Full length articleRelaxation behavior of densified sodium aluminoborate glass
Graphical abstract
Introduction
Being a non-equilibrium state of matter, glass continuously relaxes towards the supercooled liquid state and relaxation is an intrinsic and universal feature of glasses. Even though this phenomenon is well-known and has been actively investigated, the full understanding of glass relaxation remains a challenging problem of glass science [1]. Different methods have been applied to investigate relaxation processes. In most cases, the observed relaxation laws are rather complex and cannot be described by a single exponent function. Therefore, more sophisticated mathematical models are widely used to fit the experimental data. In particular, the stretched exponential function is often found to describe well the experimental relaxation data obtained by different techniques [2], [3], [4], [5], [6]. The most common form of the function is:where A is a preexponential constant, τ the relaxation time, β the dimensionless “stretching” factor (0 < β ≤ 1)
The model of diffusion of excitations into traps, developed by Grassberger and Proccacia [7], and experimentally supported by Philipps [8], provided a physical foundation for use of the stretched exponential function to describe relaxation phenomena in glasses and some specific values of the stretching factor were proposed [8]. In practice, the mean relaxation times, obtained as the result of the fit using the stretched exponential function, are often used to determine the activation energies of the relaxation. However, the stretching factor, which could be used to identify the origin of the relaxation mechanism, is often taken for granted and/or does not match the theoretically predicted values of 3/5 and 3/7 [3,4,6]. Moreover, the stretched exponential function (with β≠1) is not always the best mathematical model to describe the relaxation kinetics of some physical properties [2,[9], [10], [11]].
Analysis of the relaxation decay functions is a reverse problem with many possible numerical solutions. This type of analysis is widely used and has been conducted for decades in fluorescence spectroscopy - time-resolved luminescence measurements and subsequent rather sophisticated analyses are now routine procedures in this field of science [12]. To correctly solve the reverse problem of the decay function analysis, it is necessary to properly choose the mathematical model and to acquire decay curves with high signal-to-noise ratio and high temporal resolution for a long enough period. Simultaneous treatment of several decay curves obtained from the same system, but at slightly different conditions, improves the reliability of the analysis.
Different types of experimental data, such as density [3,6], refractive index [13], linear dimensions [11], birefringence [2,5], fictive temperature [5], X-ray scattering [14,15], Raman and Brillouin spectroscopies [13], and others, can be used to track glass relaxation. There are several processes occurring during relaxation, usually identified as α-, β- and γ- relaxation, with the typical relaxation time depending on the dominant mode and temperature [16], [17], [18], [19]. For detailed investigation of the relaxation processes, it is crucial to precisely control the temperature during the glass relaxation and, ideally, monitor the changes in situ [4,9,14]. It has been demonstrated that α-, β- and γ- relaxation processes contribute differently to various macro- and microscopic parameters of the analyzed glass [20,21]. Therefore, it is interesting to perform simultaneous cooperative investigation of the relaxation process using different experimental techniques. Recently, it has been demonstrated that Raman and Brillouin spectroscopies can be simultaneously used to monitor phase transitions in situ during differential scanning calorimetry (DSC) scan, allowing simultaneous measurements of structural and elastic properties [22]. Mechanical spectroscopy can be used to explore internal friction relaxation processes, i.e. β- and γ- relaxation processes, whereas α-relaxation corresponds to the network relaxation of the glass. So, different relaxation processes should be accessible by means of Raman and Brillouin spectroscopies.
The objective of this work is to utilize the recent experimental advances to critically evaluate the relaxation behavior in a pressure-quenched densified glass, since the densification process leads to both structure and property changes relative to the as-melted glass [23], [24], [25], [26]. In order to reveal different relaxation processes, Raman and Brillouin spectroscopies are chosen as the main experimental tools. Moreover, all the measurements are performed in situ inside a DSC, enabling precise control of the temperature. Experimental data obtained by these techniques are considered as relaxation curves and analyzed using different mathematical approaches. The relaxation kinetics obtained with Raman and Brillouin spectroscopies as well as calorimetry are compared and the activation energies of the different relaxation mechanisms are estimated.
Section snippets
Experimental
The object of this work is glass with the composition 25.5 Na2O – 20.4 Al2O3 – 54.1 B2O3 (mol%), which was obtained by standard melt quenching technique and then subjected to isostatic compression at 1 GPa at its glass transition temperature (Tg) of 449 °C. This glass was chosen as it undergoes significant volume densification (from 2.24 to 2.38 g/cm3) as well as structural transformations (e.g., increase in boron and aluminum coordination numbers). A detailed description of the glass
Structure and properties of densified and fully relaxed glasses
Different physical properties and structural parameters obtained for the densified and the relaxed glass state are summarized in Table 1.
According to the previous results, the as-prepared glass has density of 2.24 g/cm3, whereas the densification process leads to a value of 2.38 g/cm3 [23]. Refractive indices nD and nF increase upon densification, from 1.497 to 1.526 and from 1.506 to 1.533, respectively, in agreement with Newton-Drude model.
The fractions of aluminum and boron species have been
Discussion
Strong modification of the different glass properties is observed upon high-temperature densification, which can be described in terms of the fictive temperature concept. The common approach to determine the Tf using DSC shows a rather mild variation of the Tf. The fictive temperature was also determined using the analysis of the Brillouin and Raman spectra on heating. Although all the three experimental techniques give quite close values of the fictive temperature for the relaxed glass, the Tf
Conclusions
A densified sodium aluminoborate glass is studied in detail by means of Raman, Brillouin spectroscopies and DSC methods. The changes of elastic properties upon densification cannot be described by the change of the B and Al speciation and depend on the structural modifications of the glass network. The larger amount of BO4 units in the densified glass state results in conversion of pentaborate units into diborate and di-pentaborate groups. Densification also leads to formation of NBOs, which
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
M.M.S. acknowledges Kacper Januchta (Aalborg University) for experimental assistance. A.V. and D.L. acknowledge Michael Bergler (FAU Erlangen-Nuremberg) for additional ex situ Brillouin measurements. M.M.S. acknowledges the support from VILLUM FONDEN (research grant no. 13253).
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