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Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives
NOC-17855; No of Pages 7 Journal of Non-Crystalline Solids xxx (2016) xxx–xxx
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives Yang Bai a,b, Lian Peng a,⁎, Qingshan Zhu a,⁎, Zhigang Hao c a b c
State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China China National Bluestar (Group) Co., Ltd, Beijing 100029, PR China
a r t i c l e
i n f o
Article history: Received 28 January 2016 Received in revised form 6 May 2016 Accepted 14 May 2016 Available online xxxx Keywords: Lithium disilicate glass Non-isothermal crystallization kinetics Crystallization activation energy
a b s t r a c t In this study, a rapid and simple calculation procedure to determine the non-isothermal crystallization kinetic parameters of a glass was proposed based on the work of Matusita et al. The crystal growth index (n) was firstly determined with the equation proposed by Matusita in 1979 and the value of morphology index (m) could be determined according to the relationship between n and m. The activation energy for crystal growth was determined using the modified-Kissinger equation proposed by Matusita in 1980. To verify the validity of this efficient and rapid method, four compositions in the Li2O-SiO2-Al2O3-P2O5 glass system were investigated by scanning electron microscopy (SEM) and X-ray diffractometry (XRD). The crystallization mechanisms as identified by the characterization show good agreement with those predicted by the new calculation procedure, verifying the validity of the calculation procedure. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The lithium disilicate-based glass-ceramic is one of the most promising dental restorative materials and has been the model system of many theoretical studies [1,2]. To obtain the glass-ceramics with outstanding properties, some oxide additives are commonly used, for example, P2O5 is used as an efficient nucleating agent [3,4] and Al2O3 is used to reduce immiscibility in alkali silicate systems [5,6]. Up to the present, improvement of the performance of the lithium disilicatebased glass-ceramic through the Al2O3 and P2O5 addition still needs to be further explored [1,7,8]. It is well-known that the properties of glass-ceramics are determined by the precipitated crystals and their microstructures in the glass matrix [7,9], which is closely related to the crystallization mechanism of a parent glass. Therefore, understanding of the crystallization kinetics of a parent glass is a critical issue for the development of glassceramics. Crystallization kinetic parameters, providing the crystallization mechanism of a glass [10], include the activation energy of crystallization E, the crystal growth index n and the morphology index m. The activation energy E reflects the sensitivity of a glass to temperature variation and thus affects the controllability of a crystallization process [11], and the n and m reflect the crystallization mechanism. The Kissinger equation is widely applied to calculate the crystallization activation energy E [10,12,13]. With the assumption - that the
⁎ Corresponding authors. E-mail addresses: [email protected] (L. Peng), [email protected] (Q. Zhu).
crystallization process is a first-order chemical reaction [14,15], the E can then be obtained without accounting the n and m. The crystallization mechanism is usually determined by the Matusita equation (refer to as the “M equation” hereafter) [10,12], which is proposed by Matusita et al. [16] in 1979. In 1980, Matusita et al. [17] investigated the relationship between the crystallization mechanism and the activation energy for crystal growth. They derived the modified-Kissinger equation on the basis of the nucleation and crystal growth theory to calculate the activation energy. Then they determined the activation energy E for a viscous flow by experiments, which has been reported to be equal to that of crystal growth in the Li2O·2SiO2 glass [18]. By comparing the Eη with different values of E, it was found that the actual activation energy E was associated with the crystallization mechanism. Therefore, they concluded that the E for crystal growth could be calculated only after being aware of the crystallization mechanism of a glass. Moreover, Donald et al. [19,20] also pointed out that the precise crystallization mechanism should be known for a reliable determination of E by the non-isothermal method. Therefore, to investigate the crystallization kinetics of a lithium zinc silicate glass, both the isothermal and nonisothermal methods were used to determine the E, n and m. They firstly determined the crystallization activation energy Eisothermal by the isothermal method. Then n and m were determined by the trial and error method, i.e. comparing E calculated by the modified Kissinger-type equation, using different n and m, with the Eisothermal. When the E is close to the Eisothermal, the corresponding n and m were considered to represent the actual crystallization mechanism [19]. Using this method, the crystallization kinetic parameters E, n and m can be all determined. However, although crystallization kinetic parameters can be
http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032 0022-3093/© 2016 Elsevier B.V. All rights reserved.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Y. Bai et al. / Journal of Non-Crystalline Solids xxx (2016) xxx–xxx
determined for a glass by the combined isothermal and non-isothermal method, it is quite time-consuming. It is therefore quite meaningful to develop a simple method to determine n, m and E only by the nonisothermal method. In the present study, a simple and quick calculation procedure was established for determining the non-isothermal crystallization kinetic parameters n, m and E, and the as-determined parameters were verified by experimental data. 2. Theory background The crystal growth index (n), which is related to the nucleation and crystallization mechanism [19], was determined according to the Eq. (1) developed by Matusita and Sakka [16,21]. ln ½− ln ð1−χÞ ¼ −nlnβ–1:052mE=RTp þ const: Z χT ¼ Z
T Ts Tf Ts
ð1Þ
C ðT ÞdT ð2Þ
Table 1 Values for n and m used in Eq. (1). Crystallization mechanism
n
m
Bulk crystallization with an increasing number of nuclei (i.e. an as-quenched sample with the number of nuclei inversely proportional to the heating rate) Three-dimensional growth of crystals 4 3 Two-dimensional growth of crystals 3 2 One-dimensional growth of crystals 2 1 Surface crystallization 1 1
Table 2 The composition of parent glasses (mol%). Glass
SiO2
Li2O
P2O5
Al2O3
SiO2/Li2O
P2O5/Al2O3
A1 A2 A3 A4
64.00 63.55 62.92 62.30
32.00 31.70 31.42 31.20
3.00 2.85 2.83 2.80
1.00 1.90 2.83 3.70
2:1 2:1 2:1 2:1
3:1 3:2 3:3 3:4
C ðT ÞdT
where C(T) is the DSC curve of the exothermic peak as shown in Fig. 1. χ represents the volume fraction crystallized at a given temperature and defined as the ratio of the integral area from Ts to T, to the total integral area of the exothermic peak between the outset crystallization temperature Ts and the terminal crystallization temperature Tf. The n and m are the constants depending on the crystallization mechanism, where under the volume crystallization mechanism n equals to m + 1 and m for glasses without nuclei and containing a fixed number of nucleus, respectively. While, when surface crystallization is dominant, n = m = 1 [22,12]. Values of n and m are summarized in Table 1 for different crystallization mechanism [23]. The apparent activation energy E can then be calculated from the variation of peak temperatures with heating rate by the modified Kissinger equation as: Ln βn =Tp2 ¼ −mE=RTp þ const:
ð3Þ
where β is the heating rate, Tp is the peak crystallization temperature, E is the crystallization activation energy and R is the gas constant. 3. Experimental procedures
uniformly, the mixture was melted in a Pt crucible at 1500 °C for 2 h using an electric resistance furnace and the melt was then quenched into water to obtain a glass frit. After that, the frit was milled for a few minutes and sieved to obtain the particles $_amp_$lt;74 μm. The crystallization temperatures were investigated using differential scanning calorimetry (DSC, Linseis, STA PT-1600, Germany), with the nominal accuracy of ±0.05 K and ±0.3 μW for temperature and heat respectively. Moreover, the temperature of the equipment is calibrated by standard material of Indium. The DSC analyses were performed using Al2O3 crucibles and the glass powders were heated from room temperature to 1200 °C with different heating rates (β = 5, 10, 15, 20 and 25 °C min−1). All glass samples were heated at respective peak temperatures for 1 h and the crystalline phases were then identified using Xray diffractometry (XRD, PANalytical, X'PERT-PRO MPD) with the Cu Kα radiation. To study the bulk crystallization behavior, the glass powders of A1 and A3 were remelted at 1300 °C for 2 h and cooled to room temperature to form glass blocks of about 1 g. The glass blocks were then annealed at their respective peak temperatures for 30 s, followed by XRD characterizations to determine the as-formed crystalline phases. In addition, the glass block of A3 was further heat treated at its peak crystallization temperature for 2 min. After the heat treatments, all
Lithium disilicate glasses of stoichiometric composition were prepared using analytic grade (purity ≥99%) Li2CO3 (for Li2O), SiO2, Al2O3 and (NH4)2HPO4 (for P2O5). Table 2 presents the detailed compositions of the parent glass investigated. After mixing the raw materials
Fig. 1. Method for determining the crystallized fraction χ.
Fig. 2. DSC plots for glass A1 at different heating rates.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
Y. Bai et al. / Journal of Non-Crystalline Solids xxx (2016) xxx–xxx
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4. Results 4.1. DSC results The non-isothermal method has been widely used for obtaining crystallization kinetic parameters by analyzing the data derived from non-isothermal DSC studies. The crystallization temperature obtained from a DSC curve increases with increasing the heating rate [24,25]. The DSC plots of the parent glass A1 with different heating rates (5,10,15,20 and 25 °C min− 1) are shown in Fig. 2 and the DSC plots for the A2–A4 glass show the same tendency as Fig. 2 and therefore are not depicted. Fig. 3 shows the peak crystallization temperatures of each glass at different heating rates. 4.2. Crystallization kinetic results
Fig. 3. The peak temperatures of A1–A4 determined by DSC at different heating rates. The lines are drawn as guides to the eyes.
samples were ground and polished with successive SiC papers. The polished samples were then etched by a 2 vol% HF solution for 2 min. After that, the microstructures of A1 and A3 were charactered by scanning electron microscopy (SEM, Semicon, JSM-7001F).
In the present study, the crystallization mechanism was firstly determined and the corresponding activation energy E was calculated by the modified-Kissinger equation. The crystallized fractions (χ) versus temperature plots for A1–A4 at different heating rates are shown in Fig. 4, from which the crystallized fraction (χ) at a fixed temperature could be directly obtained. Fig. 5 shows the plots of ln[−ln(1 − χ)] versus lnβ (derived from the M equation), together with the linear fitting using the least square method. The slope of the straight line represents the value of n. Once the values of n were obtained, m values can be determined from which have been
Fig. 4. Evolution of crystallized fraction χ for A1–A4 at different heating rates.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Fig. 5. Variation of ln(−ln(1 − χ))with lnβ for A1–A4 at fixed temperatures.
presented in Table 1. The crystallization activation energy E was determined by plotting ln(βn/Tp2) versus 1000 m/RTp, according to Eq. (3), as shown in Fig. 6. The data in Fig. 6 were also linearly fitted by the least square method. Using the above calculation procedure, the calculated values of the average n, m and E are listed in Table 3. It can be
Fig. 6. Plots of ln(βn/Tp2) versus 1000 m/RTp for A1–A4.
Table 3 The n, m and E for A1–A4 glasses. Composition
n
m
E/kJ mol−1
R2
A1 A2 A3 A4
0.76 ± 0.12 1.29 ± 0.15 1.56 ± 0.09 1.88 ± 0.12
1 1 1 1
1063.61 709.48 672.78 767.36
0.997 0.996 0.992 0.997
Fig. 7. X-ray diffraction patterns for glass samples A1–A4 after heat treatment at their respective peak temperatures for 1 h.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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4.3. XRD results
Table 4 Summary of crystalline phases. Glasses Heat treatment temperature (°C)
Major crystalline phase
Minor crystalline phases
A1 A2 A3
787 761 742
Li2Si2O5 Li2Si2O5 Li2Si2O5
A4
708
Li2Si2O5
Li3PO4, LixAlxSi3-xO6 Li3PO4, LixAlxSi3-xO6 Al2PO4SiO6, LixAlxSi3-xO6, Li2SiO3 Al2PO4SiO6, LixAlxSi3-xO6, Li2SiO3
Fig. 7 exhibits the X-ray diffraction patterns of the glasses A1-A4 after being annealed at respective peak temperatures for 1 h. Table 4 shows the crystalline phases in A1-A4. The crystalline phases of lithium disilicate and LixAlxSi3-xO6 exist in all samples, and more Al2O3 favors the formation of the LixAlxSi3-xO6 phase rather than the lithium disilicate. In addition, the Li3PO4 only exists in A1 and A2. The peaks related to the lithium metasilicate and aluminum phosphate silicate phase appear in A3 and A4. 5. Discussion
seen that the values of n vary from 0.76 to 1.88 for A1–A4, and the A3 has the lowest activation energy (672.78 kJ mol−1). As shown in Table 1, the crystallization process is dominated by the surface crystallization mechanism for n = m = 1 and by the bulk crystallization mechanism for n = 2, m = 1. It is therefore that the surface crystallization dominates in A1, the values of n and m are 1; for A2– A4, the value of n varies from 1 to 2, the values of m are also 1.
Previously, the crystallization kinetic parameters can be determined by the non-isothermal method with the minimum experiments. However, it is notable that the crystallization mechanism should be known before determining the reliable activation energy. The present investigation proposed a new calculation procedure to determine the crystallization kinetic parameters, e.g. the crystallization mechanism can be firstly derived by the M equation, and the activation energy can then be subsequently determined by the modified-Kissinger equation.
Fig. 8. Microstructures of A1 and A3 after heat treatments at their respective peak temperatures for 30 s (etched with 2 vol.% HF solution for 2 min). (a) A1, including the surface area (1) and the bulk area (2) (×200); (b) a high magnification image of the surface area (1) in (a) (×3000); (c) a high magnification image of the bulk area (2) in (a) (×3000); (d) A3, including the surface area (1) and the bulk area (2) (×200); (e) a high magnification image of the surface area (1) in (d) (×3000); (f) a high magnification image of the bulk area (2) in (d) (×3000).
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Fig. 9. X-ray diffraction patterns for glass samples A1 and A3 after annealed at their respective peak temperatures for 30 s.
It is necessary to overcome a certain potential barrier when an amorphous glass transforms to a crystalline phase, which is known as the crystallization activation energy E. Generally speaking, a glass system with relatively lower activation energy is easily controllable during the crystallization process [11]. In the present investigation, the glass system A3 has the lowest crystallization activation energy among the glasses investigated. Therefore, the crystallization of glass A3 should be the most easily controlled as compared with those of the other glasses. To confirm this prediction, the glass system A1, with the highest crystallization activation energy, and A3 were both heat treated at their respective peak temperatures for 30 s. After the heat treatment, the surface of A1 exhibited slight devitrification and the inner of the glass remained to be almost transparent, whereas, A3 was entirely transparent. Fig. 8 shows the microstructure of A1 and A3 after being annealed at their respective peak temperatures for 30 s. The samples after the heat treatment were etched with a 2 vol.% HF solution for 2 min to dissolve the amorphous phase. Fig .8(a) shows the low magnification microstructure of A1, including the surface area (marked as (1)) and the bulk area (marked as (2)). It is obviously noticed from Fig. 8(a) that the microstructure of the surface area is different from that of the bulk area. Fig. 8(b) and (c) respectively correspond to the high magnification microstructures of the surface area and the bulk area in Fig. 8(a). As shown in Fig. 8(b) and (c), rapid crystallization occurs in the surface area rather than the bulk area, demonstrating not only the difficulty in controlling the crystallization of A1 but also the nature of the surface crystallization mechanism of A1. On the contrary, the surface area and the bulk area in A3 show the same microstructure with few crystals,
as shown in Fig. 8(d–f). The drastic difference of A1 and A3 could also be seen from Fig. 9. Large amount of crystals precipitated in the specimen of A1, while less crystals precipitated in A3. Based on the above results, it is confirmed that the A3 glass with low activation energy is more easily controlled than the A1 glass system, which proves the validity of the predicted results (E) of our calculating procedure. It is generally accepted that there are two kinds of crystallization mechanisms: bulk and surface crystallization. In most cases the two crystallization mechanisms occur simultaneously [26]. As shown in Table 3, the lowest value of n was obtained for A1, demonstrating that A1 crystallizes via the surface crystallization mechanism, which has been confirmed in Fig. 8(a). The n value is 1.56 for A3, indicating that the crystallization of A3 occurred via both the surface and the bulk mechanism. Fig. 10 reveals the microstructure of A3 after heat treatment at its peak temperature for 2 min. Fig. 10(a) exhibits the monolithic microstructure of A3, from which it can be concluded that there is no difference between the surface and bulk area. Fig. 10(b) and (c) are the high magnification microstructures of the surface and bulk area of A3, respectively, which exhibits the same microstructure. It is concluded that the crystallization behavior of A3 mainly shows a bulk crystallization, which agrees with the predicted n value of 1.56. Based on the SEM and XRD results, the newly-proposed calculation procedure is verified to be valid, that is, n, m and E can be reliably obtained by the M equation and the modified-Kissinger equation. 6. Conclusion In this study, a rapid and efficient calculation procedure to analyze the non-isothermal crystallization kinetics of a glass was proposed based on the work by Matusita. Firstly the crystallization mechanism was determined by the M equation and then the activation energy E was calculated using the modified-Kissinger equation. To verify the validity of the calculation procedure, four different compositions in the Li2O-SiO2-Al2O3-P2O5 glass system were investigated by DSC, XRD and SEM techniques. The crystallization kinetic results of our calculation procedure showed that the glass system Al had the highest E and A3 had the lowest E. As a result, A1 is more difficult to control the crystallization process as compared with that of A3, as confirmed by the XRD and SEM characterizations. It was further showed by the XRD and SEM characterizations that A1 exhibited surface crystallization and A3 mainly occurred bulk crystallization, which are in good agreement with that predicted by the new calculation procedure. In addition, the main crystallization mechanism changes from surface-type crystallization to volumetrictype crystallization for A1 to A4. Acknowledgements The authors gratefully acknowledge the financial support from National Natural Science Foundation of China under the Contract No. 21325628.
Fig. 10. Microstructures of A3 after heat treatment at its peak temperature for 2 min (etched with 2 vol.% HF solution for 2 min). (a) A3, including the surface area (1) and the bulk area (2) (×200); (b) a high magnification image of the surface area (1) in (a) (×3000); (c) a high magnification image of the bulk area (2) in (a) (×3000).
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives Yang Bai a,b, Lian Peng a,⁎, Qingshan Zhu a,⁎, Zhigang Hao c a b c
State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China China National Bluestar (Group) Co., Ltd, Beijing 100029, PR China
a r t i c l e
i n f o
Article history: Received 28 January 2016 Received in revised form 6 May 2016 Accepted 14 May 2016 Available online xxxx Keywords: Lithium disilicate glass Non-isothermal crystallization kinetics Crystallization activation energy
a b s t r a c t In this study, a rapid and simple calculation procedure to determine the non-isothermal crystallization kinetic parameters of a glass was proposed based on the work of Matusita et al. The crystal growth index (n) was firstly determined with the equation proposed by Matusita in 1979 and the value of morphology index (m) could be determined according to the relationship between n and m. The activation energy for crystal growth was determined using the modified-Kissinger equation proposed by Matusita in 1980. To verify the validity of this efficient and rapid method, four compositions in the Li2O-SiO2-Al2O3-P2O5 glass system were investigated by scanning electron microscopy (SEM) and X-ray diffractometry (XRD). The crystallization mechanisms as identified by the characterization show good agreement with those predicted by the new calculation procedure, verifying the validity of the calculation procedure. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The lithium disilicate-based glass-ceramic is one of the most promising dental restorative materials and has been the model system of many theoretical studies [1,2]. To obtain the glass-ceramics with outstanding properties, some oxide additives are commonly used, for example, P2O5 is used as an efficient nucleating agent [3,4] and Al2O3 is used to reduce immiscibility in alkali silicate systems [5,6]. Up to the present, improvement of the performance of the lithium disilicatebased glass-ceramic through the Al2O3 and P2O5 addition still needs to be further explored [1,7,8]. It is well-known that the properties of glass-ceramics are determined by the precipitated crystals and their microstructures in the glass matrix [7,9], which is closely related to the crystallization mechanism of a parent glass. Therefore, understanding of the crystallization kinetics of a parent glass is a critical issue for the development of glassceramics. Crystallization kinetic parameters, providing the crystallization mechanism of a glass [10], include the activation energy of crystallization E, the crystal growth index n and the morphology index m. The activation energy E reflects the sensitivity of a glass to temperature variation and thus affects the controllability of a crystallization process [11], and the n and m reflect the crystallization mechanism. The Kissinger equation is widely applied to calculate the crystallization activation energy E [10,12,13]. With the assumption - that the
⁎ Corresponding authors. E-mail addresses: [email protected] (L. Peng), [email protected] (Q. Zhu).
crystallization process is a first-order chemical reaction [14,15], the E can then be obtained without accounting the n and m. The crystallization mechanism is usually determined by the Matusita equation (refer to as the “M equation” hereafter) [10,12], which is proposed by Matusita et al. [16] in 1979. In 1980, Matusita et al. [17] investigated the relationship between the crystallization mechanism and the activation energy for crystal growth. They derived the modified-Kissinger equation on the basis of the nucleation and crystal growth theory to calculate the activation energy. Then they determined the activation energy E for a viscous flow by experiments, which has been reported to be equal to that of crystal growth in the Li2O·2SiO2 glass [18]. By comparing the Eη with different values of E, it was found that the actual activation energy E was associated with the crystallization mechanism. Therefore, they concluded that the E for crystal growth could be calculated only after being aware of the crystallization mechanism of a glass. Moreover, Donald et al. [19,20] also pointed out that the precise crystallization mechanism should be known for a reliable determination of E by the non-isothermal method. Therefore, to investigate the crystallization kinetics of a lithium zinc silicate glass, both the isothermal and nonisothermal methods were used to determine the E, n and m. They firstly determined the crystallization activation energy Eisothermal by the isothermal method. Then n and m were determined by the trial and error method, i.e. comparing E calculated by the modified Kissinger-type equation, using different n and m, with the Eisothermal. When the E is close to the Eisothermal, the corresponding n and m were considered to represent the actual crystallization mechanism [19]. Using this method, the crystallization kinetic parameters E, n and m can be all determined. However, although crystallization kinetic parameters can be
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Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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determined for a glass by the combined isothermal and non-isothermal method, it is quite time-consuming. It is therefore quite meaningful to develop a simple method to determine n, m and E only by the nonisothermal method. In the present study, a simple and quick calculation procedure was established for determining the non-isothermal crystallization kinetic parameters n, m and E, and the as-determined parameters were verified by experimental data. 2. Theory background The crystal growth index (n), which is related to the nucleation and crystallization mechanism [19], was determined according to the Eq. (1) developed by Matusita and Sakka [16,21]. ln ½− ln ð1−χÞ ¼ −nlnβ–1:052mE=RTp þ const: Z χT ¼ Z
T Ts Tf Ts
ð1Þ
C ðT ÞdT ð2Þ
Table 1 Values for n and m used in Eq. (1). Crystallization mechanism
n
m
Bulk crystallization with an increasing number of nuclei (i.e. an as-quenched sample with the number of nuclei inversely proportional to the heating rate) Three-dimensional growth of crystals 4 3 Two-dimensional growth of crystals 3 2 One-dimensional growth of crystals 2 1 Surface crystallization 1 1
Table 2 The composition of parent glasses (mol%). Glass
SiO2
Li2O
P2O5
Al2O3
SiO2/Li2O
P2O5/Al2O3
A1 A2 A3 A4
64.00 63.55 62.92 62.30
32.00 31.70 31.42 31.20
3.00 2.85 2.83 2.80
1.00 1.90 2.83 3.70
2:1 2:1 2:1 2:1
3:1 3:2 3:3 3:4
C ðT ÞdT
where C(T) is the DSC curve of the exothermic peak as shown in Fig. 1. χ represents the volume fraction crystallized at a given temperature and defined as the ratio of the integral area from Ts to T, to the total integral area of the exothermic peak between the outset crystallization temperature Ts and the terminal crystallization temperature Tf. The n and m are the constants depending on the crystallization mechanism, where under the volume crystallization mechanism n equals to m + 1 and m for glasses without nuclei and containing a fixed number of nucleus, respectively. While, when surface crystallization is dominant, n = m = 1 [22,12]. Values of n and m are summarized in Table 1 for different crystallization mechanism [23]. The apparent activation energy E can then be calculated from the variation of peak temperatures with heating rate by the modified Kissinger equation as: Ln βn =Tp2 ¼ −mE=RTp þ const:
ð3Þ
where β is the heating rate, Tp is the peak crystallization temperature, E is the crystallization activation energy and R is the gas constant. 3. Experimental procedures
uniformly, the mixture was melted in a Pt crucible at 1500 °C for 2 h using an electric resistance furnace and the melt was then quenched into water to obtain a glass frit. After that, the frit was milled for a few minutes and sieved to obtain the particles $_amp_$lt;74 μm. The crystallization temperatures were investigated using differential scanning calorimetry (DSC, Linseis, STA PT-1600, Germany), with the nominal accuracy of ±0.05 K and ±0.3 μW for temperature and heat respectively. Moreover, the temperature of the equipment is calibrated by standard material of Indium. The DSC analyses were performed using Al2O3 crucibles and the glass powders were heated from room temperature to 1200 °C with different heating rates (β = 5, 10, 15, 20 and 25 °C min−1). All glass samples were heated at respective peak temperatures for 1 h and the crystalline phases were then identified using Xray diffractometry (XRD, PANalytical, X'PERT-PRO MPD) with the Cu Kα radiation. To study the bulk crystallization behavior, the glass powders of A1 and A3 were remelted at 1300 °C for 2 h and cooled to room temperature to form glass blocks of about 1 g. The glass blocks were then annealed at their respective peak temperatures for 30 s, followed by XRD characterizations to determine the as-formed crystalline phases. In addition, the glass block of A3 was further heat treated at its peak crystallization temperature for 2 min. After the heat treatments, all
Lithium disilicate glasses of stoichiometric composition were prepared using analytic grade (purity ≥99%) Li2CO3 (for Li2O), SiO2, Al2O3 and (NH4)2HPO4 (for P2O5). Table 2 presents the detailed compositions of the parent glass investigated. After mixing the raw materials
Fig. 1. Method for determining the crystallized fraction χ.
Fig. 2. DSC plots for glass A1 at different heating rates.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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4. Results 4.1. DSC results The non-isothermal method has been widely used for obtaining crystallization kinetic parameters by analyzing the data derived from non-isothermal DSC studies. The crystallization temperature obtained from a DSC curve increases with increasing the heating rate [24,25]. The DSC plots of the parent glass A1 with different heating rates (5,10,15,20 and 25 °C min− 1) are shown in Fig. 2 and the DSC plots for the A2–A4 glass show the same tendency as Fig. 2 and therefore are not depicted. Fig. 3 shows the peak crystallization temperatures of each glass at different heating rates. 4.2. Crystallization kinetic results
Fig. 3. The peak temperatures of A1–A4 determined by DSC at different heating rates. The lines are drawn as guides to the eyes.
samples were ground and polished with successive SiC papers. The polished samples were then etched by a 2 vol% HF solution for 2 min. After that, the microstructures of A1 and A3 were charactered by scanning electron microscopy (SEM, Semicon, JSM-7001F).
In the present study, the crystallization mechanism was firstly determined and the corresponding activation energy E was calculated by the modified-Kissinger equation. The crystallized fractions (χ) versus temperature plots for A1–A4 at different heating rates are shown in Fig. 4, from which the crystallized fraction (χ) at a fixed temperature could be directly obtained. Fig. 5 shows the plots of ln[−ln(1 − χ)] versus lnβ (derived from the M equation), together with the linear fitting using the least square method. The slope of the straight line represents the value of n. Once the values of n were obtained, m values can be determined from which have been
Fig. 4. Evolution of crystallized fraction χ for A1–A4 at different heating rates.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Fig. 5. Variation of ln(−ln(1 − χ))with lnβ for A1–A4 at fixed temperatures.
presented in Table 1. The crystallization activation energy E was determined by plotting ln(βn/Tp2) versus 1000 m/RTp, according to Eq. (3), as shown in Fig. 6. The data in Fig. 6 were also linearly fitted by the least square method. Using the above calculation procedure, the calculated values of the average n, m and E are listed in Table 3. It can be
Fig. 6. Plots of ln(βn/Tp2) versus 1000 m/RTp for A1–A4.
Table 3 The n, m and E for A1–A4 glasses. Composition
n
m
E/kJ mol−1
R2
A1 A2 A3 A4
0.76 ± 0.12 1.29 ± 0.15 1.56 ± 0.09 1.88 ± 0.12
1 1 1 1
1063.61 709.48 672.78 767.36
0.997 0.996 0.992 0.997
Fig. 7. X-ray diffraction patterns for glass samples A1–A4 after heat treatment at their respective peak temperatures for 1 h.
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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4.3. XRD results
Table 4 Summary of crystalline phases. Glasses Heat treatment temperature (°C)
Major crystalline phase
Minor crystalline phases
A1 A2 A3
787 761 742
Li2Si2O5 Li2Si2O5 Li2Si2O5
A4
708
Li2Si2O5
Li3PO4, LixAlxSi3-xO6 Li3PO4, LixAlxSi3-xO6 Al2PO4SiO6, LixAlxSi3-xO6, Li2SiO3 Al2PO4SiO6, LixAlxSi3-xO6, Li2SiO3
Fig. 7 exhibits the X-ray diffraction patterns of the glasses A1-A4 after being annealed at respective peak temperatures for 1 h. Table 4 shows the crystalline phases in A1-A4. The crystalline phases of lithium disilicate and LixAlxSi3-xO6 exist in all samples, and more Al2O3 favors the formation of the LixAlxSi3-xO6 phase rather than the lithium disilicate. In addition, the Li3PO4 only exists in A1 and A2. The peaks related to the lithium metasilicate and aluminum phosphate silicate phase appear in A3 and A4. 5. Discussion
seen that the values of n vary from 0.76 to 1.88 for A1–A4, and the A3 has the lowest activation energy (672.78 kJ mol−1). As shown in Table 1, the crystallization process is dominated by the surface crystallization mechanism for n = m = 1 and by the bulk crystallization mechanism for n = 2, m = 1. It is therefore that the surface crystallization dominates in A1, the values of n and m are 1; for A2– A4, the value of n varies from 1 to 2, the values of m are also 1.
Previously, the crystallization kinetic parameters can be determined by the non-isothermal method with the minimum experiments. However, it is notable that the crystallization mechanism should be known before determining the reliable activation energy. The present investigation proposed a new calculation procedure to determine the crystallization kinetic parameters, e.g. the crystallization mechanism can be firstly derived by the M equation, and the activation energy can then be subsequently determined by the modified-Kissinger equation.
Fig. 8. Microstructures of A1 and A3 after heat treatments at their respective peak temperatures for 30 s (etched with 2 vol.% HF solution for 2 min). (a) A1, including the surface area (1) and the bulk area (2) (×200); (b) a high magnification image of the surface area (1) in (a) (×3000); (c) a high magnification image of the bulk area (2) in (a) (×3000); (d) A3, including the surface area (1) and the bulk area (2) (×200); (e) a high magnification image of the surface area (1) in (d) (×3000); (f) a high magnification image of the bulk area (2) in (d) (×3000).
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Fig. 9. X-ray diffraction patterns for glass samples A1 and A3 after annealed at their respective peak temperatures for 30 s.
It is necessary to overcome a certain potential barrier when an amorphous glass transforms to a crystalline phase, which is known as the crystallization activation energy E. Generally speaking, a glass system with relatively lower activation energy is easily controllable during the crystallization process [11]. In the present investigation, the glass system A3 has the lowest crystallization activation energy among the glasses investigated. Therefore, the crystallization of glass A3 should be the most easily controlled as compared with those of the other glasses. To confirm this prediction, the glass system A1, with the highest crystallization activation energy, and A3 were both heat treated at their respective peak temperatures for 30 s. After the heat treatment, the surface of A1 exhibited slight devitrification and the inner of the glass remained to be almost transparent, whereas, A3 was entirely transparent. Fig. 8 shows the microstructure of A1 and A3 after being annealed at their respective peak temperatures for 30 s. The samples after the heat treatment were etched with a 2 vol.% HF solution for 2 min to dissolve the amorphous phase. Fig .8(a) shows the low magnification microstructure of A1, including the surface area (marked as (1)) and the bulk area (marked as (2)). It is obviously noticed from Fig. 8(a) that the microstructure of the surface area is different from that of the bulk area. Fig. 8(b) and (c) respectively correspond to the high magnification microstructures of the surface area and the bulk area in Fig. 8(a). As shown in Fig. 8(b) and (c), rapid crystallization occurs in the surface area rather than the bulk area, demonstrating not only the difficulty in controlling the crystallization of A1 but also the nature of the surface crystallization mechanism of A1. On the contrary, the surface area and the bulk area in A3 show the same microstructure with few crystals,
as shown in Fig. 8(d–f). The drastic difference of A1 and A3 could also be seen from Fig. 9. Large amount of crystals precipitated in the specimen of A1, while less crystals precipitated in A3. Based on the above results, it is confirmed that the A3 glass with low activation energy is more easily controlled than the A1 glass system, which proves the validity of the predicted results (E) of our calculating procedure. It is generally accepted that there are two kinds of crystallization mechanisms: bulk and surface crystallization. In most cases the two crystallization mechanisms occur simultaneously [26]. As shown in Table 3, the lowest value of n was obtained for A1, demonstrating that A1 crystallizes via the surface crystallization mechanism, which has been confirmed in Fig. 8(a). The n value is 1.56 for A3, indicating that the crystallization of A3 occurred via both the surface and the bulk mechanism. Fig. 10 reveals the microstructure of A3 after heat treatment at its peak temperature for 2 min. Fig. 10(a) exhibits the monolithic microstructure of A3, from which it can be concluded that there is no difference between the surface and bulk area. Fig. 10(b) and (c) are the high magnification microstructures of the surface and bulk area of A3, respectively, which exhibits the same microstructure. It is concluded that the crystallization behavior of A3 mainly shows a bulk crystallization, which agrees with the predicted n value of 1.56. Based on the SEM and XRD results, the newly-proposed calculation procedure is verified to be valid, that is, n, m and E can be reliably obtained by the M equation and the modified-Kissinger equation. 6. Conclusion In this study, a rapid and efficient calculation procedure to analyze the non-isothermal crystallization kinetics of a glass was proposed based on the work by Matusita. Firstly the crystallization mechanism was determined by the M equation and then the activation energy E was calculated using the modified-Kissinger equation. To verify the validity of the calculation procedure, four different compositions in the Li2O-SiO2-Al2O3-P2O5 glass system were investigated by DSC, XRD and SEM techniques. The crystallization kinetic results of our calculation procedure showed that the glass system Al had the highest E and A3 had the lowest E. As a result, A1 is more difficult to control the crystallization process as compared with that of A3, as confirmed by the XRD and SEM characterizations. It was further showed by the XRD and SEM characterizations that A1 exhibited surface crystallization and A3 mainly occurred bulk crystallization, which are in good agreement with that predicted by the new calculation procedure. In addition, the main crystallization mechanism changes from surface-type crystallization to volumetrictype crystallization for A1 to A4. Acknowledgements The authors gratefully acknowledge the financial support from National Natural Science Foundation of China under the Contract No. 21325628.
Fig. 10. Microstructures of A3 after heat treatment at its peak temperature for 2 min (etched with 2 vol.% HF solution for 2 min). (a) A3, including the surface area (1) and the bulk area (2) (×200); (b) a high magnification image of the surface area (1) in (a) (×3000); (c) a high magnification image of the bulk area (2) in (a) (×3000).
Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032
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Please cite this article as: Y. Bai, et al., Non-isothermal crystallization kinetics of stoichiometric lithium disilicate-based glasses with Al2O3 additives, J. Non-Cryst. Solids (2016), http://dx.doi.org/10.1016/j.jnoncrysol.2016.05.032