**3. Results**

#### *3.1. Particle Size Distributions Related to Stress Conditions*

The sizes of the quartz particles show complex correlations with pressure undergone and linear correlations between the rate of increase in pressure and the average size.

The particle size curves (Figure 3) obtained from the tests show a distribution of variable shape:


**Figure 3.** CE diameter distribution curves of quartz particles (the meaning of CE is "circle equivalent"; the curves are obtained from the smoothing by average of 41 readings; the results are expressed in *x-y* graphs and not in histograms, due to the high number of reading channels; and gr is the weight of sample, e.g., 0.102 gr as grams, 102 mg).

Figure 4 shows the correlation between the total length of the fractures per unit of quartz weight (calculated on the basis of the total perimeter of the particles) and stress rate.

**Figure 4.** Correlation between the stress rate and total fracture length.

#### *3.2. Determination of the Morphological Characteristics of the Fractures*

The morphologies of the fractures in the quartz granules after the cutting effort are extremely varied and interesting, showing that the fracture phenomenon of this mineral is very complex and connected to a large number of parameters. We analyzed the data obtained from the analysis of the images, starting from the samples that underwent the least intense pressures, to end with those that underwent the greatest pressure.

In Figure 5, the fracture forms left on the quartz granules by stress rates of about 0.5 MPa/s are observed. Stress creates a first series of conchoidal-shaped fractures. Around it, there are "sawtooth" shapes of homogeneous dimensions. The average height of the teeth is 2.3 μm. The area filled with these teeth is extremely large and covers several hundred μm2. We initially thought that these forms were related to a Dauphine twinning; after careful examination we decided not to include this result, as it is still unclear. Dauphine gemination is however compatible with the stress regime to which quartz crystals are subjected in our experiments; in particular, Laughner et al. [12] demonstrated that the stress required to produce twins can be lower than 88 MPa. Since the strength of quartz on compression is 200–300 MPa, Dauphiné twinning generally precedes brittle fracture.

In samples subjected to stress of greater intensity and rate (5–50 Mpa/s), simpler fractures are generated that extend for distances from a few units to a few tens of μm. Figure 6 is a mosaic of eight photos taken on a quartz particles with some ridges and fractures. These fractures (Figure 6) show a profile raised above the surface with a vaguely triangular section and an average length of 20–30 μm from the beginning of the fracture until the first bifurcation, which invariably occurs at angles of 27◦. In larger grains, the fractures end with euhedral shaped craters of very variable sizes, from 150 nm to 1–2 μm (Figure 7). The shapes of the craters are regular, with hexagonal, square and trigonal geometries; only the smaller craters are elliptical (Figure 7). Most of these craters are aligned in directions inclined with respect to the direction of the fractures. These alignments reach conspicuous dimensions, often exceeding 100 μm. In some areas, where the density of craters is of the order of one every 2–3 μm, the craters unite and form open fractures, ranging from a few to ten μm wide and proportional lengths of up to 100 μm. In the fragments of the samples subjected to the maximum stress, the presence of "bubbles" is observed on the surface of the material with fractures on the surface (Figure 7C). These bubbles open in some places, forming small craters (50–100 nm), resembling real "hot spots" with a raised edge of apparently melted material (Figure 8). At the apex of some fractures, there are also real "protrusions" (Figure 9), while in rare areas, there are open fractures and craters filled with quartz crystals, that are elongated and small, with diameters of 0.5–0.8 μm and lengths of 1–1.5 μm, and often twinned (Figure 10). The same phenomenon can be observed in some open fractures, completely covered by newly formed quartz crystals, from which the crystals are arranged according to a design that mimics an exit direction of the precursor material. Along the fractures, detachments of filamentous material are observed, starting from the starting point of the fracture (Figure 11). These filaments are composed of silica alone. These fibers are characterized by diameters between 50 and 200 nm and lengths of from a few μm to tens of μm, and they follow the fractures until they detach, and, then, they can take on twisted, curled or meandering shapes. Their section is slightly flattened, almost as if they were ribbons. On the points of the greatest concentration of fractures, hundreds of these filaments are observed, which start from the fractures in a crystallographic direction and then tend to detach (Figure 11).

**Figure 5.** Sawtooth forms generated by the combination of two conchoidal fractures on the surface of the quartz granules; stress rate: 0.5 MPa/s.

**Figure 6.** Fractures on the surface of a quartz granule subjected to 100 MPa; the bifurcations show angles of about 27◦ (taken from the work of Martinelli et al. [5]).

**Figure 7.** Fractures in the granules at 150–200 MPa; in photo (**A**) the euhedral shapes of the craters at the apex of fractures of a few microns are well observed. Photo (**B**) shows the formation of several generations of fractures starting from the craters. In photo (**C**), there are open fractures formed by the coalescence of the craters that form at the end of the fractures; on the left, aligned bubbles, barely visible on the surface of the granules. In white, the apparent directions taken by the fractures, in black the visible directions.

**Figure 8.** Quartz, 120 MPa: "hot spot" on quartz particle surfaces.

**Figure 9.** Quartz, 220 MPa: amorphous silica extruded from a fracture on quartz surface.

**Figure 10.** Quartz, 230 MPa: crystallization and growth of quartz microcrystals from silica near fractures and hot spots.

**Figure 11.** Filamentous forms of silica that are an integral part of fractures of the type shown in Figure 6.
