**1. Introduction**

The possibility that fractured quartz turns into cristobalite and tridymite poses serious problems in the safe management of industrial milling. In the last twenty years, numerous laboratories have sprung up all over the world conducting experiments on rocks in the conditions of friction typical of technologies utilized in rock grinding. To a large extent, these experiments are carried out trying to correlate the friction coefficient with stress (tangential and normal), the speed and the spaces covered by the simulated fault [1,2]. At the same time, attention has grown towards the "dynamometamorphic" phenomena suffered by rocks and linked to stress: heating, gas dissociation, partial or total melting of the friction layers. In the recent past, several working groups have focused their attention on the role of quartz in the sliding phenomena of rocks, and the idea is that the heating of the contact surface by friction produces a partial melting of the material, the formation of a silica layer amorphous which is quickly hydrated by ambient moisture, which thus becomes a lubricating gel that drastically reduces the friction coefficient of the defects [3,4]. In a recent publication, we formulated another hypothesis to explain the lowering of the coefficient of friction in experiments on quartz-containing rocks. This hypothesis is based on the progressive formation of nanocrystalline cristobalite, which works as a solid lubricant [5,6]. The silica polymorph called cristobalite has the particularity of being an auxetic material, i.e., with a negative Poisson ratio, both in the form of low temperature (alpha) and in that of high temperature (beta). If a layer of cristobalite is found in shear conditions, it can reduce its contact area as a result of the volume contraction and equally reduces the friction coefficient.

The hypothesis is that quartz, subjected to a prolonged reticular distortion over time, tends to take on a structure with ever greater disturbance, but formed by cristobalite nanophases. This phase would be nanocrystalline, not visible by X diffraction but visible by Raman spectroscopy. The accumulation of this phase in the interface between the sliding surfaces would cause the friction coefficient to decay more or less rapidly, depending on the intensity of the dynamometamorphic action [6]. Furthermore, quartz's structural decay is marked by the decay of the electromagnetic signals generated by its fracturing, which diminishes over time as fracturing and damage of the original crystalline structure proceed [5,6]. A key element is missing in this theory: how and when the patina of cristobalite is generated. The purpose of present work is to contribute to a better understanding of the processes related to quartz tribochemistry.

#### **2. Experimental Procedure**

The task of this experimental work is to understand the mechanisms that link the progressive demolition of the crystal structure of quartz and the appearance of polymorphic phases during the application of sliding stresses. In two previous works [5,6], the authors of this work reported details on the polymorphic phases of silica that are formed during fracturing and on the correlations between fractures and the amount of very low frequency electromagnetic energy emitted by the crystals during the fracturing.

An innovative "piston cylinder" was used to carry out these studies. It is equipped with two steel pistons which compress the sample and which represent the armatures of a condenser, equipped with an insulating Teflon jacket, which allows the containment of the material. Thanks to Teflon, the pressure distribution exerted is anisotropic, and this is due to the materials that make up the cell itself. The materials that exert the pressure (stainless steel) and the containment material (Teflon) are different in terms of elasticity, coefficient of Poisson and compressive strength. This determines a condition of anisotropy in the exercise of compression: the mineral is not subjected to equal stresses in all directions, but greater according to the direction of the piston and less in the directions perpendicular to it. This anisotropy allows one to create a fracturing system by shear, which generates fractures favoring the development of a network of microcracks. The entire piston cylinder is first evacuated and subsequently subjected to an analytical grade nitrogen flow to ensure an anhydrous atmosphere. The system was created taking into account similar systems published in the past by various authors [7–10]. The pressure is applied through a motorized hydraulic press, which develops a maximum load of 4.9 kN.

The quartz-α samples come from natural quartz crystals, purchased at Ward (Ward, West Henrietta, NY, USA; www.wardsci.com), previously analyzed in optical microscopy to detect any defects, such as inclusions and fractures. The crystals were chosen in the weight range from 0.05 to 1.5 g. Each test generated powders and fragments that were analyzed for shape, size, area and volume, through the new Morphology G3ID image analysis system (Malvern, UK) based on optical scanning microscopy. The automated scanning system allows one to measure and analyze about 1 million particles per hour and to know the values of the perimeter, area and volume of each particle, from 300 μm to 1 μm. This scanning microscope has already been used previously by the authors for investigations on asbestos fibers in soils and recently on quartz crystals [5,6]. To determine the morphologies, the particles are dispersed on the surface of the optical plate. Scanning takes place at constant magnification on all particles following an *x-y* scanning mechanism; the depth of the particles is reconstructed through the "*z*-stacking" mechanism that allows one to shoot the same image of the particle on different focal planes.

In this work, we used the data of the optical scan to estimate the quantities of "new" surfaces generated by the fracture, the statistics on morphologies (equivalent diameter, area for every particle). These data were compared to the entity of the stress rate. The calculation of the real volume deserves special mention. The instrument software measures the volume by the diameter equivalent to the sphere (SE Volume), but this value is very far from reality. Therefore, we used an algorithm that is based on the measurement of the attenuation of the intensity of light transmitted by the particle. For non-scattering media, the Beer–Lambert law (BL, or absorption law) is well recognized to describe the relationship between transmittance and sample thickness as:

$$T = \exp(-\mu\_\text{a} d) \tag{1}$$

where *T* is the transmittance, *d* is the sample thickness, and μ<sup>a</sup> is the absorption coefficient (cm−1). This expression is based on the random nature of stochastic light absorption, characterized by the rate constant μa. Since the transmitted light intensity is measured for each particle, and since we are always in the presence of quartz, which has an absorption coefficient from 664 cm−<sup>1</sup> at 450 nm to 312 cm−<sup>1</sup> at 650 nm [10], the thickness "*d*" can be derived for all particles. Figure 1A shows the effect of fracturing on quartz grains; the images have been modified after Zhao, B. et al. [11]. On the left, we can see the two-dimensional projection of the particles obtained from the compression fracturing of a quartz grain. The perimeter of the granule, obtained from the two-dimensional projection, is expressed in green. The perimeters of the projections of the individual particles obtained from the fracturing are indicated in red. In Figure 1B, images of the original crystal, a tip weighing 207 mg and some of the particles obtained from the fracturing can be observed.

**Figure 1.** (**A**) Breakage of a grain: on the left, projection images of particles created by the breaking of first grain; on the right, original perimeter (green) and new perimeter (red). (**B**) On the left, the image of the original crystal fragment, 207 mg in weight; on the right, the 12 largest fragments of the left crystal; each fragment of the crystal, from 0.3 mm to 1 μm, was analyzed from the morphological and dimensional point; in total, the left crystal produced over 320,000 fragments; the black barindicates 150 μm.

The surfaces of the "internal" granules are, in fact, the new fracture surfaces, created when the imposed stress exceeds the critical stress level. The sum of the surfaces of the particles will be equivalent to the sum of the new surfaces created by the fractures, *Stot*, plus the original surface. In this way, it is possible to calculate the total area created by the fractures. By extrapolating this concept, it is also possible to calculate the total length of the fractures. The total perimeter of all particles is correlated with the total length of the fractures, minus the original perimeter of the crystal and the loss of data due to the two-dimensional transposition of the three-dimensional particles. The latter error is reduced if the particles analyzed by microscopy are in very large numbers. For this reason, the analyses in morphology must be carried out on a high number of particles, usually above 100,000 particles.

In order to determine the nature of silica polymorphs, a Raman microprobe inserted in the Morphology G3ID was used, which uses a 785 nm laser with a spot of 2 microns in diameter. The Raman laser power is 40 mW.

To determine the stress to which the crystal is subjected, a measurement method was developed using the image of the shattered crystal printed on a pressure sensitive film (Pressurex Inc., Madison, NJ, USA; www.sensorprod.com). These films have an ink layer that produces a color, and the intensity of which is proportional to pressure. Figure 2 shows the pressure marks left on the film by different quartz crystals

**Figure 2.** Images of the films impressed by several compressed crystals; on the right, a calibration test. The numbers represent the weight of samples in mg.

Finally, we used scanning electron microscopy to determine the microscopic characteristics of fractures at different stress levels (Zeiss EVO MA10, Zeiss Gmbh, Ulm, Germany). The samples to be analyzed in the SEM were left in their original condition, without cleaning, since debris on the surfaces of the granules can provide important information.
