Relaxation behavior of densified sodium aluminoborate glass

Abstract

In this work, we study the relaxation behavior of a densified sodium aluminoborate glass by means of coupled Raman spectroscopy, Brillouin spectroscopy, and differential scanning calorimetry analyses. First, we show that the changes in elastic properties upon densification are largely associated with structural modifications in the glass network at short- and medium-range orders. Then, the evolution of the structural and elastic properties of the densified glass has been monitored in situ in the coupled DSC-Brillouin-Raman setup during isothermal annealing at different temperatures below the glass transition temperature. The stretched exponential function is found to well describe the observed relaxation kinetics, however, the stretching factor β varies non-monotonically with temperature. In contrast, the Arrhenius behavior of the characteristic decay times is deduced by lifetime distribution analysis, revealing three different relaxation processes with typical activation energies of 170±25, 200±5, and 280±15 kJ/mol. The relative contributions of these processes to the overall relaxation kinetics are found to vary with the temperature as well as the type of parameter considered (structural, elastic, or thermal), and hence, the relaxation kinetics cannot be properly understood using the stretched exponent function. The possible origins of the different relaxation processes are discussed.

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:

$$f\left(t\right)=A\text{exp}\left[-{\left(t/\tau \right)}^{\beta }\right],$$

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.