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Change in Vickers hardness at the glass transition region for fragile and strong glasses
Journal of Non-Crystalline Solids 286 (2001) 141±145
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Change in Vickers hardness at the glass transition region for fragile and strong glasses T. Watanabe, Y. Benino, T. Komatsu * Department of Chemistry, Nagaoka University of Technology, Nagaoka 940-2188, Japan Received 16 October 2000; received in revised form 2 March 2001
Abstract The temperature dependence of Vickers hardness between room temperature and around the glass transition temperature Tg in a vacuum for some glasses with dierent fragile characters was measured. The hardness at T =Tg < 0:9 decreases gradually with increasing temperature, but the glasses show unique temperature dependences in the range 0:9 < T =Tg < 1:1 depending on their fragile character. A sharp decrease in hardness is observed at around T =Tg 0:9±1:0 for fragile Bi2 O3 - and TeO2 -based glasses, but 50CuOx 50P2 O5 and soda-lime silicate glasses with strong viscosity characteristics still have relatively large Vickers hardness even at Tg and the hardness drops to almost zero around T =Tg 1:05±1:1. It is suggested that for fragile glasses the b-relaxation has an important eect on the Vickers hardness change near the glass transition region, but for strong glasses it is the a-relaxation that governs the hardness near Tg . Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The concept of fragility in glass-forming supercooled liquids introduced by Angell [1] gives new insights for glass transition and structural relaxation phenomena. Glass formers are classi®ed into two types: strong glass formers which show an Arrhenius behavior in Angell's reduced plot (i.e., viscosity vs temperature) and fragile glass formers in which the temperature dependence of the viscosity is non-Arrhenius but is expressed using the Vogel±Fulcher equation [1]. It is known that oxide glass formers with well-formed tetrahedral net-
* Corresponding author. Tel.: +81-258 47 9313, fax: +81-258 47 9300. E-mail address: [email protected] (T. Komatsu).
work structure such as SiO2 belong to the category of strong liquids and ionic glass formers without directional bonds such as 2BiCl3 KCl are fragile [1]. Recently, the present authors' group [2] measured the temperature dependence of Vickers hardness of some oxide glasses and demonstrated that TeO2 -based glasses, which are considered fragile liquids from viscosity and heat capacity changes around the glass transition temperature, Tg [3,4], are fragile even from the point of view of mechanical properties, because hardness decreases sharply around Tg . It is of particular interest to examine mechanical or elastic properties around Tg for various glass-forming liquids with dierent fragile characters. Such information would be valuable not only for handling of glass products during the manufacturing process but also for a deeper understanding of the fragility concept. The
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 5 2 1 - X
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T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
temperature dependence of hardness for some strong glasses such as fused SiO2 and GeO2 has been reported by Westbrook [5]. In this paper, we measured the temperature dependences of Vickers hardness from room temperature to the glass transition region for fragile or strong glasses such as Bi2 O3 ±B2 O3 ±PbO and CuOx ±P2 O5 and found that the change in Vickers hardness around Tg is sensitive to the fragile character of glasses.
2. Experimental The nominal compositions examined in the present study are given in Table 1. These glasses have the following features: Bi2 O3 -based and TeO2 -based glasses have received much attention because of their excellent optical properties such as large third-order non-linear susceptibility. Copper phosphate glasses show unique thermal and physical properties depending on the copper valence states [6]. A soda-lime silicate glass available commercially is selected as a standard glass. The glasses were prepared using a conventional melt-quenching method. Commercial powders of reagent grade oxides were mixed and melted in a platinum crucible at 1073±1273 K for 30±40 min in an electric furnace. After melting, the melt was poured onto an iron plate heated to 423±473 K. Table 1 Nominal glass compositions, glass transition temperature Tg , and Vickers hardness at room temperature Hv in a vacuum for the glasses examined in the present study Composition (mol%)
Tg (K)
Hv (GPa)
40Bi2 O3 40B2 O3 20PbO 60Bi2 O3 20B2 O3 20PbO 15Na2 O 15ZnO 70TeO2 10K2 O 20WO3 70TeO2 15K2 O 15Nb2 O5 70TeO2 50CuOx 50P2 O5 R Cu 0 R Cu 0:42 R Cu 0:74 14Na2 O 13CaO 73SiO2
632 568 537 617 648
3.6 3.0 2.6 2.5 3.3
708 538 440 828
4.3 4.1 1.8 6.0
In 50CuOx 50P2 O5 glasses, the ratio of copper ions, i.e., R Cu Cu = Cu Cu2 , was changed using glucose addition during glass melting. Error: 2 K for Tg , 0.1 GPa for Hv .
The chemical analysis of copper valence states in 50CuOx 50P2 O5 glasses are described elsewhere [6]. Glass transition temperatures were determined by using dierential thermal analysis (DTA) at a heating rate of 10 K min 1 . The bulk glasses for Vickers indentation tests were annealed at a temperature of Tg 10 K for 10 min to eliminate internal stress in the glasses. The temperature dependence of Vickers hardness Hv of the glasses was measured using a high temperature indentation tester in the temperature range from room temperature to around Tg in a vacuum of 1:33 10 3 Pa. The applied load in each indentation test was 490 mN and the loading time was 15 s. Indentation tests at a given temperature were carried out ten times and mean values of Vickers hardness were estimated. Measuring temperatures were increased continuously from room temperature to around Tg . The temperature of the diamond pyramid indenter was kept near that of the samples within 1 K. 3. Results The values of Tg and Hv at room temperature for the glasses are summarized in Table 1. The temperature dependences of Vickers hardness of 40Bi2 O3 40B2 O3 20PbO and 60Bi2 O3 20B2 O3 20PbO glasses in a vacuum are shown in Fig. 1, in which the values of the relative Vickers hardness change, H T =H RT , are plotted as a function of the reduced temperature, T =Tg . H T and H RT are the values of Vickers hardness at temperature T and at room temperature, respectively. It is seen that the hardness decreases gradually in the temperature region well below Tg ; T =Tg < 0:9, with increasing temperature. The Vickers hardness decreases rapidly at and near Tg and is almost zero in the GPa scale at Tg . It should be, however, pointed out that 60Bi2 O3 20B2 O3 20PbO glass containing a large amount of Bi2 O3 shows a steep hardness change at lower reduced temperatures compared with 40Bi2 O3 40B2 O3 20PbO glass. The temperature dependences of Vickers hardness of 15Na2 O 15ZnO 70TeO2 and 10K2 O 20WO3 70TeO2 glasses in a vacuum are shown in Fig. 2. In these TeO2 -based glasses, the sharp de-
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
Fig. 1. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for Bi2 O3 -based glasses. (): 40Bi2 O3 40B2 O3 20PbO; : 60Bi2 O3 20B2 O3 20PbO.
Fig. 2. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for TeO2 -based glasses. (): 10K2 O 20WO3 70TeO2 ; : 15Na2 O 15ZnO 70TeO2 .
crease in the hardness is observed at around T =Tg 0:9±1:0, similar to 60Bi2 O3 20B2 O3 20PbO glass. The temperature dependences of Vickers hardness of 50CuOx 50P2 O5 glasses with dierent copper valence states, i.e., R Cu Cu = Cu Cu2 0; 0:42 and 0.74, are shown in
143
Fig. 3. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for 50CuOx 50P2 O5 glasses with dierent copper valence states R Cu Cu = Cu Cu2 . : R Cu 0; : R Cu 0:42, : R Cu 0:74.
Fig. 3. It is seen that these glasses still have relatively large Vickers hardness even at Tg , i.e., T =Tg 1:0 and the hardness becomes almost zero around T =Tg 1:05±1:1, indicating that these glasses show extremely dierent patterns in the H T =H RT vs T =Tg plots compared with Bi2 O3 and TeO2 -based glasses. As reported by Sato et al. [6], 50CuOx 50P2 O5 glasses become `strong' (in the fragility concept) with increasing Cu content due to the formation of covalent Cu ±O bonds. It is seen from Fig. 3 that the values of reduced temperature T =Tg giving Hv 0 tend to increase with increasing R Cu , implying that the temperature dependence of Vickers hardness around Tg is related to the degree of fragility. The temperature dependence of Vickers hardness of a soda-lime silicate glass is shown in Fig. 4 together with the data on the reduced Young's modulus reported by Rouxel and Sangleboeuf [7]. It is seen that the temperature dependence of Young's modulus changes at just Tg , but the change in Vickers hardness around Tg is still gradual. The data shown in Fig. 4 demonstrate that a soda-lime silicate glass is suciently `strong' even at Tg . Bourhis and Metayer [8] also reported a Vickers hardness of 3.75 GPa even at Tg for a soda-lime silicate glass.
144
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
Fig. 4. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for a soda-lime silicate glass. The data on Young's modulus are taken from [7].
4. Discussion Glass undergoes both compression and shear during the process of deformation in indentation test, and consequently the observed deformation comprises elastic deformation, plastic ¯ow and densi®cation [9]. Elastic properties are among physical properties which depend on the forces between atoms in solids. As the temperature increases, thermal expansion increases the separation between atoms and slightly decreases the forces between atoms, leading to a gradual decrease in elastic moduli, e.g. Young's modulus, with increasing temperature [7]. Yamane and Mackenzie [10] showed that Vickers hardness is proportional to Young's modulus. However, within the glass transition range, glass changes to viscous materials, i.e., viscous ¯ow is enhanced. It means elastic moduli decrease rapidly at temperatures above Tg [7]. It is known that the characteristic relaxation time s around Tg is the order of 100 s, but changes strongly with the temperature. For example, Rouxel and Sangleboeuf [7] reported that the values of s for a soda-lime silicate glass with Tg 818 K are 10 min at 808 K and 1 s at 853 K. In the present study, the loading time of Vickers indenter was 15 s, indicating that the time for loading is comparable to the value of s around
Tg . Therefore, we can expect that the Vickers hardness in glass at temperatures far below Tg decreases gradually with increasing temperature, and decreases steeply in the glass transition region. Indeed, for all glasses examined in the present study such a temperature dependence of Vickers hardness is observed as seen in Figs. 1±3. The present results demonstrate that Vickers hardness at and near Tg depends strongly on the glass systems and compositions. It is well known that TeO2 -based glasses belong to the category of fragile glass-forming system, meaning that bond breakings and atomic rearrangements occur easily around Tg [3,4]. Bi2 O3 -based glasses containing large Bi2 O3 contents are also fragile [11]. The results shown in Figs. 1 and 2 suggest that signi®cant glass structure changes giving a rapid decrease in hardness start at around T =Tg 0:9±0:95 in these Bi2 O3 - and TeO2 -based glasses. On the other hand, copper phosphate and soda-lime silicate glasses consisting of the so-called typical network former oxides of SiO2 and P2 O5 are basically stronger compared to TeO2 - and Bi2 O3 -based glasses in the strong/fragile classi®cation concept, although the degree of the fragility of silicate and copper phosphate glasses depends on the amounts of alkali metal or alkaline earth metal oxides and on the Cu /Cu2 ratio [1,6]. The results shown in Figs. 3 and 4 suggest that such relatively strong glasses have a high resistance against bond breaking and atomic rearrangements under the applied load (490 mN in this study) even at just Tg . In other words, the temperature dependence of Vickers hardness around Tg under the same indentation condition depends strongly on the fragility of glass-forming liquids. It is well recognized that there are two type structural relaxations in glass. One is called a-relaxation which is cooperative for atomic displacements/rearrangements and is directly related to the glass transition [12]. That is, a-relaxation is a primary relaxation and is observed at temperatures above Tg . The other is b-relaxation, and this secondary relaxation is observed even at temperatures below Tg [12,13]. Although the microscopic origin of b-relaxation in glass is still open to discussion [13], it has been suspected that b-relaxation corresponds to non-cooperative atomic movements
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
[12]. Structural relaxation of glass and supercooled liquids, i.e., relaxation times, could be, therefore, characterized by two dierent temperatures, when glass is heated: the ®rst is the temperature at which only b-relaxation starts; the second is the glass transition temperature Tg at which the appearance of a-relaxation is observed. Considering the above structural relaxation model, it is suggested that the b-relaxation has an important eect on the Vickers hardness change near the glass transition region for fragile glasses with extremely weak network structures such as Bi2 O3 and TeO2 -based glasses. On the other hand, for strong glasses consisting of well-de®ned strongly bonded network structures, it is the a-relaxation that governs the Vickers hardness near Tg . Westbrook [5] reported that the slope of the hardness±temperature relation changes around 873 K in fused silica. It is obvious that this temperature is much lower than the glass transition temperature (Tg 1473 K). Silica glass is known as an example of strong glasses [1]. It is, however, also well known that silica glass shows an extremely dierent deformation behavior during the indentation test compared with soda-lime silica glass [9,14]. That is, the main deformation mechanism in silica glass is densi®cation (not plastic ¯ow), and the densi®cation introduced at room temperature recovers (decreases) by annealing at temperatures around 873 K [14]. Further study will be needed to understand the microscopic mechanism of the temperature dependence of hardness for silica glass. 5. Conclusions Vickers hardness for some glasses with dierent fragile character was measured between room temperature and around Tg in a vacuum. The hardness for T =Tg < 0:9 decreases gradually with increasing temperature for all glasses examined in the present study, but the glasses show unique temperature dependences in the range 0:9 < T =Tg < 1:1 depending on their strong or
145
fragile character. A sharp decrease in hardness is observed at around T =Tg 0:95±1:0 for fragile Bi2 O3 - and TeO2 -based glasses, but for 50CuOx 50P2 O5 and soda-lime silicate glasses with strong character the hardness becomes almost zero only around T =Tg 1:1. The present study demonstrates that measurements of Vickers hardness in the glass transition region are informative for an indepth understanding of the strong/fragile concept in glass-forming liquids. As a further study, it is desired to measure creep and stress relaxation behaviors at temperatures of T =Tg 0:9±1:0 for fragile glasses. Acknowledgements This work was supported by a Grant of The Sumitomo Foundation and the Grant-in-Aid for Scienti®c Research from the Ministry of Education, Science, Sports and Culture, Japan. References [1] C.A. Angell, J. Non-Cryst. Solids 131±133 (1991) 13. [2] T. Watanabe, Y. Benino, K. Ishizaki, T. Komatsu, J. Ceram. Soc. Jpn. 107 (1999) 1140. [3] T. Komatsu, R. Ike, R. Sato, K. Matusita, Phys. Chem. Glasses 36 (1995) 216. [4] K. Aida, Y. Benino, V. Dimitrov, T. Komatsu, R. Sato, J. Am. Ceram. Soc. 83 (2000) 1192. [5] J.H. Westbrook, Phys. Chem. Glasses 1 (1960) 32. [6] R. Sato, T. Komatsu, K. Matusita, J. Non-Cryst. Solids 201 (1996) 222. [7] T. Rouxel, J.C. Sangleboeuf, J. Non-Cryst. Solids 271 (2000) 224. [8] E. Le Bourhis, D. Metayer, J. Non-Cryst. Solids 272 (2000) 34. [9] C.R. Kurjian, G.W. Kammlott, M.M. Chaudhuri, J. Am. Ceram. Soc. 78 (1995) 737. [10] M. Yamane, J.D. Mackenzie, J. Non-Cryst. Solids 15 (1974) 153. [11] Y. Benino, T. Komatsu, unpublished data. [12] J. Rault, J. Non-Cryst. Solids 271 (2000) 177. [13] R. Bohmer, C.A. Angell, in: R. Richert, A.Blumen (Eds.), Disorder Eects on Relaxational Processes, Springer, Berlin, 1994, p. 11. [14] J.E. Neely, J.D. Mackenzie, J. Mater. Sci. 3 (1968) 603.
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Change in Vickers hardness at the glass transition region for fragile and strong glasses T. Watanabe, Y. Benino, T. Komatsu * Department of Chemistry, Nagaoka University of Technology, Nagaoka 940-2188, Japan Received 16 October 2000; received in revised form 2 March 2001
Abstract The temperature dependence of Vickers hardness between room temperature and around the glass transition temperature Tg in a vacuum for some glasses with dierent fragile characters was measured. The hardness at T =Tg < 0:9 decreases gradually with increasing temperature, but the glasses show unique temperature dependences in the range 0:9 < T =Tg < 1:1 depending on their fragile character. A sharp decrease in hardness is observed at around T =Tg 0:9±1:0 for fragile Bi2 O3 - and TeO2 -based glasses, but 50CuOx 50P2 O5 and soda-lime silicate glasses with strong viscosity characteristics still have relatively large Vickers hardness even at Tg and the hardness drops to almost zero around T =Tg 1:05±1:1. It is suggested that for fragile glasses the b-relaxation has an important eect on the Vickers hardness change near the glass transition region, but for strong glasses it is the a-relaxation that governs the hardness near Tg . Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The concept of fragility in glass-forming supercooled liquids introduced by Angell [1] gives new insights for glass transition and structural relaxation phenomena. Glass formers are classi®ed into two types: strong glass formers which show an Arrhenius behavior in Angell's reduced plot (i.e., viscosity vs temperature) and fragile glass formers in which the temperature dependence of the viscosity is non-Arrhenius but is expressed using the Vogel±Fulcher equation [1]. It is known that oxide glass formers with well-formed tetrahedral net-
* Corresponding author. Tel.: +81-258 47 9313, fax: +81-258 47 9300. E-mail address: [email protected] (T. Komatsu).
work structure such as SiO2 belong to the category of strong liquids and ionic glass formers without directional bonds such as 2BiCl3 KCl are fragile [1]. Recently, the present authors' group [2] measured the temperature dependence of Vickers hardness of some oxide glasses and demonstrated that TeO2 -based glasses, which are considered fragile liquids from viscosity and heat capacity changes around the glass transition temperature, Tg [3,4], are fragile even from the point of view of mechanical properties, because hardness decreases sharply around Tg . It is of particular interest to examine mechanical or elastic properties around Tg for various glass-forming liquids with dierent fragile characters. Such information would be valuable not only for handling of glass products during the manufacturing process but also for a deeper understanding of the fragility concept. The
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 5 2 1 - X
142
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
temperature dependence of hardness for some strong glasses such as fused SiO2 and GeO2 has been reported by Westbrook [5]. In this paper, we measured the temperature dependences of Vickers hardness from room temperature to the glass transition region for fragile or strong glasses such as Bi2 O3 ±B2 O3 ±PbO and CuOx ±P2 O5 and found that the change in Vickers hardness around Tg is sensitive to the fragile character of glasses.
2. Experimental The nominal compositions examined in the present study are given in Table 1. These glasses have the following features: Bi2 O3 -based and TeO2 -based glasses have received much attention because of their excellent optical properties such as large third-order non-linear susceptibility. Copper phosphate glasses show unique thermal and physical properties depending on the copper valence states [6]. A soda-lime silicate glass available commercially is selected as a standard glass. The glasses were prepared using a conventional melt-quenching method. Commercial powders of reagent grade oxides were mixed and melted in a platinum crucible at 1073±1273 K for 30±40 min in an electric furnace. After melting, the melt was poured onto an iron plate heated to 423±473 K. Table 1 Nominal glass compositions, glass transition temperature Tg , and Vickers hardness at room temperature Hv in a vacuum for the glasses examined in the present study Composition (mol%)
Tg (K)
Hv (GPa)
40Bi2 O3 40B2 O3 20PbO 60Bi2 O3 20B2 O3 20PbO 15Na2 O 15ZnO 70TeO2 10K2 O 20WO3 70TeO2 15K2 O 15Nb2 O5 70TeO2 50CuOx 50P2 O5 R Cu 0 R Cu 0:42 R Cu 0:74 14Na2 O 13CaO 73SiO2
632 568 537 617 648
3.6 3.0 2.6 2.5 3.3
708 538 440 828
4.3 4.1 1.8 6.0
In 50CuOx 50P2 O5 glasses, the ratio of copper ions, i.e., R Cu Cu = Cu Cu2 , was changed using glucose addition during glass melting. Error: 2 K for Tg , 0.1 GPa for Hv .
The chemical analysis of copper valence states in 50CuOx 50P2 O5 glasses are described elsewhere [6]. Glass transition temperatures were determined by using dierential thermal analysis (DTA) at a heating rate of 10 K min 1 . The bulk glasses for Vickers indentation tests were annealed at a temperature of Tg 10 K for 10 min to eliminate internal stress in the glasses. The temperature dependence of Vickers hardness Hv of the glasses was measured using a high temperature indentation tester in the temperature range from room temperature to around Tg in a vacuum of 1:33 10 3 Pa. The applied load in each indentation test was 490 mN and the loading time was 15 s. Indentation tests at a given temperature were carried out ten times and mean values of Vickers hardness were estimated. Measuring temperatures were increased continuously from room temperature to around Tg . The temperature of the diamond pyramid indenter was kept near that of the samples within 1 K. 3. Results The values of Tg and Hv at room temperature for the glasses are summarized in Table 1. The temperature dependences of Vickers hardness of 40Bi2 O3 40B2 O3 20PbO and 60Bi2 O3 20B2 O3 20PbO glasses in a vacuum are shown in Fig. 1, in which the values of the relative Vickers hardness change, H T =H RT , are plotted as a function of the reduced temperature, T =Tg . H T and H RT are the values of Vickers hardness at temperature T and at room temperature, respectively. It is seen that the hardness decreases gradually in the temperature region well below Tg ; T =Tg < 0:9, with increasing temperature. The Vickers hardness decreases rapidly at and near Tg and is almost zero in the GPa scale at Tg . It should be, however, pointed out that 60Bi2 O3 20B2 O3 20PbO glass containing a large amount of Bi2 O3 shows a steep hardness change at lower reduced temperatures compared with 40Bi2 O3 40B2 O3 20PbO glass. The temperature dependences of Vickers hardness of 15Na2 O 15ZnO 70TeO2 and 10K2 O 20WO3 70TeO2 glasses in a vacuum are shown in Fig. 2. In these TeO2 -based glasses, the sharp de-
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
Fig. 1. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for Bi2 O3 -based glasses. (): 40Bi2 O3 40B2 O3 20PbO; : 60Bi2 O3 20B2 O3 20PbO.
Fig. 2. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for TeO2 -based glasses. (): 10K2 O 20WO3 70TeO2 ; : 15Na2 O 15ZnO 70TeO2 .
crease in the hardness is observed at around T =Tg 0:9±1:0, similar to 60Bi2 O3 20B2 O3 20PbO glass. The temperature dependences of Vickers hardness of 50CuOx 50P2 O5 glasses with dierent copper valence states, i.e., R Cu Cu = Cu Cu2 0; 0:42 and 0.74, are shown in
143
Fig. 3. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for 50CuOx 50P2 O5 glasses with dierent copper valence states R Cu Cu = Cu Cu2 . : R Cu 0; : R Cu 0:42, : R Cu 0:74.
Fig. 3. It is seen that these glasses still have relatively large Vickers hardness even at Tg , i.e., T =Tg 1:0 and the hardness becomes almost zero around T =Tg 1:05±1:1, indicating that these glasses show extremely dierent patterns in the H T =H RT vs T =Tg plots compared with Bi2 O3 and TeO2 -based glasses. As reported by Sato et al. [6], 50CuOx 50P2 O5 glasses become `strong' (in the fragility concept) with increasing Cu content due to the formation of covalent Cu ±O bonds. It is seen from Fig. 3 that the values of reduced temperature T =Tg giving Hv 0 tend to increase with increasing R Cu , implying that the temperature dependence of Vickers hardness around Tg is related to the degree of fragility. The temperature dependence of Vickers hardness of a soda-lime silicate glass is shown in Fig. 4 together with the data on the reduced Young's modulus reported by Rouxel and Sangleboeuf [7]. It is seen that the temperature dependence of Young's modulus changes at just Tg , but the change in Vickers hardness around Tg is still gradual. The data shown in Fig. 4 demonstrate that a soda-lime silicate glass is suciently `strong' even at Tg . Bourhis and Metayer [8] also reported a Vickers hardness of 3.75 GPa even at Tg for a soda-lime silicate glass.
144
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
Fig. 4. The relative change in Vickers hardness H T =H RT obtained in a vacuum of 1:33 10 3 Pa as a function of the reduced temperature T =Tg for a soda-lime silicate glass. The data on Young's modulus are taken from [7].
4. Discussion Glass undergoes both compression and shear during the process of deformation in indentation test, and consequently the observed deformation comprises elastic deformation, plastic ¯ow and densi®cation [9]. Elastic properties are among physical properties which depend on the forces between atoms in solids. As the temperature increases, thermal expansion increases the separation between atoms and slightly decreases the forces between atoms, leading to a gradual decrease in elastic moduli, e.g. Young's modulus, with increasing temperature [7]. Yamane and Mackenzie [10] showed that Vickers hardness is proportional to Young's modulus. However, within the glass transition range, glass changes to viscous materials, i.e., viscous ¯ow is enhanced. It means elastic moduli decrease rapidly at temperatures above Tg [7]. It is known that the characteristic relaxation time s around Tg is the order of 100 s, but changes strongly with the temperature. For example, Rouxel and Sangleboeuf [7] reported that the values of s for a soda-lime silicate glass with Tg 818 K are 10 min at 808 K and 1 s at 853 K. In the present study, the loading time of Vickers indenter was 15 s, indicating that the time for loading is comparable to the value of s around
Tg . Therefore, we can expect that the Vickers hardness in glass at temperatures far below Tg decreases gradually with increasing temperature, and decreases steeply in the glass transition region. Indeed, for all glasses examined in the present study such a temperature dependence of Vickers hardness is observed as seen in Figs. 1±3. The present results demonstrate that Vickers hardness at and near Tg depends strongly on the glass systems and compositions. It is well known that TeO2 -based glasses belong to the category of fragile glass-forming system, meaning that bond breakings and atomic rearrangements occur easily around Tg [3,4]. Bi2 O3 -based glasses containing large Bi2 O3 contents are also fragile [11]. The results shown in Figs. 1 and 2 suggest that signi®cant glass structure changes giving a rapid decrease in hardness start at around T =Tg 0:9±0:95 in these Bi2 O3 - and TeO2 -based glasses. On the other hand, copper phosphate and soda-lime silicate glasses consisting of the so-called typical network former oxides of SiO2 and P2 O5 are basically stronger compared to TeO2 - and Bi2 O3 -based glasses in the strong/fragile classi®cation concept, although the degree of the fragility of silicate and copper phosphate glasses depends on the amounts of alkali metal or alkaline earth metal oxides and on the Cu /Cu2 ratio [1,6]. The results shown in Figs. 3 and 4 suggest that such relatively strong glasses have a high resistance against bond breaking and atomic rearrangements under the applied load (490 mN in this study) even at just Tg . In other words, the temperature dependence of Vickers hardness around Tg under the same indentation condition depends strongly on the fragility of glass-forming liquids. It is well recognized that there are two type structural relaxations in glass. One is called a-relaxation which is cooperative for atomic displacements/rearrangements and is directly related to the glass transition [12]. That is, a-relaxation is a primary relaxation and is observed at temperatures above Tg . The other is b-relaxation, and this secondary relaxation is observed even at temperatures below Tg [12,13]. Although the microscopic origin of b-relaxation in glass is still open to discussion [13], it has been suspected that b-relaxation corresponds to non-cooperative atomic movements
T. Watanabe et al. / Journal of Non-Crystalline Solids 286 (2001) 141±145
[12]. Structural relaxation of glass and supercooled liquids, i.e., relaxation times, could be, therefore, characterized by two dierent temperatures, when glass is heated: the ®rst is the temperature at which only b-relaxation starts; the second is the glass transition temperature Tg at which the appearance of a-relaxation is observed. Considering the above structural relaxation model, it is suggested that the b-relaxation has an important eect on the Vickers hardness change near the glass transition region for fragile glasses with extremely weak network structures such as Bi2 O3 and TeO2 -based glasses. On the other hand, for strong glasses consisting of well-de®ned strongly bonded network structures, it is the a-relaxation that governs the Vickers hardness near Tg . Westbrook [5] reported that the slope of the hardness±temperature relation changes around 873 K in fused silica. It is obvious that this temperature is much lower than the glass transition temperature (Tg 1473 K). Silica glass is known as an example of strong glasses [1]. It is, however, also well known that silica glass shows an extremely dierent deformation behavior during the indentation test compared with soda-lime silica glass [9,14]. That is, the main deformation mechanism in silica glass is densi®cation (not plastic ¯ow), and the densi®cation introduced at room temperature recovers (decreases) by annealing at temperatures around 873 K [14]. Further study will be needed to understand the microscopic mechanism of the temperature dependence of hardness for silica glass. 5. Conclusions Vickers hardness for some glasses with dierent fragile character was measured between room temperature and around Tg in a vacuum. The hardness for T =Tg < 0:9 decreases gradually with increasing temperature for all glasses examined in the present study, but the glasses show unique temperature dependences in the range 0:9 < T =Tg < 1:1 depending on their strong or
145
fragile character. A sharp decrease in hardness is observed at around T =Tg 0:95±1:0 for fragile Bi2 O3 - and TeO2 -based glasses, but for 50CuOx 50P2 O5 and soda-lime silicate glasses with strong character the hardness becomes almost zero only around T =Tg 1:1. The present study demonstrates that measurements of Vickers hardness in the glass transition region are informative for an indepth understanding of the strong/fragile concept in glass-forming liquids. As a further study, it is desired to measure creep and stress relaxation behaviors at temperatures of T =Tg 0:9±1:0 for fragile glasses. Acknowledgements This work was supported by a Grant of The Sumitomo Foundation and the Grant-in-Aid for Scienti®c Research from the Ministry of Education, Science, Sports and Culture, Japan. References [1] C.A. Angell, J. Non-Cryst. Solids 131±133 (1991) 13. [2] T. Watanabe, Y. Benino, K. Ishizaki, T. Komatsu, J. Ceram. Soc. Jpn. 107 (1999) 1140. [3] T. Komatsu, R. Ike, R. Sato, K. Matusita, Phys. Chem. Glasses 36 (1995) 216. [4] K. Aida, Y. Benino, V. Dimitrov, T. Komatsu, R. Sato, J. Am. Ceram. Soc. 83 (2000) 1192. [5] J.H. Westbrook, Phys. Chem. Glasses 1 (1960) 32. [6] R. Sato, T. Komatsu, K. Matusita, J. Non-Cryst. Solids 201 (1996) 222. [7] T. Rouxel, J.C. Sangleboeuf, J. Non-Cryst. Solids 271 (2000) 224. [8] E. Le Bourhis, D. Metayer, J. Non-Cryst. Solids 272 (2000) 34. [9] C.R. Kurjian, G.W. Kammlott, M.M. Chaudhuri, J. Am. Ceram. Soc. 78 (1995) 737. [10] M. Yamane, J.D. Mackenzie, J. Non-Cryst. Solids 15 (1974) 153. [11] Y. Benino, T. Komatsu, unpublished data. [12] J. Rault, J. Non-Cryst. Solids 271 (2000) 177. [13] R. Bohmer, C.A. Angell, in: R. Richert, A.Blumen (Eds.), Disorder Eects on Relaxational Processes, Springer, Berlin, 1994, p. 11. [14] J.E. Neely, J.D. Mackenzie, J. Mater. Sci. 3 (1968) 603.