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The glassy state of the amorphous V2O5–NiO–TeO2 samples
Journal of Physics and Chemistry of Solids 72 (2011) 1381–1385
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
The glassy state of the amorphous V2O5–NiO–TeO2 samples Seyed Ali Salehizadeh a, Dariush Souri b,n a b
Young Researchers Club, Varamin-Pishva Branch, Islamic Azad University, Varamin, Iran Department of Physics, Faculty of Science, Malayer University, Malayer, Iran
a r t i c l e i n f o
abstract
Article history: Received 10 April 2011 Received in revised form 19 July 2011 Accepted 19 August 2011 Available online 25 August 2011
The glass transition temperature dependence to heating rate and therefore the activation energy (DHn) of the glass transition of (60-x)V2O5–xNiO–40TeO2 oxide glasses with 0 r x r 20 (in mol%) were investigated at heating rates j ( ¼ 3 6, 9, 10 and 12 K/min) using differential scanning calorimetry (DSC). The heating rate dependence of Tg was used to investigate the applicability of different theoretical models describing the glass transition. Using the application of Moynihan and Kissinger et al. models to the present data, different values of (DHn) at each different heating-rate regions were obtained. The fragility parameter (m¼ DHn/R Tg) was 24.98 for x ¼ 10 mol%, suggesting that this glass may be considered as a rather strong glass (fragility index m 4 20 is an indication of fragile glass). Also the compositional dependence of Tg and DHn was investigated. & 2011 Elsevier Ltd. All rights reserved.
Keywords: A. Amorphous materials A. Glasses C. Differential scanning calorimetry (DSC) D. Phase transitions D. Specific heat
1. Introduction Because of the technical, scientific and technological interest of tellurite glasses, an understanding of their structure and their physical properties is very important [1–15]. Study in structural characteristics of glasses by spectral analyzing and DSC curve can be a suitable way to understand the behavior of glasses [16]. The glass transition and associated anomaly of relaxation behavior is the subject of many theoretical and experimental investigations [17–19]. In spite of the extensive research devoted to understand the phenomenon of glass transition, there is no satisfactory description of this phenomenon and more work is needed to overcome this difficulty. The differential scanning calorimetry (DSC) technique is widely used to investigate the glass transformation in glassy materials. The kinetics of the glass transition as studied by the DSC method is important in investigating the nature of the glass transformation process. Moreover, the kinetic aspect of the glass transition is evident from the dependence of Tg on the heating rate. This behavior can be used to identify different mechanisms involved in the transition process. One of the key kinetic parameters, which can be determined by DSC measurements, is the activation energy, DHn, of the glass transition. DHn can be determined from the dependence of Tg on heating rate [20]. Glasses, which strongly resist any structural changes with changing temperature, are characterized as strong glasses [21–23]. Consequently, the strong glasses show only
n
Corresponding author. Tel./fax: þ 98 851 333 99 83. E-mail addresses: [email protected], [email protected] (D. Souri).
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a small change in heat capacity in the glass transition region. In contrast, the glasses, whose structures undergo a large change with changing temperature and which show a large change in heat capacity in the glass transition region, are referred to as fragile glasses. In classifying strong–fragile characteristics for glasses, Angell used [21] a log viscosity (Z) vs. reduced temperature (Tg/T, Tg being the glass transition temperature) plot such as the one shown schematically in Fig. 1. Strong glasses [22–23] have a highly polymerized, mostly covalently bonded, network and the temperature dependence of Z near the glass transition region for such liquids is nearly Arrhenian (log Z vs. 1/T plot is linear). For fragile glasses (Chalcogenide [24–27], iron phosphate [28]), whose network is ionic or molecular type, the temperature dependence of Viscosity is typically non-Arrehenian, and the log Z vs. 1/T plots for these liquids deviate from linearity. The slope at any point on the curves in Fig. 1 yields the value for DHZ/Tg, where DHZ is the activation energy for viscous flow. Thus, for strong glasses, DHZ/Tg is nearly constant with temperature near the glass transition region, but it is temperature dependent and increases rapidly with decreasing temperature near the glass transition region for typical fragile glasses. The fragile glasses are characterized generally by a high value of DHZ/Tg. For most glass forming liquids the activation energy for glass transition, DHn, is indistinguishable from DHZ near the glass transition region [25–26]. Thus, measuring and evaluating the values for DHn are often used to determine the strong–fragile characters of glasses [25–26]. So, in my previous work [7], the optical properties of the present samples have been investigated, but there is no report on their glass transition properties. The present paper reports the
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15 3.5
7
Heat Flow (mW) Exo-Up
Log (viscosity, Pa.s)
4.5
11 Slope
Hη/Tg
Strong
3
Fregile
1.5 Tg
0.5 -0.5
-1 -5
heating rate=3 K /min
2.5
TCr
-1.5 150
0
0.2
0.4
0.6
0.8
1
200
1.2
250
300
350
400
450
500
450
500
450
500
Temperature (°C)
Tg/T
glass transition behavior for V2O5–NiO–TeO2 oxide glasses with the purpose of (1) evaluating their strong/fragile character, which is related to the degree of structural reorganization with temperature near the glass transition region, (2) to investigate the effect of heating rate on the glass transition, (3) to investigate the variation of the activation energy of the glass transition and (4) to use the experimental data to test a number of theoretical models proposed to describe the glass transition.
Heat Flow (mW) Exo-Up
Fig. 1. Schematic plot of temperature dependence of log(viscosity) for ‘strong’ and ‘fragile’ glasses [21].
3. Results and discussion 3.1. XRD patterns XRD characterization of 40TVNx samples has been carried out on different samples, confirming the amorphous nature of them; results have been reported in our previous work [7]. 3.2. Thermal analysis and activation energy for glass transition (DHn) The representative DSC outputs of the 40TVN10 sample obtained at different selected heating rates are shown in Fig. 2 (this figure is only an illustration and the main information are summarized in Table 1). The measured data for other samples are presented in Table 1.
400
Temperature (°C) 12 Heat Flow(mW) Exo-Up
2. Experimental procedure The tri-component (60-x)V2O5–xNiO–40TeO2 glasses with 0rxr20 (in mol%), hereafter termed as 40TVNx, were prepared by the usual rapid melt quenching technique. During the sample production, the melt was mixed every 5 min to prevent the separation of the three components. The melt was poured on to a polished steel block and immediately pressed by another polished steel block, where the blocks were kept at room temperature. The characterization of the glass systems was carried out by x-ray diffraction (XRD) studies using a Bruker diffractometer (AXS D8 Advance, CuKa, Germany). The density (r) of each sample was calculated by Archimedes’s method using para-xylene as an immersion liquid; results of density, XRD patterns and glass transition temperature have been previously reported [7]. Also, the glass transition temperature (Tg) of these samples was obtained using differential scanning calorimetry (DSC: Pyris1, USA) under dynamic N2 gas atmosphere (at a constant rate of 20 cm3/min); also for each DSC measurement, the heating rates (j) of 3, 6, 9, 10 and 12 K/min were used to obtain the DSC curves.
11 9 heating rate= 9 K /min 7 5 3 1 -1 -3 -5 -7 -9 -11 150 200 250 300 350
7
heating rate= 12 K /min
2 -3 -8 150
200
250
300
350
400
Temperature (°C) Fig. 2. DSC curves of the 40TVN10 glass at different selected heating rates a: j ¼3 K/min, b: j ¼ 9 K/min, c: j ¼ 12 K/min; (For better clarity, plots are shown separately).
In the absence of thermal events, the position of the baseline in such a plot is proportional to the specific heat of the sample. The presence of an endothermic peak, superimposed on the baseline, indicates the occurrence of a heat-absorbing event such as glass transition or melting. On the other hand, an exothermic peak occurs as a result of some sort of heat-releasing event such as crystallization [29]. The structural transformation is characterized by two temperatures Tg, TCr. The glass transition temperature, Tg, as defined by the endothermic change in the DSC trace indicates a change of viscosity, marking a transformation from amorphous solid phase to supercooled liquid state; furthermore, viscosity changes continuously in the whole temperature range and even it is not claimed that the steepest change occurs at the experimentally determined Tg; besides, the temperature dependence of viscosity is not essentially Arrhenian. As the output of the DSC during heating is proportional to the heat capacity, it is a straightforward and convenient method of detecting the glass transition and investigating its kinetics. For example, the heatingrate dependence of the glass transition temperature Tg can be used to determine the activation energy of the transition from glassy to liquid state [19–20,29–30]. In this work, the middle point of the endothermic trace was used to define Tg. Other definitions for Tg were used by different workers. For instance, Abu-Sehly et al. [20] and Moynihan et al. [26] used different
S.A. Salehizadeh, D. Souri / Journal of Physics and Chemistry of Solids 72 (2011) 1381–1385
1383
Table 1 Activation energy for glass transition DHn determined using Eqs. (2) and (3) at lower and higher heating rate regions, fragility (m) at higher heating rates, glass transition temperature (Tg) and crystallization temperature (Tcr) for 40TVNx glasses at the different heating rates (j). Glass
j (K/min)
Tg (1C)
Tcr (1C)
40TVN0
3 6 9 10 12
227.7 232.68 234.4 234.8 235.96
267.16 283.2 286.8 287.5 290.64
3 6 9 10 12
246.3 251.5 255.8 258.08 261.9
355.8 352.7 362.8 392.9 374.6
3 6 9 12
287.8 287 291.7 294.4
357.3 377.9 342.6 427.9
40TVN10
40TVN20
m
58.85
ln (Φ)
1.8 1.4
521
524
527 Tg (K)
530
533
536
Fig. 3. Representative plot of ln j against the glass transition temperature Tg. The solid and dashed lines represent fit to Eq. (1) at different heating rate regions, which imply strongly to temperature dependence of activation energy. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
definitions of Tg that included the extrapolated onset, the inflection point and the maximum point of the endothermic trace. Using these definitions of Tg, the result of extracting the activation energy for different glasses was found to be the same. The exothermic peak temperature Tcr is used to identify the crystallization process. As listed in Table 1, both Tcr and Tg shift to higher temperatures with increasing heating rate. The heatingrate dependence of Tg is clearly indicated in the Fig. 2 and Table 1. The kinetic aspect of the glass transition is evident from the pronounced shift in Tg. It is worth observing that an order of magnitude increase in j causes a shift in Tg of 5 K. It has been widely observed that the dependence of the Tg on the heating-rate j follows empirical Lasocka’s formula [31]: T g ¼ a þb ln j
From Eq. (2) 293.2
From Eq. (2): 506.09
From Eq. (3): 284.83
From Eq. (3): 497.66
From Eq. (2): 265.64
From Eq. (2): 111.16
From Eq. (3): 256.92
From Eq. (3): 102.32
From Eq. (2): 2263.68 From Eq. (3): 2254.37
From Eq. (2): 277.71 From Eq. (3): 268.32
24.98
40TVN10
1 518
DHn (kJ/mol) at higher j
119.56
2.6 2.2
DHn (kJ/mol) at lower j
ð1Þ
where a and b are constants for a given glass composition. In order to see if Eq. (1) describes the heating-rate dependence of Tg, the Tg is plotted against ln j as shown in Fig. 3 representatively for 40TVN10 sample. As evident from this figure, the present data cannot be fitted to Eq. (1) for the whole range of j and there are two different linear regions. As pointed out by Mehta et al. [32], the values of a and b are sensitive to the cooling rate of the melt. This behavior indicates that the physical significance of a and b is related to the nature of the structural relaxation within the glass transition region. It is evident from Fig. 3 that the values of a and b are different for different heating rate regions; these different values of a and b obtained in the present work may be related to a change in the transformation processes involved in the glass transition.
Based on the structural relaxation models, the heating and cooling rate dependence of the glass transition temperature was investigated by many authors [26,33–36]. As presented in continuation, two frequently used equations for the structural relaxation are Moynihan [25] and Kissinger [37]. In spite of the fact that Kissinger and Moynihan equations are basically and originally for the determination of the activation energy for the crystallization process, it has been shown that the same equations can be used for the evaluation of the activation energy of the glass transition process [38] (to a high degree of approximation); conditions necessary for the validity of these equations are that the structural relaxation be describable by a temperature-independent distribution of relaxation times and that the glass be cooled from a starting temperature well above the transition region and subsequently reheated at the same rate starting from a temperature well below the transition region; therefore, it should be mentioned that the activation energies, calculated in this work, are of phenomenological effective values determined on the basis of Arrhenian activation process. Upon the above explanations, the model frequently used to determine the activation energy (DHn) for structural relaxation in the glass transition region is given by Moynihan [25] as dðln jÞ=dð1=T g Þ ¼ DHn =R
ð2Þ
where Tg is the glass transition temperature determined from the DSC curve measured at a heating rate of j and R is the gas constant. The value of DHn is determined from the slope of the plots, ln j vs. 1/Tg. On the other hand, a Kissinger-type equation [37], which is generally used to determine the activation energy for structural relaxation, is also used to determine DHn, and is given by d½ln ðj=T 2 g Þ=dð1=T g Þ ¼ DHn =R
ð3Þ /T2g)
Thus, the slope of the ln (j vs. 1/Tg plot gives the value for DHn. Both types of plots, ln (j) vs. 1/Tg (Eq. (2)) and ln (j/T2g ) vs. 1/Tg (Eq. (3)), for the present glasses show, as expected, linear relationship with a linear correlation factor better than 0.9986. Such plots are shown in Figs. 4 and 5 for 40TVNx glasses. Furthermore, as is evident from Figs. 4 and 5, two regions can be identified in the plots. This leads to two different values for the activation energy in each heating rate region; the obtained data of DHn are listed in Table 1, for example in the case of 40TVN10 sample upon the Moynihan model (Eq. 2), in the low-j region, the activation energy for the glass transition is 265.64 kJ/mole and in the highj region the activation energy is 111.16 kJ/mole; on the other
S.A. Salehizadeh, D. Souri / Journal of Physics and Chemistry of Solids 72 (2011) 1381–1385
ln (Φ)
2.2 1.8 x= 0 mol%
1.4
x= 10 mol% x= 20 mol%
1 1.86
1.88
1.9
1.92
1.94
1000/ Tg
1.96
1.98
2
(K-1)
Fig. 4. Plots of ln j vs. 1000/Tg (Eq. (1)) for 40TVNx glasses. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
-9.8
ln (Φ/Tg2)
-10.1 -10.4 -10.7 -11 -11.3
x=0 mol% x=10 mol% x=20 mol%
-11.6 1.86 1.88
1.9
1.92 1.94 1.96 1.98
2
1000/ Tg (K-1) Fig. 5. Plots of ln [j/T2g ] vs. 1000/Tg (Eq. (1)) for 40TVNx glasses. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
hand, upon the Kissinger et al. model (Eq. (3)), in the low-j region, the activation energy for the glass transition is 256.92 kJ/ mole and in the high-j region the activation energy is 102.32 kJ/ mole for the same sample. This deviation (existence of two j-regions) from Moynihan or Kissinger et al. predictions shows that the glass transition process cannot be described by constant activation energy. It is worth mentioning that although Moynihan and Kissinger equations are based on different theoretical models, they both led to similar values of the activation energies in the lower and the higher heating rate regions, which suggest that both equations are useful in determining DHn; however, the DHn values from Eq. (2), on the average, 9 kJ/mol differ from those from Eq. (3). It should be mentioned here that the above analysis showed that even on the basis of Moynihan and Kissinger models, the process of glass transition cannot be described by single activation energy. Generally, it is believed that Moynihan and Kissinger equations are physically equivalent for the isokinetic processes and are valid only in narrow temperature ranges; therefore the obtained activation energies from these models are nearly the same. [25,39]The role of shear modulus as an important thermodynamic and kinetic parameter governing the properties and relaxation of the glassy state has been emphasized ; furthermore, in general, temperature dependence of shear modulus does not depend on heating rate at T4Tg; in other words, at ToTg shear viscosity depends on heating rate and is responsible for structural relaxation and related viscoelasticity [39]. Thus, it seems that the activation energies determined in the present work are the activation energy of the shear viscosity [25]. As will be shown below, this behavior was observed and suggests the heating-rate dependence of the activation energy. It is therefore tempting to investigate the dependence of the glass transition activation energy on the heating rates, so, the values of DHn
determined from the slope of such straight lines are given in Table 1 and are shown in Fig. 6 as a function of glass composition. Table 1 and Fig. 6 show that DHn for the present glasses has a behavior change at x ¼10 mol%, in both heating rate regions. For example, at higher j-region, 40TVN10 has the less DHn equal to 111.16 kJ/mol, suggesting the decrease of the concentration of non-bridging oxygens (NBOs), which means the structural change in the system 40TVNx at x ¼10 mol%. The decrease of NBO’s means the decrease of fragility of the glass as can be seen in evaluating the fragility. On the other hand, the DSC data reported in Table 1 show that for the different compositions of the system at different heating rates, the glass transition temperature increases with the increasing antimony oxide content and all the other heating rates indicate similar behavior. This variation is shown in Fig. 7, where Tg is seen to increase with increasing x or with decreasing V-content for each heating rate. Furthermore, using the results of our previous work [5] and results presented in Fig. 7, Tg data show that the glass transition temperature is sensitive to the NiO concentration. Increasing Tg can be interpreted as increasing the thermal stability of the glass. The thermal stability of the glass is a result of the glass structure; in other words, in this work, the change in Tg indicates a change related to the manner in which V2O5 and NiO get arranged in the glass. The thermally stable glasses will have a close packed structure, while the unstable glasses will have a loose packed structure [40]. Thus the addition of NiO increases the stability of the glass and the rigidity of the network, which is in agreement with the data of the glass density (a criterion of packing) (reported in [7]). It has been reported [7] that the data of density r increase with the increase in NiO content. Since NiO has a high relative molecular mass, thus, it is an expected result. This means that the glass-transition temperature increases if the average coordination number increases. This may be due to the decrease in the number of V–V bonds and the increase of the V–Ni bonds as a result of the increase of the nickel oxide content (x) and the decrease of the V content. In other
ΔH* (kJ/mol)
2.6
600
2100
lower rates
1700
higher rates
500 400
1300 900
300
500
200 100
100 10
0
20
x: NiO content (mol%) Fig. 6. Plot of DHn against NiO content (x) at different j-regions, for 40TVNx glasses.
570
Φ =3 K/min Φ =6 K/min Φ =9 K/min Φ =10 K/min Φ =12 K/min
560 550 Tg (K)
1384
540 530 520 510 500 0
10
20
x: NiO content (mol%) Fig. 7. Variation of Tg with NiO concentration (x) at different heating rates.
S.A. Salehizadeh, D. Souri / Journal of Physics and Chemistry of Solids 72 (2011) 1381–1385
120
x¼10, which can be considered as a rather strong glass. Thus, the glass with x ¼10 mol% has probably resistance against thermal shocks and is a good candidate for fabrication.
100 Fragility (m)
1385
80 60
References
40 20 0
10 x: NiO content (mol%)
20
Fig. 8. The fragility parameter, m, for 40TVNx glasses.
words, the cross-linking provided by Ni atoms increases for 40TVNx samples, which in turn affects the structure in a manner to increase the Tg. A parameter, m, known as the ‘fragility parameter’ and defined [41] as m ¼ DHn =RT g was calculated and plotted as a function of composition in Fig. 8, see also Table 1, which has a behavior change at x¼10 mol% as discussed previously; the calculated m-values for 40TVNx glasses are in the range 24–120. Although there is no sharp limit to determine strong–fragile characters of glasses on the basis of m-values, a value of mo 20 is typical of strong glasses and for m 4 20 is a fragile glass [42]. Thus, glasses with x a10 mol% are considered to be fragile glasses and glass with x¼10 mol% (with m ¼24.98) can be considered as a rather strong glass; upon this discussion, glass with x¼10 mol% probably has a good resistance against thermal shocks and so is a suitable candidate for technological applications.
4. Conclusions
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Investigation of heating-rate dependence of the glass transition temperature in (60-x)V2O5–40TeO2–xNiO glasses was carried out using DSC technique. It was observed that Tg shifted to higher temperatures with the increasing heating rates. The observed dependence was discussed in terms of different theoretical models describing glass transition. It was shown in this work that the transition process cannot be described in terms of single activation energy. The present work shows that the assumption that the glass activation energy does not vary during the glass transition process is not valid. The activation energy DHn and fragility m were determined for the present glasses. The fragility characteristics of these glasses have a behavior change at x ¼10 mol%, which is in accordance with the variations of DHn. Generally, these glasses are in the fragile glass category except for
[29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
The glassy state of the amorphous V2O5–NiO–TeO2 samples Seyed Ali Salehizadeh a, Dariush Souri b,n a b
Young Researchers Club, Varamin-Pishva Branch, Islamic Azad University, Varamin, Iran Department of Physics, Faculty of Science, Malayer University, Malayer, Iran
a r t i c l e i n f o
abstract
Article history: Received 10 April 2011 Received in revised form 19 July 2011 Accepted 19 August 2011 Available online 25 August 2011
The glass transition temperature dependence to heating rate and therefore the activation energy (DHn) of the glass transition of (60-x)V2O5–xNiO–40TeO2 oxide glasses with 0 r x r 20 (in mol%) were investigated at heating rates j ( ¼ 3 6, 9, 10 and 12 K/min) using differential scanning calorimetry (DSC). The heating rate dependence of Tg was used to investigate the applicability of different theoretical models describing the glass transition. Using the application of Moynihan and Kissinger et al. models to the present data, different values of (DHn) at each different heating-rate regions were obtained. The fragility parameter (m¼ DHn/R Tg) was 24.98 for x ¼ 10 mol%, suggesting that this glass may be considered as a rather strong glass (fragility index m 4 20 is an indication of fragile glass). Also the compositional dependence of Tg and DHn was investigated. & 2011 Elsevier Ltd. All rights reserved.
Keywords: A. Amorphous materials A. Glasses C. Differential scanning calorimetry (DSC) D. Phase transitions D. Specific heat
1. Introduction Because of the technical, scientific and technological interest of tellurite glasses, an understanding of their structure and their physical properties is very important [1–15]. Study in structural characteristics of glasses by spectral analyzing and DSC curve can be a suitable way to understand the behavior of glasses [16]. The glass transition and associated anomaly of relaxation behavior is the subject of many theoretical and experimental investigations [17–19]. In spite of the extensive research devoted to understand the phenomenon of glass transition, there is no satisfactory description of this phenomenon and more work is needed to overcome this difficulty. The differential scanning calorimetry (DSC) technique is widely used to investigate the glass transformation in glassy materials. The kinetics of the glass transition as studied by the DSC method is important in investigating the nature of the glass transformation process. Moreover, the kinetic aspect of the glass transition is evident from the dependence of Tg on the heating rate. This behavior can be used to identify different mechanisms involved in the transition process. One of the key kinetic parameters, which can be determined by DSC measurements, is the activation energy, DHn, of the glass transition. DHn can be determined from the dependence of Tg on heating rate [20]. Glasses, which strongly resist any structural changes with changing temperature, are characterized as strong glasses [21–23]. Consequently, the strong glasses show only
n
Corresponding author. Tel./fax: þ 98 851 333 99 83. E-mail addresses: [email protected], [email protected] (D. Souri).
0022-3697/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2011.08.021
a small change in heat capacity in the glass transition region. In contrast, the glasses, whose structures undergo a large change with changing temperature and which show a large change in heat capacity in the glass transition region, are referred to as fragile glasses. In classifying strong–fragile characteristics for glasses, Angell used [21] a log viscosity (Z) vs. reduced temperature (Tg/T, Tg being the glass transition temperature) plot such as the one shown schematically in Fig. 1. Strong glasses [22–23] have a highly polymerized, mostly covalently bonded, network and the temperature dependence of Z near the glass transition region for such liquids is nearly Arrhenian (log Z vs. 1/T plot is linear). For fragile glasses (Chalcogenide [24–27], iron phosphate [28]), whose network is ionic or molecular type, the temperature dependence of Viscosity is typically non-Arrehenian, and the log Z vs. 1/T plots for these liquids deviate from linearity. The slope at any point on the curves in Fig. 1 yields the value for DHZ/Tg, where DHZ is the activation energy for viscous flow. Thus, for strong glasses, DHZ/Tg is nearly constant with temperature near the glass transition region, but it is temperature dependent and increases rapidly with decreasing temperature near the glass transition region for typical fragile glasses. The fragile glasses are characterized generally by a high value of DHZ/Tg. For most glass forming liquids the activation energy for glass transition, DHn, is indistinguishable from DHZ near the glass transition region [25–26]. Thus, measuring and evaluating the values for DHn are often used to determine the strong–fragile characters of glasses [25–26]. So, in my previous work [7], the optical properties of the present samples have been investigated, but there is no report on their glass transition properties. The present paper reports the
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15 3.5
7
Heat Flow (mW) Exo-Up
Log (viscosity, Pa.s)
4.5
11 Slope
Hη/Tg
Strong
3
Fregile
1.5 Tg
0.5 -0.5
-1 -5
heating rate=3 K /min
2.5
TCr
-1.5 150
0
0.2
0.4
0.6
0.8
1
200
1.2
250
300
350
400
450
500
450
500
450
500
Temperature (°C)
Tg/T
glass transition behavior for V2O5–NiO–TeO2 oxide glasses with the purpose of (1) evaluating their strong/fragile character, which is related to the degree of structural reorganization with temperature near the glass transition region, (2) to investigate the effect of heating rate on the glass transition, (3) to investigate the variation of the activation energy of the glass transition and (4) to use the experimental data to test a number of theoretical models proposed to describe the glass transition.
Heat Flow (mW) Exo-Up
Fig. 1. Schematic plot of temperature dependence of log(viscosity) for ‘strong’ and ‘fragile’ glasses [21].
3. Results and discussion 3.1. XRD patterns XRD characterization of 40TVNx samples has been carried out on different samples, confirming the amorphous nature of them; results have been reported in our previous work [7]. 3.2. Thermal analysis and activation energy for glass transition (DHn) The representative DSC outputs of the 40TVN10 sample obtained at different selected heating rates are shown in Fig. 2 (this figure is only an illustration and the main information are summarized in Table 1). The measured data for other samples are presented in Table 1.
400
Temperature (°C) 12 Heat Flow(mW) Exo-Up
2. Experimental procedure The tri-component (60-x)V2O5–xNiO–40TeO2 glasses with 0rxr20 (in mol%), hereafter termed as 40TVNx, were prepared by the usual rapid melt quenching technique. During the sample production, the melt was mixed every 5 min to prevent the separation of the three components. The melt was poured on to a polished steel block and immediately pressed by another polished steel block, where the blocks were kept at room temperature. The characterization of the glass systems was carried out by x-ray diffraction (XRD) studies using a Bruker diffractometer (AXS D8 Advance, CuKa, Germany). The density (r) of each sample was calculated by Archimedes’s method using para-xylene as an immersion liquid; results of density, XRD patterns and glass transition temperature have been previously reported [7]. Also, the glass transition temperature (Tg) of these samples was obtained using differential scanning calorimetry (DSC: Pyris1, USA) under dynamic N2 gas atmosphere (at a constant rate of 20 cm3/min); also for each DSC measurement, the heating rates (j) of 3, 6, 9, 10 and 12 K/min were used to obtain the DSC curves.
11 9 heating rate= 9 K /min 7 5 3 1 -1 -3 -5 -7 -9 -11 150 200 250 300 350
7
heating rate= 12 K /min
2 -3 -8 150
200
250
300
350
400
Temperature (°C) Fig. 2. DSC curves of the 40TVN10 glass at different selected heating rates a: j ¼3 K/min, b: j ¼ 9 K/min, c: j ¼ 12 K/min; (For better clarity, plots are shown separately).
In the absence of thermal events, the position of the baseline in such a plot is proportional to the specific heat of the sample. The presence of an endothermic peak, superimposed on the baseline, indicates the occurrence of a heat-absorbing event such as glass transition or melting. On the other hand, an exothermic peak occurs as a result of some sort of heat-releasing event such as crystallization [29]. The structural transformation is characterized by two temperatures Tg, TCr. The glass transition temperature, Tg, as defined by the endothermic change in the DSC trace indicates a change of viscosity, marking a transformation from amorphous solid phase to supercooled liquid state; furthermore, viscosity changes continuously in the whole temperature range and even it is not claimed that the steepest change occurs at the experimentally determined Tg; besides, the temperature dependence of viscosity is not essentially Arrhenian. As the output of the DSC during heating is proportional to the heat capacity, it is a straightforward and convenient method of detecting the glass transition and investigating its kinetics. For example, the heatingrate dependence of the glass transition temperature Tg can be used to determine the activation energy of the transition from glassy to liquid state [19–20,29–30]. In this work, the middle point of the endothermic trace was used to define Tg. Other definitions for Tg were used by different workers. For instance, Abu-Sehly et al. [20] and Moynihan et al. [26] used different
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Table 1 Activation energy for glass transition DHn determined using Eqs. (2) and (3) at lower and higher heating rate regions, fragility (m) at higher heating rates, glass transition temperature (Tg) and crystallization temperature (Tcr) for 40TVNx glasses at the different heating rates (j). Glass
j (K/min)
Tg (1C)
Tcr (1C)
40TVN0
3 6 9 10 12
227.7 232.68 234.4 234.8 235.96
267.16 283.2 286.8 287.5 290.64
3 6 9 10 12
246.3 251.5 255.8 258.08 261.9
355.8 352.7 362.8 392.9 374.6
3 6 9 12
287.8 287 291.7 294.4
357.3 377.9 342.6 427.9
40TVN10
40TVN20
m
58.85
ln (Φ)
1.8 1.4
521
524
527 Tg (K)
530
533
536
Fig. 3. Representative plot of ln j against the glass transition temperature Tg. The solid and dashed lines represent fit to Eq. (1) at different heating rate regions, which imply strongly to temperature dependence of activation energy. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
definitions of Tg that included the extrapolated onset, the inflection point and the maximum point of the endothermic trace. Using these definitions of Tg, the result of extracting the activation energy for different glasses was found to be the same. The exothermic peak temperature Tcr is used to identify the crystallization process. As listed in Table 1, both Tcr and Tg shift to higher temperatures with increasing heating rate. The heatingrate dependence of Tg is clearly indicated in the Fig. 2 and Table 1. The kinetic aspect of the glass transition is evident from the pronounced shift in Tg. It is worth observing that an order of magnitude increase in j causes a shift in Tg of 5 K. It has been widely observed that the dependence of the Tg on the heating-rate j follows empirical Lasocka’s formula [31]: T g ¼ a þb ln j
From Eq. (2) 293.2
From Eq. (2): 506.09
From Eq. (3): 284.83
From Eq. (3): 497.66
From Eq. (2): 265.64
From Eq. (2): 111.16
From Eq. (3): 256.92
From Eq. (3): 102.32
From Eq. (2): 2263.68 From Eq. (3): 2254.37
From Eq. (2): 277.71 From Eq. (3): 268.32
24.98
40TVN10
1 518
DHn (kJ/mol) at higher j
119.56
2.6 2.2
DHn (kJ/mol) at lower j
ð1Þ
where a and b are constants for a given glass composition. In order to see if Eq. (1) describes the heating-rate dependence of Tg, the Tg is plotted against ln j as shown in Fig. 3 representatively for 40TVN10 sample. As evident from this figure, the present data cannot be fitted to Eq. (1) for the whole range of j and there are two different linear regions. As pointed out by Mehta et al. [32], the values of a and b are sensitive to the cooling rate of the melt. This behavior indicates that the physical significance of a and b is related to the nature of the structural relaxation within the glass transition region. It is evident from Fig. 3 that the values of a and b are different for different heating rate regions; these different values of a and b obtained in the present work may be related to a change in the transformation processes involved in the glass transition.
Based on the structural relaxation models, the heating and cooling rate dependence of the glass transition temperature was investigated by many authors [26,33–36]. As presented in continuation, two frequently used equations for the structural relaxation are Moynihan [25] and Kissinger [37]. In spite of the fact that Kissinger and Moynihan equations are basically and originally for the determination of the activation energy for the crystallization process, it has been shown that the same equations can be used for the evaluation of the activation energy of the glass transition process [38] (to a high degree of approximation); conditions necessary for the validity of these equations are that the structural relaxation be describable by a temperature-independent distribution of relaxation times and that the glass be cooled from a starting temperature well above the transition region and subsequently reheated at the same rate starting from a temperature well below the transition region; therefore, it should be mentioned that the activation energies, calculated in this work, are of phenomenological effective values determined on the basis of Arrhenian activation process. Upon the above explanations, the model frequently used to determine the activation energy (DHn) for structural relaxation in the glass transition region is given by Moynihan [25] as dðln jÞ=dð1=T g Þ ¼ DHn =R
ð2Þ
where Tg is the glass transition temperature determined from the DSC curve measured at a heating rate of j and R is the gas constant. The value of DHn is determined from the slope of the plots, ln j vs. 1/Tg. On the other hand, a Kissinger-type equation [37], which is generally used to determine the activation energy for structural relaxation, is also used to determine DHn, and is given by d½ln ðj=T 2 g Þ=dð1=T g Þ ¼ DHn =R
ð3Þ /T2g)
Thus, the slope of the ln (j vs. 1/Tg plot gives the value for DHn. Both types of plots, ln (j) vs. 1/Tg (Eq. (2)) and ln (j/T2g ) vs. 1/Tg (Eq. (3)), for the present glasses show, as expected, linear relationship with a linear correlation factor better than 0.9986. Such plots are shown in Figs. 4 and 5 for 40TVNx glasses. Furthermore, as is evident from Figs. 4 and 5, two regions can be identified in the plots. This leads to two different values for the activation energy in each heating rate region; the obtained data of DHn are listed in Table 1, for example in the case of 40TVN10 sample upon the Moynihan model (Eq. 2), in the low-j region, the activation energy for the glass transition is 265.64 kJ/mole and in the highj region the activation energy is 111.16 kJ/mole; on the other
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ln (Φ)
2.2 1.8 x= 0 mol%
1.4
x= 10 mol% x= 20 mol%
1 1.86
1.88
1.9
1.92
1.94
1000/ Tg
1.96
1.98
2
(K-1)
Fig. 4. Plots of ln j vs. 1000/Tg (Eq. (1)) for 40TVNx glasses. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
-9.8
ln (Φ/Tg2)
-10.1 -10.4 -10.7 -11 -11.3
x=0 mol% x=10 mol% x=20 mol%
-11.6 1.86 1.88
1.9
1.92 1.94 1.96 1.98
2
1000/ Tg (K-1) Fig. 5. Plots of ln [j/T2g ] vs. 1000/Tg (Eq. (1)) for 40TVNx glasses. Straight lines are drawn for the guide for eye to distinct the different heating rate regions.
hand, upon the Kissinger et al. model (Eq. (3)), in the low-j region, the activation energy for the glass transition is 256.92 kJ/ mole and in the high-j region the activation energy is 102.32 kJ/ mole for the same sample. This deviation (existence of two j-regions) from Moynihan or Kissinger et al. predictions shows that the glass transition process cannot be described by constant activation energy. It is worth mentioning that although Moynihan and Kissinger equations are based on different theoretical models, they both led to similar values of the activation energies in the lower and the higher heating rate regions, which suggest that both equations are useful in determining DHn; however, the DHn values from Eq. (2), on the average, 9 kJ/mol differ from those from Eq. (3). It should be mentioned here that the above analysis showed that even on the basis of Moynihan and Kissinger models, the process of glass transition cannot be described by single activation energy. Generally, it is believed that Moynihan and Kissinger equations are physically equivalent for the isokinetic processes and are valid only in narrow temperature ranges; therefore the obtained activation energies from these models are nearly the same. [25,39]The role of shear modulus as an important thermodynamic and kinetic parameter governing the properties and relaxation of the glassy state has been emphasized ; furthermore, in general, temperature dependence of shear modulus does not depend on heating rate at T4Tg; in other words, at ToTg shear viscosity depends on heating rate and is responsible for structural relaxation and related viscoelasticity [39]. Thus, it seems that the activation energies determined in the present work are the activation energy of the shear viscosity [25]. As will be shown below, this behavior was observed and suggests the heating-rate dependence of the activation energy. It is therefore tempting to investigate the dependence of the glass transition activation energy on the heating rates, so, the values of DHn
determined from the slope of such straight lines are given in Table 1 and are shown in Fig. 6 as a function of glass composition. Table 1 and Fig. 6 show that DHn for the present glasses has a behavior change at x ¼10 mol%, in both heating rate regions. For example, at higher j-region, 40TVN10 has the less DHn equal to 111.16 kJ/mol, suggesting the decrease of the concentration of non-bridging oxygens (NBOs), which means the structural change in the system 40TVNx at x ¼10 mol%. The decrease of NBO’s means the decrease of fragility of the glass as can be seen in evaluating the fragility. On the other hand, the DSC data reported in Table 1 show that for the different compositions of the system at different heating rates, the glass transition temperature increases with the increasing antimony oxide content and all the other heating rates indicate similar behavior. This variation is shown in Fig. 7, where Tg is seen to increase with increasing x or with decreasing V-content for each heating rate. Furthermore, using the results of our previous work [5] and results presented in Fig. 7, Tg data show that the glass transition temperature is sensitive to the NiO concentration. Increasing Tg can be interpreted as increasing the thermal stability of the glass. The thermal stability of the glass is a result of the glass structure; in other words, in this work, the change in Tg indicates a change related to the manner in which V2O5 and NiO get arranged in the glass. The thermally stable glasses will have a close packed structure, while the unstable glasses will have a loose packed structure [40]. Thus the addition of NiO increases the stability of the glass and the rigidity of the network, which is in agreement with the data of the glass density (a criterion of packing) (reported in [7]). It has been reported [7] that the data of density r increase with the increase in NiO content. Since NiO has a high relative molecular mass, thus, it is an expected result. This means that the glass-transition temperature increases if the average coordination number increases. This may be due to the decrease in the number of V–V bonds and the increase of the V–Ni bonds as a result of the increase of the nickel oxide content (x) and the decrease of the V content. In other
ΔH* (kJ/mol)
2.6
600
2100
lower rates
1700
higher rates
500 400
1300 900
300
500
200 100
100 10
0
20
x: NiO content (mol%) Fig. 6. Plot of DHn against NiO content (x) at different j-regions, for 40TVNx glasses.
570
Φ =3 K/min Φ =6 K/min Φ =9 K/min Φ =10 K/min Φ =12 K/min
560 550 Tg (K)
1384
540 530 520 510 500 0
10
20
x: NiO content (mol%) Fig. 7. Variation of Tg with NiO concentration (x) at different heating rates.
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120
x¼10, which can be considered as a rather strong glass. Thus, the glass with x ¼10 mol% has probably resistance against thermal shocks and is a good candidate for fabrication.
100 Fragility (m)
1385
80 60
References
40 20 0
10 x: NiO content (mol%)
20
Fig. 8. The fragility parameter, m, for 40TVNx glasses.
words, the cross-linking provided by Ni atoms increases for 40TVNx samples, which in turn affects the structure in a manner to increase the Tg. A parameter, m, known as the ‘fragility parameter’ and defined [41] as m ¼ DHn =RT g was calculated and plotted as a function of composition in Fig. 8, see also Table 1, which has a behavior change at x¼10 mol% as discussed previously; the calculated m-values for 40TVNx glasses are in the range 24–120. Although there is no sharp limit to determine strong–fragile characters of glasses on the basis of m-values, a value of mo 20 is typical of strong glasses and for m 4 20 is a fragile glass [42]. Thus, glasses with x a10 mol% are considered to be fragile glasses and glass with x¼10 mol% (with m ¼24.98) can be considered as a rather strong glass; upon this discussion, glass with x¼10 mol% probably has a good resistance against thermal shocks and so is a suitable candidate for technological applications.
4. Conclusions
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Investigation of heating-rate dependence of the glass transition temperature in (60-x)V2O5–40TeO2–xNiO glasses was carried out using DSC technique. It was observed that Tg shifted to higher temperatures with the increasing heating rates. The observed dependence was discussed in terms of different theoretical models describing glass transition. It was shown in this work that the transition process cannot be described in terms of single activation energy. The present work shows that the assumption that the glass activation energy does not vary during the glass transition process is not valid. The activation energy DHn and fragility m were determined for the present glasses. The fragility characteristics of these glasses have a behavior change at x ¼10 mol%, which is in accordance with the variations of DHn. Generally, these glasses are in the fragile glass category except for
[29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]
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