluids.

[3] TEM investigations on the structure of synthetic forsterite, K-feldspar, and YAG grain boundaries confirm the compact structure of grain boundaries [Heinemann et al., 2001, 2005; Marquardt et al., 2010]. Nevertheless, grain boundary voids resulting in material failure are not uncommon, for example, in metals, and are usually associated with applied stress [Hull and Rimmer, 1959; Shewmon and Anderson, 1998], growing under the influence of intracrystalline defects [Speight and Beere, 1975]. In experiments as well as in nature, nanometer-wide channels along triple-line grain junctions and voids are observed, which may allow pervasive fluid flow through otherwise compact crystalline material [Lee et al., 1991; Mancktelow and Pennacchioni, 2004; Watson and Brenan, 1987]. Diffusivity along the channels is regarded as dependent on fluid chemistry and grain and phase boundaries away from these channels are seen as nonpermeable structures [Hay and Evans, 1988; Watson and Brenan, 1987].

[4] In our TEM- and 3D FIB-SEM-based study, we present data from metamorphic rocks, which show that quartz grain boundaries from various geological environments are partially open to a large extent on the nanometer to micrometer scale and not preferentially along grain junctions. The voids along the grain boundaries form a connected network of pores. This possibly is a common phenomenon in low- to medium-grade metamorphic rocks.

2 Geological Setting and Samples

[5] Quartz grain boundaries from rocks with different P-T-t-deformation conditions and history were investigated: (i) quartzite from the contact aureole of the Ballachulish Intrusive Igneous Complex (Scotland) and (ii) from the surrounding regional-metamorphic Dalradian and (iii) quartz from granite of the northern part of the Aar Massif (Central Alps of Switzerland). For these regions detailed geological, petrologic, mineralogical, and structural studies exist [Frey et al., 1976; Voll, 1976; Voll et al., 1991].

2.1 Ballachulish Complex

[6] The late Caledonian Ballachulish Igneous Complex intruded the Dalradian metasediments at 412 ± 28 Ma [Troll and Weiss, 1991], long time after the regional metamorphism that affected the metasedimentary sequence (ca. 590 – 500 Ma). Conditions of metamorphism and deformation prior to and during intrusion of the igneous complex are discussed and summarized by Pattison and Voll [1991]. Peak temperatures of regional metamorphism are estimated at 400–450°C west and at ca. 550°C southeast of the intrusion, at a pressure of ca. 0.6 GPa. The temperature at the time of intrusion was probably as low as ca. 250°C and pressure down to ca. 0.3 GPa. During regional metamorphism and deformation clastic quartz grains of the quartzite developed mainly prism-parallel subgrain boundaries and recrystallized to an amount of 50%–90%. The recrystallized grains reach average diameters of 140 µm and are weakly deformed. Boundaries between recrystallized as well as host grains are sutured [Buntebarth and Voll, 1991; Figure 1a]. Late intracrystalline cracks are rare.

Figure 1.

Photomicrographs of quartzites from outside and inside the Ballachulish contact aureole and from the northern Aar Massif; crossed polars. (a) Appin Quartzite from Port Appin with sutured and flattened quartz grains from low-T regional metamorphism; sample B10-86. (b) Ballachulish contact, quartzite with weakly polygonal quartz grains, coarsened during contact metamorphism, and K-feldspar (Kf); sample 4874, section 2. (c) Locations of TEM foils cut across quartz grain boundaries and quartz–K-feldspar phase boundaries (broken arrows) and of serial sections (black arrows); same sample. (d) Granite from the Northern Aar massif; quartz (qtz) recrystallized during low-T regional metamorphism between coarse magmatic quartz (Qtz) sample KR4716.

[7] During and after the intrusion the maximum temperature in the wall rocks reached 750°C–800°C directly at the contact and ca. 500°C at distances of ca. 1.9 and 0.8 km, respectively, depending on the position in the aureole [Pattison, 1991]. With respect to fluid availability and fluid flow in the quartzite, Harte et al. [1991] conclude that (i) fluid developed during late stages of magmatic crystallization and was generated in pelitic and calcareous rocks, (ii) aureole rocks are strongly dehydrated, due to previous regional metamorphism, and show limited permeability, (iii) no widespread fluid flow and no system of hydrothermal fluid circulation was established. Based on thermal modeling, cooling of major parts of the aureole to 350–400°C during a period of roughly 1 Ma can be inferred [Buntebarth, 1991].

[8] Sample 4874 comes from a quartzite layer inside the Leven Schists along a forest road near Allt na Leachd. Because the sample location is at the univariant reaction curve muscovite = corundum + K-feldspar + H2O [Pattison and Harte, 1991] ca. 40 m east of the contact of the Ballachulish Igneous Complex, the sample experienced a maximum temperature of 655°C–670°C [Masch and Heuss-Aßbichler, 1991; Pattison, 1991] at a pressure of ca. 0.3 GPa. The elevated temperature led to grain coarsening of quartz with only weak grain boundary suturing [Buntebarth and Voll, 1991, Figures 1b and 1c]. The lack of deformation features indicates absence of deformation during and after contact metamorphism.

[9] The location of the two samples B5-86B and B10-86 of Appin quartzite is Port Appin, ca. 13 km southwest of the contact. Both samples experienced regional metamorphism and deformation at a pressure of ca. 0.6 GPa, with T-max of ca. 400°C [Buntebarth and Voll, 1991; Pattison and Voll, 1991], but no contact metamorphism. Relatively coarse grain boundary suturing and only rare weak polygonization (Figure 1a) indicate annealing after deformation.

2.2 Aar Massif

[10] The Aar Massif is composed of a variegated series of Hercynian basement rocks and of granitoids that crystallized at ca. 280 Ma [Frey et al., 1976]. All rocks experienced Alpine deformation and metamorphism in the Lepontine Metamorphic “High” [Trümpy, 1980], with temperatures increasing from 300°C in the north to 500°C at the southern margin of the Gotthard Massif [Frey et al., 1976]. South of Erstfeld the Alpine deformation of the late Hercynian Central Aare Granite led to polygonization and incomplete recrystallization of the millimeter-sized magmatic quartz grains (Figure 1d). Late intracrystalline cracks are rare. During prograde metamorphism of the granite at lower greenschist facies conditions water was available, as indicated by chlorite formation and wide-spread and coarse alteration of plagioclase. In addition, water was set free by quartz recrystallization [Voll, 1976].

[11] Sample KR4716 was collected from the central Aare Granite from a road cut at the dam of the reservoir Wassen, 8 km south of Amsteg and 1 km north of Wassen. According to this position and the distances to the 300°C and 500°C isograds of Alpine metamorphism, T-max was ca. 350°C. The maximum pressure during T-peak can be estimated as 0.2 – 0.3 GPa [Frey et al., 1976]. Lack of internal deformation features in the recrystallized polygonal grains (Figure 1d) indicates annealing after deformation.

3 Sample Preparation and Measurements

[12] Focused ion beam (FIB) sample preparation, transmission electron microscopy (TEM), and 3D slice and view imaging were performed at GeoForschungsZentrum Potsdam. Electron transparent foils used for TEM with the dimensions 15 × 10 × 0.150 µm were prepared from thin sections without glass cover. At an optical microscope scale, the grain or phase boundaries do not display any peculiarities such as unusual width. The foils were cut normal to the trace of the quartz grain boundaries on the surface of the thin section applying the FIB technique. The TEM ready foils are placed onto a perforated carbon membrane on a copper TEM grid. No further carbon coating of the foil was applied. Details of the FIB sample preparation for TEM use are given elsewhere [Wirth, 2004, 2009].

4 3D Visualization of Grain Boundaries

[13] The 3D cross section of a grain boundary between two quartz grains was possible through the “slice-and-view” application of the FEI Quanta 3D dual beam (FIB/SEM) machine at GFZ-Potsdam. For this procedure, we first deposited a 1.5 µm thick strip of platinum on top of the grain boundary of interest. Subsequently, we have excavated three trenches normal to each other along the sides of this protective layer of platinum, by sputtering Ga ions with the focused ion beam [Wirth, 2009]. Ion sputtering occurred using an accelerating voltage of 30 keV and beam current of 30 nA. The trenches were polished with a beam current of 7 nA, and the frontal surface was repolished using 1 nA. For the cross-sectioning, we have acquired 100 sequential images. After each image acquisition, 100 nm of material was removed by sputtering with the Ga ion beam. That is a step width of 100 nm. The beam current for sputtering was 1 nA. The images were acquired applying the electron gun (Schottky field emitter) in the secondary electron imaging mode using an accelerating voltage of 5 keV and beam current of 95 pA. The grain boundary 3D model was designed with the freeware software Fiji ( and the animation from the 100 images (see Supplementary Material) was created using iMovie.

[14] We have to emphasize that FIB sample preparation or the slice and view technique cannot and do not introduce artifacts like cracks or cavities to the specimen. This statement is based on the experience of approximately 3000 TEM foils sputtered with FIB from different materials and studied with TEM by one of the authors (RW).

[15] Transmission electron microscopy was performed with a Tecnai F20 X-twin TEM with a Schottky field emitter as electron source. The TEM is equipped with a Gatan Tridiem™ Imaging Filter GIF, a Fishione high-angle annular darkfield (HAADF) detector camera and an EDAX X-ray analyzer. Bright-field images are usually acquired as energy filtered images applying a 20 eV window to the zero loss peak. Quartz is very sensitive to electron irradiation damage. Therefore, at lower magnification images were generally acquired in the scanning transmission mode as high-angle annular darkfield images (HAADF), thus reducing the irradiation damage substantially. Most of the grain boundary images, bright-field as well as high-angle annular darkfield images, show the perforated carbon film, the FIB-prepared membrane rests on, as shadow image.

5 Observations and Results

[16] Geometry and crystallographic orientation of 25 grain boundaries from four samples were analyzed. The samples represent the three different geological environments described above: quartzite from high-T contact metamorphism (sample 4874), quartzite from low-T regional metamorphism close to contact aureole (samples B10-86 and B5-86B), and granite from low-T regional metamorphism (sample KR4716).

[17] Based on TEM images from foils prepared normal to the grain boundary plane (Figure 1c), in combination with polarized light microscopy, observations on geometry and crystallography of the grain boundaries are reported as follows.

[18] (1) In the high-T contact sample (4874) nearly all boundaries are partially open, with a width of 150 to more than 500 nm (Figures 2b–2d). These open grain boundaries are represented by two individual quartz surfaces separated from each other by a void. That means that in 2D the two grains meet along certain grain boundary sections, forming a “usual” grain boundary, and along other sections, a gap/void exists between the two grains (henceforth “open grain boundary”). In the three low-T regional metamorphic samples (B10-86, B5-86B, KR4716), the boundaries are also partly open with ca. 40 – 100 nm wide gaps (Figures 2a and 3a). Boundaries may be also marked by arrays of cavities with euhedral shape (see further below).

Figure 2.

HAADF TEM images of open sections of quartz grain boundaries. White bands (Pt) are protective layers of platinum covering the thin-section surface prior to FIB milling. (a) Sample B10-86 from low-T region outside the Ballachulish contact aureole; foil 2256. White arrows indicate short-distance curvature connecting straight segments of grain boundary. A small depression occurs where the grain boundary meets the thin-section surface. (b) Sample 4874, section 2, foil 2075. The grain boundary is weakly segmented into micrometer-long straight sections (white arrows). A small grain fragment is rotated into the open grain boundary (curved black arrow), probably during the process of thin-section polishing. (c) Same sample, foil 1935. A triangular cavity (c) bound by straight segments (white arrows) of one neighboring quartz grain occurs along the open grain boundary. A small depression occurs where the grain boundary meets the thin-section surface. (d) Same sample, foil 1933. Open grain boundary with cone-shaped cavities (c) on one side and euhedral crystal faces on the other side, connected by short-distance curvature (broken line arrow). Small cavities are developed where dislocations meet the open grain boundaries (white arrow). On the faces of the neighboring quartz crystals small quartz grains are grown (black arrow).

Figure 3.

TEM bright-field images of quartz grain boundaries. (a) Roughly less than 1–2 µm long and 100–200 nm wide open sections (white arrows) of quartz grain boundaries from low-T regional metamorphism outside the Ballachulish contact with several µm long straight closed segments (broken arrows). Sample B5-86B; foil 2436. (b) Dislocation line ending at the surface of a quartz grain forming an open grain boundary. A cone-shaped euhedral depression is visible around the dislocation line. Sample 4874, foil 1946. White contrast represents epoxy.

[19] The shapes of the grain surfaces along the open boundaries are polygonal, i.e., they form nm to several micrometer-long straight segments (facets) with only few degrees deviation in orientation (Figures 2a, 2b, and 2d). Larger differences in orientation are rare. The transition from one to the next facet is not absolutely sharp but curved over a distance of several nm (Figures 2a and 2d). On the one hand, this segmentation is similar to the one on the micrometer scale known from sutured quartz grain boundaries [Kruhl and Peternell, 2002]. On the other hand, this grain boundary geometry on the nanometer-scale does not appear self-similar as reported from micrometer-sized grain boundaries of metamorphic quartz [Kruhl and Nega, 1996] and as obviously also true for the micrometer-sized grain boundaries of the investigated samples (Figures 1a and 2b). In general, both sides of open grain boundaries run parallel to each other (Figure 2). Locally, opposite polygon corners suggest opening directions oblique to the trend of the boundary (Figure 4a). Phase boundaries between quartz and K-feldspar are also partially open (Figure 5a), with widths of ca. 110 nm (Table 1).

Figure 4.

(a) HAADF TEM image of an open quartz grain boundary with two additional polygonal cavities (hatched areas). Arrows indicate opening direction oblique to parts of the grain boundary. Sample 4874, foil 2096. Dark contrast with bubbles is due to epoxy filling the open grain boundary. (b) TEM bright-field image of one grain surface at an open section of a quartz grain boundary. Prism-parallel wall of open quartz grain boundary, segmented by short probably rhombohedral steps. Prism-parallel orientation is determined by diffraction pattern. Sample 4874, foil 1946. The epoxy-filled open part of the grain boundary is labeled ogb.

Figure 5.

(a) TEM bright-field image of an open quartz–K-feldspar phase boundary, roughly 100 nm wide. The generally curved boundary is built by smaller partly straight segments. Sample 4874, foil 2216. (b) TEM bright-field image of an open quartz grain boundary (ogb). The roughly 150 nm wide grain boundary at the thin-section surface (white double arrow), covered by a protective layer of platinum (Pt), opens toward the interior of the thin section. On one side the cavity develops euhedral shape (white arrows). The opposite side shows small cone-shaped depressions where dislocations meet the grain boundary (black arrows). Sample 4874, foil 1942.

Table 1. Measured Grain and Grain Boundary Data Based on TEM Imagesa
(a) Number of Sample and Thin-Section Area(b) Foil Number(c) Grain Diameter (µm)(d) Open Grain Boundary Width (µm)(e) Open grain- Boundary Width in Percent of Grain Diameter(f) Grain Boundary Length (µm)(g) Open Grain Boundary area (µm2)(h) Area of Cavities (µm2)
  1. a

    Grain diameters (c) are determined as the sum of the half-diameters of the two neighboring grains. Widths of open zones along grain boundaries (d) are measured as vertical distance between the faces of the neighboring grains. Since these faces generally run exactly parallel to each other (Figure 2), inaccuracy of measurement is not more than ca. 10 nm. Numbers in parentheses = widths of inclusions along closed grain boundaries, probably smaller than width of open grain boundary. Grain boundary length (f) is the total length of grain boundaries visible in the foil. Values in parentheses = closed grain boundaries. n.d. = not determinable. Volumes of open grain boundaries and of cavities per volume unit are based on grain boundary length determinations in thin sections.

4874-2(1)20895220.2840.05417.953 (5.984)1.4760.190
4874-2(2)19386380.2720.0439.284 (2.564)1.8280.445
Grain boundary area (mm2) / 1 mm3 quartz volume:3.282  
Open grain boundary volume (µm3) / grain boundary area (µm2) 0.257 
Cavity volume (µm3) / grain boundary area (µm2)  0.109
Open grain boundary volume (% of quartz volume) 0.084 
Cavity volume (% of quartz volume)  0.036
Grain boundary area (mm2) / 1 mm3 quartz volume17.755  
Open grain boundary volume (µm3) / grain boundary area (µm2) 0.123 
Cavity volume (µm3) / grain boundary area (µm2)  0.018
Open grain boundary volume (% of quartz volume) 2.184 
Cavity volume (% of quartz volume)  0.032
B5-86B(1)2436819(0.148) 12.000 (9.540)--0
B5-86B(2)2439595(0.069) 2.300 (1.967)--0
B5-86B(1)2441n.d.(0.073) 6.800 (4.800)n.d.5.706
B5-86B(2)24431.233n.d. 8.148n.d.18.544
Grain boundary area (mm2) / 1 mm3 quartz volume13.708  
Open grain boundary volume (µm3) / grain boundary area (µm2) -- 
Cavity volume (µm3) / grain boundary area (µm2)  0.829
Open grain boundary volume (% of quartz volume) -- 
Cavity volume (% of quartz volume)  1.136
Grain boundary area (mm2) / 1 mm3 quartz volume10.933  
Open grain boundary volume (µm3) / grain boundary area (µm2) 0.075 
Cavity volume (µm3) / grain boundary area (µm2)  0.024
Open grain boundary volume (% of quartz volume) 0.082 
Cavity volume (% of quartz volume)  0.027
4874-2 Kf-Qtz22163400.110 8.1540.8970
4874-2 Kf-Qtz22253200.044 4.8790.2150.070
    Average 0.05813.0331.1120.070

[20] (2) Cavities frequently occur along the open grain boundaries and only there. They can be easily recognized as deviation from parallel geometry of the opposite grain faces (Figures 2c, 2d, and 4a). Their geometry varies from small pockets to long sections of increased opening width and larger variously shaped regions of several times the “normal” opening width (Figure 5b). The boundaries of the cavities are crystallographically controlled, i.e., they are polygonal with facets parallel to specific crystallographic planes. Prism-parallel cavity boundaries are segmented by short oblique steps, probably in rhombohedral orientations (Figure 4b) as known from euhedral quartz grown in fluid-filled geodes or open fissures.

[21] From the animation generated with a stack of 100 pictures (see movie in the Supplementary Material), it is obvious that in three dimensions the larger cavities are interconnected and form channel-like structures which “migrate” along the grain boundaries and change in dimension and shape (Figures 6a–6f). Consequently, the cavities form a pathway for fluid percolation. Locally, small euhedral quartz crystals occur within the open grain boundaries and cavities (Figure 2d).

Figure 6.

Snapshots of the slice-and-view process along a grain boundary between two quartz grains (animation in the Supplementary Material). The image (a) indicates the initial setup for the slice-and-view process with the frontal and lateral grooves excavated with the FIB and also the place of TEM foil extraction. The trace of the grain boundary on the thin section is indicated by the dashed line on the images (a) to (e). Images (b) to (e) show the same grain boundary at different depths in 3D presenting different stages of grain openings and closings, with variation on the space between crystals (c). Note that in some places the boundary is truncated and develops a small step with a different orientation of the general grain boundary (d) and that grain boundary can be “healed” again (e). The image (f) is a 3D model of the space between the two grain boundaries based on the 100 images of the slice-and-view, showing “wave” behavior of these structures when observed in 3D. The view direction of this image is the same as of the snapshots and the animation. Sample 4874.

[22] A second slice-and-view animation composed of 100 individual images demonstrates the varying opening and closing of cavities in the third dimension along the quartz-feldspar phase boundaries (see animation in the Supplementary Material). Interestingly, the animation shows that the K-feldspar grain contains a series of cavities with changing diameter while quartz does not. In the 3D cross section of the grain boundary, it is also impressive to see how “fast” the position of the interface moves following the phase boundary and how quickly a grain boundary opens and closes. From the second animation, it is clear that we do not observe a “normal” phase boundary plane but a system of partly open sections of quartz and K-feldspar surfaces followed by closed phase boundary sections.

[23] (3) A third type of open space is represented by small depressions of the faces of the open grain boundaries (Figure 5b). These depressions are generally connected to lattice defects such as dislocations. Toward the defect, straight boundary segments are formed, which include angles of ca. 90°–120° (Figures 6 and 3b). Where several dislocation lines meet open grain boundaries each of them form small triangular grooves, i.e., cone-shaped grooves in 3D, which occur as a series of grooves along the otherwise straight boundary. Several dislocations may cause larger cavities that, again, show segmented outlines.

[24] (4) The grain diameters, widths of open grain boundaries, grain boundary lengths visible in the TEM foils, and the area of cavities have been determined for the four investigated samples, based on TEM images and thin sections (Table 1). Even if the 25 measured boundaries are not representative, they give an estimate of the porosity caused by open grain boundaries and cavities. The pore space of the open grain boundaries is ca. 0.082%–2.2%, that of the cavities ca. 0.027%–1.136%.

[25] (5) The widths of the open grain boundaries roughly correlate with the diameters of the two neighboring quartz crystals (Figure 7). Given the uncertainty of grain diameter determination, due to cut effects, this correlation appears significant. Boundaries from the high-T contact metamorphic sample with grain diameters of ca. 0.5–1 mm show opening widths of ca. 150–500 nm, whereas boundaries from two samples with low-T regional metamorphism and grain sizes of ca. 50–800 µm show only widths of ca. 40–100 nm (Table 1). All measurements follow the same trend. On average the widths of the open grain boundaries are ca. 0.058% of the half-diameter sum of the two neighboring quartz grains.

Figure 7.

Correlation between widths of 19 open quartz grain boundaries and grain diameters, based on data given in Table 1. Quartz from high-T contact and low-T regional metamorphism. The widths are determined based on TEM images (as shown in Figure 4a) as perpendicular distance between opposite parallel grain boundary segments, unless “opening” oblique to the segments is indicated. The grain diameters are calculated as sum of the half diameters of the two neighboring quartz grains, measured in thin section. The two broken lines indicate minimum and maximum width of open grain boundaries in percentage of the cell dimension a, as shown in Table 2. See text for details.

Table 2. Changes of Quartz Cell Dimensions in Relation to Temperature and Pressurea
Sample300 → 25°C0.3 → 0 GPa0.36 → 0 GPa0.214 → 0 GPaTotal ContractionContraction DifferencePercentage of a at 25°C / 0 GPa
  1. a

    Changes of quartz cell dimensions (Å) parallel a in both neighboring grains (= [a]) and parallel a in one and parallel c in the other neighboring grain (= [1/2(a + c)]) during cooling (reduction) below the diffusion threshold (ca. 300°C) and decompression (expansion) from the pressures at 300°C for the four analyzed samples to 0 GPa. Values are determined on the basis of data given by Kihara [1990] and Levien et al. [1980]. The third last column contains the total contraction that results from cooling contraction versus decompression expansion. The second last column shows the difference between contraction at boundaries perpendicular to a and c in neighboring grains and at boundaries perpendicular to a in neighboring grains (Figure 8b, gray). The last column contains this difference as percentage of the cell dimension a = 5.16 Å, taken as the average of the values given by Kihara [1990] and Levien et al. [1980] for 25°C and 0 GPa.

4874 [1/2(a+c)]−0.0188+0.01024  −0.008560.00242 [Å]0.047%
4874 [a]−0.0226+0.01162  −0.01098
B5-86B & B10-86 [1/2(a+c)]−0.0188 +0.01229 −0.006510.00215 [Å]0.042%
B5-86B & B10−86 [a]−0.0226 +0.01394 −0.00866
KR4716 [1/2(a+c)]−0.0188  +0.0073−0.011500.00279 [Å]0.054%
KR4716 [a]−0.0226  +0.00831−0.01429

6 Discussion

[26] There are some principal arguments that the “openings” along the grain or phase boundaries are not a FIB induced artifact as suggested by Trepmann et al. [2010]. The first is a geometrical argument. During FIB milling the Ga-ion beam has an extremely small angle of incidence (approximately 1.5°) with the sputtered surface, which means that the ion beam operates almost parallel to the desired surface. We know from numerous FIB-prepared foils that even nanopores are not opened or widened by the Ga ion beam. Very often the original surface is covered by redeposited Ga or sputtered material [Wirth, 2004, 2009]. A second argument derives from the nanometer-sized microstructures. Steps on the atomic scale can be observed in high-resolution lattice fringe images up to the surface of the grain boundary (Figure 4b). If the open grain boundary would have been sputtered by the Ga ion beam we would certainly see an amorphous layer right at the edge where the sample is thinner than 50 nm. This is because during sputtering Ga atoms are always implanted into the surface resulting in an amorphous surface layer of variable thickness, depending essentially on the average Z number of the target material, the accelerating voltage and the beam current used. Consequently, approaching a thickness of <50 nm (using a single beam FIB at 30 keV) the whole sample gets more and more amorphous. This was not observed here, as we observe diffraction contrast in the grains separated by the boundary. The third reason is that the 3D cross-sectioning along the grain boundary clearly shows the local variation of the widths of the open sections and cavities, where sometimes the open grain boundary closes and reopens again. In addition, all the open grain or phase boundaries are filled with epoxy, which was used to embed the sample. The presence of epoxy after FIB milling proves that open space must have been present prior to FIB sample preparation.

[27] The open grain boundaries are also not an artifact of thin section preparation. This is convincingly demonstrated in the animations from the cross sections normal to the grain or phase boundary planes and the varying width of the open sections in the 3D imaging (Figure 6). Grain boundaries show similar opening width along their entire exposed length (Figure 2). They do not open toward the thin section surface but in certain cases even toward the thin-section interior, where they form larger cavities (Figure 5b). Cavity walls are planar, i.e., most probably crystallographically controlled. New quartz crystals are grown within cavities (Figure 2d). No open fractures are visible, neither at the surface nor in the interior of the thin section.

[28] Since the observed partial opening of quartz grain boundaries is not an artifact of thin section or FIB preparation, it necessarily results from processes in the metamorphic history of the rocks. In order to understand these processes, it is helpful to keep in mind that three different types of open space occur: (i) approximately 40–500 nm wide zones that follow, with absolutely constant width, exactly the geometry of the grain boundaries, i.e., their polygonal structure (Figure 2), (ii) larger cavities of variable shape and up to micrometer size in the grains along their open boundaries, and (iii) cone-shaped, nanometer-sized depressions along the open boundaries, which are related to dislocations (Figure 3b). This spatial correlation already argues for the formation of the large as well as small cone-shaped cavities subsequent to the formation of the open grain boundary parallel zones. Geometries and widths of these zones are surprisingly uniform, principally because the samples represent different types of rocks that experienced different metamorphism and deformation.

[29] The widths of the open zones correlate with the diameters of the neighboring quartz grains (Figure 7). Even the contact metamorphic sample (4874) that experienced much higher maximum temperatures in the high-quartz field fits the trend. Like other minerals, quartz contracts during cooling and expands during decompression. Both processes are anisotropic. Under the P-T conditions of the analyzed samples, cooling contraction is generally stronger than decompression-expansion [Fei, 1995; Levien et al., 1980]. Consequently, the quartz fabric should open, preferentially at sites of lowest strength, such as grain boundaries. On the other hand, the open space should be simultaneously closed by the confining pressure above ca. 0.06 GPa [Schön, 2004] as well as by volume diffusion at elevated temperatures [Poirier, 1985]. Below a threshold temperature of ca. 300°C (“recrystallization temperature”) [Voll, 1976] diffusion in quartz is extremely slow and grain boundary migration is not observed [Buntebarth and Voll, 1991; Voll, 1976]. Voids would stay open because quartz shrinks during cooling and expands during decompression more strongly in a-direction than in c-direction [Fei, 1995; Levien et al., 1980].

[30] In a simplified conceptual model, we consider the crystal structure of quartz to consist of three orthogonal axes c, a, and a (Figure 8a). In arrays of such quartz grains with the different axes being randomly but exclusively parallel oriented, the c axes of one ninth, the a axes of four ninth, and the c and a axes of four ninth of the neighboring grains are parallel to each other (Figure 8b). These orientations lead to different volume reduction values because at a-a grain boundaries the volume reduction during cooling and decompression, i.e., the difference between contraction by cooling and expansion by decompression, is larger than at c-c and a-c boundaries (Table 2). In sintered porous metal powder, below ca. 50% porosity the material gains measurable strength [Tharp, 1983] and in a crystal-melt mush a minimum of ca. 50% of the crystals are supposed to form a stress supporting network [Vigneresse et al., 1996]. In analogy we assume that in a situation of roughly 50% of closed grain boundaries the grains form a stress-supporting network and the remaining open boundaries would stay open. In our case all c-c and most a-c boundaries would be closed and mainly the a-a boundaries would stay open. During cooling from 300 to 25°C and decompression from 0.214–0.3 to 0 GPa (Figure 9), the gaps along a-a boundaries amount to a-a contraction reduced by approximately the value of a-c contraction, i.e., ca. 0.00242 Å for sample 4874, 0.00215 Å for samples B5-86B and B10-86, and 0.00279 Å for sample KR4716 (Table 2). These values correspond 0.047%, 0.042% and 0.054%, respectively, of the cell dimension a at 25°C and 0 MPa and are similar to the average percentage of measured width of open grain boundaries of 0.058% (Table 1, Figure 7). This shows that the model is in good agreement with the measurements.

Figure 8.

Conceptual 2D model of anisotropic volume change in quartz during cooling and decompression. (a) Quartz is considered to consist of three orthogonal axes a, a, and c. The anisotropy of cooling contraction and decompression expansion along c changes an original 2D quadratic shape to rectangular and the comparatively stronger cooling contraction leads to area reduction (gray). (b) Cooling and decompression related area reduction in a quartz grain fabric with random orientation of a and c axes. The shapes of the originally cubic grains change to rectangular in a-c sections. Mainly boundaries perpendicular to c (arrows) are kept closed by the confining pressure and boundaries perpendicular to a in both neighboring grains stay open (gray areas).

Figure 9.

Temperature- and pressure-related changes of quartz cell dimensions parallel a and c in both neighboring grains ( = ½(a + c) ). Stars and solid lines mark the reduction of the cell dimension during cooling from ca. 500°C to 25°C (after Kihara [1990]). The broken lines mark the expansion of the cell dimension during decompression from the initial P-T conditions as well as P conditions at 300°C (circles) of the four analyzed samples to 0 GPa (after Levien et al. [1980]). The different slopes of the curves already indicate that the effect of cooling contraction is larger than the effect of decompression extension.

[31] Most of the observed grain boundaries are partly open. It is important to note that the FIB-prepared TEM foil represents only a section of the overall grain boundary considered because of the dimension of the foil (15 µm × 10 µm × 0.150 µm). Even if the true amount of open grain boundary length is possibly smaller, due to nonrepresentative selection of measurement sites, a portion of ca. 50% as required by our model still rises the question “what holds the rocks together”? Currently the possible answer would be that the strength of the rocks is related to the remaining ca. 50% closed boundaries in connection with the interlocking of neighboring grains along their sutured boundaries. The locally changing structure of such a partially open grain or phase boundary is visible in Figures 6b–6e and in the animations in the supplementary material.

[32] The small cone-shaped depressions and the larger cavities were generated by dissolution processes. We assume the presence of a fluid in the open section of the grain and phase boundaries. It is unlikely that the open space would be filled by gases only. Where dislocations meet the grain faces along the open boundaries, which are sites of increased solubility of the crystal due to the local stress field around the dislocation core, small cavities are formed and follow the strain field of the dislocation cores (Figures 3b and 5b). Similar dislocation-related grooves (etch pits) are frequently reported from weathered crystal surfaces and related to increased solubility [Berner, 1978; Brantley et al., 1986]. Along the open grain boundaries larger cavities form wide bays with dislocations at their corners. At the transitions to the open grain boundaries crystal faces are frequently round. All this argues for the cavities being formed by dissolution through a fluid phase. Locally, small quartz crystals are attached to the cavities' boundaries (Figure 2d) and long prism-parallel boundaries are segmented by small rhombohedral steps (Figure 4b) as typical for quartz from geodes or open fissures. This indicates that not only dissolution was a significant process but also precipitation, as typical for metamorphic rocks. Fluid flow is expected to be high in all studied samples during prograde metamorphism [Harte et al., 1991; Voll, 1976]. Interestingly, the amount of dissolved as well as newly crystallized matter is small and we never observed any kind of “quench phase” from the dissolved material. The reason for that might be that (i) the grain boundaries opened during retrograde conditions and (ii) below 300°C and p < 0.5 GPa the solubility of quartz in aqueous solutions is very low [Manning, 1994]. As an example, the quartz solubility at 300°C and 0.1 GPa is ca. 600 ppm of Si per 100 parts of water [Morey et al., 1962]. This is in agreement with our model predicting grain boundary opening during cooling below 300°C, i.e., at temperature conditions where only minor amount of dissolution and reprecipitation is expected.

[33] The absence of any “quench” material in the investigated TEM foils might be explained by partial crack healing. It was experimentally demonstrated that microcracks in quartz can heal within hours at 600°C and 0.2 GPa [Brantley et al., 1990]. This could explain the absence of a “quench” phase and the occurrence of growth steps on some of the quartz surfaces. Another earlier experimental approach to microcrack healing also demonstrated the very rapid healing of quartz cracks in the presence of a fluid that can dissolve and reprecipitate quartz at comparatively low temperatures of 200°C–600°C at a pressure of 0.2 GPa [Smith and Evans, 1984]. It might be the case that parts of the open grain boundaries described in this paper have been partially closed again in the presence of a fluid and dissolved silica by a sort of crack-healing process.

7 Conclusions

[34] TEM imaging of quartz from a metamorphic contact aureole and from greenschist facies regional metamorphism shows that quartz grain boundaries are partly open. The opening probably results from general reduction of cell dimensions during decompression and cooling below the diffusion threshold of quartz (ca. 300°C), in combination with the anisotropy of volume reduction.

[35] In addition, dissolution leads to the formation of cavities along open grain boundaries. TEM analyses coupled with SEM/FIB sequential imaging along these grain boundaries demonstrate the presence of three different types of voids: (i) up to 500 nm wide openings with constant width; (ii) up to few microns-sized cavities of different shapes, and (iii) dislocation-related nanometer-sized and cone-shaped depressions. It is likely that the open grain boundaries form an at least partially connected network that generates permeability in the rock. This permeability, together with cavities in general, may have an important effect on the physical properties of these rocks, such as strength and shear resistance, fluid flow and reactivity, elasticity, storage capability, etc.

[36] Because the cell volume of any crystalline material is temperature and pressure dependent and because cooling contraction and decompression expansion of most of the minerals are anisotropic, the process of grain boundary opening, as described above for quartz, is expected to become common during cooling and decompression of all metamorphic and igneous rocks. The same process will also occur along phase boundaries and intracrystalline cracks or cleavage planes. During decreasing temperatures diffusion ceases in feldspars at ca. 500°C [Passchier and Trouw, 2005, and references therein; Voll, 1976] and in pyroxenes and amphiboles at uppermost amphibolite facies conditions as a minimum [Brodie and Rutter, 1985; Kruhl and Huntemann, 1991]. Since feldspars, amphiboles and pyroxenes are dominant in middle and lower crustal rocks, open grain and phase boundaries should be a common phenomenon. Widths of open grain boundaries will be even larger in volcanic rocks crystallizing at low pressures, i.e., without much influence of decompression expansion. This would most prominently affect basalts of the oceanic crust, with all consequences for their physical properties as well as transport of water into the upper mantle.


[37] We gratefully acknowledge the help of Anja Schreiber, who prepared all of the TEM foils with FIB, and Christian Stäb, who measured grain sizes and determined grain boundary orientations and areas. Thanks are due to Günter Buntebarth and Ludwig Masch for providing samples from the Ballachulish area and to Yves Bernabé and Richard Spiess for helpful reviews. The investigation was financially supported by the German Research Council under grant KR 691/33.