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Compression creep and dynamic viscoelastic studies of binarysodium and lithium silicate glasses around deformationtemperature
Naoyuki KITAMURA³
National Institute of Advanced Industrial Science and Technology, 1–8–31 Midorigaoka, Ikeda, Osaka 563–8577, Japan
Mold pressing of glasses has been used in the past half centuryas the fabrication process of optical components, such as precisionlenses for digital still cameras and pick-up devices, micro-lenses,gratings, and prisms. Recently, this technique has been expandingto form sub-wavelength periodic structures on the surface of glasscomponents for a generation of new functions such as diffraction,antireflection, and retardation.1)4) In many cases, injection withhigh aspect ratio and precise transfer of mold shape are importantproblems that remain unsolved. For example, Kitamura et al.4)
reported thermal nano-imprinting of a two-dimensional periodicstructure with 300 nm pitch on high-refractive index phosphateglasses. The imprinted round shape was quite different from theoriginal cone shape of the mold. They5) also reported differencesin the transferability of a one-dimensional periodic structure ontwo kinds of phosphate glasses when pressed under pressure-timeconditions at the same viscosity. Moreover, in the general mold-ing process of optical lenses, sink marks of elements also havesimilar problems. The difficulty of molding relates strongly to themechanical and thermal properties of glass materials. In particular,the viscoelastic nature of the glass is most important for achievinga precise transfer of the shape of the mold and injection with highaspect ratio in thermal molding processes.
Viscoelastic properties such as internal friction,6),7) delayedelasticity up to glass transition temperature,8) and stress relaxa-tion9) have been extensively studied in silicate systems from halfa century ago. For example, Forry6) and Rötger7) reported thattwo structural relaxations due to diffusion alkali ions and mov-ing non-bridging oxygen were found at around ¹5050°C and150300°C for binary alkali silicate glasses from internal frictionmeasurement. Argon8) reported that the delayed elasticity of asoda-lime-silica glass is explained by a molecular arrangementmechanism with a distribution of activation energies. Crichtonet al.9) attempted to explain the stress relaxation of soda limeglass at high temperature by multiple Maxwell type modelshaving some relaxation time. Although the viscoelastic nature ataround the deformation temperature is very important for thermalmolding processes, as mentioned above, much less work hasbeen reported on this property.In the present study, the viscoelastic measurements of basic
binary sodium and lithium silicate glasses were performed byuniaxial compression creep tests and dynamic viscoelastic mea-surement. The effect of modifying the oxide and difference in thekind of modifying cation on the viscoelastic nature are discussedbased on an injection test into a narrow pore.
2. Experimental procedure
Na2OxSiO2 (x = 2, 3, and 4 in molar ratio) and Li2O2SiO2
glasses were prepared by a conventional melt-quench method.Na2CO3 (99%, Wako Chemicals), Li2CO3 (99%, KojundoChemicals, 99%), and SiO2 (99.99%, Nitchitsu) were used as
ature At were determined by thermal mechanical analysis (TMA/SS-6300, Seiko Instruments) under conditions of a load of 100mN and a heating rate of 5 °C/min. The density μ of the samplewas measured by Archimedes method with distilled water withan error of less than «1 kg/m3.A uniaxial compression creep test was performed by using a
were measured at room temperature by an ultrasonic pulse-echo method. A 10MHz longitudinal transducer and a 5MHztransverse transducer were used with a pulse transmitter/receiver(DPR300, JSR Ultrasonics). The cylinder sample for the creep testwas used for this ultrasonic measurement. Instantaneous shearmodulus G0, Poisson’s ratio ¯, instantaneous elastic modulus E0,and bulk modulus K0 were determined from both the velocitiesand the density of the sample as follows:
G0 ¼ μv2T ; ð1Þ
¯ ¼ 1
2
ðv2L � 2v2T Þðv2L � v2T Þ
; ð2Þ
E0 ¼ 2ð1þ ¯ÞG0; ð3ÞK0 ¼
E0
3ð1� 2¯Þ : ð4ÞThe details of the measurement and calculation of elastic
moduli are described elsewhere.10),11) These values were used forthe calculation of the creep function and the relaxation modulusin the analysis of the creep test.Dynamic viscoelastic measurement was performed by using a
viscoelasticy measuring instrument (DMS-6300, Seiko Instru-ments). The center of the beam sample, where the sample wasfixed, was modulated at thirteen different frequencies f : 0.01,0.02, 0,05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, and 100Hz.The recorded time histories of strain and stress were convertedto storage elastic modulus EB(½) and loss elastic modulusEBB(½),12),13) where ½ is angular frequency and ½ = 2³f.Measurements were carried out from room temperature to aroundthe deformation temperature with a heating rate of 0.3 °C/min.Injection tests were carried out by using the precision pressing
machine mentioned above. A flat glassy carbon mold (GC20SS,Tokai Carbon) and a glassy carbon mold having a narrow pore ofdiameter 200¯m and depth 700¯m were placed on the pressingarms. A cylinder sample was pressed by these molds with a loadof 1.5 kN under vacuum conditions at the temperature at which
Fig. 1. History of displacement of cylindrical sample height for thecreep test of (a)(c) Na2OxSiO2 (x = 2, 3, and 4) glasses and (d) Li2O2SiO2 glass.
Kitamura: Compression creep and dynamic viscoelastic studies of binary sodium and lithium silicate glasses around deformation
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3.2 Physical properties and mechanical prop-erties measured by the ultrasonic pulse-echomethod
The glass transition temperature Tg and deformation tem-perature At of the glass samples are listed on the left side ofTable 1 along with the density μ. The longitudinal and transversevelocities vL and vT at room temperature are listed in the middleof the table. The instantaneous shear modulus G0, Poisson’s ratio¯, instantaneous elastic modulus E0, and bulk modulus K0 arealso listed in the right columns in the table. The E0 and G0 forsodium system decrease with increasing Na2O content. Thevalues for Li2O2SiO2 glass are larger than those for sodiumsilicate glasses.
3.3 Dynamic viscoelastic measurementThe temperature dependence of the storage elastic modulus
EB(½) and loss elastic modulus EBB(½) are shown in Figs. 3(a)3(d) for Na2OxSiO2 (x = 2, 3, and 4) and Li2O2SiO2 glasses,respectively. Five frequencies, f = 0.01, 0.1, 1, 10, and 100Hz,are chosen as representative frequencies. Vertical lines indicatethe Tg and At for each glass. As seen in the figures, EB(½) starts todecrease and EBB(½) starts to increase slightly below the Tg, andsome fluctuation is observed at around At for only frequencieshigher than 1Hz. Figure 4 shows the EBB(½) curve for f = 1Hzbelow 400°C. A broad bump is observed at around 150300°C inEBB(½) of the sodium system, while it is not clear in the lithiumsystem. The frequency dependence of the storage elastic modulusEB(½) and loss elastic modulus EBB(½) are shown in Figs. 5(a)5(d) for Na2OxSiO2 (x = 2, 3, and 4) and Li2O2SiO2 glasses,respectively. Graphs on the left and right sides show EB(½) andEBB(½), respectively. The EB(½) is almost flat at low temperaturesand high frequencies, but decreases in the low frequency region.This decreasing tendency becomes remarkable at higher tempera-tures. Moreover, the decrease in EB(½) with increasing tempera-
Table 1. Glass transition (Tg) and deformation (At) temperatures, density (μ) of Na2OxSiO2 (x = 2, 3, and 4) and Li2O2SiO2 glasses.Right columns represent ultrasonic wave velocities of longitudinal and transverse waves (vL and vT), instantaneous elastic moduli E0,instantaneous shear moduli G0, Poisson’s ratio ¯ and bulk modulus K0 calculated from the velocities at room temperature
Fig. 3. Temperature dependence of storage elastic modulus EB(½)[closed circles], loss elastic modulus EBB(½) [open circles], and tan ¤[closed triangles] of (a)(c) Na2OxSiO2 (x = 2, 3, and 4) glasses and(d) Li2O2SiO2 glass from 300°C to around the deformation tempera-ture. The data for modulation frequencies of 0.01, 0.1, 1, 10, and 100Hzare selected as representative examples. Vertical thin solid lines representthe glass transition Tg and deformation At temperatures as listed inTable 1.
Fig. 4. Loss elastic modulus EBB(½) of Na2O2SiO2 glass (frequency =1Hz) for the low temperature range.
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ture is more remarkable in Li2O2SiO2 glass than sodium silicateglasses. EB(½) curves for Li2O2SiO2 glass shows an irregulardecrease only at 536 and 545°C, whereas EBB(½) shows almostthe same profile for sodium silicate glasses and has a broad peakat higher temperatures at a glance. Crystallization of the samplewas observed after measurement of Li2O2SiO2 glass.
3.4 Injection testA small round bump was formed on the glass surface after the
injection test. Figure 6 shows the dependence of the injectedvolume on pressing time for all glasses. The volume increasesmonotonically with pressing time and follows the same trajectoryfor Na2OxSiO2 (x = 2, 3, and 4) glasses. In contrast, the volumefor Li2O2SiO2 glass tends to be suppressed on the pressing for600 s, although all cylinder samples showed almost the same
4.1 Uniaxial compression creep testAs seen in Figs. 1(a)1(d), the displacements of the sample
exceed 50% of the initial height, so that true stress was intro-duced according to Arai’s method18) to avoid an estimation errorof the creep function J(t) due to large deformation. In the present
Fig. 5. Frequency dependence of (left side) storage elastic modulus EB(½) and (right side) loss elastic modulus EBB(½) of(a)(c) Na2OxSiO2 (x = 2, 3, and 4) glasses and (d) Li2O2SiO2 glass at several temperatures around the deformationtemperature (Table 1).
Kitamura: Compression creep and dynamic viscoelastic studies of binary sodium and lithium silicate glasses around deformation
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study, the creep function J(t) was fitted by a 10-term powerfunction,
JðtÞ ¼ 1
E0
þX10i¼1
aiti; ð6Þ
for a conventional calculation of the shear relaxation modulusG(t) on the inverse Laplace transformation.19) In Eq. (6), t is thetime, and ai is the regression coefficient of the i-th term. Theinstantaneous creep function J0 at t = 0 was assumed by a recip-rocal Young’s modulus 1/E0. The G(t) of Na2O2SiO2 glass esti-mated by inverse Laplace transformation is shown in Fig. 8(a).Similar curves are obtained for Na2O3SiO2 and 4SiO2 glassesas seen in Figs. 8(b) and 8(c). The profile of G(t) is also similarfor Li2O2SiO2 glass [see Fig. 8(d)], but the temperature shift islarger than the sodium silicate system. As seen in these figures,taking logarithmic time for the horizontal axis, the relaxationmodulus at each temperature has almost the same profile, namelythe relaxation rate changes with temperature according to thetimetemperature superposition principle.20) Shift factor ln¡T
was obtained by superimposing the G(t) curve at each temper-ature onto a curve at the deformation temperature At. Figure 9shows the ln¡T plotted against the reciprocal of temperatureT. The factor obeys 1/T linearly well, that is, the activationenergy ¦H of structural relaxation can be estimated by usingNarayanaswamy’s equation, which is based on the Arrheniustype relationship as follows,21)
ln¡TðT Þ ¼�H
R
1
At
� 1
T
� �; ð7Þ
where R is the molar gas constant, 8.314 JK¹1mol¹1. The activa-tion energies ¦H estimated from the slope of the curve are441, 424, 417, and 449 Jmol¹1 for Na2OxSiO2 (x = 2, 3, and 4)and Li2O2SiO2 glasses, respectively. The energy decreases withdecreasing Na2O content for the sodium system, while Li2O2SiO2 glass shows higher energy than the sodium system. Inanalogy to polymer materials, slipping between network clustersseparated by modifying cations at non-bridging oxygen mightbe the main structural relaxation for inorganic glass.22) The in-crease in activation energy with Na2O content seems to contradictthe decrease in cluster size. Therefore, the concept of free vol-ume23),24) or variation in configurational entropy25) is expectedto relate to the increase in energy as discussed by Perez et al.26)
even though the mechanism is not still clear.The G(t) curve generally obeys the classical Maxwell model18)
terms and G¨ are listed in Table 2 against the ¸1. As seen in theresults, theG1 of the Li2O2SiO2 glass is larger than that of Na2OxSiO2 glasses. A similar tendency is found in the instantaneouselastic and shear moduli. These are consistent with the decrease incovalent character of the glass, which can be estimated by Sun’s
Fig. 9. Relationship between the shift factor ln¡T and reciprocal oftemperature T for Na2OxSiO2 (x = 2, 3, and 4) and Li2O2SiO2 glasses.
Fig. 8. Time dependence of shear relaxation moduli G(t) of (a)(c)Na2OxSiO2 (x = 2, 3, and 4) glasses and (d) Li2O2SiO2 glass.
Fig. 10. Schematic illustration of the two-term Maxwell model for therelaxation modulus.
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report,27) although the composition dependence of the G1 is notseen in the sodium system. However, the ¸1 of Li2O2SiO2 glassis shorter than that of Na2O2SiO2 glass. Even though the molarconcentrations of glass modifying oxides are the same, it is foundthe structural relaxation at the temperature, which might be due toslipping between glass network clusters, easily proceeds in thelithium silicate glass.
4.2 Dynamic viscoelastic measurementFigure 4 shows the broad contour of the stored elasticity
EBB(½) found in the region around 150300°C for the sodiumsystem. Since it has a wide temperature region, this indicates apresence of some structural relaxation, which may have a widedistribution of activation energy. The change in magnitude, how-ever, is quite small. Forry6) and Rötger7) observed two peaks dueto energy loss by internal friction measurement in binary silicateglasses. A peak from ¹50 to 50°C was attributed to diffusionof alkali ions.28) Another peak was located around 150250°C.Coenen29) suggested the energy loss peak, which was found inthe region, originates from the motion of non-bridging oxygens.Taylor28) also suggested the possibility of proton motion as theorigin of this peak. Moreover, the higher temperature peak ininternal friction was not remarkable for the lithium silicateglass.30) This is similar to the present result in Li2O2SiO2 glass.The region at higher temperatures is consistent with the presentbroad contour in the EBB(½) curve, though the origin of the peakis still controversial and macroscopic large deformation is notexpected to occur by these mechanisms.In the high temperature region above 400°C, EB(½) starts
to decrease around the glass transition temperature as seen inFigs. 3(a)3(c). The degree of drop at Tg tends to increase withincreasing Na2O concentration. As mentioned above, structuralrelaxation is expected due to slipping between network clustersaround non-bridging oxygens terminated by modifying cations.Therefore, a decrease in covalent characteristic around the non-bridging oxygens should lead to a rapid decrease in the elasticityEB(½) at Tg. Complex fluctuations are also observed in EB(½) andEBB(½) at vibration frequencies above 1Hz. Since this regioncorresponds to that of super-cooled liquid state, the network clus-ters are expected to break down into smaller sizes. The energyfor breaking down the network is expected to vary, resultingin complex fluctuations. Thus subdivision of the network isexpected to grow complicatedly in frequency with increasingtemperature above Tg. At the temperature where the bond breakdown occurs, elastic properties do not obey the time (frequency)temperature superposition principle. Koide et al.13) introducedln¡T both in the horizontal and vertical axes to make a mastercurve. A ln¡T in the vertical axis may be reasonable, because
relaxations due to diffusion of alkali ions and motion of non-bridging oxygens continuously exist even at high temperatures,and because thermal expansion may affect the shift of elasticmodulus. The EB(½) and EBB(½) curves were superposed onto acurve at the glass transition temperature by using the usual hori-zontal and vertical ln¡T. Figures 11(a)11(d) show the mastercurves of EB(½) and EBB(½) for Na2OxSiO2 (x = 2, 3 and 4) andLi2O2SiO2 glasses. As seen in the figures, the EB(½) and EBB(½)curves for sodium silicate glasses show almost the same profile.This suggests that the mechanism of structural relaxation, that is,distribution of structural relaxation time is independent of theNa2O content. Some departures from the curve are observed onthe higher frequency side of the EBB(½) curves. These departurescorrespond to complex fluctuations around the deformationtemperature which is observed to have temperature dependence(Fig. 3) only at high frequencies as expected from the abovediscussion. Moreover, other departures in the lower frequencyregion are observed only in the EBB(½) curve of Li2O2SiO2
glass. These data correspond to the results at high temperatures.As seen in Fig. 3(d), the EB(½) and EBB(½) values are scatteredat high temperatures above 550°C. These departures at lowerfrequencies are deduced to be due to crystallization. Eliminatingsome anomalous departures, therefore, the broad profile in theEBB(½) is expected to be strongly related to structural relaxationdue to slipping among the network clusters. In contrast, Li2O2SiO2 glass shows a similar profile in the EBB(½) master curve.However, the low frequency side below around 10¹2Hz in theprofile is missing compared to the sodium silicate glasses as seenin Fig. 11(d). This indicates that structural relaxation of Li2O2SiO2 glass is expected to proceed faster than sodium silicateglasses. The faster relaxation is in good agreement with theshorter relaxation time found in the analysis of G(t). The fasterrelaxation is also well consistent with the shorter ¸1 of about 30 s(Table 2) for the lithium silicate glass.
4.3 Injection testAs seen in both Figs. 6 and 7, Na2OxSiO2 (x = 2, 3, and 4)
glasses shows almost the same behavior on the injected volumeagainst pressing time and viscosity. This is consistent with theseglasses having the same frequency dependence as seen in theEB(½) and EBB(½) master curves. The loss elastic modulus extendsto lower frequencies than 10¹2 Hz and has long relaxation times:75, 178, and 268 s (Table 2) for Na2OxSiO2 (x = 2, 3, and 4)glasses, respectively. Therefore, deformation is not expected inthe sodium silicate glasses in a short period of the injection testexcept 600 s. In contrast, the injection seems to proceed faster inLi2O2SiO2 glass than sodium silicate glasses. The EBB(½) curveof Li2O2SiO2 glass does not have the structural relaxation partbelow 10¹2 Hz and also has a shorter relaxation time of 29 s inthe Maxwell model (Table 2), that is, faster relaxation than 100 sorder relaxation. It is deduced that the lack of slow relaxationcorresponds well with the faster injection in longer pressingperiods above 30 s for Li2O2SiO2 glass.
Kitamura: Compression creep and dynamic viscoelastic studies of binary sodium and lithium silicate glasses around deformation
temperatureJCS-Japan
726
¸1 increased with decreasing Na2O content, which correspondsto decreasing size of network cluster units. In contrast, the ¸1 ofLi2O2SiO2 glass was about one-third of that of Na2O2SiO2
Acknowledgement This work was carried out as a study ofCSTI, SIP Project (Development of Advanced Glass ProcessingTechnologies).
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Fig. 11. Master curves of (left side) storage elastic modulus EB(½) and (right side) loss elastic modulus EBB(½) of (a)(c)Na2OxSiO2 (x = 2, 3, and 4) glasses and (d) Li2O2SiO2 glass at each glass transition temperature (Table 1) as a standardtemperature. The curves were obtained by the time-temperature superposition principle using data shown in Fig. 5.
Journal of the Ceramic Society of Japan 125 [10] 721-727 2017 JCS-Japan