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Enthalpy relaxation in hyperquenched glasses of different fragility
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Journal of Non-Crystalline Solids 354 (2008) 1862–1870 www.elsevier.com/locate/jnoncrysol
Enthalpy relaxation in hyperquenched glasses of different fragility Lasse Hornbøll, Yuanzheng Yue
*
Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark Received 1 March 2007; received in revised form 15 September 2007
Abstract The enthalpy relaxation in hyperquenched (HQ) glasses with a wide range of fragilities is studied by performing annealing and differential scanning calorimetric (DSC) experiments. In this work, the enthalpy relaxation behavior of annealed HQ glasses is characterized in terms of the excess heat capacity (Cp,exc) given by the difference between the first and the second DSC measurements on the HQ glasses. The shape of the Cp,exc curves depends on the fragility of the glass system, which implies that during annealing the mechanism of the structural relaxation of the HQ strong systems differs from that of the HQ fragile systems. The details of the fragility dependence of the Cp,exc curves have been discussed in terms of the energy landscape and the structure of the liquids. 2007 Elsevier B.V. All rights reserved. PACS: 64.70.Pf; 65.60.+a; 81.40.Gh Keywords: Glass transition; Germania; Silicates; Fragility; Structural relaxation
1. Introduction In recent years, the study of enthalpy relaxation in hyperquenched (HQ) glasses has attracted considerable interests of glass scientists because it provides rich information on the structural relaxation in glasses and the potential energy landscape of liquids [1–6]. Hyperquenching here refers to a cooling process at a rate of 106 to 108 K/min. A calorimetric temperature scan on HQ glasses at a rate of 20 K/min results in a large exothermic enthalpy relaxation response prior to the glass transition, when compared to glasses cooled at the standard rate of 20 K/min [4–7]. This response is usually characterized by the difference in isobaric heat capacity (Cp) between the HQ glass and the standard glass. When the glass is hyperquenched, high energy states are frozen in. The enthalpy relaxation response is therefore a direct outcome of the distribution
*
Corresponding author. Tel.: +45 96358522; fax: +45 96350558 E-mail addresses: [email protected] (L. Hornbøll), [email protected] (Y. Yue). 0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.10.023
of frozen-in states, and thus a semi-direct measure of the energy landscape of a liquid. Measurements of annealed HQ glass are very useful to obtain further information on the energy landscape [6,8,9]. Annealing of the HQ glass in the temperature range from the glass transition temperature (Tg) to 0.6Tg results in a decreasing amount of relaxed enthalpy [6,8,9]. For basaltic glass this decrease is predominantly seen in the low temperature regime of the relaxation exotherm for low annealing temperatures (Ta) [6]. The change in the relaxation spectrum resulting from annealing at different time and temperature shows a number of features, which have been discussed thoroughly for basaltic glass [6]. The most prominent of these is the sub-Tg endotherm, which has been detected for a number of glass systems [2,6,8– 10] and which has provided new information on the glass transition of water [11]. Previously, experiments on the enthalpy relaxation of HQ glasses have been used to calculate the fictive temperature (Tf) of the glasses [12] and from this to calculate the cooling rate of the fibers by using information on the liquid relaxation properties [13]. This is of high technological
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importance, because Tf is an important parameter for controlling the forming and annealing conditions of glass products. Tf for any glass is defined as the temperature of the melt, at which the structure of the glass equals that of the melt [14]. In terms of configurational entropy (Sc), Tf of a glass corresponds to the temperature of the liquid with the same amount of Sc. As Sc is directly coupled to structure, it is evident that any change in structure will result in a change in Tf, including changes in the structure from external forces during glass formation. Fiber drawing is a widely used method to obtain HQ glass [4,7,15]. In fiber drawing the high cooling rate is obtained by a rapid increase in surface area and simultaneously a rapid decrease in temperature. The surface increase requires a high directional force, which leads to an oriented structure in the glass [16]. As this is also a structural change, it will evidently change the enthalpy relaxation response and Tf. In the Tool–Narayanaswamy model Tf is a measure of the total relaxation time in the glass [14,17]. Because the total relaxation time in glasses is not a simple function, but rather is made up from several distributions of relaxation times [18], the Tf is not a detailed measure of the relaxation behavior of the glass [19]. Rather it is a sum of all relaxation times in the glass corresponding to the microstructures within the glass. In the view of these arguments it is not enough to model a glass by the fictive temperature, and interpreting this temperature as corresponding to a liquid with a given structure. Although the features observed in DSC experiments of both HQ and annealed HQ have been well described for basaltic glasses, it is not known whether these features are universal for HQ glasses or whether they depend on chemical composition. To establish this we here present results on the enthalpy relaxation for six different glass compositions. The compositions are chosen to be oxideglass-forming systems of different origin, with the basic idea to achieve a wide distribution of fragilities, without taking specific chemical composition into account. In the concept of fragility, all glass-forming systems can be attributed a fragility index (m), based on the dependence of the relaxation time of the liquid on the temperature [20]. The more non-Arrhenian this dependence is, the more fragile is the melt (higher m). Vitreous GeO2 was chosen as the strongest glass and two different calcium-silicate compositions as the most fragile. To cover the intermediate fragility range two standard glasses and a basaltic composition were measured.
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2. Experimental Six glass systems were prepared as HQ glasses by fiber drawing. One system was the standard glass NIST 710a obtained from National Institute of Standards and Technology (see Table 1 for the composition). Another was GeO2 glass fibers obtained by melting the crystalline material directly in the fiber drawing crucible. The chemical composition of the remaining four systems as obtained by X-ray fluorescence analysis is given in Table 1. ST is a basaltic composition made from a mixture of natural minerals. For the compositions labeled E and CS both glass fibers and glass for viscosity measurements were prepared from pure raw chemicals obtained from Fluka: SiO2, Al2O3, CaCO3, MgO, and B2O3. Each batch was prepared by careful hand mixing for 15 min. The batch was melted in an electrical furnace in a Pt/Rh crucible at 1500 C for 2 h, quenched in water, remelted at 1500 C for 4 h and then cast in a graphite form. The same melting procedure was used for NIST and ST. Continuous fibers from compositions E, Ge and NIST were drawn from a Pt crucible through a 1.8–2 mm die in the bottom by means of a high speed spinning wheel of Ø 35 cm. The drawing speed was 1.2 m/s. The resulting fibers were homogeneous and approximately 10 lm thick with only small variation in fiber thickness and no sign of crystallization or inhomogeneities. Before annealing experiments and DSC measurements the fibers were cut into small pieces of lengths ranging from 0.1 to 1 mm. Fibers of CS and ST samples were made by a cascade process, where the melt was poured directly onto the high speed spinning wheel and the fibers collected on the wall surrounding the wheel. The resulting fibers were of diameters (d) between 5 and 50 lm and of lengths between 1 and 5 mm. Before annealing experiments and DSC measurements the fibers were sieved in a 63 lm sieve to separate fibers from the large amount of droplets formed by the cascade process. Annealing was carried out in a muffle furnace sustaining temperatures in the range from 400 K to 1300 K with a precision within 1 K. Annealing was done in ambient conditions for pressure, atmosphere and humidity. Annealing was carried out by placing a platinum crucible with the sieved or crushed sample directly into a preheated furnace. After annealing the sample was removed from the furnace and left to cool under ambient conditions. For each system annealing was carried out systematically at 2–5 different
Table 1 Chemical composition of the measured glass-forming systems in molar%
GeO2 NIST 710a E-glass Basalt 45CaO Æ 55SiO2 55CaO Æ 45SiO2
SiO2
CaO
Al2O3
MgO
100% GeO2 68 55 40 55 45
8 17 18 45 55
2 15 21
5 8
FeO
Na2O
TiO2
8
K2O
B2O3
9
4 8
7
2
2
1
ZnO
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1.8 1.6
3 -1 -1
annealing temperatures between Ta = 0.5Tg and Ta = 0.9Tg. For each Ta, annealing was carried out for different periods of annealing time (ta) ranging from 10 min to 44 days. DSC measurements were carried out on a heat flux DSC instrument (Netzsch, STA 449C Jupiter). The measurements included 4 DSC scans: Correction with empty crucibles to reduce background noise, standard scan with an empty reference crucible and a sapphire reference material as the sample, fresh fiber as sample, and the same fiber sample cooled within the DSC instrument with 20 C/min. The Cp curve for a measurement was calculated relative to the Cp of the standard sapphire crystal after subtraction of the correction run to remove the background noise. Measurements were carried out in purged Argon gas atmosphere. The sample mass was between 18 and 22 mg. For the determination of the glass transition temperature (Tg) a cooling (Qc) and heating (Qh) rate of 10 K/min was used to apply to DIN 53765. The high temperature viscosity measurements were carried out with a load-controlled rheometer (Paar-Physica MC1 rheolab). The rheometer was mounted on top of a furnace with a temperature stability of ±1 K. The measurement geometry was a cup/cylinder with the cylinder cone formed in the ends. The stress applied in the measurements was between 7 Pa and 7000 Pa and the resulting shear rates were between 0.5 and 27.
Cp (J K g )
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1.4
2
4
1.2
5 6
1 0.8
1 0.6 400
600
800
1000
T (K) Fig. 1. Glass transitions of the six samples from Table 1 determined at a heating rate of 10 K/min subsequent to a cooling rate of 10 K/min. Numbers correspond as follows: (1) GeO2, (2)NIST, (3) Basalt, (4) Eglass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2. Values of Tg for the samples estimated from these measurements are shown in Table 2.
12
3. Results
8
log (η (Pa s))
For all the compositions shown in Table 1 Tg was determined by a DSC scan at 10 K/min according to the standard procedure for estimating Tg. Fig. 1 shows the DSC upscans for all six glass compositions. The Tg is determined from the DSC measurements by extrapolating lines fitted to the sharp rise at the transition zone and a straight line fitted to the glass heat capacity (Cpg) (as shown in Fig. 2). The Tg is then given by the intercept of the lines and is shown in Table 2 for all the compositions. The Tg determined this way corresponds within 2 K to the temperature of the inflection point on the recorded downscan with a rate of 10 K/min. In addition the figure shows the large difference in the thermal response of the GeO2 glass compared to the others. The small jump in Cp at Tg results in a higher uncertainty on measurements on the GeO2 glass. Viscosity data for all six compositions are shown in Fig. 2. The high temperature data for the CS compositions are taken from [21]. The figure clearly shows the wide variety in the crystallization behavior of the melts as the lowest temperature where viscosity can be measured. Where the GeO2 and NIST melts have no tendency to crystallize at all, the calcium-silicates readily crystallize leaving no chance of glass formation without hyperquenching. Measured values at temperatures below 1500 K obtained for the calcium-silicates were not reproducible, probably because of phase separation of some kind taking place [22]. In the figure, the viscosity data are plotted in a fragil-
10
6 4 2 0 -2 -4 0
0.2
0.4
0.6
0.8
T/Tg (K/K) Fig. 2. Viscosity measurements and Tg from Table 2 viewed in a fragility plot. Open squares: GeO2, closed squares: NIST, open diamonds: E-glass, closed diamonds: Basalt, open circles: 45CaO Æ 55SiO2, closed circles: 55CaO Æ 45SiO2. The measurements are fitted with Eq. (1). The value of the fragility parameter (m) determined by Eq. (2) is shown in Table 2.
ity plot [23] using the Tg values from Table 2. In a fragility plot the viscosity is plotted against Tg/T. In Fig. 2 the data are fitted with Eq. (1) [24] by a Levenberg–Marquadt fitting procedure, adjusting g0, T0, and D: DT 0
g ¼ g0 eðT T 0 Þ :
ð1Þ
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Table 2 Characteristic parameters of the glasses determined by viscosity measurements and DSC Tdraw (K) GeO2 NIST 710a E-glass Basalt 45CaO Æ 55SiO2 55CaO Æ 45SiO2
1673 1523 1563 1773 1803 1803
Qc (K/s) 4
7 · 10 9 · 104 11 · 104 9 · 105 10 · 105 12 · 105
m
Tg (K)
DCp (J/g K)
Hexc (J/g)
Tf (K)
17.5 44.6 51.2 62.5 90.4 141.2
830 831 962 943 1025 1056
0.045 0.14 0.26 0.34 0.33 0.37
22 34 54 79 50 59
1271 1000 1135 1215 1150 1250
Tdraw is the temperature of the melt during fiber drawing. Qc is the estimated cooling rate. m is the fragility index determined by Eq. (2). DCp is the difference between the Cp of the liquid and the Cp of the glass taken at Tg. Hexc is the sum of enthalpy released in the relaxation peak seen in Fig. 4. Tf is the fictive temperature determined as shown in Fig. 3.
From the fits the fragility indices for the six systems were determined according to Eq. (2) [23]: 1 T gT 0 D: ln 10 ðT g T 0 Þ2
ð2Þ
The determined fragility indexes are listed in Table 2. The DSC upscans shown in Fig. 1 are all made on samples previously cooled from above the glass transition with the specific rate of 10 K/min. This allows for direct comparison between the different glasses studied in this work. To be able to compare the enthalpy relaxation functions of these systems as well it is necessary to have a standard spectrum to compare with. To obtain a standard spectrum the following measuring scheme was followed for all the measured samples: (1) hyperquenching (unknown cooling rate); (2) annealing (when applied); (3) DSC upscan (Qh = 20 K/min); (4) DSC downscan (Qc = 20 K/min) and (5) DSC upscan (Qh = 20 K/min). Steps 3–5 are performed within the DSC, and the result is Cp-measurements during two upscans. The second can be considered a ‘standard scan’ on a glass system with the well known thermal history of Qc = 20 K/min. This procedure was first introduced in [12]. Fig. 3 shows the two upscans made following this procedure on a sample of E glass. In the figure it is clear that the as-drawn raw fibers show different spectra when measured because of the fast cooling. Four important parameters can be extracted from the Cp curves shown in Fig. 3 The isobaric heat capacity of the liquid (Cpl) is assumed to be temperature independent, and taken as the average of the values of the measurement at the highest temperatures. The isobaric heat capacity of the glass (Cpg) is fitted by a linear function at temperatures just below Tg and then the value of this function at Tg is reported. The Tg is evaluated as described previously. The total released enthalpy (Hexc) is determined as the area enclosed by the two curves. In the figure Tf is indicated, determined by the area matching method [12,25]. The values determined in this way for all six samples are shown in Table 2. Regardless of the high level of information in the properties from the Cp spectra shown in Table 2, they do not show the temperature dependence of the enthalpy relaxation. As the relaxation of frozen-in enthalpy in HQ and annealed HQ systems is our main concern, we introduce
1.6
Cp (J K-1 g-1)
m¼
C pl
1.4
1.2
Cpg
1
Tf
0.8
Tg 400
600
800
1000
1200
T (K) Fig. 3. Measured values of Cp for E-glass. The lower curve is the first upscan on the HQ sample. The upper curve is the second upscan on the sample cooled with 20 K/min. Both upscans are with 20 K/min. The figure shows how Cpl, Cpg, and Tg are estimated by linear extrapolations. The total excess enthalpy Hexc is determined as the integral of the area enclosed by the two upscan curves. Tf is determined by the area matching method, which is based on the equality of the two light gray areas in the figure.
the Cp,exc relaxation spectrum. This is simply the difference between the second and the first DSC scans on the original sample. The Cp,exc spectrum is thus a plot of the excess enthalpy of the HQ sample. For a well annealed sample, or a sample cooled with a cooling rate slower than 20 K/ min Cp,exc is endothermic, whereas a fast cooled sample has an exothermic Cp,exc. Fig. 4 shows Cp,exc for as-drawn fibers from all measured compositions. The measurement shown in Fig. 3 is included (No. 4) and clearly shows the advantage of this kind of representation. For the strong glass, GeO2, the spectrum looks quite symmetrical. For the most fragile composition (55CaO Æ 45SiO2) on the other hand, the relaxation spectrum is clearly a two-domain type peak: a major peak close to Tg (the a-domain), and a smaller ‘shoulder’ at lower temperature (the b-domain). Fig. 5 shows raw data as obtained. In the figure the relative uncertainty of the method is seen as the level of noise on
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0.3
Cp.exc (J g-1 K-1 )
4 0.2
0.1
2 6
5 3
1
0 0.4
0.6
0.8
1
T/Tg (K/K) Fig. 4. Cp,exc for the HQ fibers from all six compositions, shown against temperature relative to Tg. Numbers correspond as follows: (1) GeO2, (2) NIST, (3) Basalt, (4) E-glass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2.
the measurements. This uncertainty becomes pronounced for GeO2 because of the low intensity of the relaxation peak. The uncertainty from the handling of the sample can be estimated by analysis of the ‘zero’ line at low temperatures. Theoretically the line should have an absolute value of 0 because no difference is expected in Cp for the first and second upscans at temperatures below the onset. Fig. 5 shows clearly that there is a difference between the highest and lowest ‘zero’ lines, which is then a measure of the error on the experiment. Fig. 5 is presented to give the overall picture of the enthalpy relaxation for different fragilities, as this shows a number of features which is difficult to extract from raw data in a satisfactory way. For each sample a number of annealing temperatures are presented at a number of times. But as the figure is intended for clarification of overall trends, the measurements are not labeled independently. The values of ta are of course shorter for samples showing more enthalpy release at the same Ta and at a given ta the increasing Ta results in less enthalpy release. Fig. 6 shows three problems often experienced when measuring the Cp spectra shown in Fig. 5. The curves shown in the figure are all measurements on E-glass. The first problem is associated with changes in the packing density of the fiber sample during the measurement. This is shown in the figure in the measurement presented with the dashed curves. The two curves are the first and second upscans. The outcome of the problem is a clearly visible deviation of the first upscan from the second one at low temperatures. Assumably this deviation will persist throughout the whole measurement and thus measurements with a large deviation have been discarded. The second problem is the possible baseline drift. This case is shown by the dotted line, which is a second upscan.
The dotted line shows that the measured Cp decreases with increasing temperature when approaching Tg. If such an effect is from a baseline problem the first upscan can be assumed to show the same effect. Thus the Cp,exc spectrum will not be affected and is therefore still usable. In this case the determination of Tf from the second upscan is of course not possible. The third problem appears when sample handling includes crushing of the fibers subsequent to annealing. If such a treatment is done to a sufficiently high degree of disintegration a prepeak appears in the Cp,exc spectrum. The solid curves in the figure show this peak in the first upscan. The peak is not very intense and is therefore not detectable on the upscan on the HQ fiber. Neither is the peak observed in a sample crushed prior to annealing, because the excess enthalpy from the crushing is annealed out parallel to the structural relaxation. In the figure the peak is shown for an annealed sample. For some of these experiments it is possible to subtract the prepeak, but unfortunately it has been required to discard some measurements as well. 4. Discussion In general, the detailed features of the enthalpy relaxation of glasses depend on glass composition, hence, glass structure, and thermal history. Different chemical compositions give different fragilities. Thus, we should see a relation between the enthalpy relaxation features and the fragility, i.e. a relation between a thermodynamic and a dynamic feature, since the enthalpy relaxation is a thermodynamic response, whereas fragility is a dynamic feature. In this work we focus on the details of the impact of fragility on the enthalpy relaxation, both for HQ and annealed HQ fibers. The fragility parameter is an outcome of the structure of the liquid and thus might be connected to the way the enthalpy is frozen in on cooling. The samples studied in this work cover a wide range of fragility from m = 30 (for GeO2) to 150 (for CS55). For the CS glasses, nuclear magnetic resonance spectra show no indication of crystallinity [26], and thus the formed glasses are highly amorphous. Two different fiber drawing methods were used to produce the fibers. Both methods are expected to introduce some amount of anisotropy and thereby mechanical structure change in the samples. Such effects have been ignored because of suggestions that the enthalpy excitation with this origin is very small compared to the amount from thermal quenching [16,27]. The amount of released enthalpy during the DSC scan is strongly dependent on thermal history. Thus the cooling rate is very important when comparing the Cp,exc curve for the different compositions. The cooling rate depends on the temperature of the liquid when the fibers are made and on the drawing speed. Even though these two numbers are well known during the continuous fiber drawing, it is in fact impossible to calculate the precise cooling rate for two reasons. Firstly, the temperature decay is not constant, but
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0.2
1
2
3
4
5
6
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0.1
0
-0.1
0.3
-1 -1
Cp.exc (J K g )
0.2
0.1
0
-0.1
0.2
0.1
0
-0.1 500
700
900
1100
500
700
900
1100
T (K) Fig. 5. Cp,exc spectra from all compositions at a number of different Ta and ta. The compositions are shown in the order of increasing fragility, from left to right. The numbers on the figure thus correspond to the compositions as follows: (1) GeO2, (2) NIST, (3) Basalt, (4) E-glass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2. The spread around zero at the lowest temperature on each graph is a measure for the absolute error of the measurements.
rather exponential, according to normal heat diffusion. The liquid thus move through an exponentially decaying temperature reservoir with high constant speed. Secondly, the glass transition zone on freezing-in at high speed is very broad, probably covering several hundreds of degrees, leading to a difficulty in attributing a certain transition temperature. In Table 2 are given the values for the cooling rate calculated ad hoc by assuming a constant temperature decay for the exponential around Tg, and then calculating the distance from the die, where the temperature is 100 K below Tg. The cooling rate can then be calculated from the drawing speed. For the cascade fiber process the draw-
ing speed is not well known, but from simulations on this process a maximum velocity is calculated to be between 15 m/s and 30 m/s [13]. In the case of the cascade fibers this value is used to calculate an estimated cooling rate in the same way as for the continuous fibers. Due to the problems described above we have not been able to obtain the same cooling rates for the samples investigated. However, because it is evident that changing the cooling rate only changes the intensity of the enthalpy release spectrum for a given material and not the shape, we are still able to compare the spectra from different compositions. In addition, it is not to be expected from
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describe dielectric relaxation in terms of Johari–Goldstein b relaxations [28].
1.8
4.2. Effect of annealing
1.6
-1
-1
Cp (J g K )
1.4
1.2
1
0.8
0.6 400
600
800
1000
T (K) Fig. 6. Common errors seen in measurements of Cp. Measurements on Eglass are shown as examples. The solid lines are first and second upscans on E-glass annealed for 2 days at 800 K, showing a pronounced prepeak from 600 to 800 K. The dashed lines show a difference in the glass Cp between the two upscans, using E-glass annealed for 3.5 h at 750 K. The dotted line is a second upscan for E-glass, showing a decreasing Cpg.
considerations of the values of Cp that the same thermal history for two different materials will result in the same amount of frozen-in enthalpy. Rather we expect that this do depend significantly on the absolute value of Cp. Fig. 5 shows the DSC results from measurements on the six glasses annealed at different temperatures and times. The figure clearly confirms the results presented earlier on basaltic fibers, where three important features have been described [6]: (1) a relaxation distributed in two domains; (2) a decrease in the relaxation function on annealing starting from low temperature; and (3) a sub-Tg endotherm appearing at high Ta and ta. Each of these three important phenomena is described below with the focus on the fragility dependence of these phenomena.
4.1. Relaxation distributed in two domains The extent of the two domain relaxation function for the measured samples is shown in Figs. 4 and 5, the six samples are shown in the order of increasing fragility from left to right. In both representations the change in the shape of the Cp,exc peak is seen as an increasing b domain when fragility increases. For GeO2 the relaxation does not have any pronounced b domain, while the figure shows that this is indeed the case for ST and CS samples. This increase has been suggested to be explainable by models used to
Annealing causes the relaxation spectrum to diminish in a typical way for all fibers. Annealing for short times and at low temperatures (around 0.65–0.75Tg) only relaxes the b domain, so that the peak becomes a Gaussian shape. Only with fairly high annealing temperatures (around 0.85– 0.90Tg) the main relaxation decreases. In Fig. 5 this can be seen for the ST sample where long time at Ta = 800 causes complete relaxation. This is typical for the fragile samples, which all have a pronounced b domain. The results for the strong GeO2 composition and partly those for NIST show a quite different annealing behavior. It seems from the figure that the annealing effect is equivalently distributed over the whole range of the relaxation peak, so that the intensity of the entire peak relaxes by annealing. This agrees well with the fact that no pronounced b domain is seen for these strong systems. In the framework of the energy landscape [29], the explanation for these observations would include a more and more pronounced splitting of the mega basin responsible for the a relaxation into sub-basins where the activation energy is lower with increasing fragility. Fragile systems with such a splitting will then have a structure partly filling the sub-basins. With sufficient activation energy (i.e. Ta) these basins can change their internal occupancy and thus structural relaxation is possible. The activation energy for viscous flow (a relaxation, mega basin potential) is higher and thus requires a higher Ta to change occupancy and this part of structural relaxation is thus not possible at low annealing temperatures. For the ST sample this is clearly visible. For a number of annealing experiments up to a limiting Ta only annealing of the b domain takes place. Only above the limiting value of Ta the temperature is sufficiently high to relax the a domain. The same observations are done for the other samples, but not nearly as pronounced as for the ST sample. 4.3. The sub-Tg endotherm The sub-Tg endotherm is not pronounced for any compositions apart from ST. The E sample shows it, but not as pronounced as the ST sample. The reason for this could be found in the difference in fragility. The E sample is less fragile than the ST and therefore the difference between the activation energies for the two relaxations is smaller. This means that the a domain will relax simultaneously with the b domain. In such a situation no sub-Tg endotherm is expected to occur. For the most fragile CS systems the endotherm is not pronounced either. It is not evident why this is not the case from the measurements presented here. There is evidently no phase separation or crystallization problems during annealing, and the system is very fragile. A small endotherm is observed after sufficient
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4.4. Development of an additional exothermic peak
1.4
1.3
Cpl /Cpg
annealing, but for this glass the main relaxation also changes during the appearance of this sub-Tg endotherm. It has been suggested that for glasses with a crystal content as low as 0.2%, no endotherm appears [30]. Such small crystal content is in the detection limit of the NMR measurements used to test the CS sample for crystal content and therefore the reason for the missing endotherm might be connected to this problem.
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1.2
A fourth very striking observation in addition to the three observations described above is apparent from Fig. 5. At high temperatures, above Tg, the systems seem to show a more and more pronounced sharp exothermic peak as fragility increases. For GeO2 no peak is seen at all. NIST shows a small tendency for a narrowing of the highest part of the a domain into a small peak on annealing. For the E glass a high temperature sharp peak is clearly the outcome of annealing, the peak being a part of the original a domain. For the Basalt glass the a domain is seen to have an additional sharp peak developing during annealing. For the two calcium-silicates the high temperature peak is a striking feature of the spectrum and is actually not disappearing for any of the shown measurements. The peak eventually disappears for Ta > 0.9Tg. This observation has not been previously reported to our knowledge, and should be a subject for further experiments. Evidently, fragility has an impact on the enthalpy relaxation of the samples, and it seems as if the effect systematically changes the relaxation spectra of glasses.
1.1
1
0
50
100
150
m Fig. 7. Fragility dependence of the ratio Cpl/Cpg at the glass transition.
the difficulty in establishing a relationship between the fragility index and the thermodynamic glass transition. The amount of released enthalpy is dependent on cooling rate and can probably not be compared between the different compositions. For the same composition, however, we expect Hexc to decrease with increasing Ta and ta. Fig. 8 shows the dependence of calculated values of Hexc on ta. To compare the systems independent of the absolute value of Hexc, the figure shows the relative value Hexc(ta)/
4.5. Fragility and the glass transition
0.8
Hexc(tA)/Hexc(tA=0)
Several suggestions to a possible connection between parameters extracted from the thermodynamic glass transition and the kinetic fragility have been proposed [31–34]. Originally the fragility was suggested to be connected to the size of the jump in heat capacity observed in DSC measurements at Tg [31]. Later on this has been opposed based on measurements on a range of substances [33,34]. Because of the large amount of standard measurements of Cp on each composition available from the second upscans performed, we have the possibility to investigate the connection between the fragility and the calorimetric glass transition closer. Fig. 7 shows the average Cp jump observed at the glass transition. The quantity is shown as Cpl relative to Cpg, and thus gives values above 1 for all samples. The error bar represents the standard deviation in the estimations. The result for each composition is the mean value for all second upscans. The figure shows an increase in the jump with increasing fragility, but does not show any linear dependence. This supports the conclusions presented earlier [34]. The error bars in the figure are quite substantial and show the problem with exact estimation of heat capacities, even with the high number of measurements used here. This might be one of the reasons for
0.6
0.4
0.2
0 -1
0
1
2
3
4
log (tA(min)) Fig. 8. Influence of annealing time on the Hexc. The Hexc is shown relative to the Hexc of the HQ glass to compare the results for different systems. Filled circles are GeO2 at 650 K, filled squares are NIST at 650 K, diamonds are E-glass at 750 K, open squares are Basalt at 750 K, open circles are 45CaO Æ 55SiO2 at 800 K, and triangles are 55CaO Æ 45SiO2 at 700 K.
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Hexc(HQ), where Hexc(HQ) is the absolute value of the release for the HQ glass. A specific annealing temperature is selected for each of the six samples so that Ta/Tg is approximately 0.77. From Fig. 5 it is expected that the calculated value decreases with increasing annealing time. The time is shown logarithmically to be able to see the whole range of times. Generally an exponentially decreasing trend is observed with increasing ta. In the figure linear fits are not included to avoid too much crowding, but in a first approximation this seems likely. Also errors bars are not included, but these are around 10–15%, which is the uncertainty on the estimation of Hexc. An exponential decrease (a straight line) in Hexc with increasing time supports a model featuring energy barriers with heights corresponding to activation energies. 5. Conclusions HQ glasses with a wide range of fragilities are measured using a DSC before and after annealing at temperatures below Tg for various durations. The results indicate that the relaxation of the HQ glasses during annealing depends on the fragility of the system. For strong systems, the enthalpy relaxation is manifested by a continuous decrease in the intensity of the entire Cp,exc peak with increasing the annealing degree (Ta and ta). In contrast, for fragile systems annealing at low temperatures results in a continuous decrease of only a part of the Cp,exc peak. This is manifested by a shift of the low temperature cutoff of the peak while the high temperature part remains unchanged. The results clearly illustrate the need to further consider a possible structure change of fragile liquids from the high end of the viscous liquids to the high viscosity regime. By further experiments on glass-forming systems with well determined relaxation properties in the viscous liquid regime, much more detailed information on the possible reason for the non-Ahrrenian temperature dependence of fragile systems could be achieved. Acknowledgment This work was supported by the Danish Research Council under Grant No. 26-03-0096.
References [1] L.M. Wang, V. Velikov, C.A. Angell, J. Chem. Phys. 117 (2003) 10184. [2] E. Cernoskova, Z. Cernosek, J. Holubova, J. Non-Cryst. Solids 326 (2003) 141. [3] Z. Cernosek, J. Holubova, E. Cernoskova, M. Liska, J. Optoelectron. Adv. Mater. 4 (2002) 489. [4] C.A. Angell, Y.Z. Yue, L.M. Wang, J.R.D. Copley, S. Borick, S. Mossa, J. Phys.: Condens. Matter 15 (2003) 1051. [5] N. Giovambattista, C.A. Angell, F. Sciortino, H.E. Stanley, Phys. Rev. E 72 (2005) 1. [6] Y.Z. Yue, Phys. Chem. Glasses 46 (2005) 354. [7] J. Huang, P.K. Gupta, J. Non-Cryst. Solids 139 (1992) 239. [8] C.A. Angell, J. Therm. Anal. 69 (2002) 794. [9] S. Vyazovkin, I. Dranca, Thermochim. Acta 446 (2006) 140. [10] G.P. Johari, J. Phys. Chem. B 107 (2003) 9063. [11] Y.Z. Yue, C.A. Angell, Nature 427 (2004) 717. [12] Y.Z. Yue, J.de C. Christiansen, S.L. Jensen, Chem. Phys. Lett. 357 (2002) 20. [13] R. Von der Ohe, PhD thesis, Aalborg Univesity, 2003. [14] A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240. [15] J.-P. Ducroux, S.M. Rekhson, F.L. Merat, J. Non-Cryst. Solids 172– 174 (1994) 541. [16] H. Stockhorst, R. Bruckner, J. Non-Cryst. Solids 49 (1982) 471. [17] O.S. Narayanaswamy, J. Am. Ceram. Soc. 54 (1971) 491. [18] G.P. Johari, M. Goldstein, J. Chem. Phys. 53 (1970) 2372. [19] G.W. Scherer, Relaxation in Glass and Composites, John Wiley, NY, USA, 1986. [20] R. Bo¨hmer, C.A. Angell, Phys. Rev. B 45 (1992) 10091. [21] J.O’M. Bockris, D.C. Lowe, Proc. Roy. Soc. A 226 (1954) 423. [22] P. Saravanapavan, L.L. Hench, J. Non-Cryst. Solids 318 (2003) 1. [23] C.A. Angell, J. Non-Cryst. Solids 131–133 (1991) 13. [24] H. Vogel, Physik. Zeitschr. 22 (1921) 645. [25] C.T. Moynihan, A.J. Easteal, M.A. DeBolt, J. Tucker, J. Am. Ceram. Soc. 59 (1976) 12. [26] L. Hornbøll, PhD thesis, Aalborg University, 2007. [27] L. Hornbøll, N. Lonnroth, Y.Z. Yue, J. Am. Ceram. Soc. 89 (2006) 70. [28] L. Hornbøll, Y. Yue, J. Non-Cryst. Solids, in press, doi:10.1016/ j.jnoncrysol.2007.06.101. [29] F.H. Stillinger, Science 267 (1995) 1935. [30] G.P. Johari, J. Chem. Phys. 119 (2003) 2935. [31] C.A. Angell, in: K.L. Ngai, G.B. Wright (Eds.), Relaxations in Complex Systems, National Technical Information Service, US Department of Commerce, Springfield, VA, 1985, p. 3. [32] L.M. Wang, C.A. Angell, R. Richert, J. Chem. Phys. 125 (2006) 074505-1. [33] C.M. Roland, P.G. Santangelo, C.G. Robertson, K.L. Ngai, J. Chem. Phys. 118 (2003) 10351. [34] D.H. Huang, G.B. McKenna, J. Chem. Phys. 114 (2001) 5621.
Journal of Non-Crystalline Solids 354 (2008) 1862–1870 www.elsevier.com/locate/jnoncrysol
Enthalpy relaxation in hyperquenched glasses of different fragility Lasse Hornbøll, Yuanzheng Yue
*
Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark Received 1 March 2007; received in revised form 15 September 2007
Abstract The enthalpy relaxation in hyperquenched (HQ) glasses with a wide range of fragilities is studied by performing annealing and differential scanning calorimetric (DSC) experiments. In this work, the enthalpy relaxation behavior of annealed HQ glasses is characterized in terms of the excess heat capacity (Cp,exc) given by the difference between the first and the second DSC measurements on the HQ glasses. The shape of the Cp,exc curves depends on the fragility of the glass system, which implies that during annealing the mechanism of the structural relaxation of the HQ strong systems differs from that of the HQ fragile systems. The details of the fragility dependence of the Cp,exc curves have been discussed in terms of the energy landscape and the structure of the liquids. 2007 Elsevier B.V. All rights reserved. PACS: 64.70.Pf; 65.60.+a; 81.40.Gh Keywords: Glass transition; Germania; Silicates; Fragility; Structural relaxation
1. Introduction In recent years, the study of enthalpy relaxation in hyperquenched (HQ) glasses has attracted considerable interests of glass scientists because it provides rich information on the structural relaxation in glasses and the potential energy landscape of liquids [1–6]. Hyperquenching here refers to a cooling process at a rate of 106 to 108 K/min. A calorimetric temperature scan on HQ glasses at a rate of 20 K/min results in a large exothermic enthalpy relaxation response prior to the glass transition, when compared to glasses cooled at the standard rate of 20 K/min [4–7]. This response is usually characterized by the difference in isobaric heat capacity (Cp) between the HQ glass and the standard glass. When the glass is hyperquenched, high energy states are frozen in. The enthalpy relaxation response is therefore a direct outcome of the distribution
*
Corresponding author. Tel.: +45 96358522; fax: +45 96350558 E-mail addresses: [email protected] (L. Hornbøll), [email protected] (Y. Yue). 0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.10.023
of frozen-in states, and thus a semi-direct measure of the energy landscape of a liquid. Measurements of annealed HQ glass are very useful to obtain further information on the energy landscape [6,8,9]. Annealing of the HQ glass in the temperature range from the glass transition temperature (Tg) to 0.6Tg results in a decreasing amount of relaxed enthalpy [6,8,9]. For basaltic glass this decrease is predominantly seen in the low temperature regime of the relaxation exotherm for low annealing temperatures (Ta) [6]. The change in the relaxation spectrum resulting from annealing at different time and temperature shows a number of features, which have been discussed thoroughly for basaltic glass [6]. The most prominent of these is the sub-Tg endotherm, which has been detected for a number of glass systems [2,6,8– 10] and which has provided new information on the glass transition of water [11]. Previously, experiments on the enthalpy relaxation of HQ glasses have been used to calculate the fictive temperature (Tf) of the glasses [12] and from this to calculate the cooling rate of the fibers by using information on the liquid relaxation properties [13]. This is of high technological
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importance, because Tf is an important parameter for controlling the forming and annealing conditions of glass products. Tf for any glass is defined as the temperature of the melt, at which the structure of the glass equals that of the melt [14]. In terms of configurational entropy (Sc), Tf of a glass corresponds to the temperature of the liquid with the same amount of Sc. As Sc is directly coupled to structure, it is evident that any change in structure will result in a change in Tf, including changes in the structure from external forces during glass formation. Fiber drawing is a widely used method to obtain HQ glass [4,7,15]. In fiber drawing the high cooling rate is obtained by a rapid increase in surface area and simultaneously a rapid decrease in temperature. The surface increase requires a high directional force, which leads to an oriented structure in the glass [16]. As this is also a structural change, it will evidently change the enthalpy relaxation response and Tf. In the Tool–Narayanaswamy model Tf is a measure of the total relaxation time in the glass [14,17]. Because the total relaxation time in glasses is not a simple function, but rather is made up from several distributions of relaxation times [18], the Tf is not a detailed measure of the relaxation behavior of the glass [19]. Rather it is a sum of all relaxation times in the glass corresponding to the microstructures within the glass. In the view of these arguments it is not enough to model a glass by the fictive temperature, and interpreting this temperature as corresponding to a liquid with a given structure. Although the features observed in DSC experiments of both HQ and annealed HQ have been well described for basaltic glasses, it is not known whether these features are universal for HQ glasses or whether they depend on chemical composition. To establish this we here present results on the enthalpy relaxation for six different glass compositions. The compositions are chosen to be oxideglass-forming systems of different origin, with the basic idea to achieve a wide distribution of fragilities, without taking specific chemical composition into account. In the concept of fragility, all glass-forming systems can be attributed a fragility index (m), based on the dependence of the relaxation time of the liquid on the temperature [20]. The more non-Arrhenian this dependence is, the more fragile is the melt (higher m). Vitreous GeO2 was chosen as the strongest glass and two different calcium-silicate compositions as the most fragile. To cover the intermediate fragility range two standard glasses and a basaltic composition were measured.
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2. Experimental Six glass systems were prepared as HQ glasses by fiber drawing. One system was the standard glass NIST 710a obtained from National Institute of Standards and Technology (see Table 1 for the composition). Another was GeO2 glass fibers obtained by melting the crystalline material directly in the fiber drawing crucible. The chemical composition of the remaining four systems as obtained by X-ray fluorescence analysis is given in Table 1. ST is a basaltic composition made from a mixture of natural minerals. For the compositions labeled E and CS both glass fibers and glass for viscosity measurements were prepared from pure raw chemicals obtained from Fluka: SiO2, Al2O3, CaCO3, MgO, and B2O3. Each batch was prepared by careful hand mixing for 15 min. The batch was melted in an electrical furnace in a Pt/Rh crucible at 1500 C for 2 h, quenched in water, remelted at 1500 C for 4 h and then cast in a graphite form. The same melting procedure was used for NIST and ST. Continuous fibers from compositions E, Ge and NIST were drawn from a Pt crucible through a 1.8–2 mm die in the bottom by means of a high speed spinning wheel of Ø 35 cm. The drawing speed was 1.2 m/s. The resulting fibers were homogeneous and approximately 10 lm thick with only small variation in fiber thickness and no sign of crystallization or inhomogeneities. Before annealing experiments and DSC measurements the fibers were cut into small pieces of lengths ranging from 0.1 to 1 mm. Fibers of CS and ST samples were made by a cascade process, where the melt was poured directly onto the high speed spinning wheel and the fibers collected on the wall surrounding the wheel. The resulting fibers were of diameters (d) between 5 and 50 lm and of lengths between 1 and 5 mm. Before annealing experiments and DSC measurements the fibers were sieved in a 63 lm sieve to separate fibers from the large amount of droplets formed by the cascade process. Annealing was carried out in a muffle furnace sustaining temperatures in the range from 400 K to 1300 K with a precision within 1 K. Annealing was done in ambient conditions for pressure, atmosphere and humidity. Annealing was carried out by placing a platinum crucible with the sieved or crushed sample directly into a preheated furnace. After annealing the sample was removed from the furnace and left to cool under ambient conditions. For each system annealing was carried out systematically at 2–5 different
Table 1 Chemical composition of the measured glass-forming systems in molar%
GeO2 NIST 710a E-glass Basalt 45CaO Æ 55SiO2 55CaO Æ 45SiO2
SiO2
CaO
Al2O3
MgO
100% GeO2 68 55 40 55 45
8 17 18 45 55
2 15 21
5 8
FeO
Na2O
TiO2
8
K2O
B2O3
9
4 8
7
2
2
1
ZnO
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1.8 1.6
3 -1 -1
annealing temperatures between Ta = 0.5Tg and Ta = 0.9Tg. For each Ta, annealing was carried out for different periods of annealing time (ta) ranging from 10 min to 44 days. DSC measurements were carried out on a heat flux DSC instrument (Netzsch, STA 449C Jupiter). The measurements included 4 DSC scans: Correction with empty crucibles to reduce background noise, standard scan with an empty reference crucible and a sapphire reference material as the sample, fresh fiber as sample, and the same fiber sample cooled within the DSC instrument with 20 C/min. The Cp curve for a measurement was calculated relative to the Cp of the standard sapphire crystal after subtraction of the correction run to remove the background noise. Measurements were carried out in purged Argon gas atmosphere. The sample mass was between 18 and 22 mg. For the determination of the glass transition temperature (Tg) a cooling (Qc) and heating (Qh) rate of 10 K/min was used to apply to DIN 53765. The high temperature viscosity measurements were carried out with a load-controlled rheometer (Paar-Physica MC1 rheolab). The rheometer was mounted on top of a furnace with a temperature stability of ±1 K. The measurement geometry was a cup/cylinder with the cylinder cone formed in the ends. The stress applied in the measurements was between 7 Pa and 7000 Pa and the resulting shear rates were between 0.5 and 27.
Cp (J K g )
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1.4
2
4
1.2
5 6
1 0.8
1 0.6 400
600
800
1000
T (K) Fig. 1. Glass transitions of the six samples from Table 1 determined at a heating rate of 10 K/min subsequent to a cooling rate of 10 K/min. Numbers correspond as follows: (1) GeO2, (2)NIST, (3) Basalt, (4) Eglass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2. Values of Tg for the samples estimated from these measurements are shown in Table 2.
12
3. Results
8
log (η (Pa s))
For all the compositions shown in Table 1 Tg was determined by a DSC scan at 10 K/min according to the standard procedure for estimating Tg. Fig. 1 shows the DSC upscans for all six glass compositions. The Tg is determined from the DSC measurements by extrapolating lines fitted to the sharp rise at the transition zone and a straight line fitted to the glass heat capacity (Cpg) (as shown in Fig. 2). The Tg is then given by the intercept of the lines and is shown in Table 2 for all the compositions. The Tg determined this way corresponds within 2 K to the temperature of the inflection point on the recorded downscan with a rate of 10 K/min. In addition the figure shows the large difference in the thermal response of the GeO2 glass compared to the others. The small jump in Cp at Tg results in a higher uncertainty on measurements on the GeO2 glass. Viscosity data for all six compositions are shown in Fig. 2. The high temperature data for the CS compositions are taken from [21]. The figure clearly shows the wide variety in the crystallization behavior of the melts as the lowest temperature where viscosity can be measured. Where the GeO2 and NIST melts have no tendency to crystallize at all, the calcium-silicates readily crystallize leaving no chance of glass formation without hyperquenching. Measured values at temperatures below 1500 K obtained for the calcium-silicates were not reproducible, probably because of phase separation of some kind taking place [22]. In the figure, the viscosity data are plotted in a fragil-
10
6 4 2 0 -2 -4 0
0.2
0.4
0.6
0.8
T/Tg (K/K) Fig. 2. Viscosity measurements and Tg from Table 2 viewed in a fragility plot. Open squares: GeO2, closed squares: NIST, open diamonds: E-glass, closed diamonds: Basalt, open circles: 45CaO Æ 55SiO2, closed circles: 55CaO Æ 45SiO2. The measurements are fitted with Eq. (1). The value of the fragility parameter (m) determined by Eq. (2) is shown in Table 2.
ity plot [23] using the Tg values from Table 2. In a fragility plot the viscosity is plotted against Tg/T. In Fig. 2 the data are fitted with Eq. (1) [24] by a Levenberg–Marquadt fitting procedure, adjusting g0, T0, and D: DT 0
g ¼ g0 eðT T 0 Þ :
ð1Þ
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Table 2 Characteristic parameters of the glasses determined by viscosity measurements and DSC Tdraw (K) GeO2 NIST 710a E-glass Basalt 45CaO Æ 55SiO2 55CaO Æ 45SiO2
1673 1523 1563 1773 1803 1803
Qc (K/s) 4
7 · 10 9 · 104 11 · 104 9 · 105 10 · 105 12 · 105
m
Tg (K)
DCp (J/g K)
Hexc (J/g)
Tf (K)
17.5 44.6 51.2 62.5 90.4 141.2
830 831 962 943 1025 1056
0.045 0.14 0.26 0.34 0.33 0.37
22 34 54 79 50 59
1271 1000 1135 1215 1150 1250
Tdraw is the temperature of the melt during fiber drawing. Qc is the estimated cooling rate. m is the fragility index determined by Eq. (2). DCp is the difference between the Cp of the liquid and the Cp of the glass taken at Tg. Hexc is the sum of enthalpy released in the relaxation peak seen in Fig. 4. Tf is the fictive temperature determined as shown in Fig. 3.
From the fits the fragility indices for the six systems were determined according to Eq. (2) [23]: 1 T gT 0 D: ln 10 ðT g T 0 Þ2
ð2Þ
The determined fragility indexes are listed in Table 2. The DSC upscans shown in Fig. 1 are all made on samples previously cooled from above the glass transition with the specific rate of 10 K/min. This allows for direct comparison between the different glasses studied in this work. To be able to compare the enthalpy relaxation functions of these systems as well it is necessary to have a standard spectrum to compare with. To obtain a standard spectrum the following measuring scheme was followed for all the measured samples: (1) hyperquenching (unknown cooling rate); (2) annealing (when applied); (3) DSC upscan (Qh = 20 K/min); (4) DSC downscan (Qc = 20 K/min) and (5) DSC upscan (Qh = 20 K/min). Steps 3–5 are performed within the DSC, and the result is Cp-measurements during two upscans. The second can be considered a ‘standard scan’ on a glass system with the well known thermal history of Qc = 20 K/min. This procedure was first introduced in [12]. Fig. 3 shows the two upscans made following this procedure on a sample of E glass. In the figure it is clear that the as-drawn raw fibers show different spectra when measured because of the fast cooling. Four important parameters can be extracted from the Cp curves shown in Fig. 3 The isobaric heat capacity of the liquid (Cpl) is assumed to be temperature independent, and taken as the average of the values of the measurement at the highest temperatures. The isobaric heat capacity of the glass (Cpg) is fitted by a linear function at temperatures just below Tg and then the value of this function at Tg is reported. The Tg is evaluated as described previously. The total released enthalpy (Hexc) is determined as the area enclosed by the two curves. In the figure Tf is indicated, determined by the area matching method [12,25]. The values determined in this way for all six samples are shown in Table 2. Regardless of the high level of information in the properties from the Cp spectra shown in Table 2, they do not show the temperature dependence of the enthalpy relaxation. As the relaxation of frozen-in enthalpy in HQ and annealed HQ systems is our main concern, we introduce
1.6
Cp (J K-1 g-1)
m¼
C pl
1.4
1.2
Cpg
1
Tf
0.8
Tg 400
600
800
1000
1200
T (K) Fig. 3. Measured values of Cp for E-glass. The lower curve is the first upscan on the HQ sample. The upper curve is the second upscan on the sample cooled with 20 K/min. Both upscans are with 20 K/min. The figure shows how Cpl, Cpg, and Tg are estimated by linear extrapolations. The total excess enthalpy Hexc is determined as the integral of the area enclosed by the two upscan curves. Tf is determined by the area matching method, which is based on the equality of the two light gray areas in the figure.
the Cp,exc relaxation spectrum. This is simply the difference between the second and the first DSC scans on the original sample. The Cp,exc spectrum is thus a plot of the excess enthalpy of the HQ sample. For a well annealed sample, or a sample cooled with a cooling rate slower than 20 K/ min Cp,exc is endothermic, whereas a fast cooled sample has an exothermic Cp,exc. Fig. 4 shows Cp,exc for as-drawn fibers from all measured compositions. The measurement shown in Fig. 3 is included (No. 4) and clearly shows the advantage of this kind of representation. For the strong glass, GeO2, the spectrum looks quite symmetrical. For the most fragile composition (55CaO Æ 45SiO2) on the other hand, the relaxation spectrum is clearly a two-domain type peak: a major peak close to Tg (the a-domain), and a smaller ‘shoulder’ at lower temperature (the b-domain). Fig. 5 shows raw data as obtained. In the figure the relative uncertainty of the method is seen as the level of noise on
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0.3
Cp.exc (J g-1 K-1 )
4 0.2
0.1
2 6
5 3
1
0 0.4
0.6
0.8
1
T/Tg (K/K) Fig. 4. Cp,exc for the HQ fibers from all six compositions, shown against temperature relative to Tg. Numbers correspond as follows: (1) GeO2, (2) NIST, (3) Basalt, (4) E-glass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2.
the measurements. This uncertainty becomes pronounced for GeO2 because of the low intensity of the relaxation peak. The uncertainty from the handling of the sample can be estimated by analysis of the ‘zero’ line at low temperatures. Theoretically the line should have an absolute value of 0 because no difference is expected in Cp for the first and second upscans at temperatures below the onset. Fig. 5 shows clearly that there is a difference between the highest and lowest ‘zero’ lines, which is then a measure of the error on the experiment. Fig. 5 is presented to give the overall picture of the enthalpy relaxation for different fragilities, as this shows a number of features which is difficult to extract from raw data in a satisfactory way. For each sample a number of annealing temperatures are presented at a number of times. But as the figure is intended for clarification of overall trends, the measurements are not labeled independently. The values of ta are of course shorter for samples showing more enthalpy release at the same Ta and at a given ta the increasing Ta results in less enthalpy release. Fig. 6 shows three problems often experienced when measuring the Cp spectra shown in Fig. 5. The curves shown in the figure are all measurements on E-glass. The first problem is associated with changes in the packing density of the fiber sample during the measurement. This is shown in the figure in the measurement presented with the dashed curves. The two curves are the first and second upscans. The outcome of the problem is a clearly visible deviation of the first upscan from the second one at low temperatures. Assumably this deviation will persist throughout the whole measurement and thus measurements with a large deviation have been discarded. The second problem is the possible baseline drift. This case is shown by the dotted line, which is a second upscan.
The dotted line shows that the measured Cp decreases with increasing temperature when approaching Tg. If such an effect is from a baseline problem the first upscan can be assumed to show the same effect. Thus the Cp,exc spectrum will not be affected and is therefore still usable. In this case the determination of Tf from the second upscan is of course not possible. The third problem appears when sample handling includes crushing of the fibers subsequent to annealing. If such a treatment is done to a sufficiently high degree of disintegration a prepeak appears in the Cp,exc spectrum. The solid curves in the figure show this peak in the first upscan. The peak is not very intense and is therefore not detectable on the upscan on the HQ fiber. Neither is the peak observed in a sample crushed prior to annealing, because the excess enthalpy from the crushing is annealed out parallel to the structural relaxation. In the figure the peak is shown for an annealed sample. For some of these experiments it is possible to subtract the prepeak, but unfortunately it has been required to discard some measurements as well. 4. Discussion In general, the detailed features of the enthalpy relaxation of glasses depend on glass composition, hence, glass structure, and thermal history. Different chemical compositions give different fragilities. Thus, we should see a relation between the enthalpy relaxation features and the fragility, i.e. a relation between a thermodynamic and a dynamic feature, since the enthalpy relaxation is a thermodynamic response, whereas fragility is a dynamic feature. In this work we focus on the details of the impact of fragility on the enthalpy relaxation, both for HQ and annealed HQ fibers. The fragility parameter is an outcome of the structure of the liquid and thus might be connected to the way the enthalpy is frozen in on cooling. The samples studied in this work cover a wide range of fragility from m = 30 (for GeO2) to 150 (for CS55). For the CS glasses, nuclear magnetic resonance spectra show no indication of crystallinity [26], and thus the formed glasses are highly amorphous. Two different fiber drawing methods were used to produce the fibers. Both methods are expected to introduce some amount of anisotropy and thereby mechanical structure change in the samples. Such effects have been ignored because of suggestions that the enthalpy excitation with this origin is very small compared to the amount from thermal quenching [16,27]. The amount of released enthalpy during the DSC scan is strongly dependent on thermal history. Thus the cooling rate is very important when comparing the Cp,exc curve for the different compositions. The cooling rate depends on the temperature of the liquid when the fibers are made and on the drawing speed. Even though these two numbers are well known during the continuous fiber drawing, it is in fact impossible to calculate the precise cooling rate for two reasons. Firstly, the temperature decay is not constant, but
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0.2
1
2
3
4
5
6
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0.1
0
-0.1
0.3
-1 -1
Cp.exc (J K g )
0.2
0.1
0
-0.1
0.2
0.1
0
-0.1 500
700
900
1100
500
700
900
1100
T (K) Fig. 5. Cp,exc spectra from all compositions at a number of different Ta and ta. The compositions are shown in the order of increasing fragility, from left to right. The numbers on the figure thus correspond to the compositions as follows: (1) GeO2, (2) NIST, (3) Basalt, (4) E-glass, (5) 45CaO Æ 55SiO2, and (6) 55CaO Æ 45SiO2. The spread around zero at the lowest temperature on each graph is a measure for the absolute error of the measurements.
rather exponential, according to normal heat diffusion. The liquid thus move through an exponentially decaying temperature reservoir with high constant speed. Secondly, the glass transition zone on freezing-in at high speed is very broad, probably covering several hundreds of degrees, leading to a difficulty in attributing a certain transition temperature. In Table 2 are given the values for the cooling rate calculated ad hoc by assuming a constant temperature decay for the exponential around Tg, and then calculating the distance from the die, where the temperature is 100 K below Tg. The cooling rate can then be calculated from the drawing speed. For the cascade fiber process the draw-
ing speed is not well known, but from simulations on this process a maximum velocity is calculated to be between 15 m/s and 30 m/s [13]. In the case of the cascade fibers this value is used to calculate an estimated cooling rate in the same way as for the continuous fibers. Due to the problems described above we have not been able to obtain the same cooling rates for the samples investigated. However, because it is evident that changing the cooling rate only changes the intensity of the enthalpy release spectrum for a given material and not the shape, we are still able to compare the spectra from different compositions. In addition, it is not to be expected from
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describe dielectric relaxation in terms of Johari–Goldstein b relaxations [28].
1.8
4.2. Effect of annealing
1.6
-1
-1
Cp (J g K )
1.4
1.2
1
0.8
0.6 400
600
800
1000
T (K) Fig. 6. Common errors seen in measurements of Cp. Measurements on Eglass are shown as examples. The solid lines are first and second upscans on E-glass annealed for 2 days at 800 K, showing a pronounced prepeak from 600 to 800 K. The dashed lines show a difference in the glass Cp between the two upscans, using E-glass annealed for 3.5 h at 750 K. The dotted line is a second upscan for E-glass, showing a decreasing Cpg.
considerations of the values of Cp that the same thermal history for two different materials will result in the same amount of frozen-in enthalpy. Rather we expect that this do depend significantly on the absolute value of Cp. Fig. 5 shows the DSC results from measurements on the six glasses annealed at different temperatures and times. The figure clearly confirms the results presented earlier on basaltic fibers, where three important features have been described [6]: (1) a relaxation distributed in two domains; (2) a decrease in the relaxation function on annealing starting from low temperature; and (3) a sub-Tg endotherm appearing at high Ta and ta. Each of these three important phenomena is described below with the focus on the fragility dependence of these phenomena.
4.1. Relaxation distributed in two domains The extent of the two domain relaxation function for the measured samples is shown in Figs. 4 and 5, the six samples are shown in the order of increasing fragility from left to right. In both representations the change in the shape of the Cp,exc peak is seen as an increasing b domain when fragility increases. For GeO2 the relaxation does not have any pronounced b domain, while the figure shows that this is indeed the case for ST and CS samples. This increase has been suggested to be explainable by models used to
Annealing causes the relaxation spectrum to diminish in a typical way for all fibers. Annealing for short times and at low temperatures (around 0.65–0.75Tg) only relaxes the b domain, so that the peak becomes a Gaussian shape. Only with fairly high annealing temperatures (around 0.85– 0.90Tg) the main relaxation decreases. In Fig. 5 this can be seen for the ST sample where long time at Ta = 800 causes complete relaxation. This is typical for the fragile samples, which all have a pronounced b domain. The results for the strong GeO2 composition and partly those for NIST show a quite different annealing behavior. It seems from the figure that the annealing effect is equivalently distributed over the whole range of the relaxation peak, so that the intensity of the entire peak relaxes by annealing. This agrees well with the fact that no pronounced b domain is seen for these strong systems. In the framework of the energy landscape [29], the explanation for these observations would include a more and more pronounced splitting of the mega basin responsible for the a relaxation into sub-basins where the activation energy is lower with increasing fragility. Fragile systems with such a splitting will then have a structure partly filling the sub-basins. With sufficient activation energy (i.e. Ta) these basins can change their internal occupancy and thus structural relaxation is possible. The activation energy for viscous flow (a relaxation, mega basin potential) is higher and thus requires a higher Ta to change occupancy and this part of structural relaxation is thus not possible at low annealing temperatures. For the ST sample this is clearly visible. For a number of annealing experiments up to a limiting Ta only annealing of the b domain takes place. Only above the limiting value of Ta the temperature is sufficiently high to relax the a domain. The same observations are done for the other samples, but not nearly as pronounced as for the ST sample. 4.3. The sub-Tg endotherm The sub-Tg endotherm is not pronounced for any compositions apart from ST. The E sample shows it, but not as pronounced as the ST sample. The reason for this could be found in the difference in fragility. The E sample is less fragile than the ST and therefore the difference between the activation energies for the two relaxations is smaller. This means that the a domain will relax simultaneously with the b domain. In such a situation no sub-Tg endotherm is expected to occur. For the most fragile CS systems the endotherm is not pronounced either. It is not evident why this is not the case from the measurements presented here. There is evidently no phase separation or crystallization problems during annealing, and the system is very fragile. A small endotherm is observed after sufficient
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4.4. Development of an additional exothermic peak
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annealing, but for this glass the main relaxation also changes during the appearance of this sub-Tg endotherm. It has been suggested that for glasses with a crystal content as low as 0.2%, no endotherm appears [30]. Such small crystal content is in the detection limit of the NMR measurements used to test the CS sample for crystal content and therefore the reason for the missing endotherm might be connected to this problem.
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A fourth very striking observation in addition to the three observations described above is apparent from Fig. 5. At high temperatures, above Tg, the systems seem to show a more and more pronounced sharp exothermic peak as fragility increases. For GeO2 no peak is seen at all. NIST shows a small tendency for a narrowing of the highest part of the a domain into a small peak on annealing. For the E glass a high temperature sharp peak is clearly the outcome of annealing, the peak being a part of the original a domain. For the Basalt glass the a domain is seen to have an additional sharp peak developing during annealing. For the two calcium-silicates the high temperature peak is a striking feature of the spectrum and is actually not disappearing for any of the shown measurements. The peak eventually disappears for Ta > 0.9Tg. This observation has not been previously reported to our knowledge, and should be a subject for further experiments. Evidently, fragility has an impact on the enthalpy relaxation of the samples, and it seems as if the effect systematically changes the relaxation spectra of glasses.
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m Fig. 7. Fragility dependence of the ratio Cpl/Cpg at the glass transition.
the difficulty in establishing a relationship between the fragility index and the thermodynamic glass transition. The amount of released enthalpy is dependent on cooling rate and can probably not be compared between the different compositions. For the same composition, however, we expect Hexc to decrease with increasing Ta and ta. Fig. 8 shows the dependence of calculated values of Hexc on ta. To compare the systems independent of the absolute value of Hexc, the figure shows the relative value Hexc(ta)/
4.5. Fragility and the glass transition
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Hexc(tA)/Hexc(tA=0)
Several suggestions to a possible connection between parameters extracted from the thermodynamic glass transition and the kinetic fragility have been proposed [31–34]. Originally the fragility was suggested to be connected to the size of the jump in heat capacity observed in DSC measurements at Tg [31]. Later on this has been opposed based on measurements on a range of substances [33,34]. Because of the large amount of standard measurements of Cp on each composition available from the second upscans performed, we have the possibility to investigate the connection between the fragility and the calorimetric glass transition closer. Fig. 7 shows the average Cp jump observed at the glass transition. The quantity is shown as Cpl relative to Cpg, and thus gives values above 1 for all samples. The error bar represents the standard deviation in the estimations. The result for each composition is the mean value for all second upscans. The figure shows an increase in the jump with increasing fragility, but does not show any linear dependence. This supports the conclusions presented earlier [34]. The error bars in the figure are quite substantial and show the problem with exact estimation of heat capacities, even with the high number of measurements used here. This might be one of the reasons for
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log (tA(min)) Fig. 8. Influence of annealing time on the Hexc. The Hexc is shown relative to the Hexc of the HQ glass to compare the results for different systems. Filled circles are GeO2 at 650 K, filled squares are NIST at 650 K, diamonds are E-glass at 750 K, open squares are Basalt at 750 K, open circles are 45CaO Æ 55SiO2 at 800 K, and triangles are 55CaO Æ 45SiO2 at 700 K.
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Hexc(HQ), where Hexc(HQ) is the absolute value of the release for the HQ glass. A specific annealing temperature is selected for each of the six samples so that Ta/Tg is approximately 0.77. From Fig. 5 it is expected that the calculated value decreases with increasing annealing time. The time is shown logarithmically to be able to see the whole range of times. Generally an exponentially decreasing trend is observed with increasing ta. In the figure linear fits are not included to avoid too much crowding, but in a first approximation this seems likely. Also errors bars are not included, but these are around 10–15%, which is the uncertainty on the estimation of Hexc. An exponential decrease (a straight line) in Hexc with increasing time supports a model featuring energy barriers with heights corresponding to activation energies. 5. Conclusions HQ glasses with a wide range of fragilities are measured using a DSC before and after annealing at temperatures below Tg for various durations. The results indicate that the relaxation of the HQ glasses during annealing depends on the fragility of the system. For strong systems, the enthalpy relaxation is manifested by a continuous decrease in the intensity of the entire Cp,exc peak with increasing the annealing degree (Ta and ta). In contrast, for fragile systems annealing at low temperatures results in a continuous decrease of only a part of the Cp,exc peak. This is manifested by a shift of the low temperature cutoff of the peak while the high temperature part remains unchanged. The results clearly illustrate the need to further consider a possible structure change of fragile liquids from the high end of the viscous liquids to the high viscosity regime. By further experiments on glass-forming systems with well determined relaxation properties in the viscous liquid regime, much more detailed information on the possible reason for the non-Ahrrenian temperature dependence of fragile systems could be achieved. Acknowledgment This work was supported by the Danish Research Council under Grant No. 26-03-0096.
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