Journal of Non-Crystalline Solids 349 (2004) 185–188 www.elsevier.com/locate/jnoncrysol
Fracture-induced change in the internal energy of silicate glasses Jun Matsuoka a,*, Mamoru Sumita a, Minoru Numaguchi a, Satoshi Yoshida a, Naohiro Soga b b
a Department of Materials Science, The University of Shiga Prefecture, Hassaka 2500, Hikone, Shiga 522-8533, Japan National Institute of Advanced Industrial Science and Technology, Kasumigaseki 1-3-1, Chiyoda-ku, Tokyo 100-8921, Japan
Available online 2 November 2004
Abstract Crushing a silicate glass is known to cause fracture-induced permanent strain. In this study, the magnitude of this strain is estimated for SiO2, 15Na2O Æ 10CaO Æ 75SiO2, and 10K2O Æ 38PbO Æ 52SiO2 glasses from the viewpoint of a change in internal energy. Samples were crushed with a percussion mortar and subsequently annealed. Heat of solution to HFaq was measured and the difference in heat of solution between as-crushed and well-annealed samples was regarded as the fracture-induced change in internal energy. This value is about 10 kJ/mol-SiO2 for SiO2, 7 kJ/mol-SiO2 for soda-lime silicate, and 2 kJ/mol-SiO2 for lead silicate glasses. The annealing behavior indicates that the fracture-induced permanent change is due to densification. The compositional dependence of the permanent change should be due to the difference in free volume of glasses, i.e., glass with large free volume will exhibit large fracture-induced structural change. Ó 2004 Published by Elsevier B.V. PACS: 61.43.Fs; 62.20.Mk; 68.35.Gy
1. Introduction Glass is known as brittle material, and linear fracture mechanics can be used to analyze the fracture of glass. This means that fracture occurs without large plastic deformation in glass. However, because of the fact that the quasi-static fracture surface energy is about an order of magnitude larger than the static surface energy, not only the formation of new surface but also other energy consumption processes must be related with the fracture surface energy of glass. On the other hand, crushing a glass is known to cause the fracture-induced permanent strain around the surface, which can be detected as the non-uniformity in refractive index [1] and as the formation of electronic defect [2]. This means that the energy consumption process contains the structural change in *
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[email protected] (J. Matsuoka). 0022-3093/$ - see front matter Ó 2004 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2004.08.183
the case of dynamic fracture process. However, the nature of this fracture-induced structural change around the surface is not clarified yet, and the magnitude of the energy consumption for this process also remains as an unsolved problem. In this study, the magnitude of fracture-induced structural change for SiO2 glass, soda lime silicate, and lead silicate glasses is estimated from the viewpoint of change in internal energy. Estimation is carried out by comparing the heat of solution of as-fractured and well-annealed glass samples to hydrofluoric acid. The nature of fracture-induced structural change is discussed using the relaxation behavior of internal energy observed in the annealing of fractured glass. 2. Experimental Glasses used in this study are SiO2 (Toshiba Ceramics, T-2030; OH content is 1 ppm), 15Na2O–10CaO– 75SiO2, and 10K2O–38PbO–52SiO2. Soda lime and lead
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silicate glasses were prepared from reagent grade Na2CO3, CaCO3, K2CO3, PbO and SiO2 by melting and subsequent annealing. Glass transition temperature is 1220 °C for SiO2, 565 °C for soda lime silicate, and 400 °C for lead silicate glasses. Samples were crushed with an automatic alumina percussion mortar, and then sieved to be in the mesh size between 53 and 75 lm. The crushing was carried out in air with the temperature in the range from 18 to 28 °C and the humidity in the range from 50% to 80%. After that, crushed glass powders were heat-treated at a prescribed temperature below Tg to cause the relaxation. Maximum heat-treatment temperature was determined as the temperature where no change in the shape of glass powder, such as blunting of the edge and sintering of powders, was observed by scanning electron microscopy. Heat of solution was measured by dissolving the obtained glass powders to 24 mass% HF aqueous solution (hydrofluoric acid) at 25 °C. A twin isoperibol calorimeter (Tokyo Riko, TIC-22) was used for the measurement. Difference of the formation energy between bulk glass and crushed glass powder after structural relaxation by annealing is the surface energy of glass, and that between bulk glass and as-crushed glass powder is the summation of the surface energy and the increase in internal energy due to the structural change caused with fracture. Therefore, the difference of the formation energy between annealed and as-crushed glass powders is the increase in internal energy by fracture. On the other hand, when we dissolve the glass powder to HF aqueous solution, the internal energy of the dissolved state of glass samples is the same between the annealed and ascrushed powders. This means that the difference of the heat of solution to HFaq for annealed and as-crushed powders is just the same with the increase in internal energy by fracture.
Fig. 1. Heat of solution of crushed SiO2 glass samples as a function of the post-fracture heat-treatment time. Lines are guide to the eyes.
3. Results Fig. 1 shows the heat of solution of SiO2 glass samples as a function of heat-treatment time. Heat of solution decreases with heat-treatment, indicating the presence of structural relaxation. The difference in heat of solution between the as-fractured glass and the glass heat-treated at 1000 °C for 96 h is about 10.5 kJ mol1, which is about 7% of the heat of solution. When the heat-treatment temperature was set lower, the magnitude of relaxation became small. In addition, relaxation at a temperature below 900 °C completes within 24 h, i.e., further heat-treatment causes no further change. Fig. 2 shows the heat of solution of the silicate glasses as a function of heat-treatment time when the heat-treatment temperature was set to T/Tg = 0.85. The vertical ax
Fig. 2. Heat of solution of the silicate glasses as a function of heattreatment time when the heat-treatment temperature was set to T/ Tg = 0.85. The vertical ax in this figure is plotted as the heat of solution of glass per mole of SiO2. Lines are guide to the eyes.
in this figure is the heat of solution of glass per mole of SiO2. Change of the heat of solution by annealing is small for lead silicate glass (about 2 kJ mol-SiO21), intermediate for soda lime silicate (about 7 kJ molSiO21), and large for SiO2 glass (10.5 kJ mol-SiO21). In the case of lead silicate glass, increase of the heattreatment temperature to T/Tg = 0.89 gives only a small change compared with the case in Fig. 2 (T/Tg = 0.85), and the difference is within the experimental error.
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Further increase of the temperature to T/Tg = 0.92 caused the surface smoothening and sintering of the glass powder, which prevented the accurate measurement. In the case of soda lime silicate glass, increase of the heat-treatment temperature to T/Tg = 0.94 makes the heat of solution 1.5 kJ mol-SiO21 lower than the annealed value in Fig. 2 (T/Tg = 0.85). In this case, change in the heat of solution completes within 24 h.
4. Discussion Relaxation of the fracture-induced increase in internal energy for SiO2 glass shows that the magnitude of relaxation strongly depends on the heat-treatment temperature, but the characteristic time of relaxation slightly depends on the temperature. This indicates that this behavior cannot be explained by a simple Debyetype (single exponential) relaxation in which the characteristic time of relaxation follows the Arrhenius equation. Furthermore, because of the absence of the long time tail in relaxation and of the dependence of the final state of relaxation on the heat-treatment temperature, this behavior cannot be explained also by stretched exponential function. Therefore, non-Debye relaxation in this case should be due to the distribution of activation energy for relaxation [3], and precise analysis is difficult. We must note that a similar behavior is observed on the relaxation of densified bulk SiO2 glass [4]. In order to clarify the nature of fracture-induced structural change in SiO2 glass, apparent activation energy at the initial stage of relaxation is deduced by using the next equation rðT 2 Þ E 1 1 ¼ exp ; ð1Þ rðT 1 Þ R T1 T2 where r(Ti) is the initial relaxation rate at temperature Ti, E* the apparent activation energy, and R the gas constant [5]. Fig. 3 shows the relation between the initial relaxation rate and the inverse heat-treatment temperature. From the slope of this figure, apparent activation energy of 56 kJ/mol is obtained. This value is similar to that of the relaxation of the refractive index in densified SiO2 glass, which is 42 kJ/mol [5], and far from the activation energy of viscous flow, 511 kJ/mol. Therefore, the nature of the fracture-induced structural change observed in the present study should be the densification of glass, and strains in bond angle and dihedral angle caused by densification would be the origin of the increase in internal energy. Fig. 2 indicates that large composition dependence exists on the fracture-induced structural change in silicate glasses. When we assume that the structural change is the densification not only in the case of SiO2 glass but also the cases of lead silicate and soda lame silicate, the difference should be due to the difference in free volume.
Fig. 3. Relation between the initial relaxation rate and the inverse heat-treatment temperature of SiO2 glass. Solid line indicates the least square fit of the data. Slope corresponding to the activation energy for viscous flow is also plotted as dashed line.
Free volume of glass is related with the solubility of inert gas to the glass [6]. In silicate glasses, increase of the network modifier drastically decreases the solubility of He (or the free volume) in glass, e.g., the solubility of He at 200 °C for 12.5Na2O Æ 12.5CaO Æ 75SiO2 glass is an order of magnitude smaller than that for SiO2 glass [7]. Using this relation, solubility of He in lead silicate glass used in this study is expected to be more than an order of magnitude smaller than that of SiO2 glass, and that in soda lime silicate used in this study be about one seventh of that of SiO2 glass. This difference in free volume should be the origin of the composition dependence of the magnitude of fracture-induced structural change in the present three glasses.
5. Conclusion Fracture-induced structural change is estimated from the viewpoint of change in internal energy for SiO2, 15Na2O–10CaO–75SiO2, and 10K2O–38PbO–52SiO2 glasses. Heat of solution to HFaq for glass samples, which are crushed and subsequently annealed, was measured to evaluate the change in internal energy by crushing. Annealing behavior indicates that the nature of fracture-induced structural change is densification. Composition dependence of the magnitude seems to be due to the difference in free volume of glasses, i.e., glass with large free volume will give large fracture-induced structural change.
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