Cr2O3 Doping Effect on Silica Glass Cooling Rate

In this paper we present the results on the effect of the SiO2 melt cooling rate on the morphology of its surface. The method of atomic force microscopy explores a surface roughness of the silica glass cooled at different rates after its heating up to more than 2100 °C. The study compares three modes of cooling glass rods with a diameter of 14 mm: convective heat exchange with the surrounding air, quenching with dropping the sample into a vessel with water, and radiation of silica glass doped with 0.1 wt% Cr2O3. The surface roughness of silica glass in the second and third modes of cooling was significantly less than in the conditions of convective heat exchange. Doping the silica glass with Cr2O3 increases the heat exchange coefficient by 2 times and decreases the surface roughness. The results of the research can contribute to improving the mechanical and optical properties of silica glass light guides.


Introduction
Silica glass (SG) has a unique high strength, which is equal to  GPa according to theoretical forecasts [1]. Therefore, silica fibers are promising reinforcing filler for lightweight high-strength composite structural materials. However, despite various methods of such fiber production, their strength does not exceed 6 GPa [2]. Works [3][4][5][6][7] consider the factors constraining the development of the processes to obtain fibers with strength close to the theoretical level for SG.
As known, cracks on glass surface initiate its destruction [8,9]. In [10], it is assumed that temperature fluctuations can generate cracks, leading to decrease in the SG strength by 2 times compared to its theoretical estimate.
The strength of commercial optical fiber made of SG with a diameter of 125 microns (6 GPa) corresponds to the depth of a critical surface crack ≈ 6 nm, calculated based on experimental dependence (1) of fiber strength (σ) on defect size (r) on its surface [3]: where D is a constant ≈ 0.474 × 10 -3 GPa × m 0.5 .
Extrapolation of Eq. (1) to the defect size equal to the length of the Si − O bond of the SG grid (0.16 nm) gives a strength value equal to 37.5 GPa, corresponding to theoretical estimates [1]. Experimental studies [5] showed that the strength of particularly thin SG fibers with a diameter of 120 nm, measured at natural ambient humidity, is equal to 26 GPa. Reducing the equilibrium pressure of water vapor in the surrounding atmosphere to 10 -2 Pa according to the results of [7] can lead to a twofold increase in the strength of such fibers.
The globular nature of the glass structure [11][12][13] can determine the specifics of its surface morphology and regularity of distribution of nanoscale cracks in depth. Therefore, the high strength of particularly thin silica fiber may result from the decrease of SG surface roughness due to its high cooling rate when drawing the fiber [14,15].
Thus, the high cooling rate of the fiber in comparison with the preform leads to a decrease in the surface roughness of the SG [16]. At the same time, water quenching of the preform heated to 2300 °C reduces the level of its surface roughness by 10 times due to the high cooling rate compared to cooling in air [17]. However, such a SG cooling method cannot be implemented in the process of fiber drawing. Therefore, this work aims to study the effect of different cooling conditions on the SG surface roughness measured by atomic force microscopy (AFM).

Materials and Research Methods
According to Kirchhoff's radiation law, heated bodies lose thermal energy due to radiation; its spectral region corresponds to the wavelength of absorption by this substance. Silica glass at high temperatures is transparent in the optical spectrum of the visible range [18]. However, in this spectral region the SG impurities of transition metals intensively absorb radiation [19] and hence they effectively emit, reducing the temperature of SG.
As known [19], SG containing a Cr admixture has the greatest absorption capacity compared to other coloring impurities: Ni, V, Co and Fe (Table 1). Therefore, intentional additions of Cr 2 O 3 to silica glass should be expected to provide the greatest effect of its cooling due to radiation in the visible range of the optical spectrum.
For experiments, samples were SG rods with a diameter of 14 mm.: samples with a core diameter of 5.5 mm were obtained on the MCVD lathe by melting quartz grains inside a tube of silica glass type KV (Russian brand name). In sample No. 1 the core was made of pure quartz grains, while in sample No. 2 it contained 0.1 wt % Cr 2 O 3 .
A SG rod rotating at a speed of 45 revolutions per minute was heated by the flame of an oxygen-hydrogen burner using an automated system OFC-12-729 manufactured by Nextrom. The surface temperature of the samples was measured with a standard optical pyrometer at a radiation wavelength of ≈ 5 microns. In this region of the optical spectrum, SG is not transparent [20].
After reaching a constant temperature value at maximum power of the burner, it was turned off and an automated record of temperature changes over time with an error of the IK optical pyrometer not more than 1% was made.
The samples were cooled under two different conditions: -during the heat exchange of samples with the ambient air; -discharging of sample No. 1 (for no more than 1 s) into a vessel with water.
The SG surface roughness was studied using an AFM Solver PRO-M (NT-MDT, Russia). The measurements were made by the contact method using the ETALON tip with the curvature radius less than 10 nm. A horizontal resolution is better than 20 nm, and vertical resolution is about 0.1 nm.

Results
The experiments have shown that the steady-state surface temperature of a sample heated by a flame stream is significantly affected by the radiation of the core glass in the visible transparency region of SG. Thus, the addition of 0.1% wt % Cr 2 O 3 in the SG core reduces the surface temperature of the sample at maximum burner power from 2300 to 2175 °C (Fig. 1). The cooling time of sample No. 2 doped with Cr from the maximum heating temperature to 1000 °C (30 s) is two times less than that of sample No. 1 of pure SG (60 s). Figure 2 shows a diagram of heat flows while cooling sample No. 2, where, in comparison with sample No. 1, heat flow QRc is added to the radiation from the core into the environment. It should be noted that the heat flow to radiation from the SG surface (QR) is significantly less than the heat flow to radiation from the core (QRc) doped with chromium oxide. This occurs in accordance with Wien's law, the maximum radiation energy with a body temperature increase shifts to the short-wave region of the optical spectrum, in which Cr in the wavelength region of 600-800 nm has the greatest emissivity. The melt of pure SiO 2 emits in the longwavelength region of the optical spectrum (at a wavelength of more than 2000 nm [20]), while remaining transparent to the radiative flow from Cr 2 O 3 . The measurement results of the SG surface relief on AFM (Fig. 3) showed that: -the roughness of the water quenching sample No. 1 is significantly less than with the convective heat exchange with the surrounding air; -comparison of the samples surface roughness indicates the same cooling rate of SG both for the conditions of its quenching in water and due to the emissivity of chromium. Figure 4 shows the shapes of the bulb under the same drawing conditions in a furnace with a graphite heater of 125 microns fiber diameter from samples No. 1 and 2. The length of the bulb doped with Cr 2 O 3 is significantly less than that of a bulb made of pure SG. This is due to the different values of the heat transfer coefficient from the heated sample to the environment.

Discussion
The bulb shapes after drawing and cooling were photographed. The diameter changes as a function of axial distance in the neck-down regions were determined from the magnified pictures.
Based on the distribution of diameter (d) along length (z) in the bulb zone, it is possible to calculate the constant (B) [21] proportional to the heat transfer coefficient during SG cooling of according to Eq. (2): where d f is the fiber diameter equal to 0.125 mm; d 0 is the normalized diameter ≈ 5 mm.
Constant B is determined by the slope of straight lines for dependence ln ln (d/df) on the z coordinate along the axis of the bulb (Fig. 5). The value of B for the sample without Cr 2 O 3 is equal to 0.38 cm −1 , which differs from the value of this constant ≈ 0.65 cm −1 for the silica fiber being drawn by heating with a similar graphite heater [21]. Such a difference may be due to the different drawing speed of the fiber.
The ratio of this constant value for two samples is ≈ 2, which indicates a significant increase in the heat transfer coefficient when doping the core with chromium. Therefore, the cooling time up to 1000 °C for samples No. 1 and 2 differs twice (Fig. 1).
It is obvious that the shape of the bulb and its surface relief, depending on the cooling rate of the SG, is determined both by the Cr 2 O 3 concentration and thickness of the cladding. The paper shows a significant dependence of the SG surface roughness on its cooling rate. The height of the relief peaks of the SG cooled in the air atmosphere is 7 nm, while at water glass quenching and chromium radiation cooling the profile peaks do not exceed 1.5 nm.
Previously, it was found that defects in the surface of silica fiber that reduce its strength [22] are usually caused by the presence of micro-admixture of coloring elements (Cr and Fe). Their high emissivity leads to local cooling and an increase in the SG viscosity, which prevents its plastic deformation. Therefore, the size of such defects does not change in the process of fiber drawing, which determines its low-strength state. The presence of a chromium-doped radiating SG can prevent such behavior of localized defects containing coloring impurities. The cooling rate increase also contributes to the hardening of the high-temperature homogeneous state of the doped silica glass, which is prone to liquation. In the technology of the active light guides doped with rare earth elements (Er, Yb, etc.), it can lead to a decrease in optical losses.

Conclusions
The research results indicate a significant influence of the cooling rate of the SG heated to more than 2000 °C on its surface relief. It is shown that an increase in the emissivity of glass in the visible region of the spectrum due to Cr 2 O 3 doping doubles the cooling rate and smooths its surface roughness. This behavior of SG is probably due to the specifics of the globular structure of the glass matrix, which affects both the surface morphology and structure of the silicon dioxide melt in a quenched state. Therefore, the cooling rate of the SG heated to more than 2000 °C can affect both the strength and optical properties of products based on it.