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Crystal nucleation rates in a Na2O–SiO2 glass
Journal of Non-Crystalline Solids 261 (2000) 163±168
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Crystal nucleation rates in a Na2O±SiO2 glass Lori L. Burgner, Michael C. Weinberg * Arizona Materials Laboratories, Materials Science and Engineering Department, University of Arizona, Tucson, AZ 85721-0012, USA Received 28 May 1999; received in revised form 2 September 1999
Abstract Nucleation of sodium metasilicate crystals in sodium silicate glass of composition 43Na2 O±57SiO2 is investigated. Two-stage isothermal heating and optical microscopy techniques are utilized to determine the steady-state nucleation rates at temperatures between 390°C and 455°C. The results of this investigation are compared to the results we obtained for the temperature dependence of the nucleation rate in these glasses via a DTA technique which we presented in a previous study. It is found that the results of the two techniques are in agreement within experimental error. It is observed that the peak nucleation rate for this composition occurs near 410°C, which is about 50°C lower than that reported for nucleation in the 46Na2 O±54SiO2 glass composition. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Crystal nucleation in glasses continues to be an important and active area of inquiry due to its technological and scienti®c importance. In the realm of technology, knowledge of crystal nucleation rates in glasses at dierent temperatures is essential for preparing glass±ceramics, wherein nucleation must be promoted, as well as for applications in which nucleation must be avoided, such as optical ®bers. To the scienti®c community, glasses provide an ideal media for studying nucleation phenomena in a condensed system and for quantitatively testing standard nucleation theories. Glasses that appear to nucleate homogeneously within the volume are traditionally studied within the realm of classical nucleation theory (CNT). However, discrepancies between theoreti-
* Corresponding author. Tel.: +1-520 621 6909; fax: +1-520 621 8059. E-mail address: [email protected] (M.C. Weinberg).
cal predictions and experimental results, along with observations of metastable phase formation, have called into the question the validity of applying CNT to describe the nucleation process in these glasses. Of the few glass-forming systems that exhibit volume nucleation without the aid of nucleating agents, the binary sodium silicate is one of the simplest systems. However, this system has received scant attention due to problems with glass formation. In the binary sodium silicate system, it is known that internal (volume) nucleation does not occur for glasses of disilicate (NS2 ) composition [1]. However, glasses close to the metasilicate composition do exhibit internal nucleation [2,3]. It is therefore of interest to study the nucleation and crystallization behavior of this system as a function of composition to ascertain the composition region which exhibits internal nucleation. Also, we wish to investigate how the magnitudes of the nucleation rates vary with glass composition. In the present investigation, we use two-stage heating and optical microscopy techniques to
0022-3093/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 9 7 - 9
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L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
study the steady-state nucleation rates in a sodium silicate glass of composition 43Na2 O±57SiO2 (mol%). In a previous study [4], we presented and utilized a novel DTA method for determining the temperature dependence of the steady-state nucleation rate for the same glass composition used in the present investigation. Hence, another goal of this study is to compare the results obtained by the two dierent techniques. 2. Experimental A sodium silicate glass of nominal composition 43Na2 O±57SiO2 (mol%) was prepared using standard analytical grade Na2 CO3 and SiO2 . The batched precursor powders were rolled on a ball mill in a glass jar for 2 h, then transferred to a platinum crucible and melted at 1250°C for 2 h in an electric furnace. To ensure homogeneity, the melt was periodically stirred with a platinum rod. The melt was quenched (in air) rapidly by pressing between steel plates. The chemical composition of the prepared glass was determined by index of refraction measurements. According to the data of Morey and Merwin [5], the deviation of the prepared glass composition from the batch was within 0.2 mol%. To determine the glass transition temperature (Tg ) of the prepared glass, dierential thermal analysis (DTA) was employed. DTA was performed on bulk form samples using a system with a platinum crucible at a heating rate of 10°C minÿ1 . X-ray diraction measurements were performed using CuKa radiation. Samples were ground to ®ne powder then dusted onto a 20 mm square glass slide and scanned at a rate of 2° minÿ1 . with scattering angle, 2h, values from 0° to 90°. The development technique, which employs two-stage isothermal heating and optical microscopy, was utilized to obtain nucleation rate data. Isothermal heat-treatments were carried out by placing samples in a platinum boat and heating them in a horizontal tube furnace constant to within 1°C. Samples were ®rst subjected to isothermal heating at temperatures between 390°C and 455°C for various times to bring about crystal
nucleation. Nucleated samples were subsequently heated at 610°C for short times to grow the crystals to observable dimensions for the optical microscope. Optical microscopy was performed using a polarizing microscope. To observe and photograph internal crystals, heat-treated samples were mechanically ground and optically polished on both sides. The resulting samples, between 50 and 80 lm thick, were examined between cross-polarizers to observe and photograph the birefringence resulting from the crystalline phases. Ten to twenty micrographs were obtained for samples of each nucleation temperature, Tn , nucleation time, tn , combination. Knowledge of the magni®cation and glass thickness allowed the volume of sample represented by each micrograph to be determined. Sample thickness was measured with the aid of a micrometer. Since the crystal concentrations produced were low and the sample thicknesses were less than the depth of ®eld at the desired magni®cation, the number density data were found directly from the optical micrographs by counting the number of crystals present in each micrograph. 3. Results The glass transition temperature, Tg , of the prepared glass was determined by DTA. From the DTA trace of the bulk form sample, Tg was found to be 420 2°C. The number density data obtained by optical microscopy were plotted as a function of nucleation heat-treatment time for each nucleation heat-treatment temperature: 390°C, 400°C, 410°C, 415°C, 425°C, 440°C and 455°C. Data collected indicated the presence of transient eects for nucleation temperatures 6 425°C. The slopes of the linear regions of the kinetic curves, which yield the magnitudes of the steady-state nucleation rates, Is , were found by a least squares ®t. The error associated with each slope (and thus Is ) was calculated using standard error analysis procedures. The steady-state region of the kinetic curves for nucleation temperatures 390°C, 410°C, 425°C and 455°C are shown in Fig. 1(a), (b), (c) and (d), respectively. As noted, multiple micrographs were
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
165
Fig. 1. (a) Linear region of kinetic curve for nucleation temperature of 390°C. (b) Linear region of kinetic curve for nucleation temperature of 410°C. (c) Linear region of kinetic curve for nucleation temperature of 425°C. (d) Linear region of kinetic curve for nucleation temperature of 455°C.
obtained for each heat-treatment and the data points in Fig. 1(a)±(d) represent the average Nv values. The standard deviations from the average values are represented by the vertical error bars. Table 1 shows the magnitudes of steady-state nucleation rates and associated errors for each nucleation temperature, Tn , as determined from
the aforementioned procedures. Fig. 2, which shows the magnitude and temperature dependence of the steady-state nucleation rate, Is , for the bi-
Table 1 Steady-state nucleation rates of sodium metasilicate crystals Tn (°C)
Is ´ 10ÿ2 (cmÿ3 minÿ1 )
Errors () ´ 10ÿ2 (cmÿ3 minÿ1 )
390 400 410 415 425 440 455
0.12 3.01 71.84 56.17 35.39 19.64 10.88
0.02 0.58 4.75 4.67 1.50 3.33 1.80
Fig. 2. Magnitude and temperature dependence of the steadystate nucleation rate for 43Na2 O±57SiO2 (mol%) glass composition.
166
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
nary sodium silicate glass composition 43Na2 O± 57SiO2 (mol%), was generated from the data in Table 1. As depicted in Fig. 2, the steady-state nucleation rate curve has the form of an asymmetric peak with a maximum rate, Imax , of 7.2 ´ 103 (cmÿ3 minÿ1 ) occurring at a temperature, Tmax , of 410°C. Also, from Fig. 2 it appears that the nucleation range for this glass composition is approximately 385±465°C. It should be noted that the line connecting the experimental data points in Fig. 2 (and in subsequent ®gures) has no theoretical signi®cance and is only present for the purpose of providing a guide for the eye of the reader. Heat-treated samples with removed surface layers were analyzed by XRD. As expected, the crystal phase precipitated by internal nucleation for this composition was found to be sodium metasilicate. 4. Discussion In a previous study [4], the authors presented a novel DTA method for determining the temperature dependence of the steady-state nucleation rate and illustrated the use of this method for the same glass composition used in the present investigation. The DTA technique relies on producing identical number densities for dierent thermal histories. The parameter of interest in the DTA method is the peak shift, DTp , de®ned as the difference between peak temperatures of maximum crystallization of as-quenched and previously isothermally nucleated glass. If the same peak shift is produced for two dierent nucleation temperatures for two dierent nucleation times, using the same scan rate, the number densities must be identical (provided that the data are outside the transient nucleation regime and that there is no signi®cant overlap of nucleation and growth). Therefore, the inverse ratio of the two nucleation times gives the ratio of the nucleation rates at the two dierent nucleation temperatures. Thus, the DTA technique yields the relative nucleation rates as a function of temperature, but not the magnitudes of the nucleation rates. To test the accuracy of the DTA method, the nucleation rate data obtained at various Tn in the
present study were normalized to the rate at 440°C, since this is the temperature to which the data were normalized in Ref. [4]. Fig. 3 shows the normalized data from the present investigation along with the data from Ref. [4]. The absence of error bars for the DTA experimental points notwithstanding, it is apparent from Fig. 3 that the results from the two dierent techniques agree within experimental error (data points from the DTA technique do not show error bars because it is not obvious how to calculate the errors associated with this method). Although the two techniques agree well, it does appear that the data in the present study generally lie above the DTA technique data. Although this could be explained by dierences in water content, this possibility is remote because the glass used in both investigations came from the same batch. Further, as shown in Fig. 3, the steady-state nucleation rates for nucleation temperatures 390°C and 400°C are relatively small. Thus, as exempli®ed by Fig. 1(a), the number densities of crystals produced at these Tn remains small for long times. Although the development technique is sensitive to such small crystal number densities, the DTA technique is not. As described in Ref. [4], to produce a detectable peak shift, DTp , the number densities must be suciently large. Due to the small nucleation rates in this glass at temperatures of 390°C and 400°C, the nucleation times employed ( 6 24 h) in Ref. [4] would not produce large enough number densities to enable genera-
Fig. 3. Comparison of experimental data from present work (normalized to rate at 440°C) and experimental data from Ref. [4].
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
tion of nucleation rate data for these temperatures by the DTA method. To our knowledge, only two other works [2,3] have investigated internal nucleation rates in binary sodium silicate glasses. The salient features of the prior works and the present work are shown in Table 2. These data reveal an emergent trend in nucleation kinetics as a function of composition. Both the temperature of maximum nucleation, Tmax , and the magnitude of the maximum nucleation rate, Imax , increase in value as composition tends towards stoichiometric sodium metasilicate. Although strictly speaking the classical expression for the steady-state nucleation rate is not correct for o-composition pseudo one component internal nucleation, it is reasonable to invoke this expression for predicting qualitative trends. There are three critical factors to consider when interpreting the change in nucleation kinetics with composition, namely, the kinetic barrier, the thermodynamic barrier and the surface energy. Not much is known about the compositional dependence of the surface energy and no attempt will be made here to speculate about the in¯uence of this factor on the observed trend. According to CNT, the nucleation rate is a monotonically decreasing function of viscosity. Therefore, the above features could be a result of disparate water contents in the glasses used by the dierent investigators. Increased water content could decrease the viscosity of the glass. This in turn would decrease the kinetic barrier to nucleation, thus increasing Is . If we assume the water contents to be similar, the same argument can be made based on compositional eects since increasing Na2 O content also decreases the viscosity [6]. However, it does not seem likely that the re-
duction in the kinetic barrier to nucleation over this small composition range would be large enough to account for the signi®cant variation in observed nucleation rates. The aforementioned features are more readily explained based on thermodynamic arguments. According to the binary Na2 O±SiO2 phase diagram [7], the liquidus temperature (TL ) shows a sharp decrease from the metasilicate composition to about the 62SiO2 (wt%) composition. Therefore, for a given temperature, T, below the liquidus, the undercooling DT (where DT DTL ÿ T) increases as the SiO2 content decreases. Consequently, the thermodynamic driving force at temperature T increases and the thermodynamic barrier decreases as SiO2 content decreases and Is would increase accordingly. Based on the above, we can conclude that the thermodynamic driving force dominates the nucleation behavior over this compositional range. Barker et al. [8] found similar behavior for the composition dependence of Imax in a nucleation rate study conducted on the binary Li2 O±SiO2 system and they drew a similar conclusion regarding the origin of this behavior. The data of Barker et al. showed that Tmax and Imax of the 40Li2 O± 60SiO2 (mol%) composition were higher than Tmax and Imax of the 36Li2 O±64SiO2 (mol%) composition. According to the phase diagram for the binary Li2 O±SiO2 system [9], the liquidus temperature sharply decreases with increasing SiO2 content over this composition range. 5. Summary The nucleation of sodium metasilicate crystals in a binary sodium silicate glass of composition 43Na2 O±57SiO2 (mol%) was investigated over the
Table 2 Summary of present and prior works Composition (mol%) a
46Na2 O±54SiO2 44Na2 O±56SiO2 b 43Na2 O±57SiO2 c a
Ref. [2]. Ref. [3]. c This work. b
167
Nucleation range (°C)
Tmax (°C)
Imax (cmÿ3 minÿ1 )
410±490 400±470 385±465
460 427 410
360 ´ 106 183 ´ 103 72 ´ 102
168
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
temperature range 390±455°C. The magnitude and temperature dependence of the steady-state nucleation rate was determined by the development technique. The magnitude of the maximum nucleation rate was found to be 7.2 ´ 103 (cmÿ3 minÿ1 ). The temperature at which the maximum nucleation rate occurred was 410°C, which is near Tg for this glass. The results of this study were compared to the results obtained for the temperature dependence of the steady-state nucleation rate via a DTA technique, which we demonstrated in a previous study for the same glass. The results of the two dierent techniques agree within experimental error. These results validate the DTA technique for determining the temperature dependence of steady-state nucleation rates, provided the number densities are suciently large. Acknowledgements M.C.W. extends his appreciation to the Oce of Basic Energy Sciences of the US Department of Energy for ®nancial support of this work.
References [1] W.D. Scott, J.A. Pask, J. Am. Ceram. Soc. 44 (4) (1961) 181. [2] V.N. Filopovich, A.M. Kalinina, G.A. Sycheva, Neorg. Mater. 11 (1975) 1305. [3] V.M. Fokin, N.S. Yuritsyn, Glass Phys. Chem. 23 (3) (1997) 236. [4] T.W. Wakasugi, L.L. Burgner, M.C. Weinberg, J. NonCryst. Solids 244 (1999) 63. [5] G.W. Morey, H.E. Merwin, J. Opt. Soc. Am. 22 (1932) 632. [6] R. Knoche, D.B. Dingwell, F.A. Seifert, S.L. Webb, Chem. Geo. 116 (1994) 1. [7] F.C. Kracek, J. Phys. Chem. 34 (1930) 1588. [8] M.F. Barker, T. Wang, P.F. James, Phys. Chem. Glasses 29 (6) (1988) 240. [9] F.C. Kracek, J. Phys. Chem. 34 (Part II) (1930) 2645.
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Crystal nucleation rates in a Na2O±SiO2 glass Lori L. Burgner, Michael C. Weinberg * Arizona Materials Laboratories, Materials Science and Engineering Department, University of Arizona, Tucson, AZ 85721-0012, USA Received 28 May 1999; received in revised form 2 September 1999
Abstract Nucleation of sodium metasilicate crystals in sodium silicate glass of composition 43Na2 O±57SiO2 is investigated. Two-stage isothermal heating and optical microscopy techniques are utilized to determine the steady-state nucleation rates at temperatures between 390°C and 455°C. The results of this investigation are compared to the results we obtained for the temperature dependence of the nucleation rate in these glasses via a DTA technique which we presented in a previous study. It is found that the results of the two techniques are in agreement within experimental error. It is observed that the peak nucleation rate for this composition occurs near 410°C, which is about 50°C lower than that reported for nucleation in the 46Na2 O±54SiO2 glass composition. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Crystal nucleation in glasses continues to be an important and active area of inquiry due to its technological and scienti®c importance. In the realm of technology, knowledge of crystal nucleation rates in glasses at dierent temperatures is essential for preparing glass±ceramics, wherein nucleation must be promoted, as well as for applications in which nucleation must be avoided, such as optical ®bers. To the scienti®c community, glasses provide an ideal media for studying nucleation phenomena in a condensed system and for quantitatively testing standard nucleation theories. Glasses that appear to nucleate homogeneously within the volume are traditionally studied within the realm of classical nucleation theory (CNT). However, discrepancies between theoreti-
* Corresponding author. Tel.: +1-520 621 6909; fax: +1-520 621 8059. E-mail address: [email protected] (M.C. Weinberg).
cal predictions and experimental results, along with observations of metastable phase formation, have called into the question the validity of applying CNT to describe the nucleation process in these glasses. Of the few glass-forming systems that exhibit volume nucleation without the aid of nucleating agents, the binary sodium silicate is one of the simplest systems. However, this system has received scant attention due to problems with glass formation. In the binary sodium silicate system, it is known that internal (volume) nucleation does not occur for glasses of disilicate (NS2 ) composition [1]. However, glasses close to the metasilicate composition do exhibit internal nucleation [2,3]. It is therefore of interest to study the nucleation and crystallization behavior of this system as a function of composition to ascertain the composition region which exhibits internal nucleation. Also, we wish to investigate how the magnitudes of the nucleation rates vary with glass composition. In the present investigation, we use two-stage heating and optical microscopy techniques to
0022-3093/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 9 7 - 9
164
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
study the steady-state nucleation rates in a sodium silicate glass of composition 43Na2 O±57SiO2 (mol%). In a previous study [4], we presented and utilized a novel DTA method for determining the temperature dependence of the steady-state nucleation rate for the same glass composition used in the present investigation. Hence, another goal of this study is to compare the results obtained by the two dierent techniques. 2. Experimental A sodium silicate glass of nominal composition 43Na2 O±57SiO2 (mol%) was prepared using standard analytical grade Na2 CO3 and SiO2 . The batched precursor powders were rolled on a ball mill in a glass jar for 2 h, then transferred to a platinum crucible and melted at 1250°C for 2 h in an electric furnace. To ensure homogeneity, the melt was periodically stirred with a platinum rod. The melt was quenched (in air) rapidly by pressing between steel plates. The chemical composition of the prepared glass was determined by index of refraction measurements. According to the data of Morey and Merwin [5], the deviation of the prepared glass composition from the batch was within 0.2 mol%. To determine the glass transition temperature (Tg ) of the prepared glass, dierential thermal analysis (DTA) was employed. DTA was performed on bulk form samples using a system with a platinum crucible at a heating rate of 10°C minÿ1 . X-ray diraction measurements were performed using CuKa radiation. Samples were ground to ®ne powder then dusted onto a 20 mm square glass slide and scanned at a rate of 2° minÿ1 . with scattering angle, 2h, values from 0° to 90°. The development technique, which employs two-stage isothermal heating and optical microscopy, was utilized to obtain nucleation rate data. Isothermal heat-treatments were carried out by placing samples in a platinum boat and heating them in a horizontal tube furnace constant to within 1°C. Samples were ®rst subjected to isothermal heating at temperatures between 390°C and 455°C for various times to bring about crystal
nucleation. Nucleated samples were subsequently heated at 610°C for short times to grow the crystals to observable dimensions for the optical microscope. Optical microscopy was performed using a polarizing microscope. To observe and photograph internal crystals, heat-treated samples were mechanically ground and optically polished on both sides. The resulting samples, between 50 and 80 lm thick, were examined between cross-polarizers to observe and photograph the birefringence resulting from the crystalline phases. Ten to twenty micrographs were obtained for samples of each nucleation temperature, Tn , nucleation time, tn , combination. Knowledge of the magni®cation and glass thickness allowed the volume of sample represented by each micrograph to be determined. Sample thickness was measured with the aid of a micrometer. Since the crystal concentrations produced were low and the sample thicknesses were less than the depth of ®eld at the desired magni®cation, the number density data were found directly from the optical micrographs by counting the number of crystals present in each micrograph. 3. Results The glass transition temperature, Tg , of the prepared glass was determined by DTA. From the DTA trace of the bulk form sample, Tg was found to be 420 2°C. The number density data obtained by optical microscopy were plotted as a function of nucleation heat-treatment time for each nucleation heat-treatment temperature: 390°C, 400°C, 410°C, 415°C, 425°C, 440°C and 455°C. Data collected indicated the presence of transient eects for nucleation temperatures 6 425°C. The slopes of the linear regions of the kinetic curves, which yield the magnitudes of the steady-state nucleation rates, Is , were found by a least squares ®t. The error associated with each slope (and thus Is ) was calculated using standard error analysis procedures. The steady-state region of the kinetic curves for nucleation temperatures 390°C, 410°C, 425°C and 455°C are shown in Fig. 1(a), (b), (c) and (d), respectively. As noted, multiple micrographs were
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
165
Fig. 1. (a) Linear region of kinetic curve for nucleation temperature of 390°C. (b) Linear region of kinetic curve for nucleation temperature of 410°C. (c) Linear region of kinetic curve for nucleation temperature of 425°C. (d) Linear region of kinetic curve for nucleation temperature of 455°C.
obtained for each heat-treatment and the data points in Fig. 1(a)±(d) represent the average Nv values. The standard deviations from the average values are represented by the vertical error bars. Table 1 shows the magnitudes of steady-state nucleation rates and associated errors for each nucleation temperature, Tn , as determined from
the aforementioned procedures. Fig. 2, which shows the magnitude and temperature dependence of the steady-state nucleation rate, Is , for the bi-
Table 1 Steady-state nucleation rates of sodium metasilicate crystals Tn (°C)
Is ´ 10ÿ2 (cmÿ3 minÿ1 )
Errors () ´ 10ÿ2 (cmÿ3 minÿ1 )
390 400 410 415 425 440 455
0.12 3.01 71.84 56.17 35.39 19.64 10.88
0.02 0.58 4.75 4.67 1.50 3.33 1.80
Fig. 2. Magnitude and temperature dependence of the steadystate nucleation rate for 43Na2 O±57SiO2 (mol%) glass composition.
166
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
nary sodium silicate glass composition 43Na2 O± 57SiO2 (mol%), was generated from the data in Table 1. As depicted in Fig. 2, the steady-state nucleation rate curve has the form of an asymmetric peak with a maximum rate, Imax , of 7.2 ´ 103 (cmÿ3 minÿ1 ) occurring at a temperature, Tmax , of 410°C. Also, from Fig. 2 it appears that the nucleation range for this glass composition is approximately 385±465°C. It should be noted that the line connecting the experimental data points in Fig. 2 (and in subsequent ®gures) has no theoretical signi®cance and is only present for the purpose of providing a guide for the eye of the reader. Heat-treated samples with removed surface layers were analyzed by XRD. As expected, the crystal phase precipitated by internal nucleation for this composition was found to be sodium metasilicate. 4. Discussion In a previous study [4], the authors presented a novel DTA method for determining the temperature dependence of the steady-state nucleation rate and illustrated the use of this method for the same glass composition used in the present investigation. The DTA technique relies on producing identical number densities for dierent thermal histories. The parameter of interest in the DTA method is the peak shift, DTp , de®ned as the difference between peak temperatures of maximum crystallization of as-quenched and previously isothermally nucleated glass. If the same peak shift is produced for two dierent nucleation temperatures for two dierent nucleation times, using the same scan rate, the number densities must be identical (provided that the data are outside the transient nucleation regime and that there is no signi®cant overlap of nucleation and growth). Therefore, the inverse ratio of the two nucleation times gives the ratio of the nucleation rates at the two dierent nucleation temperatures. Thus, the DTA technique yields the relative nucleation rates as a function of temperature, but not the magnitudes of the nucleation rates. To test the accuracy of the DTA method, the nucleation rate data obtained at various Tn in the
present study were normalized to the rate at 440°C, since this is the temperature to which the data were normalized in Ref. [4]. Fig. 3 shows the normalized data from the present investigation along with the data from Ref. [4]. The absence of error bars for the DTA experimental points notwithstanding, it is apparent from Fig. 3 that the results from the two dierent techniques agree within experimental error (data points from the DTA technique do not show error bars because it is not obvious how to calculate the errors associated with this method). Although the two techniques agree well, it does appear that the data in the present study generally lie above the DTA technique data. Although this could be explained by dierences in water content, this possibility is remote because the glass used in both investigations came from the same batch. Further, as shown in Fig. 3, the steady-state nucleation rates for nucleation temperatures 390°C and 400°C are relatively small. Thus, as exempli®ed by Fig. 1(a), the number densities of crystals produced at these Tn remains small for long times. Although the development technique is sensitive to such small crystal number densities, the DTA technique is not. As described in Ref. [4], to produce a detectable peak shift, DTp , the number densities must be suciently large. Due to the small nucleation rates in this glass at temperatures of 390°C and 400°C, the nucleation times employed ( 6 24 h) in Ref. [4] would not produce large enough number densities to enable genera-
Fig. 3. Comparison of experimental data from present work (normalized to rate at 440°C) and experimental data from Ref. [4].
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
tion of nucleation rate data for these temperatures by the DTA method. To our knowledge, only two other works [2,3] have investigated internal nucleation rates in binary sodium silicate glasses. The salient features of the prior works and the present work are shown in Table 2. These data reveal an emergent trend in nucleation kinetics as a function of composition. Both the temperature of maximum nucleation, Tmax , and the magnitude of the maximum nucleation rate, Imax , increase in value as composition tends towards stoichiometric sodium metasilicate. Although strictly speaking the classical expression for the steady-state nucleation rate is not correct for o-composition pseudo one component internal nucleation, it is reasonable to invoke this expression for predicting qualitative trends. There are three critical factors to consider when interpreting the change in nucleation kinetics with composition, namely, the kinetic barrier, the thermodynamic barrier and the surface energy. Not much is known about the compositional dependence of the surface energy and no attempt will be made here to speculate about the in¯uence of this factor on the observed trend. According to CNT, the nucleation rate is a monotonically decreasing function of viscosity. Therefore, the above features could be a result of disparate water contents in the glasses used by the dierent investigators. Increased water content could decrease the viscosity of the glass. This in turn would decrease the kinetic barrier to nucleation, thus increasing Is . If we assume the water contents to be similar, the same argument can be made based on compositional eects since increasing Na2 O content also decreases the viscosity [6]. However, it does not seem likely that the re-
duction in the kinetic barrier to nucleation over this small composition range would be large enough to account for the signi®cant variation in observed nucleation rates. The aforementioned features are more readily explained based on thermodynamic arguments. According to the binary Na2 O±SiO2 phase diagram [7], the liquidus temperature (TL ) shows a sharp decrease from the metasilicate composition to about the 62SiO2 (wt%) composition. Therefore, for a given temperature, T, below the liquidus, the undercooling DT (where DT DTL ÿ T) increases as the SiO2 content decreases. Consequently, the thermodynamic driving force at temperature T increases and the thermodynamic barrier decreases as SiO2 content decreases and Is would increase accordingly. Based on the above, we can conclude that the thermodynamic driving force dominates the nucleation behavior over this compositional range. Barker et al. [8] found similar behavior for the composition dependence of Imax in a nucleation rate study conducted on the binary Li2 O±SiO2 system and they drew a similar conclusion regarding the origin of this behavior. The data of Barker et al. showed that Tmax and Imax of the 40Li2 O± 60SiO2 (mol%) composition were higher than Tmax and Imax of the 36Li2 O±64SiO2 (mol%) composition. According to the phase diagram for the binary Li2 O±SiO2 system [9], the liquidus temperature sharply decreases with increasing SiO2 content over this composition range. 5. Summary The nucleation of sodium metasilicate crystals in a binary sodium silicate glass of composition 43Na2 O±57SiO2 (mol%) was investigated over the
Table 2 Summary of present and prior works Composition (mol%) a
46Na2 O±54SiO2 44Na2 O±56SiO2 b 43Na2 O±57SiO2 c a
Ref. [2]. Ref. [3]. c This work. b
167
Nucleation range (°C)
Tmax (°C)
Imax (cmÿ3 minÿ1 )
410±490 400±470 385±465
460 427 410
360 ´ 106 183 ´ 103 72 ´ 102
168
L.L. Burgner, M.C. Weinberg / Journal of Non-Crystalline Solids 261 (2000) 163±168
temperature range 390±455°C. The magnitude and temperature dependence of the steady-state nucleation rate was determined by the development technique. The magnitude of the maximum nucleation rate was found to be 7.2 ´ 103 (cmÿ3 minÿ1 ). The temperature at which the maximum nucleation rate occurred was 410°C, which is near Tg for this glass. The results of this study were compared to the results obtained for the temperature dependence of the steady-state nucleation rate via a DTA technique, which we demonstrated in a previous study for the same glass. The results of the two dierent techniques agree within experimental error. These results validate the DTA technique for determining the temperature dependence of steady-state nucleation rates, provided the number densities are suciently large. Acknowledgements M.C.W. extends his appreciation to the Oce of Basic Energy Sciences of the US Department of Energy for ®nancial support of this work.
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