**4. Discussion of Data**

The data obtained in this study should be seen in the light of the most recent literature on the effects of shear stress on alpha quartz, literature to which the authors have also contributed [5,6]. The fractures we have observed show an evolution which, we believe, depends substantially on the stress rate rather than on the pressure itself. In fact, we have verified that even a pressure of 50 MPa, supplied in times exceeding one minute, generates a more intense fragmentation than a pressure of 100 MPa supplied in times of a few tens of seconds. The most relevant phenomena observed on quartz granules that have undergone increasing stress are as follows:


From Figure 4 it can be observed that the fracture length increases exponentially with the increase in the stress rate. This is reasonable, since the total length is related to the number of particles and this to the number of bifurcations of the cracks that are generated during the breaking of the quartz crystals. Cracks that reach critical speed tend to divide into two cracks (bifurcations) with an acute angle between them, as demonstrated by Tromans and Meech [13–15]. Consequently, if the stress velocity is greater, the cracks' opening speed will also be greater, and this will produce more fractures and a greater number of particles.

In Figure 6, the ridges indicate the presence of fractures under the surface. The crests indicate an increase in volume propagated linearly along the fractures. The fractures separate into two sections with an acute angle of 27◦. As is known, the angle of forking varies with the stress state. In particular, the bifurcation angle indicates the relationship between shear stress and normal stress τ/σ*n*. An angle of 27◦ corresponds to a ratio from −0.3 to −0.5, which essentially indicates a bending stress (Richter, 2003) [16]. Both the total length of the fractures and the amplitude of the bifurcation angle are parameters to be framed in a wider context of energy analysis of the fracturing phenomenon, for which the reader is referred to the cited bibliography. In this context, it is sufficient to remember that the fracture length is connected with the fracturing speed [13–15]. The cited authors calculate that in alpha quartz, the fractures split in two when the propagation speed reaches the *climit* (limit speed of 1990 m/s). At that moment, the ratio between the size of the new fracture, *ai* and the initial size, *a*, is equal to 2, and the speeds of the two daughter fractures is reduced to 30–50% of *climit*. The two fractures thus formed increase their speed and must again fork when they reach *climit* and at an *ai*/*a* ratio of 4, according to relation:

$$(a\_{\vec{\nu}}a)\_{\text{branch}\u{\mathfrak{h}}} = \mathfrak{Z}(a\_{\vec{\nu}}a)\_{\text{branch}\u{\mathfrak{h}}} = \mathfrak{Z}(a\_{\vec{\nu}}a)\_{\text{branch}\u{\mathfrak{h}}} = \mathfrak{Z}(a\_{\vec{\nu}}a)\_{\text{branch}\u{\mathfrak{h}}} = \mathfrak{Z}(a\_{\vec{\nu}}a)\_{\text{clinit}\u{\mathfrak{h}}}$$

It is important to note that an increase in the propagation speed leads to a higher frequency of bifurcations and therefore to a greater fragmentation. This is confirmed by the observations made with the analysis of the morphological image of the particles, where it is evident that a higher stress rate increases the number of particles and the total fracture length (Figure 4). It is noteworthy that the propagation of fractures in the minerals causes an accumulation of deformation energy, and this energy must dissipate; in mineral mechanics, the ways of disposing of the plastic deformation energy are essentially two: the bifurcation of fractures and, above all, the increase in temperatures in the deformation areas at the fracture tip [17,18].

The formation of the craters visible in Figure 7A–C is consequential to the propagation of fractures. In Figure 7A,B it is observed that the fractures end with a regular-shaped crater, often mimicking a crystalline form with five to six faces. The volume of matter removed from these craters seems independent of the visible (or superficial) length of the fractures. We believe that the loss of fragments of material with crystalline forms is linked to the presence of fracture lines already existing in the crystal, parallel to crystallographic directions. The reader should also note the correspondence between the apex of the fracture and the corresponding crater. We believe this is due to the undermining of the material by the wave at ultrasonic speed connected to the propagation of the fractures. Figure 7C shows the presence of surface bubbles that show cracks of about 40 nm width and lengths of about 1 μm. The bubbles also appear aligned, according to directions that lie at 60◦ with respect to the fractures. We believe that these bubbles are the superficial manifestation of the melting effect at ultrasonic speed that occurs inside the quartz grains during the crack propagation and which produces most of the phenomena we are describing. The same phenomenon is responsible for the formation of the craters aligned with the amorphous silica extrusions, visible in Figure 8, the silica extrusions in Figure 9, the recrystallized quartz from silica extrusion in Figure 10 and, finally, the filamentous fibers in Figure 11 that are, perhaps, the most interesting part of the discoveries made in this work. The Raman analysis performed on the silica fibers associated with the fractures shows that this silica is organized in the form of α-cristobalite and tridymite (Figure 12). The presence of cristobalite had already been highlighted by the authors of this work [5,6], where the structural changes of quartz in

nanocrystalline cristobalite were described when alpha quartz was subjected to shear stresses. In the aforementioned work, we have shown that the action of prolonged shear stress on the quartz crystals determines a reticular distortion so large as to lead the quartz itself to an amorphization; in this "amorphous silica", the radial distribution function analysis (RDF) has highlighted the formation of short-term clusters with a six-tetrahedron organization, similar to cristobalite and tridymite and no longer to four tetrahedrons [6]. It has also been shown that, if these amorphous phases are brought to 1200 ◦C, they tend to transform nano-cristobalite into a well-crystallized cristobalite, well visible in X-ray diffraction analysis [6]. The same association of minerals had been reported in a paper of Brodie and Rutter (2000) on quartz samples subjected first to tensile stress and then to heating at 1200 ◦C [17].

To explain the data collected, we hypothesized a mechanism that can materialize thanks to the speed of propagation of the fractures. The heart of the mechanism is tensile stress, which induces the opening of a large number of fractures in the quartz volume. Fracture propagation occurs at an estimated speed between 50% and 60% of the shear wave, therefore between 650 and 1000 m/s, and for this reason we can speak of ultrasonic speed. At these speeds, the fractures tend to fork after just 25–30 μm, and the crack tip transit times are therefore in the order of 30 ÷ 50ns. In such a short fraction of time, the amount of heat produced by the passage of the crack tip cannot have transferred to the volume outside the fracture. Weichert had already measured temperatures above 2000 K on the fractured quartz, and this has been confirmed by other authors [18,19]. These temperature increases generate channels of fused silica, which has a decidedly lower density than quartz (2.2 g/cm3 against 2.65 g/cm3). The decrease in density causes an immediate expansion in volume which causes surface fracturing. In actual fact, we can say that during the melting, the molar volume increases from 22.688 cm3/mol to 27.20 cm3/mol, with an expansion of 16.5% [19], more than enough to open the surface over the crack and bring out the fused and clotted silica filament that is inside it.

The events we have described are summarized in the diagrams in Figure 13. In the first one, we observe the simulation of the silica filaments growth, starting from the fractures; Figure 13B shows the formation of fractures ending with the euhedral craters and the formation of bullous-shaped growths. Figure 13C shows the pattern of crater formation ("hot spot") and silica protrusion from subsurface melted areas. Our data demonstrate that the friction action applied to quartz in totally anhydrous conditions leads to the formation of amorphous silica, which quickly organizes itself into nanostructures of cristobalite and tridymite [5,6]. Cristobalite has a structure consisting of rings with 6 tetrahedra, with structural arrangements that show an auxetic behavior, that is, with a negative Poisson's ratio [20,21] (Table 1). This means that a tangential compression produces a reduction in length in the normal direction and not an expansion, as expected from solids with a positive Poisson's ratio. The effect is particularly felt by the alpha cristobalite, whose Poisson ratio reaches the considerable negative value of −0.169. In practice, if the tangential contraction is 100 mm, the normal contraction will be 16.9 mm; this reduces the contact surface and correspondingly reduces its friction. It should also be taken into account that the phenomena whose generation we have verified are extremely fast, because they occur in the time interval that elapses during the final phase of propagation of the fractures. The speed of these contractions is linked to the propagation speed of the ultrasonic wave.

**Figure 13.** Scheme of propagation of fractures in quartz granules; (**A**) beginning of the phenomenon, as the fractures spread; (**B**) formation of fractures ending with the euhedral craters and superficial "elevations"; (**C**) formation of craters ("hot spots") and the protrusion of silica from the molten areas below.

**Table 1.** Mechanical parameters for silica polymorphs [13,14,20], G = Shear modulus, E = Young modulus, n = Poisson ratio, = density, ε = strain.


If the application of stress is continuous, there is an accumulation of amorphous silica that quickly transforms into cristobalite and tridymite near the fracture and sliding areas. The mechanisms described also explain the so-called "flash melting" which is observed by numerous authors in the shear stress tests on quartz and, above all, the sudden drop in the coefficient of friction that all the authors observe when the quartz is subjected to severe friction conditions [1]. Various authors support the thesis that the friction, exerted on quartz-rich rocks, generates a sort of silica gel lubricating film, an amorphous material rich in water, deriving from the environment where the test takes place. The concept of the lubricating gel is also taken up by [4], who had detected the presence of amorphous silica in the flow tracks of experiments by means of tribometric rotating friction apparatuses, such as the "pin-on-disk" on quartz [3,4]. Authors detected, via Raman spectroscopy, the peaks attributable to moganite (metastable phase of silica, quickly converted into cristobalite and tridymite) and to amorphous silica, as well as reticular distortions of alpha quartz. In addition, the authors showed spectra in FTIR microspectrophotometry to prove the presence of water in the amorphous silica of these traces of flow. The results obtained, albeit preliminary, do appear interesting. In particular, the fact that amorphous silica has hydrated with atmospheric humidity is possible, but it does not prove that it is the means of sliding the faults that insist on quartz-based rocks. In our tests, carried out under anhydrous conditions, there can be no water presence, but the same amorphous silica and cristobalite

and nanocrystalline tridymite are formed, which, as we have said, have the characteristic of reacting to efforts by decreasing the contact area, with relative reduction of the friction coefficient. At the end of this long discussion of data, we would like to summarize the events that, in our opinion, characterize the transformation of quartz into a low friction coefficient material:


In none of these events is the presence of water necessary.
