Calorimetry to Understand Structural Relaxation in Chalcogenide Glasses

Abstract

Thermal behavior of chalcogen additive materials synthesized via melt quench method can be studied by reheating the bulk samples in differential scanning calorimetry (DSC) or differential thermal analyzer (DTA) experiment. It involves kinetics of structural transformations as three basic characteristic phenomena correspond to glass transition, crystallization and melting are involved. Thermal stability and glass forming ability are important factors from technological point of view in various applications. Thermal stability of glasses can be ascertained based on calorimetric measurements. In the glass transition region (first region in reheating experiment), structural relaxation takes place. The temperature in glass transition region, its heating rate dependence and empirical approaches for estimation of apparent activation energy are useful to determine utility of these materials in various applications.

1. Introduction

Long back ago, it was believed that amorphous solids could not be semiconductors as known from the fact that that the existence of semiconductors is connected with the quantum theory of the solids, which in turn is based on the presence of long range order. The interest in amorphous materials grew in 1950’s when it was found that the non-crystalline solids and liquids that do not have any periodic structure also behave as semiconductors. Since then, extensive research initiated to explore these materials. These materials have great potential to serve as raw materials for the fabrication of electronic devices and the time is not far off when crystalline materials may be completely replaced by amorphous materials in electronic industries. It is because of the fact that the preparation technique is comparatively cheaper, processes involved are comparatively easier and the devices are of good quality in amorphous field. Amorphous materials can be regarded as amorphous semiconductors, if the energy band gap lies between 0.1 eV and 3 eV. Amorphous materials are becoming progressively popular due to their wide range of applications in solid state devices.

Glasses are those amorphous solids which are prepared by rapid cooling of the melt. In principle, any substance can be made into a glass by cooling it from the liquid state fast enough to prevent crystallization. In general, glass scientists regard the term ‘glass’ as covering ‘all non-crystalline solids that show a glass transition’ irrespective of their preparation methods. In actual practice, glass formation has been achieved with a relatively limited number of substances. The two standard methods of preparing amorphous solids are: (i) by condensation from the vapor as in thermal evaporation, sputtering, glow-discharge decomposition of gas or other methods of deposition and (ii) by cooling from a melt. The first method produces thin films, while the second method provides bulk materials. Materials that are obtained by cooling from the melt are called glasses and generally have a lesser tendency to crystallize as compared with those that can be prepared only by deposition [1]. The crystallization of an amorphous material proceeds by the processes of nucleation and growth. Glass formation is inhibition of crystallization. Glass formation becomes more probable at higher cooling rate, the smaller the sample volume and slower the crystallization rate. Whether a particular liquid can be cooled to form a glass or not, will clearly depend on the rates of the atomic or molecular transport processes involved in the nucleation and crystal growth. Liquids with small crystallization kinetic constants can thus form glasses directly from the melt. This is the basic reason as to why selenium (Se) is a good glass former in contrast to pure tellurium (Te). Silicon and germanium cannot be quenched into the glassy state even at very fast quench rates. When it was proposed that chalcogenide glasses containing large proportions of one or more chalcogen elements namely sulfur (S), selenium (Se) and tellurium (Te) instead of the conventional sixth group element oxygen (O) can act as semiconductors and continuous research in this field is going on. Moreover, the possibility of doped chalcogenide glasses in the well controlled manner has opened up many new directions for the application of chalcogenide glasses in different fields.

The alloys of chalcogenide glasses have a certain range of atomic percentages of each constituent in which they can be glassy and beyond this range they are semi-crystalline or crystalline. From literature, it can be inferred that small samples say binary, ternary or multicomponent compositions were prepared, their nature (crystalline or amorphous) were determined and consequently glass formation region is mapped out for each composition. The range of glass forming region is to some extent reliant on the quench rate or the quantity of material used during the sample preparation. Chalcogenide glasses are prepared by quenching of the liquid below melting temperature. Upon cooling a liquid below its freezing temperature, it will either crystallize or to form a glass. Glasses of different compositions have different regions of glass formation directed by the type of bonds between the constituent elements. An increased tendency to glass formation is possessed by chalcogenide compounds and alloys with predominantly covalent chemical bonds. However, the specific composition upto which glass formation in binary, ternary or multi-component system is possible, cannot be predicted in priori and has to be determined experimentally. For example, in Se-Te system, glass formation is possible upto tellurium content 30 at % [2].

When glass forming liquid is cooled, some of its properties change sharply in a narrow temperature range [3, 4]. Figure shows volume versus temperature plot during the course of temperature lowering experiment (melt quenching). Continued cooling decreases the liquid volume in a continuous fashion and the slope of the smooth volume-temperature curve defining the liquid’s volume coefficient of thermal expansion. Eventually, when the temperature is brought low enough, a liquid–solid transition takes place. Its signature in terms of low value of the expansion coefficient i.e. a smaller slope, characterizes a solid. A liquid may solidify in two ways; first one corresponds to route 1 (Figure 1) discontinuously to a crystalline solid and secondly via route 2 continuously to an amorphous solid (glass) (where T_f is freezing temperature and T_b is boiling temperature in Figure 1). The liquid-crystal transition occurred at freezing or melting temperature and an abrupt contraction is observed to the volume of the crystalline solid. However, at sufficiently high cooling rates in a melt-quenching experiment, the most materials are found to alter their behavior and follow route 2 to the solid phase. An abrupt change in the slope of the curve equal to the coefficient of volume expansion occurs at a certain temperature. This temperature is called the glass transition temperature (T_g). The liquid-glass transition occurs in a narrow temperature interval near T_g.

Figure 1.

Volume versus temperature plot for cooling an assembly of atoms can condense into the solid state.

There is no volume discontinuity, instead curve bends over to acquire the small slope characteristic of the low thermal expansion of a solid. It is significant that viscosity does not show an abrupt change at the glass transition temperature.

2. Experimental methods

2.1 Melt-quench technique

Melt-quenching technique is a widely used method to prepare the various samples of the chalcogenide glasses. The entire equipment used for preparing the alloys consists of a furnace to prepare the melt of solid mixture, a rocking arrangement to make the melt homogenous and a quenching arrangement to rapidly cooling of the melt. The furnace is operated maximum at 120 V ac and can raise the temperature up to 1200°C or more depending on type of furnace. Quartz ampoules (outer diameter ~ 1.2 cm and inner diameter ~ 1.0 cm, length ~ 10 cm) are prepared by sealing the quartz tube on one side and a neck on other side to pour the solid mixture before evacuation. To prepare glassy alloy of type Se_αIn_βPb_γTe_δ, the elemental substances (5 N) are weighed according to the exact proportions of high purity (99.999%) elements in accordance with their atomic percentages (α,β,γ,δ are the respective atomic weight percentages of Se, Te, Pb and In).

The quartz ampoules are properly cleaned with soap solution, acetone, methanol and then dried by heating in the furnace at 500°C for half an hour. The weighed mixture is poured into the ampoules and these ampoules are sealed in a vacuum of ~2 × 10⁻⁵ mbar using the diffusion pump. Then ampoules are fastened to a ceramic rod and the rod is attached to the rocking arrangement. The sealed ampoules are heated in increasing order of melting points of the constituent’s elements of the glassy alloys for 2 hours each. For example, in case of Se-Te-In, the temperature of the furnace is raised to 200°C for 2 hours, so that the indium [melting temperature, T_m = 156.6°C] diffuse into the rest of the constituents. The temperature is then raised to 300°C so that the selenium (Se) [T_m = 217°C] thoroughly mixes with other constituents. The sealed ampoules heated upto temperature 600°C in the rocking furnace initially, so that tellurium [T_m = 449°C] in respective composition mixed properly. Later, the temperature of the furnace has been raised upto 900°C and maintained at this temperature for 24 hours and rocking is done to ensure proper mixing and homogeneity of the samples. The heated ampoules are then quickly quenched in ice cooled water to get glassy alloys. Then tubes are broken, crushed, separated, ground to fine powder, labeled and kept in vacuum desiccators for further analysis.

2.2 Differential scanning calorimetry

The thermal behavior of the glasses is investigated using DSC system. The complete DSC system consists of the DSC analysis module, temperature controller, data analyzer and recorder/plotter for the preparation of hardcopy record. Working principle of DSC is shown in Figure 2. The temperature range covered in this DSC unit was from room temperature to high enough temperature (>500 degree Celsius) as per instrument make. Approximately, 3–5 mg of sample in powder form is encapsulated in standard aluminum pan in an atmosphere of dry nitrogen at a flow of 40 mL min⁻¹ and heated as per requirement under either isothermal or non-isothermal conditions. The values of glass transition temperature (T_g), the temperature of crystallization (T_c), and the melting temperature (T_m) are determined by using the microprocessor of the thermal analyzer.

Figure 2.

(a) Block diagram of working principle of DSC. (b) Heating arrangement in DSC.

3. Structural relaxation in chalcogenide glasses

Kauzmann [3] showed that glass transition occurs for many types of glasses. It has been suggested that some amorphous solids do not show a glass transition temperature (T_g), but this result has not been established. Since 2005, when I started research in the field of chalcogenide glasses for Ph.D. degree and synthesized binary, ternary and quaternary chalcogen based glasses and even after while continuing research almost 50 samples are prepared by melt quenching technique. But these samples always found to associate with T_g [5, 6, 7, 8, 9]. It is because of the fact that rearrangements in the glass structure occur during temperature lowering experiment (cooling) when the glass has the properties of liquid. Therefore, the changes are slow when the glass structure is frozen (cooling is fast enough) and it behaves like a solid. When a glass is cooled rapidly from a temperature, above the transition region into this region, it retains some properties of higher temperature. These properties ‘relax’ to the characteristics of the lower temperature with time may be pronounced more commonly as ‘structural relaxation’. The time to reach a stable or equilibrium state is longer at lower holding temperatures. If a glass material is cooled rapidly from a room temperature above the transition region, non-uniformities in its temperature during cooling lead to stresses in the glass. These stresses can weaken the glassy material and change its properties. So, it is desirable to remove them by heating the glass at an appropriate temperature in the transition region. At this annealing temperature, the stresses are removed as the glass relaxes. The rate at which annealing goes on is important in preparing glasses for use. The relaxation of glass structure from one set of properties to another after a rapid change in temperature in the glass transition region is called structural relaxation. When a glass is subjected to a stress (strain) in this region, the deformation changes with time and this process is called stress or strain relaxation. The rates of this relaxation are of practical importance and have been studied intensively in the last few years.

Figure 3 shows a typical DSC mostly observed in reheating calorimetric experiment displaying glass transition (first endothermic peak), crystallization (exothermic peak) and melting (second endothermic peak) for a chalcogenide glass. But it is pertinent to mention here that heat flow in calorimetric measurements may be different for other materials like polymers depends on materials’ characteristics. The inset of Figure 2 shows the crystallization fraction at a generic temperature T (shaded area of exothermic peak). DSC curves are characterized by first occurrence of endothermic peak which corresponds to glass transition. In this process, molar volume and enthalpy of chalcogenide material change resulting in variation of specific heat and viscosity which marks transition from solid phase to super cooled liquid phase. In other words, instantaneous change in temperature during quenching causes chalcogenide glassy material to relax from a higher enthalpy to an equilibrium state of lower enthalpy and this process is called thermal relaxation. Glass transition temperature (T_g) corresponds to point of intersection of tangents drawn to baseline and endothermic baseline shift. The onset values of characteristic temperatures are taken while defining the properties and henceforth use of glasses in technological applications. But, for in observations and hence particularly in calculations peak values of T_g, T_p and T_m are taken instead of onset values because of more accuracy in measurement of peak values than onset values. Least-squares fitting method is applied to deduce apparent activation energy and other kinetic parameters while using empirical approaches. Chalcogenide glasses generally show single T_g and single T_p indicate that the investigated system exists in single phase and homogeneous, however, a second glass transition temperature (T_g2) is also observed for Se-Te-Sn investigated samples see reference [6]. The existence of a second glass transition temperature directs unusual phase separation happening in thermal treatment. This phase separation, leading to presence of a second or more than two glass transition temperatures, may be thought of arising after super cooled melt transition or the glass may be in two phases or higher to start with itself. The phenomenon of presence of a second T_g has been found in other chalcogenides [10, 11] also.

Figure 3.

A typical DSC curve showing glass transition, crystallization and melting of a chalcogenide glass.

It is observed that characteristic temperatures shift to higher temperature with increasing heating rate. At T_g, structural relaxation time becomes equal to the relaxation time of observation τ_ob [12]. Since T_g∝ 1/ τ_ob. Thus, with the increase in heating rate, τ_ob decreases leads to increased T_g also observed in other glasses [5, 6, 7, 8, 9]. It can also be ascribed from heat dissipated so much easier at higher heating rate; therefore, decomposition begins on relatively higher temperature and has high heat of fusion. T_c is also found to increase (similar to T_g) with increasing heating rate. This could be because the materials do not get enough time for nucleation and crystallization with higher heating rate.

4. Glass transition calorimetry

In reheating experiment of glass in calorimetry, two ways can be adopted namely isothermal and non-isothermal methods. In first method i.e. under isothermal conditions, the material under investigation is placed rapidly to a temperature above T_g and the heat evolved at a constant temperature is noted as a function of time during the crystallization process. In the other method, i.e. under non-isothermal conditions, the material is heated at a fixed heating rate usually from room temperature. Again in this method also, heat evolved is noted as a function of time or temperature. A drawback of experiment under isothermal conditions is the impossibility of attainment a test temperature instantly and during the time, which system desires to stabilize, no observations are possible. However, the second method i.e. under non-isothermal conditions does not have this limitation. Due to above mentioned reasons; we have also applied this technique for the overall crystallization kinetics of investigated glassy alloys [5, 6, 7, 8, 9].

Characteristic temperature above which glassy material can have several structural arrangements and below which material is frozen in a structure which cannot change into other configuration easily is defined as glass transition temperature T_g. T_g is an indispensable parameter in studying stability of glassy materials. Furthermore, cohesive forces must be overcome for movement of atoms in glass network. So, T_g must be related to the magnitude of these forces. Therefore, theoretical models are also proposed to determine T_g which assume it to be proportional to cohesive forces, (in terms of mean bond energy < E >) and network rigidity. Tichy and Ticha [13] proposed that T_g depend on two factors; coordination number < r > and < E > after analyzing for186 glasses; T_g = 311[< E > - 0.9] (T_g so derived is in kelvin). Lankhorst [14] also devised a model for estimation of T_g from heat of atomization H_s of system and suggested empirical relation; T_g = 3.44 H_s- 480. Tanaka also gave the exponential relationship as [15]; T_g = exp(1.6 < r > + 2.3). Experimental values are sometimes closely matched with theoretically values.

Glass transition temperature depends upon the co-ordination number, bond energy and types of structural units formed. The glass transition region may be studied from glass transition temperature and its heat rate dependence, consequently, apparent activation energy of glass transition. Glass transition temperature represents the strength or rigidity of the glass structure of the glassy material. We employed three approaches to analyze the dependence of the T_g on the heating rate and estimation of apparent glass transition activation energy of bulk glasses [5, 6, 7, 8, 9]. The first one corresponds to the empirical relation given by Lasocka [16] as T_g = A + B ln(α), where A and B are constants depending upon the glass composition. From this relation, it can be easily inferred that a plot between ln(α) and T_g should be a straight line. Also, A could be deduced as T_g at a heating rate of 1 Kmin⁻¹. It is suggested by other researchers that B (determined from slope) may be correlated to the cooling rate of the melt [17, 18]. Lesser is the cooling rate of the melt, lesser is B. Thus, the physical significance of B looks to be connected with the response of the fluctuations in the configuration within the glass transformation region.

Reheating of a chalcogenide glass result into crystallization phenomenon and studies of crystallization kinetics are always connected with the concept of activation energy. Another parameter which is comprehensively used to get into structural relaxation kinetics is apparent activation energy. It is said to be that energy which is absorbed by a assembly of atoms in this region, such that a jump from one metastable state to another is possible. This apparent activation energy is involved in the molecular motion and rearrangement of atoms around glass transition temperature. The more general method used in this regard is Kissinger’s equation which is basically meant for the determination of activation energy for crystallization process. The justification of applying this method for the evaluation of the glass transition activation energy comes from the shifting of glass transition peaks at different heating rates similar to crystallization peaks. The details of this method can be noted from [19, 20] and in case of glass transition it is modified to (α/T_g²) = − E_g/ RT_g + constant. Slope of the plot between ln(α/T_g²) and 1/T_g is utilized to derive E_g. We have also used this method extensively to deduce E_g, establish a relation with other experimentally deduced parameters and thereafter to draw conclusions regarding thermal stability among the investigated glasses [5, 6, 7, 8, 9].

The other approach, using heating rate dependence of T_g is also used defined by Moynihan et al [21] in terms of the thermal relaxation phenomenon. In this kinetic interpretation, the enthalpy at a particular temperature and time H (T, t) of the glassy system, after an instantaneous isobaric change in temperature, relaxes isothermally toward a new equilibrium value H_e(T). The relaxation equation can be written in the following form [22]:

E1

where τ is a temperature—dependent structural relaxation time and is given by the following relation:

E2

where τ_o and c are constants and E_g is the activation energy of relaxation time. Using the above equations, it can be shown [21, 22, 23] that ln(α) = − E_g/RT_g + constant. Similarly, in this method i.e. using Moynihan’s relation, slope of the linear fit variation of ln(α) against 1/T_g gives E_g. E_g values so deduced are found in concordance with Kisinger’s relation [5, 6, 7, 8, 9]; therefore, one can use either of these two approaches.

Thermal stability and the ease of glass formation is a major issue in the study of glassy materials as it determines the degree of utilizing the investigated materials in various applications. It can be ascertained based on calorimetric observations. Kauzmann proposed two-third rule to determine the ease in glass formation [3] as T_rg = T_g/T_m. The composition obeying two-third rule (T_rg ≥ 0.65), indicating that the glass forming ability (GFA) for that composition of the material is high.

For a memory and switching material, the thermal stability and GFA are of vital importance. Glass transition temperature also gives the worthwhile information about the thermal stability related with strength and rigidity of glass structure. GFA is also associated with cooling of the melt bypassing crystallization. It has been stated that (T_c-T_g) is also an indicator of GFA. Higher the value of this difference, greater is GFA because higher values of this difference indicate the more kinetic resistance to crystallization. One more parameter, Hruby number K_gl is important by which thermal stability and glass formation is evaluated as (T_c-T_g)/(T_m-T_c) [24]. Higher (T_c-T_g) delays nucleation while lower (T_m-T_c) retards growth in nucleated crystals. Thus, Hruby’s parameter merges nucleation and growth information during amorphous-crystallization phase transformation. Thus, Hruby’s parameter combines the nucleation and growth aspects of phase transformation. Therefore, the composition of the glass with higher value could be taken as the most stable among studied samples.

There is no absolute measurements to define the glass formation, the empirical methods extensively used for its quantifiable properties. The fragility index (F_i) is a significant parameter to define glass forming ability and it is a measure of the rate at which the relaxation time decreases with the increase in temperature around glass transition temperature. This distict parameter is given by the relation [25, 26]; F_i = E_g/RT_gln(α). According to Vilgis [27], the glass forming liquids that show an approximate Arrhenian temperature dependence are defined as strong and specified with a lower value of F_i (F_i ≈ 16), while the other side limit i.e. fragile glass forming liquids categorized by a higher value of F_i (F_i ≈ 200). Thus, it is reasonable to state that the glasses having values of F_i within the above mentioned limit has been obtained from the good glass forming liquids.

5. Conclusions

In this chapter, use of calorimetry is discussed to understand structural relaxation in chalcogenide glasses. Some of theoretical approaches are also mentioned here that are generally used to estimate glass transition temperature before calorimetric experiment. Further, the usage of experimental data obtained from DSC or DTA for derivation of different parameters and apparent activation energy of glass transition region and hence understanding relaxation kinetics in glass transition region is also discussed in detail.