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Pressure induced nucleation in a Li2O · 2SiO2 glass
Journal of Non-Crystalline Solids 318 (2003) 157–167 www.elsevier.com/locate/jnoncrysol
Pressure induced nucleation in a Li2O 2SiO2 glass T. Fuss a
a,*
, C.S. Ray a, N. Kitamura b, M. Makihara b, D.E. Day
a
Ceramic Engineering Department and Graduate Center for Materials Research, University of Missouri-Rolla, Rolla, MO 65409, USA b Department of Optical Materials, Osaka National Research Institute, 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan Received 15 January 2002; received in revised form 12 July 2002
Abstract The concentration of nuclei (Nv ) in a Li2 O 2SiO2 (LS2 ) glass was measured using a newly developed differential thermal analysis technique, after densifying the glass at 1, 3, or 6 GPa pressure at 400 °C for 20 min. Nv increased from 38 1012 m3 for an as-melted glass to 82 1012 m3 for a glass subjected to a pressure of 1 GPa, and remained nearly constant with further increase of pressure of up to 6 GPa. This increase in Nv is equivalent to nucleating this LS2 glass at the temperature (455 °C) of its maximum nucleation rate for 2 h. The average effective activation energy for crystallization for the densified glasses, 292 10 kJ/mol, was also the same as that of the (undensified) glass nucleated at 455 °C for 2 h, but was significantly smaller than that (358 10 kJ/mol) for an as-melted (undensified and unnucleated) glass. The present results show that applying an external pressure on this LS2 glass shifts its nucleation curve to lower temperatures causing nuclei to form even at 400 °C. A decrease in viscosity at all temperatures with the application of pressure is suspected to be a reason for the enhanced nucleation observed for this LS2 glass. Ó 2002 Published by Elsevier Science B.V.
1. Introduction Knowledge of the high-pressure properties of melts, particularly silicate melts, is useful to understanding geological processes such as magma crystallization [1,2]. Many commercial glass manufacturing processes (pressing, blowing, injection molding, fiber drawing, extrusion) often involve a substantial pressure. Such pressure-aided manufacturing processes can change the properties of a glass preform in an undesirable way such as en-
*
Corresponding author. Tel.: +1-573 341 6695; fax: +1-576 341 2071. E-mail address: [email protected] (T. Fuss).
hancing the crystallization tendency of the glass [3,4]. There are a few reports [5–9] indicating that the thermodynamic driving force for nucleation, which is opposite to the energy barrier W for nucleation, is increased with increasing pressure, thereby, increasing nucleation in glass forming melts. An increase in the melting point and/or a decrease in the interfacial energy at the liquid-crystal interface at elevated pressure are suggested as the reason for the decrease in W . Some of the previous work [8,9] also postulate that a kinetic factor, namely, an increase in viscosity with increasing pressure, which may nullify or even surpass the effect of decrease in W , also simultaneously affects the nucleation rate, causing the effective nucleation rate curve (as a function of temperature) to move to higher
0022-3093/03/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 8 7 8 - 1
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temperatures with increasing pressure. However, there are reports [10–15] also of a decrease in viscosity, which favors nucleation, with increasing pressure for glass forming melts. Pressure-aided glass manufacturing processes are generally observed to be associated with some kind of tangential stress, i.e., a flow of the melt under pressure. It is argued [9] that the reason enhanced crystallization is often observed in melts that are subjected to such pressure-aided processing steps (extrusion pressing, fiber pulling) is due solely to shear thinning (a decrease in viscosity with increasing strain rate), and static pressure has virtually no role in enhancing the crystallization of the melt. It has been shown [9] further that the nucleation or crystal growth rate in most melts is decreased rather than increased by (external) static pressure alone. However, for exceptional cases such as at relatively high-pressures (GPa range) and very high DV values (difference in molar volume between the liquid and crystal phase), static pressure can increase crystallization of a melt [9]. It is clear from the above discussions that only a handful of results exist in the literature for how static pressure affects the crystallization of glass forming melts. Furthermore, these results are often in conflict with each other. It appears that the effect of static pressure on crystallization of glass forming melts, has not been fully explored. The present work was aimed at investigating the effect of isostatic pressure on nucleation for a Li2 O 2SiO2 (hereafter referred to as LS2 ) glass by measuring and comparing the nucleation density (number of nuclei per unit volume) in an as-melted glass and in a glass that was densified by applying an external pressure of 1, 3, or 6 GPa. The pressure was applied to the glass for 20 min at 400 °C, which is about 25 °C lower than the onset temperature (425 °C) for nucleation at the ambient (atmospheric) pressure for this LS2 glass. For comparison, the density of nuclei for a glass, which was not densified, but nucleated at 455 °C for 2 h was also measured. This 455 °C corresponds to the temperature of the maximum nucleation rate for the LS2 glass at ambient pressure. As will be shown later, the results of the present investigation suggest that nucleation in the LS2 glass is enhanced by pressure and the nucleation rate curve
moves to lower temperatures compared to the same curve at ambient pressure. These results are opposite to those predicted by Gutzow et al. [9] from model calculations for this glass.
2. Experimental procedures The LS2 glass was prepared by melting a homogeneous mixture of reagent grade Li2 CO3 and SiO2 at 1475 °C for 4 h in air in a platinum crucible, casting the melt onto cylindrical graphite molds of approximate dimension 8 mm ðdiameterÞ 10 mm (height), and annealing the glass at 470 °C for 1 h. After annealing, the glass was slowly cooled to room temperature by turning the power to the furnace off (furnace cool). The glass cylinders made from the same melt were then densified under 1, 3, or 6 GPa at 400 °C for 20 min using a 6–8 type multi-anvil high-pressure apparatus (UHP-2000, Sumitomo Heavy Industries, Japan) [16]. The details of the densification procedure and a description of the high-pressure apparatus are given elsewhere [17]. The pressure– temperature–time schedule that was used in densifying the glasses in the present work is shown schematically in Fig. 1. The pressure was increased at a rate of þ2 GPa/ h at room temperature (26 °C) to the desired value (1, 3, or 6 GPa) and held at that pressure for 2 h. During the second or last hour of isostatic
Fig. 1. Pressure–temperature–time schedule for densifying Li2 O 2SiO2 glass.
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hold, the temperature of the sample was increased to 400 °C at a rate of þ20 °C/min, held at 400 °C for 20 min, and then decreased to room temperature at )20 °C/min. After the sample reached room temperature, the applied pressure was decreased to zero (ambient pressure) at a rate of )2 GPa/h. The density of the densified and undensified glasses was measured by Archimedes method using distilled water as the buoyant liquid. The density (d) of the as-melted (undensified) glass was 2.34 g cm3 , while the density of the glasses densified at 1, 3, and 6 GPa was 2.39, 2.49, and 2.58 g cm3 , respectively, with an estimated error of 0.01 g cm3 . Consequently, the molar volume (VM ), calculated for one mol (0.33 Li2 O 0.67 SiO2 ) of glass, decreased from 21.38 cm3 for the undensified glass to 19.39 cm3 for the glass densified at 6 GPa pressure. The refractive index of the glasses was measured by the Becke-line technique using standard refractive index liquids. Like the density, the refractive index increased with increasing applied pressure, being 1.534 for the undensified glass and 1.544, 1.562, and 1.579 for the glasses densified at 1, 3, and 6 GPa, respectively. The estimated error in the refractive index measurements was 0.001. The number of nuclei per unit volume in the glasses was determined by a differential thermal analysis (DTA) method [18,19]. In this method, 20–30 mg of glass powder (425–500 lm particle size) is first heated in a DTA apparatus (Perkin– Elmer, Model DT7) with a heating rate of 20 °C/ min up to a temperature, TG , where the crystal growth rate (UG ) for the glass is known. The sample is then held at TG for a short time, typically between 5 and 20 min. For the present experiments with the LS2 glass, this isothermal heat treatment temperature, TG was 600 °C, where the value of UG for this glass is 2:5 108 m min1 [20]. After this isothermal heat treatment, the temperature is quickly decreased (at a rate of 40 °C/min) to 375 °C which is well below the onset temperature for nucleation (425 °C for the LS2 glass), and the sample is thermally stabilized for about 5 min. A DTA scan is then performed at a fixed 10 °C min1 heating rate until crystallization is complete as indicated by an exothermic DTA peak. A similar, second experiment is performed using a new sample of the same glass and keeping all
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the experimental parameters mentioned above constant except the heat treatment time at TG . The concentration of nuclei (Nv ) in the glass was calculated from the area of the two DTA peaks as [18,19] Nv ¼
3ðA1 m2 A2 m1 Þ ; 3 3 ðA1 m2 tG2 A2 m1 tG1 ÞpUG3
ð1Þ
where m1 is the mass of the sample, tG1 is the heat treatment time at TG , and A1 is the area of the DTA peak for the first experiments. The corresponding values for the second experiment are m2 , tG2 and A2 . Note that Eq. (1) can be further simplified if the mass of the sample in the two DTA runs is the same (m1 ¼ m2 ). The heat treatment times at 600 °C for the first and second experiments were 10 (tG1 ) and 15 (tG2 ) min, respectively. The activation energy for crystallization, E, for the glasses was determined using DTA also. In determining E, several DTA runs at constant different heating rates (u) were made and the temperature corresponding to the maximum of the crystallization peak (TP ) was determined as a function of u. TP and u are related, according to the Kissinger model [21], as lnðTP2 =uÞ / ðE=RTP Þ;
ð2Þ lnðTP2 =uÞ
where R is the gas constant. A plot of vs (1/TP ) should be a straight line (Kissinger plot) whose slope yields the value of E. The heating rates (u) used in the present experiments were 2, 4, 6, and 10 °C/min. The mass (20–30 mg) and particle size (425–500 lm) of the sample used in the experiments for measuring E were the same as used in measuring Nv . All the DTA experiments were conducted in flowing (30 cm3 min1 ) nitrogen gas using platinum containers and 99.99% pure A12 O3 powder as the reference material. The values of Nv and E for an undensified LS2 glass nucleated at 455 °C for 2 h were also measured for comparison with the same values for the densified glasses. This temperature of 455 °C was chosen since this is the temperature where the nucleation rate for an undensified LS2 glass is a maximum. The Raman spectra for these glasses were reported previously [16] and will not be repeated here. However a portion of those spectra will be
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re-analyzed in this paper to justify the conclusions made from the DTA results.
3. Results 3.1. Differential thermal analysis 3.1.1. General observations Typical DTA curves at 4 °C/min for an undensified LS2 glass and for a glass densified at 1 GPa are shown in Fig. 2. Also shown in Fig. 2, for comparison, is the DTA curve at 4 °C/min for the (undensified) LS2 glass after nucleating at 455 °C for 2 h. The DTA curves for the glasses densified at 1, 3, and 6 GPa pressure are shown in Fig. 3. The temperature, Tp , and height, (dT )p , determined from the curves in Figs. 2 and 3 at the crystallization peak maximum are given in Table 1 for all the glasses and separately shown in Fig. 4. (dT )p increases with increasing sample weight [22], and since the sample weight in the different DTA measurements was not strictly constant, the (dT )p from different experiments will be compared by using a normalized value for (dT )p , such as Ôper gramÕ of sample, which is given in Table 1 and in Fig. 4. Tp , on the other hand, does not depend on the amount of sample, but is inversely propor-
Fig. 2. DTA exotherms for undensified (0 GPa), densified (1 GPa) and nucleated (455 °C/2 h) Li2 O 2SiO2 glasses at a heating rate of 4 °C/min. Particle size 425–500 lm. Sample weight: 20.1 mg (0 GPa), 20.1 mg (455 °C/2 h), 28.4 mg (1 GPa). Atmosphere: nitrogen.
Fig. 3. DTA exotherms for densified (1, 3 and 6 GPa) Li2 O 2SiO2 glasses at a heating rate of 4 °C/min. Particle size 425–500 lm. Sample weight: 28.4 mg (1 GPa), 28.2 mg (3 GPa), 28.4 mg (6 GPa). Furnace atmosphere: nitrogen.
tional to the concentration of nuclei (Nv ) in the glass [18]. A qualitative estimate for the concentration of nuclei in the glasses can be made by comparing the values of Tp , while a comparison of (dT )p -values gives a qualitative estimate for the total number of nuclei per gram of each sample. As shown in Fig. 4 and Table 1, the Tp values for the nucleated (undensified) glass and all the densified glasses are nearly the same, but are 7–12 °C lower than that of the undensified (unnucleated) glass, see also Figs. 2 and 3. Since Tp is inversely proportional to Nv , a larger Nv should result in a smaller value for Tp . A smaller Tp value for the nucleated glass (Figs. 2 and 4, Table 1) compared to that for the unnucleated, undensified glass, is expected, since the concentration of nuclei in the nucleated glass should be higher. The lower Tp values for the densified glasses, therefore, indicate that the Nv in these glasses is higher than that in the undensified glass. The nearly equal values of Tp for the nucleated glass and all the densified glasses (Fig. 4, Table 1), suggest that the nucleation caused by a static pressure of 1, 3 or 6 GPa (at 400 °C) is equivalent to that caused by nucleation at 455 °C for 2 h at the ambient (atmospheric) pressure for this LS2 glass. It should be noted that 400 °C is about 25 °C lower than the onset temperature for nucleation
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Table 1 Thermal analysis (DTA) results for the undensified, densified and nucleated Li2 O 2SiO2 glasses Applied pressure (GPa)
Tp ð2Þ (°C)
ðdT Þp ð0:5Þ (°C/g)
Nv ð5%Þ (m3 )
Eð10Þ (kJ/mol)
0 1 3 6 0 (Nucleated at 455 °C for 2 h)
634 622 627 626 626
23.0 39.5 32.9 24.5 39.7
38 1012 81 1012 82 1012 78 1012 76 1012
358 292 281 311 286
Tp : temperature at the DTA peak maximum. (dT )p : maximum height of the DTA peak (at Tp ) per gram of sample. Nv : concentration of nuclei. E: activation energy for crystallization.
Fig. 4. Temperature (Tp ) and height (dT )p at the DTA peak maximum for the undensified, densified and nucleated (455 °C/2 h) Li2 O 2SiO2 glasses. DTA heating rate 4 °C/min.
for this glass at ambient pressure, and no additional nuclei are formed in this glass when heated at 400 °C at ambient pressure for several hours or even for several days. There is no further increase (or decrease) in the concentration of nuclei at pressures above 1 GPa. The maximum height of the crystallization peak, (dT )p , for the glass densified at 1 GPa is nearly the same as that for the nucleated glass (Fig. 4, Table 1), but is larger than that for the undensified glass. These results are consistent with the results for Tp and suggest that the total number
of nuclei in this densified glass (1 GPa) is nearly the same as that in the nucleated glass, but larger than that in the undensified glass. However, (dT )p decreases with increasing pressure when the applied pressure exceeds 1 GPa (Fig. 4), indicating a decrease in the total number of nuclei with increasing pressure >1 GPa. The reason for the decrease in (dT )p with the increasing pressure (>1 GPa) is not clearly understood, but may be due to a partial crystallization of the sample, where some of the nuclei were consumed via crystal growth. In other words, applying external pressure >1 GPa may have caused the crystal growth rate curve to move to 400 °C, which is about 150 °C lower than the onset temperature for crystal growth for this glass at ambient pressure, causing the glass to partially crystallize (at 400 °C). However, attempts to detect the crystallinity by XRD or optical microscopy for the glasses densified at pressure >1 GPa were unsuccessful. At this time, any change in the crystal growth rate with increasing pressure remains unconfirmed. 3.1.2. Nucleation density (Nv ) The nucleation density (Nv ) in the glasses was determined using a DTA technique and Eq. (1). The typical DTA curves after crystal growth heat treatment at 600 °C (TG ) for 10 (tG1 ) or 15 (tG2 ) min for the LS2 glass are shown in Fig. 5. The glass that was heat treated at 600 °C for 15 min, contained a smaller number of nuclei after the heat treatment, thus producing a smaller DTA peak than the glass that was heat treated for 10 min. The values of Nv determined using Eq. (1) and the
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Fig. 5. DTA exotherms for the Li2 O 2SiO2 glass at a heating rate of 10 °C/min after heat treatment at 600 °C for 10 or 15 min. Particle size 425–500 lm. Sample weight: 36.14 mg (10 min at 600 °C); 36.16 mg (15 min at 600 °C). Furnace atmosphere: nitrogen.
area of the DTA peaks similar to those shown in Fig. 5 are given in column 4 of Table 1 for the densified and undensified glasses. Also, included in column 4 (Table 1), for comparison, is the Nv value for the (undensified) glass nucleated at 455 °C for 2 h. As shown in Table 1 (column 4), Nv increased from 38 1012 m3 for an as-melted (undensified) glass to 82 1012 m3 (by a factor of more than 2) for a glass subjected to a pressure of 1 GPa and then remained nearly constant at pressures up to 6 GPa. The values of Nv in the densified glasses are comparable to the Nv value for the glass nucleated at 455 °C for 2 h. These results are consistent with what was qualitatively observed from the change in the DTA peak temperature (Tp ) for these glasses, see results in Section 3.1.1. The undensified glass and the glass densified at 6 GPa were given a short (10 min) crystal growth heat treatment at 618(2) °C. After light grinding and polishing (to remove surface crystallization), the polished surface was examined by optical microscopy to determine the size and number of crystals, see Fig. 6. The densified glass clearly contains a larger number of smaller crystals than
Fig. 6. Comparison of the size and number of crystals as observed by optical microscopy on a polished surface of the undensified (0 GPa) and densified (6 GPa) Li2 O 2SiO2 glasses after heat treatment at 618 °C for 10 min. Note that the undensified glass (0 GPa), contains only one large crystal, although the scanned area for both samples is the same.
the undensified glass (Fig. 6), which is consistent with the results for Nv as measured by DTA (Table 1, column 4). Both types of crystal morphology, spherullitic and prolate ellipsoidal, which are commonly observed [27] for lithium disilicate crystals, have been observed in the present work, also. However, the shape of the majority of crystals in the undensified sample is spherical, and that in the densified samples is prolate ellipsoidal, compare the two pictures in Fig. 6. The effect of static pressure on the morphology of lithium disilicate crystals is currently under investigation.
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3.1.3. Activation energy for crystallization (E) The Kissinger plots (Eq. (2)) for the undensified, nucleated (455 °C for 2 h), and all the densified glasses are shown in Fig. 7. The data for each glass fall on a straight line (correlation factor 0.997 or better) as predicted by Eq. (2). The values of E determined from the slope of these straight lines and given in column 5 of Table 1 show that E decreased from 358 kJ/mol for the undensified glass to 292 kJ/mol for the glass densified at 1 GPa. The values of E for all of the densified glasses as well as that for the glass nucleated at 455 °C for 2 h are the same within an experimental error of 10 kJ/mol. The activation energy for crystallization, E, determined by non-isothermal methods, such as DTA, generally consists of two terms. One term includes a contribution from the activation energy for nucleation while the second contains contributions from the activation energy for crystal growth. The value of E determined using Eq. (2) is close to the activation energy for crystal growth (no contribution from the activation energy for nucleation) when the formation of new nuclei can be completely prevented (a case of site-saturation or fully nucleated glass). For glasses that are not fully nucleated, the DTA method yields a higher value for E, which decreases with increasing degree of nucleation in the glass. Thus, a lower value of E for the nucleated (455 °C/2 h) glass compared to
Fig. 7. Ln (Tp2 =/) vs l/Tp plots (Kissinger) for the undensfed, densified (1, 3 and 6 GPa) and nucleated (455 °C/2 h) Li2 O 2SiO2 glass. Furnace atmosphere: nitrogen. Particle size: 425–500 lm.
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that for the undensified, unnucleated glass (column 5, Table 1) is expected. The lower value of E for all the densified glasses compared to that for the undensified glass again confirms that the concentration of nuclei in the densified glasses is higher than that in the undensified glass. 3.2. Raman spectra A portion of the Raman spectra reported in Ref. [16] for the densified and undensified LS2 glasses are reproduced in Fig. 8 after normalizing with respect to the band intensity at 1080 m1 . Fig. 8 shows only the bands at 950 and 1080 cm1 , which are of primary importance in the present investigation. The bands around 950 and 1080 cm1 are attributed [23–26] to the Si–O streching vibrations in the Q2 (where two of the four oxygen in the SiO4 tetrahedron are bridging) and Q3 (three of four oxygen in the SiO4 tetrahedron are bridging) species, respectively. Clearly, the intensity of the band at 950 cm1 increases with increasing pressure. Following the procedures in Ref. [30] the ratio of the intensities for the bands at 950 cm1 (Q2 ) and 1080 cm1 (Q3 ), IðQ2 Þ=IðQ3 Þ, was calculated from Fig. 8 to determine the relative abundance of a particular Q species in the glass, and is given in Table 2. The results in Table 2 show that
Fig. 8. A portion of the Raman spectra from Ref. [16] for the undensified and densified Li2 O SiO2 glasses after normalizing with respect to the intensity of the 1080 cm1 band.
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Table 2 Intensity of the Raman band at 950 cm1 (Q2 ) relative to that of the band at 1080 cm1 (Q3 ), IðQ2 Þ=IðQ3 Þ, for a Li2 O 2SiO2 glass after subjecting to various (static) pressures Applied pressure (GPa)
IðQ2 Þ=IðQ3 Þ
0 1 3 6
0.364 0.004 0.382 0.003 0.418 0.002 0.503 0.008
IðQ2 Þ=IðQ3 Þ increases form 0:364 0:004 for the undensified glass to 0:503 0:008 for the glass densified at 6 GPa which suggests that the relative abundance of the Q2 species increases in the glass with increasing pressure. The formation of Q2 species with increasing pressure occurs at the expense of Q3 species by the following reaction as suggested by others [2,30] for many silicate melts. 2Q3 ðexcess charge; 2Þ Q2 ðexcess charge; 2Þ þ Q4 ðno excess chargeÞ:
ð3Þ
It is interesting to note that a small side band of the primary 1080 cm1 band for Q3 appears at 1120 cm1 in the Raman spectra (Fig. 8) for these glasses, whose intensity increases with increasing pressure. The presence of such a side band in the Raman spectra has been reported before by others [25,26] for many alkali silicate, including lithium silicate, glasses. It is suggested [25,26] that
Fig. 9. Schematic of the structural rearrangement in the glass network before (A) and after (B) densification as per the transformation 2Q3 Q2 þ Q4 . The NBO in unit (2) in A becomes bridging, unit (2) in B, and one of the bridging oxygen bonds in unit (1) in A breaks to form a Q2 , unit (1) in B, after subjecting the glass to high-pressures.
the appearance of this band is connected with some kind of disordered (SiO4 ) tetrahedral units resulting from the ÔdissociationÕ of two Q3 species to one Q2 and one Q4 species, which supports the conclusion we also arrived at (Eq. (3), Fig. 9). An increasing intensity of this band at 1120 cm1 (Fig. 8) with increasing pressure further confirms that the concentration of Q2 species increases with increasing pressure in this LS2 glass.
4. Discussion The increase in the concentration of nuclei (Nv ) for the densified glasses is supported separately from the analysis of the DTA peak temperature (Section 3.1.1), the measured activation energy for crystallization (Section 3.1.3), and number of crystals found in the heat treated samples (Fig. 6). The values of Nv in the densified glasses increased by a factor of more than 2 (100–116%) compared to that for the undensified glass, see column 4 of Table 1. The increase in density (d) with increasing pressure, and a 5% experimental uncertainty in the measurements of Nv can account for an increase in Nv of only up to 15% for the densified glasses. The observed 100–116% increase in Nv is too large compared to the combined effect of the volume decrease (density increase) and experimental error. Thus, the increase in Nv for the densified glasses is considered largely the effect of static pressure. The glasses in the present investigation were densified at 400 °C for 20 min and considerable nucleation occurred in the glass at this temperature. The onset temperature for nucleation for this LS2 glass at ambient pressure is about 425 °C [18,27], meaning that no nuclei should form in this glass when heated at 400 °C at ambient pressure for hours or even for days. Clearly, applying an external static pressure of 1 GPa shifted the nucleation curve for this glass to lower temperatures causing nuclei to form even at 400 °C. Also, a pressure of 1–6 GPa, and heating at 400 °C for only 20 min produces a nucleation that is equivalent to what occurs when the glass is heated at the temperature of its maximum nucleation rate at ambient pressure (455 °C) for 2 h. Thus, it is es-
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timated that at an external pressure of 1–6 GPa, the nucleation rate in an LS2 glass at 400 °C is about six times larger than the nucleation rate at 455 °C (4.2–4:5 109 m3 s1 ) for a similar LS2 glass at the ambient pressure. The increase in density with applied pressure decreases the molar volume, VM , of the glass. A smaller VM can increase the overall rate for nucleation, I, as per the following equations 4,5 [28], by decreasing the thermodynamic energy barrier for nucleation, W . I¼
2nv V 1=3 W 1=2 kT Þ exp ; ðr lc kT 3pk3 g
ð4Þ
W ¼
16pr3 VM2 ; 3DG2
ð5Þ
where T is temperature, r1c is interfacial energy per unit area at the liquid–cluster interface, nv is number of structural units per unit volume, V is volume of structural unit, DG is the difference in free energy per mol of the crystal and liquid, k is a jump distance and g is the viscosity. However, a change in I due to any change in VM is expected to occur within the temperature range for nucleation observed at ambient pressure. The shift in the nucleation curve to lower temperature, which has been found in the present study, cannot be explained by a decrease in molar volume with applied pressure. A major contribution to the nucleation rate (I) also comes from a kinetic factor related to the viscosity parameter, g in Eq. (4). It is believed that the application of an external pressure to this LS2 glass causes its viscosity to decrease at all temperatures, which makes nuclei formation possible at temperatures lower than that for nucleation at ambient pressure. A decrease in viscosity with increasing pressure in silicate glasses has been reported [2,10–15], and has also been predicted based on MD simulations [29]. Analyses of Raman spectra suggest the formation of Q2 and Q4 species in the glasses densified at high-pressures at the expense of Q3 species (Eq. (3)). The formation of Q2 and Q4 from Q3 may occur via several processes. Whatever process is followed, the non-bridging oxygen (NBO) in one
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of the Q3 species becomes bridging (BO) by forming a bond with a neighboring SiO4 tetrahedra, see the schematic in Fig. 9. The Liþ ion associated with the NBO (unit 2 in A) should move away from unit 2. One of the Si–O–Si bonds in the other Q3 unit in A (unit 1) breaks to form a Q2 (B) and a Liþ ion moves closer to the newly formed NBO. This whole structural rearrangement process may cause a flow in the glass network, thereby, decreasing the effective viscosity of the glass. A decrease in viscosity shifts the nucleation rate curve of the glass to lower temperatures, as has been observed in the present investigation for the densified LS2 glasses. A flow in the glass network, which effectively reduces the viscosity, may also occur for the formation of 5 and/or 6-coordinated species (Si[5], Si[6]) with the increasing pressure, as shown schematically in Fig. 10. Although, this proposition is speculative at this time, since no evidence in support of the proposition is presented here, formation of Si[5] and Si[6] species in silicate glasses
Fig. 10. A schematic model showing the diffusion process via the formation of intermediate Si[5] species [30]. With the application of pressure the NBO in Q3 (unit (2)) approaches a neighboring Q4 (unit (1)) resulting in formation of five coordinated Si species (process A). Liþ ion associated with the NBO moves to unit (1) for charge compensation. This intermediate state can either return to the initial state or transform to Q3 and Q4 with different configuration (process B). In either case this structural rearrangements establish a flow in the glass network and may reduce the viscosity of the glass.
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at high-pressures has been reported [30] from the measurements of solid-state 29 Si MAS NMR spectra. Although, it is somewhat inconclusive at this time, the present results indicate that the crystal growth rate curve for this LS2 glass also moves to lower temperatures with increasing pressure. The analyses of the DTA peak height, (dT )p , suggest that crystal growth in the densified glasses occurs at 400 °C, which is about 150 °C lower than the temperature for crystal growth (550 °C) at ambient pressure. Again, a reduction in viscosity with increasing pressure, as postulated for the shift of the nucleation rate curve to lower temperatures, may also be responsible for a shift of the crystal growth rate curve to lower temperatures in the densified glasses.
5. Conclusions Applying an external static pressure of P 1 GPa to a lithium disilicate (LS2 ) glass produces nucleation at 400 °C, which is about 25 °C lower than the onset temperature for nucleation for this glass at the ambient (atmospheric) pressure. The pressure-induced nucleation rate at 400 °C was at least six times larger than the maximum nucleation rate at 455 °C for an undensified glass. Increasing the pressure up to 6 GPa had no effect on the nucleation over that achieved at 1 GPa. It is believed that applying an external pressure on a glass moves the nucleation rate (I) curve of the glass to lower temperatures as well as increases the values of I at all temperatures within the nucleation range. The crystal growth rate (U ) curve for a glass can be similarly affected by external pressures, but requires a relatively higher pressure. For the LS2 glass, crystal growth is believed to occur at pressures >1 GPa at 400 °C, which is about 150 °C lower than the onset temperature for crystal growth for this glass at atmospheric pressure. It is believed that applying a high (static) pressure on a LS2 glass, causes to form new species like Q2 , Q4 , Si[5] and Si[6] in the glass network. Forming such species produces a flow in the glass network, which effectively reduces the viscosity of
the glass at all temperatures. A smaller viscosity caused by an applied pressure is suspected to be the primary reason for the shift of the I and U curves to lower temperatures.
Acknowledgements The work was supported by National Aeronautics and Space Administration (NASA), USA, Grant #NAG8-1465 and by the Osaka National Research Institute (ONRI), AIST of Japan.
References [1] P. Richet, Y. Bottinga, Rev. Mineral. 32 (1995) 67. [2] G. Wolf, P.F. McMillan, Rev. Mineral. 32 (1995) 505. [3] E. Chanson, M. Aziz, J. Non-Cryst. Solids 130 (1991) 204. [4] B.R. Durschang, G. Carl, C. Russel, K. Marchetti, E. Roeder, Glastech. Ber. Glass Sci. Technol. 67 (1994) 171. [5] D.R. Uhlmann, J.F. Hays, D. Turnbull, Phys. Chem. Glasses 7 (1966) 159. [6] N.N. Sirota, in: N.N. Sirota (Ed.), Crystallization and Phase Transformations, Bielorussian Academy of Science, Minsk, 1962, p. 38. [7] M. Hasselblatt, Z. Anorg, Allg. Chemie. 119 (1921) 353. [8] M.J. Aziz, E. Nygren, J.F. Hays, D. Turnbull, J. Appl. Phys. 57 (1985) 2233. [9] I. Gutzow, B. Durschang, C. R€ ussel, J. Mater. Sci. 32 (1997) 5389. [10] H. Watanable, J. Phys. Earth 23 (1975) 333. [11] I. Kushiro, J. Geophys. Res. 81 (1976) 6347. [12] I. Kishuro, in: M.H. Manghnani, S. Akimoto (Eds.), High Pressure Research: Applications in Geophysics, Academic Press, 1977, p. 25. [13] I. Kushiro, Earth Planet. Sci. Lett. 41 (1978) 87. [14] C.M. Scarfe, B.O. Mysen, D. Virgo, Carnegie Inst. Washington Yearbook 78 (1979) 547. [15] C.M. Scarfe, B.O. Mysen, D. Virgo, in: B.O. Mysen (Ed.), Magmatic Processes: Physicochemical Principles, The Geochemical Society, University Park, PA, 1987, p. 59. [16] K. Kitamura, K. Fukumi, H. Mizoguchi, M. Makihara, A. Higuchi, N. Ohno, T. Fukunaga, J. Non-Cryst. Solids 274 (2000) 244. [17] A. Onodera, High Temp.-High Pressures 19 (1987) 579. [18] C.S. Ray, X. Fang, D.E. Day, J. Am. Ceram. Soc. 83 (2000) 865. [19] K.S. Ranashinghe, C.S. Ray, D.E. Day, J. Mater. Sci. 37 (2002) 547. [20] C.J.R. Gonzales-Oliver, P.S. Johnson, P.F. James, J. Mater. Sci. 14 (1979) 1159.
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H.E. Kissinger, Anal. Chem. 29 (1957) 1702. C.S. Ray, D.E. Day, J. Am. Ceram. Soc. 80 (1997) 3100. P.F. McMillan, Am. Miner. 69 (1984) 622. D.W. Matson, S.K. Sharma, J.A. Philpotts, J. Non-Cryst. Solids 58 (1983) 323. [25] E. Dowty, Phys. Chem. Miner. 14 (1987) 542. [26] A. Brawer, W.B. White, J. Chem. Phys. 63 (1975) 242. [27] P.F. James, Phys. Chem. Glasses 15 (1974) 95.
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[28] E.G. Rowlands, P.F. James, Phys. Chem. Glasses 20 (1979) 1. [29] A.C. Angell, P. Cheeseman, S. Tamaddon, Science 218 (1982) 885; A.C. Angell, P. Cheeseman, S. Tamaddon, Bull. Mineral. 106 (1983) 87. [30] X. Xue, J.F. Stebbins, M. Kanzanki, P.F. McMillan, B. Poe, Am. Miner. 76 (1991) 8.
Pressure induced nucleation in a Li2O 2SiO2 glass T. Fuss a
a,*
, C.S. Ray a, N. Kitamura b, M. Makihara b, D.E. Day
a
Ceramic Engineering Department and Graduate Center for Materials Research, University of Missouri-Rolla, Rolla, MO 65409, USA b Department of Optical Materials, Osaka National Research Institute, 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan Received 15 January 2002; received in revised form 12 July 2002
Abstract The concentration of nuclei (Nv ) in a Li2 O 2SiO2 (LS2 ) glass was measured using a newly developed differential thermal analysis technique, after densifying the glass at 1, 3, or 6 GPa pressure at 400 °C for 20 min. Nv increased from 38 1012 m3 for an as-melted glass to 82 1012 m3 for a glass subjected to a pressure of 1 GPa, and remained nearly constant with further increase of pressure of up to 6 GPa. This increase in Nv is equivalent to nucleating this LS2 glass at the temperature (455 °C) of its maximum nucleation rate for 2 h. The average effective activation energy for crystallization for the densified glasses, 292 10 kJ/mol, was also the same as that of the (undensified) glass nucleated at 455 °C for 2 h, but was significantly smaller than that (358 10 kJ/mol) for an as-melted (undensified and unnucleated) glass. The present results show that applying an external pressure on this LS2 glass shifts its nucleation curve to lower temperatures causing nuclei to form even at 400 °C. A decrease in viscosity at all temperatures with the application of pressure is suspected to be a reason for the enhanced nucleation observed for this LS2 glass. Ó 2002 Published by Elsevier Science B.V.
1. Introduction Knowledge of the high-pressure properties of melts, particularly silicate melts, is useful to understanding geological processes such as magma crystallization [1,2]. Many commercial glass manufacturing processes (pressing, blowing, injection molding, fiber drawing, extrusion) often involve a substantial pressure. Such pressure-aided manufacturing processes can change the properties of a glass preform in an undesirable way such as en-
*
Corresponding author. Tel.: +1-573 341 6695; fax: +1-576 341 2071. E-mail address: [email protected] (T. Fuss).
hancing the crystallization tendency of the glass [3,4]. There are a few reports [5–9] indicating that the thermodynamic driving force for nucleation, which is opposite to the energy barrier W for nucleation, is increased with increasing pressure, thereby, increasing nucleation in glass forming melts. An increase in the melting point and/or a decrease in the interfacial energy at the liquid-crystal interface at elevated pressure are suggested as the reason for the decrease in W . Some of the previous work [8,9] also postulate that a kinetic factor, namely, an increase in viscosity with increasing pressure, which may nullify or even surpass the effect of decrease in W , also simultaneously affects the nucleation rate, causing the effective nucleation rate curve (as a function of temperature) to move to higher
0022-3093/03/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 8 7 8 - 1
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temperatures with increasing pressure. However, there are reports [10–15] also of a decrease in viscosity, which favors nucleation, with increasing pressure for glass forming melts. Pressure-aided glass manufacturing processes are generally observed to be associated with some kind of tangential stress, i.e., a flow of the melt under pressure. It is argued [9] that the reason enhanced crystallization is often observed in melts that are subjected to such pressure-aided processing steps (extrusion pressing, fiber pulling) is due solely to shear thinning (a decrease in viscosity with increasing strain rate), and static pressure has virtually no role in enhancing the crystallization of the melt. It has been shown [9] further that the nucleation or crystal growth rate in most melts is decreased rather than increased by (external) static pressure alone. However, for exceptional cases such as at relatively high-pressures (GPa range) and very high DV values (difference in molar volume between the liquid and crystal phase), static pressure can increase crystallization of a melt [9]. It is clear from the above discussions that only a handful of results exist in the literature for how static pressure affects the crystallization of glass forming melts. Furthermore, these results are often in conflict with each other. It appears that the effect of static pressure on crystallization of glass forming melts, has not been fully explored. The present work was aimed at investigating the effect of isostatic pressure on nucleation for a Li2 O 2SiO2 (hereafter referred to as LS2 ) glass by measuring and comparing the nucleation density (number of nuclei per unit volume) in an as-melted glass and in a glass that was densified by applying an external pressure of 1, 3, or 6 GPa. The pressure was applied to the glass for 20 min at 400 °C, which is about 25 °C lower than the onset temperature (425 °C) for nucleation at the ambient (atmospheric) pressure for this LS2 glass. For comparison, the density of nuclei for a glass, which was not densified, but nucleated at 455 °C for 2 h was also measured. This 455 °C corresponds to the temperature of the maximum nucleation rate for the LS2 glass at ambient pressure. As will be shown later, the results of the present investigation suggest that nucleation in the LS2 glass is enhanced by pressure and the nucleation rate curve
moves to lower temperatures compared to the same curve at ambient pressure. These results are opposite to those predicted by Gutzow et al. [9] from model calculations for this glass.
2. Experimental procedures The LS2 glass was prepared by melting a homogeneous mixture of reagent grade Li2 CO3 and SiO2 at 1475 °C for 4 h in air in a platinum crucible, casting the melt onto cylindrical graphite molds of approximate dimension 8 mm ðdiameterÞ 10 mm (height), and annealing the glass at 470 °C for 1 h. After annealing, the glass was slowly cooled to room temperature by turning the power to the furnace off (furnace cool). The glass cylinders made from the same melt were then densified under 1, 3, or 6 GPa at 400 °C for 20 min using a 6–8 type multi-anvil high-pressure apparatus (UHP-2000, Sumitomo Heavy Industries, Japan) [16]. The details of the densification procedure and a description of the high-pressure apparatus are given elsewhere [17]. The pressure– temperature–time schedule that was used in densifying the glasses in the present work is shown schematically in Fig. 1. The pressure was increased at a rate of þ2 GPa/ h at room temperature (26 °C) to the desired value (1, 3, or 6 GPa) and held at that pressure for 2 h. During the second or last hour of isostatic
Fig. 1. Pressure–temperature–time schedule for densifying Li2 O 2SiO2 glass.
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hold, the temperature of the sample was increased to 400 °C at a rate of þ20 °C/min, held at 400 °C for 20 min, and then decreased to room temperature at )20 °C/min. After the sample reached room temperature, the applied pressure was decreased to zero (ambient pressure) at a rate of )2 GPa/h. The density of the densified and undensified glasses was measured by Archimedes method using distilled water as the buoyant liquid. The density (d) of the as-melted (undensified) glass was 2.34 g cm3 , while the density of the glasses densified at 1, 3, and 6 GPa was 2.39, 2.49, and 2.58 g cm3 , respectively, with an estimated error of 0.01 g cm3 . Consequently, the molar volume (VM ), calculated for one mol (0.33 Li2 O 0.67 SiO2 ) of glass, decreased from 21.38 cm3 for the undensified glass to 19.39 cm3 for the glass densified at 6 GPa pressure. The refractive index of the glasses was measured by the Becke-line technique using standard refractive index liquids. Like the density, the refractive index increased with increasing applied pressure, being 1.534 for the undensified glass and 1.544, 1.562, and 1.579 for the glasses densified at 1, 3, and 6 GPa, respectively. The estimated error in the refractive index measurements was 0.001. The number of nuclei per unit volume in the glasses was determined by a differential thermal analysis (DTA) method [18,19]. In this method, 20–30 mg of glass powder (425–500 lm particle size) is first heated in a DTA apparatus (Perkin– Elmer, Model DT7) with a heating rate of 20 °C/ min up to a temperature, TG , where the crystal growth rate (UG ) for the glass is known. The sample is then held at TG for a short time, typically between 5 and 20 min. For the present experiments with the LS2 glass, this isothermal heat treatment temperature, TG was 600 °C, where the value of UG for this glass is 2:5 108 m min1 [20]. After this isothermal heat treatment, the temperature is quickly decreased (at a rate of 40 °C/min) to 375 °C which is well below the onset temperature for nucleation (425 °C for the LS2 glass), and the sample is thermally stabilized for about 5 min. A DTA scan is then performed at a fixed 10 °C min1 heating rate until crystallization is complete as indicated by an exothermic DTA peak. A similar, second experiment is performed using a new sample of the same glass and keeping all
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the experimental parameters mentioned above constant except the heat treatment time at TG . The concentration of nuclei (Nv ) in the glass was calculated from the area of the two DTA peaks as [18,19] Nv ¼
3ðA1 m2 A2 m1 Þ ; 3 3 ðA1 m2 tG2 A2 m1 tG1 ÞpUG3
ð1Þ
where m1 is the mass of the sample, tG1 is the heat treatment time at TG , and A1 is the area of the DTA peak for the first experiments. The corresponding values for the second experiment are m2 , tG2 and A2 . Note that Eq. (1) can be further simplified if the mass of the sample in the two DTA runs is the same (m1 ¼ m2 ). The heat treatment times at 600 °C for the first and second experiments were 10 (tG1 ) and 15 (tG2 ) min, respectively. The activation energy for crystallization, E, for the glasses was determined using DTA also. In determining E, several DTA runs at constant different heating rates (u) were made and the temperature corresponding to the maximum of the crystallization peak (TP ) was determined as a function of u. TP and u are related, according to the Kissinger model [21], as lnðTP2 =uÞ / ðE=RTP Þ;
ð2Þ lnðTP2 =uÞ
where R is the gas constant. A plot of vs (1/TP ) should be a straight line (Kissinger plot) whose slope yields the value of E. The heating rates (u) used in the present experiments were 2, 4, 6, and 10 °C/min. The mass (20–30 mg) and particle size (425–500 lm) of the sample used in the experiments for measuring E were the same as used in measuring Nv . All the DTA experiments were conducted in flowing (30 cm3 min1 ) nitrogen gas using platinum containers and 99.99% pure A12 O3 powder as the reference material. The values of Nv and E for an undensified LS2 glass nucleated at 455 °C for 2 h were also measured for comparison with the same values for the densified glasses. This temperature of 455 °C was chosen since this is the temperature where the nucleation rate for an undensified LS2 glass is a maximum. The Raman spectra for these glasses were reported previously [16] and will not be repeated here. However a portion of those spectra will be
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re-analyzed in this paper to justify the conclusions made from the DTA results.
3. Results 3.1. Differential thermal analysis 3.1.1. General observations Typical DTA curves at 4 °C/min for an undensified LS2 glass and for a glass densified at 1 GPa are shown in Fig. 2. Also shown in Fig. 2, for comparison, is the DTA curve at 4 °C/min for the (undensified) LS2 glass after nucleating at 455 °C for 2 h. The DTA curves for the glasses densified at 1, 3, and 6 GPa pressure are shown in Fig. 3. The temperature, Tp , and height, (dT )p , determined from the curves in Figs. 2 and 3 at the crystallization peak maximum are given in Table 1 for all the glasses and separately shown in Fig. 4. (dT )p increases with increasing sample weight [22], and since the sample weight in the different DTA measurements was not strictly constant, the (dT )p from different experiments will be compared by using a normalized value for (dT )p , such as Ôper gramÕ of sample, which is given in Table 1 and in Fig. 4. Tp , on the other hand, does not depend on the amount of sample, but is inversely propor-
Fig. 2. DTA exotherms for undensified (0 GPa), densified (1 GPa) and nucleated (455 °C/2 h) Li2 O 2SiO2 glasses at a heating rate of 4 °C/min. Particle size 425–500 lm. Sample weight: 20.1 mg (0 GPa), 20.1 mg (455 °C/2 h), 28.4 mg (1 GPa). Atmosphere: nitrogen.
Fig. 3. DTA exotherms for densified (1, 3 and 6 GPa) Li2 O 2SiO2 glasses at a heating rate of 4 °C/min. Particle size 425–500 lm. Sample weight: 28.4 mg (1 GPa), 28.2 mg (3 GPa), 28.4 mg (6 GPa). Furnace atmosphere: nitrogen.
tional to the concentration of nuclei (Nv ) in the glass [18]. A qualitative estimate for the concentration of nuclei in the glasses can be made by comparing the values of Tp , while a comparison of (dT )p -values gives a qualitative estimate for the total number of nuclei per gram of each sample. As shown in Fig. 4 and Table 1, the Tp values for the nucleated (undensified) glass and all the densified glasses are nearly the same, but are 7–12 °C lower than that of the undensified (unnucleated) glass, see also Figs. 2 and 3. Since Tp is inversely proportional to Nv , a larger Nv should result in a smaller value for Tp . A smaller Tp value for the nucleated glass (Figs. 2 and 4, Table 1) compared to that for the unnucleated, undensified glass, is expected, since the concentration of nuclei in the nucleated glass should be higher. The lower Tp values for the densified glasses, therefore, indicate that the Nv in these glasses is higher than that in the undensified glass. The nearly equal values of Tp for the nucleated glass and all the densified glasses (Fig. 4, Table 1), suggest that the nucleation caused by a static pressure of 1, 3 or 6 GPa (at 400 °C) is equivalent to that caused by nucleation at 455 °C for 2 h at the ambient (atmospheric) pressure for this LS2 glass. It should be noted that 400 °C is about 25 °C lower than the onset temperature for nucleation
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Table 1 Thermal analysis (DTA) results for the undensified, densified and nucleated Li2 O 2SiO2 glasses Applied pressure (GPa)
Tp ð2Þ (°C)
ðdT Þp ð0:5Þ (°C/g)
Nv ð5%Þ (m3 )
Eð10Þ (kJ/mol)
0 1 3 6 0 (Nucleated at 455 °C for 2 h)
634 622 627 626 626
23.0 39.5 32.9 24.5 39.7
38 1012 81 1012 82 1012 78 1012 76 1012
358 292 281 311 286
Tp : temperature at the DTA peak maximum. (dT )p : maximum height of the DTA peak (at Tp ) per gram of sample. Nv : concentration of nuclei. E: activation energy for crystallization.
Fig. 4. Temperature (Tp ) and height (dT )p at the DTA peak maximum for the undensified, densified and nucleated (455 °C/2 h) Li2 O 2SiO2 glasses. DTA heating rate 4 °C/min.
for this glass at ambient pressure, and no additional nuclei are formed in this glass when heated at 400 °C at ambient pressure for several hours or even for several days. There is no further increase (or decrease) in the concentration of nuclei at pressures above 1 GPa. The maximum height of the crystallization peak, (dT )p , for the glass densified at 1 GPa is nearly the same as that for the nucleated glass (Fig. 4, Table 1), but is larger than that for the undensified glass. These results are consistent with the results for Tp and suggest that the total number
of nuclei in this densified glass (1 GPa) is nearly the same as that in the nucleated glass, but larger than that in the undensified glass. However, (dT )p decreases with increasing pressure when the applied pressure exceeds 1 GPa (Fig. 4), indicating a decrease in the total number of nuclei with increasing pressure >1 GPa. The reason for the decrease in (dT )p with the increasing pressure (>1 GPa) is not clearly understood, but may be due to a partial crystallization of the sample, where some of the nuclei were consumed via crystal growth. In other words, applying external pressure >1 GPa may have caused the crystal growth rate curve to move to 400 °C, which is about 150 °C lower than the onset temperature for crystal growth for this glass at ambient pressure, causing the glass to partially crystallize (at 400 °C). However, attempts to detect the crystallinity by XRD or optical microscopy for the glasses densified at pressure >1 GPa were unsuccessful. At this time, any change in the crystal growth rate with increasing pressure remains unconfirmed. 3.1.2. Nucleation density (Nv ) The nucleation density (Nv ) in the glasses was determined using a DTA technique and Eq. (1). The typical DTA curves after crystal growth heat treatment at 600 °C (TG ) for 10 (tG1 ) or 15 (tG2 ) min for the LS2 glass are shown in Fig. 5. The glass that was heat treated at 600 °C for 15 min, contained a smaller number of nuclei after the heat treatment, thus producing a smaller DTA peak than the glass that was heat treated for 10 min. The values of Nv determined using Eq. (1) and the
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Fig. 5. DTA exotherms for the Li2 O 2SiO2 glass at a heating rate of 10 °C/min after heat treatment at 600 °C for 10 or 15 min. Particle size 425–500 lm. Sample weight: 36.14 mg (10 min at 600 °C); 36.16 mg (15 min at 600 °C). Furnace atmosphere: nitrogen.
area of the DTA peaks similar to those shown in Fig. 5 are given in column 4 of Table 1 for the densified and undensified glasses. Also, included in column 4 (Table 1), for comparison, is the Nv value for the (undensified) glass nucleated at 455 °C for 2 h. As shown in Table 1 (column 4), Nv increased from 38 1012 m3 for an as-melted (undensified) glass to 82 1012 m3 (by a factor of more than 2) for a glass subjected to a pressure of 1 GPa and then remained nearly constant at pressures up to 6 GPa. The values of Nv in the densified glasses are comparable to the Nv value for the glass nucleated at 455 °C for 2 h. These results are consistent with what was qualitatively observed from the change in the DTA peak temperature (Tp ) for these glasses, see results in Section 3.1.1. The undensified glass and the glass densified at 6 GPa were given a short (10 min) crystal growth heat treatment at 618(2) °C. After light grinding and polishing (to remove surface crystallization), the polished surface was examined by optical microscopy to determine the size and number of crystals, see Fig. 6. The densified glass clearly contains a larger number of smaller crystals than
Fig. 6. Comparison of the size and number of crystals as observed by optical microscopy on a polished surface of the undensified (0 GPa) and densified (6 GPa) Li2 O 2SiO2 glasses after heat treatment at 618 °C for 10 min. Note that the undensified glass (0 GPa), contains only one large crystal, although the scanned area for both samples is the same.
the undensified glass (Fig. 6), which is consistent with the results for Nv as measured by DTA (Table 1, column 4). Both types of crystal morphology, spherullitic and prolate ellipsoidal, which are commonly observed [27] for lithium disilicate crystals, have been observed in the present work, also. However, the shape of the majority of crystals in the undensified sample is spherical, and that in the densified samples is prolate ellipsoidal, compare the two pictures in Fig. 6. The effect of static pressure on the morphology of lithium disilicate crystals is currently under investigation.
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3.1.3. Activation energy for crystallization (E) The Kissinger plots (Eq. (2)) for the undensified, nucleated (455 °C for 2 h), and all the densified glasses are shown in Fig. 7. The data for each glass fall on a straight line (correlation factor 0.997 or better) as predicted by Eq. (2). The values of E determined from the slope of these straight lines and given in column 5 of Table 1 show that E decreased from 358 kJ/mol for the undensified glass to 292 kJ/mol for the glass densified at 1 GPa. The values of E for all of the densified glasses as well as that for the glass nucleated at 455 °C for 2 h are the same within an experimental error of 10 kJ/mol. The activation energy for crystallization, E, determined by non-isothermal methods, such as DTA, generally consists of two terms. One term includes a contribution from the activation energy for nucleation while the second contains contributions from the activation energy for crystal growth. The value of E determined using Eq. (2) is close to the activation energy for crystal growth (no contribution from the activation energy for nucleation) when the formation of new nuclei can be completely prevented (a case of site-saturation or fully nucleated glass). For glasses that are not fully nucleated, the DTA method yields a higher value for E, which decreases with increasing degree of nucleation in the glass. Thus, a lower value of E for the nucleated (455 °C/2 h) glass compared to
Fig. 7. Ln (Tp2 =/) vs l/Tp plots (Kissinger) for the undensfed, densified (1, 3 and 6 GPa) and nucleated (455 °C/2 h) Li2 O 2SiO2 glass. Furnace atmosphere: nitrogen. Particle size: 425–500 lm.
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that for the undensified, unnucleated glass (column 5, Table 1) is expected. The lower value of E for all the densified glasses compared to that for the undensified glass again confirms that the concentration of nuclei in the densified glasses is higher than that in the undensified glass. 3.2. Raman spectra A portion of the Raman spectra reported in Ref. [16] for the densified and undensified LS2 glasses are reproduced in Fig. 8 after normalizing with respect to the band intensity at 1080 m1 . Fig. 8 shows only the bands at 950 and 1080 cm1 , which are of primary importance in the present investigation. The bands around 950 and 1080 cm1 are attributed [23–26] to the Si–O streching vibrations in the Q2 (where two of the four oxygen in the SiO4 tetrahedron are bridging) and Q3 (three of four oxygen in the SiO4 tetrahedron are bridging) species, respectively. Clearly, the intensity of the band at 950 cm1 increases with increasing pressure. Following the procedures in Ref. [30] the ratio of the intensities for the bands at 950 cm1 (Q2 ) and 1080 cm1 (Q3 ), IðQ2 Þ=IðQ3 Þ, was calculated from Fig. 8 to determine the relative abundance of a particular Q species in the glass, and is given in Table 2. The results in Table 2 show that
Fig. 8. A portion of the Raman spectra from Ref. [16] for the undensified and densified Li2 O SiO2 glasses after normalizing with respect to the intensity of the 1080 cm1 band.
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Table 2 Intensity of the Raman band at 950 cm1 (Q2 ) relative to that of the band at 1080 cm1 (Q3 ), IðQ2 Þ=IðQ3 Þ, for a Li2 O 2SiO2 glass after subjecting to various (static) pressures Applied pressure (GPa)
IðQ2 Þ=IðQ3 Þ
0 1 3 6
0.364 0.004 0.382 0.003 0.418 0.002 0.503 0.008
IðQ2 Þ=IðQ3 Þ increases form 0:364 0:004 for the undensified glass to 0:503 0:008 for the glass densified at 6 GPa which suggests that the relative abundance of the Q2 species increases in the glass with increasing pressure. The formation of Q2 species with increasing pressure occurs at the expense of Q3 species by the following reaction as suggested by others [2,30] for many silicate melts. 2Q3 ðexcess charge; 2Þ Q2 ðexcess charge; 2Þ þ Q4 ðno excess chargeÞ:
ð3Þ
It is interesting to note that a small side band of the primary 1080 cm1 band for Q3 appears at 1120 cm1 in the Raman spectra (Fig. 8) for these glasses, whose intensity increases with increasing pressure. The presence of such a side band in the Raman spectra has been reported before by others [25,26] for many alkali silicate, including lithium silicate, glasses. It is suggested [25,26] that
Fig. 9. Schematic of the structural rearrangement in the glass network before (A) and after (B) densification as per the transformation 2Q3 Q2 þ Q4 . The NBO in unit (2) in A becomes bridging, unit (2) in B, and one of the bridging oxygen bonds in unit (1) in A breaks to form a Q2 , unit (1) in B, after subjecting the glass to high-pressures.
the appearance of this band is connected with some kind of disordered (SiO4 ) tetrahedral units resulting from the ÔdissociationÕ of two Q3 species to one Q2 and one Q4 species, which supports the conclusion we also arrived at (Eq. (3), Fig. 9). An increasing intensity of this band at 1120 cm1 (Fig. 8) with increasing pressure further confirms that the concentration of Q2 species increases with increasing pressure in this LS2 glass.
4. Discussion The increase in the concentration of nuclei (Nv ) for the densified glasses is supported separately from the analysis of the DTA peak temperature (Section 3.1.1), the measured activation energy for crystallization (Section 3.1.3), and number of crystals found in the heat treated samples (Fig. 6). The values of Nv in the densified glasses increased by a factor of more than 2 (100–116%) compared to that for the undensified glass, see column 4 of Table 1. The increase in density (d) with increasing pressure, and a 5% experimental uncertainty in the measurements of Nv can account for an increase in Nv of only up to 15% for the densified glasses. The observed 100–116% increase in Nv is too large compared to the combined effect of the volume decrease (density increase) and experimental error. Thus, the increase in Nv for the densified glasses is considered largely the effect of static pressure. The glasses in the present investigation were densified at 400 °C for 20 min and considerable nucleation occurred in the glass at this temperature. The onset temperature for nucleation for this LS2 glass at ambient pressure is about 425 °C [18,27], meaning that no nuclei should form in this glass when heated at 400 °C at ambient pressure for hours or even for days. Clearly, applying an external static pressure of 1 GPa shifted the nucleation curve for this glass to lower temperatures causing nuclei to form even at 400 °C. Also, a pressure of 1–6 GPa, and heating at 400 °C for only 20 min produces a nucleation that is equivalent to what occurs when the glass is heated at the temperature of its maximum nucleation rate at ambient pressure (455 °C) for 2 h. Thus, it is es-
T. Fuss et al. / Journal of Non-Crystalline Solids 318 (2003) 157–167
timated that at an external pressure of 1–6 GPa, the nucleation rate in an LS2 glass at 400 °C is about six times larger than the nucleation rate at 455 °C (4.2–4:5 109 m3 s1 ) for a similar LS2 glass at the ambient pressure. The increase in density with applied pressure decreases the molar volume, VM , of the glass. A smaller VM can increase the overall rate for nucleation, I, as per the following equations 4,5 [28], by decreasing the thermodynamic energy barrier for nucleation, W . I¼
2nv V 1=3 W 1=2 kT Þ exp ; ðr lc kT 3pk3 g
ð4Þ
W ¼
16pr3 VM2 ; 3DG2
ð5Þ
where T is temperature, r1c is interfacial energy per unit area at the liquid–cluster interface, nv is number of structural units per unit volume, V is volume of structural unit, DG is the difference in free energy per mol of the crystal and liquid, k is a jump distance and g is the viscosity. However, a change in I due to any change in VM is expected to occur within the temperature range for nucleation observed at ambient pressure. The shift in the nucleation curve to lower temperature, which has been found in the present study, cannot be explained by a decrease in molar volume with applied pressure. A major contribution to the nucleation rate (I) also comes from a kinetic factor related to the viscosity parameter, g in Eq. (4). It is believed that the application of an external pressure to this LS2 glass causes its viscosity to decrease at all temperatures, which makes nuclei formation possible at temperatures lower than that for nucleation at ambient pressure. A decrease in viscosity with increasing pressure in silicate glasses has been reported [2,10–15], and has also been predicted based on MD simulations [29]. Analyses of Raman spectra suggest the formation of Q2 and Q4 species in the glasses densified at high-pressures at the expense of Q3 species (Eq. (3)). The formation of Q2 and Q4 from Q3 may occur via several processes. Whatever process is followed, the non-bridging oxygen (NBO) in one
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of the Q3 species becomes bridging (BO) by forming a bond with a neighboring SiO4 tetrahedra, see the schematic in Fig. 9. The Liþ ion associated with the NBO (unit 2 in A) should move away from unit 2. One of the Si–O–Si bonds in the other Q3 unit in A (unit 1) breaks to form a Q2 (B) and a Liþ ion moves closer to the newly formed NBO. This whole structural rearrangement process may cause a flow in the glass network, thereby, decreasing the effective viscosity of the glass. A decrease in viscosity shifts the nucleation rate curve of the glass to lower temperatures, as has been observed in the present investigation for the densified LS2 glasses. A flow in the glass network, which effectively reduces the viscosity, may also occur for the formation of 5 and/or 6-coordinated species (Si[5], Si[6]) with the increasing pressure, as shown schematically in Fig. 10. Although, this proposition is speculative at this time, since no evidence in support of the proposition is presented here, formation of Si[5] and Si[6] species in silicate glasses
Fig. 10. A schematic model showing the diffusion process via the formation of intermediate Si[5] species [30]. With the application of pressure the NBO in Q3 (unit (2)) approaches a neighboring Q4 (unit (1)) resulting in formation of five coordinated Si species (process A). Liþ ion associated with the NBO moves to unit (1) for charge compensation. This intermediate state can either return to the initial state or transform to Q3 and Q4 with different configuration (process B). In either case this structural rearrangements establish a flow in the glass network and may reduce the viscosity of the glass.
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at high-pressures has been reported [30] from the measurements of solid-state 29 Si MAS NMR spectra. Although, it is somewhat inconclusive at this time, the present results indicate that the crystal growth rate curve for this LS2 glass also moves to lower temperatures with increasing pressure. The analyses of the DTA peak height, (dT )p , suggest that crystal growth in the densified glasses occurs at 400 °C, which is about 150 °C lower than the temperature for crystal growth (550 °C) at ambient pressure. Again, a reduction in viscosity with increasing pressure, as postulated for the shift of the nucleation rate curve to lower temperatures, may also be responsible for a shift of the crystal growth rate curve to lower temperatures in the densified glasses.
5. Conclusions Applying an external static pressure of P 1 GPa to a lithium disilicate (LS2 ) glass produces nucleation at 400 °C, which is about 25 °C lower than the onset temperature for nucleation for this glass at the ambient (atmospheric) pressure. The pressure-induced nucleation rate at 400 °C was at least six times larger than the maximum nucleation rate at 455 °C for an undensified glass. Increasing the pressure up to 6 GPa had no effect on the nucleation over that achieved at 1 GPa. It is believed that applying an external pressure on a glass moves the nucleation rate (I) curve of the glass to lower temperatures as well as increases the values of I at all temperatures within the nucleation range. The crystal growth rate (U ) curve for a glass can be similarly affected by external pressures, but requires a relatively higher pressure. For the LS2 glass, crystal growth is believed to occur at pressures >1 GPa at 400 °C, which is about 150 °C lower than the onset temperature for crystal growth for this glass at atmospheric pressure. It is believed that applying a high (static) pressure on a LS2 glass, causes to form new species like Q2 , Q4 , Si[5] and Si[6] in the glass network. Forming such species produces a flow in the glass network, which effectively reduces the viscosity of
the glass at all temperatures. A smaller viscosity caused by an applied pressure is suspected to be the primary reason for the shift of the I and U curves to lower temperatures.
Acknowledgements The work was supported by National Aeronautics and Space Administration (NASA), USA, Grant #NAG8-1465 and by the Osaka National Research Institute (ONRI), AIST of Japan.
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