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Glass Physics and Chemistry, Vol. 28, No. 4, 2002, pp. 232–238.
Original Russian Text Copyright 2002 by Fizika i Khimiya Stekla, Startsev, Golubeva. Specific Features of Changes in the Properties
of One- and Two-Alkali Borate Glasses Containing Water:
III. Thermal Expansion and the Structural and Mechanical
Relaxation Parameters of Two-Alkali Borate Glasses
Yu. K. Startsev and O. Yu. Golubeva
Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, ul. Odoevskogo 24/2, St. Petersburg, 199155 Russia Abstract—The thermal expansion and stress relaxation in mixed alkali borate glasses containing lithium,
sodium, and potassium oxides with a total alkali oxide content of 15 mol % are measured on an inclined quartz
dilatometer and a relaxometer. The experimental data obtained are used to determine the thermal expansion
coefficients and the structural and mechanical relaxation parameters. No deviations from the additivity are
found in the concentration dependences of the thermal expansion coefficient and the calculated parameters
determining the width of the spectra of the structural and stress relaxation times. The IR absorption spectra of
the studied glasses are recorded in the range of stretching vibrations of hydroxyl groups. Analysis of the IR
spectra makes it possible to assume that the content of residual water in the structure of borate glasses affects
the manifestation of the mixed alkali effect in the properties of these glasses.
pairs of alkali oxides: Li2O–Na2O, Na2O–K2O, and The relaxation dependences of the properties in the Li2O–K2O. The total alkali oxide content was equal to glass transition range can be quantitatively described in 15 mol %. The as-batched and as-analyzed composi- the case when the kinetic parameters of the structural tions of the studied glasses and their designations were and mechanical relaxation are determined for the given in our previous work [2]. The glass designations glasses under investigation. However, no data on sys- indicate the type of alkali cations and their as-batched tematic investigations into the influence of composition content (in mol %) in the glass composition. For exam- on these parameters are available in the literature. It ple, the designation L3N12 corresponds to lithium was of interest to elucidate how the replacement of one sodium borate glass with the as-batched composition alkali oxide by another oxide in series of mixed alkali involving 3 mol % Li2O and 12 mol % Na2O.
borate glasses affects the parameters of their structural Boric acid and carbonates of the corresponding alkali metals (chemically pure) were used as the initial In our earlier work [1], we determined the tem- components for the preparation of the batch. The perature dependences of the viscosity in the range glasses were synthesized in a platinum crucible with a 1010–1013 dPa s for three series of one- and two-alkali volume of 200 ml in a Globar-heater electric furnace at borate glasses. When one alkali oxide was replaced by temperatures of 1150–1200°C for 1.5–2 h.
another oxide, we observed negative deviations from an The water content in the glasses under investigation additive behavior, i.e., the mixed alkali effect, in the was estimated by IR absorption spectroscopy. The tech- concentration dependences of the viscosity isotherms nique was described in detail in [1]. The IR spectra for the studied series of mixed alkali glasses.
were recorded on an SF-2-LSS spectrophotometer The aim of the present work was to investigate the designed at the Laboratory of Glass Properties manifestation of the mixed alkali effect in the concen- (Grebenshchikov Institute of Silicate Chemistry, Rus- tration dependences of the thermal expansion coeffi- sian Academy of Sciences) and a commercial Shi- cient, the structural relaxation parameters determined madzu IR-470 (Japan) spectrophotometer.1 from dilatometric curves, and the mechanical relax- All the glasses studied were synthesized under iden- ation parameters for two-alkali borate glasses.
tical conditions and likely involved approximatelyequal amounts of residual water. This assumption is confirmed by the estimates of water content in certain Glass synthesis. In this work, we studied three
1 We are grateful to V.Kh. Khalilov for performing the measure- series of mixed alkali borate glasses with the following ments on the IR-470 spectrophotometer.
1087-6596/02/2804-0232$27.00 2002 MAIK “Nauka /Interperiodica” SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES Designations and some properties of the studied glasses: thermal expansion coefficients below (α g) and above ( l) the glass transition range, glass transition temperatures Tg, and parameters of structural (bs and logKs) and mechanical (bσ and logKσ) glasses from the IR spectroscopic data. Since the vided a way of calculating the relaxation parameters [1] method of determining the water content in mixed of the Tool–Narayanaswamy model according to the alkali borate glasses has not been developed, the calcu- ISC algorithm [4]. The constant bs and the modulus Ks lations were carried out using the technique proposed characterizing the structural relaxation process were for one-alkali borate glasses [1]. The results of calcula- determined with a special optimizing program that tions showed that the water content in the glasses stud- minimizes the square of the difference between the computed and experimental values of the thermal Measurements of thermal expansion. The thermal
expansion in the dilatometric loops obtained upon cool- expansion of the glasses was investigated on an ing and subsequent heating at the same rate. The calcu- inclined quartz dilatometer with a small measuring load lated parameters bs and Ks are presented in the table.
[3] under thermocycling conditions. The rate of changein the temperature was equal to 3 K/min. The obtained Mechanical relaxation. The mechanical relaxation
dilatometric curves were used for determining the ther- was investigated on a relaxometer [5] whose operation mal expansion coefficients in ten-degree temperature is based on measuring the time dependence of the force ranges above the upper boundary of the glass transition under a constant deformation produced by a modified McLoughlin dynamometer [6]. Samples were prepared l ) and twenty-degree ranges below the lower boundary of the glass transition range (α in the form of cylindrical springs coiled from fibers drawn from melts of the studied glasses directly in the are listed in the table. The technique of measurements course of glass making. The prepared glass springs [7] and data processing was described in more detail in [1].
were not subjected to any additional treatment, whichruled out the possibility of reacting the samples with Structural relaxation. The dilatometer design
water vapors contained, for example, in the flame of a made it possible to perform measurements over a wide range of temperatures, including the glass transitionrange. By using this dilatometer, we measured the Numerous experiments (see, for example, [7–9]) dilatometric hysteresis loops whose processing pro- demonstrated that mechanical relaxation processes in GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002 glasses can be successfully described by the fractional Analogous signals from the reference thermocouple and the small-displacement transducer arrive at thevoltmeter and are digitized. The converter samples the corresponding channel through a multiplexer, converts the analogous signal into a binary decimal code, andtransmits it to computer memory for primary process- where σ(t) and σ0 are the stresses in the sample at the instants of time t and t = 0, respectively; τσ is the most The thermocouple thermopower and the signal from probable stress relaxation (Kohlrausch) time; and the the displacement transducer are the recorded quantities.
constant bσ (0 < bσ ≤ 1) determines the width of the The temperature with due regard for the applied correc- spectrum of the stress relaxation times τσ. The smaller tions and the displacement in terms of length are the the constant bσ, the longer the time it takes for the relaxation process to be completed. At bσ = 1, Eq. (1) The data obtained are corrected for systematic transforms into a simple exponential equation. At errors in measurements by a primary processing pro- present, in the literature on relaxation phenomena, gram. When operating with the relaxometer, one of Eq. (1) proposed by Kohlrausch [10] for representing these errors is the error of the thermopower measure- the stress relaxation in quartz fibers of electrometers is ment for a particular thermocouple. In order to allow referred to as the Kohlrausch–Williams–Watts equation for this error, the thermocouple in the operating posi- (see, for example, [11]). This equation is very conve- tion directly in the relaxometer furnace was preliminar- nient from the viewpoint of experimenters (because it ily calibrated against the melting temperatures of pure includes only two parameters!), even though it has metals followed by applying the corresponding correc- defied theoretical treatment by virtue of an infinite dis- tion to all the temperatures measured. As a conse- continuity at the time t = 0. However, this equation is quence, the error of the temperature measurement was used to advantage not only for the description of the reduced to ±0.5 K, variations in the temperature during mechanical relaxation and not only in inorganic isothermal treatments for one day did not exceed ±0.5 K, and the error of the stress measurement at a small-dis- De Bast and Gilard [12] showed that the ratio placement transducer sensitivity of 0.02 µm was as between the relaxation time τσ entering into Eq. (1) and small as ±0.5%. As a result of these errors, the errors of the viscosity of the studied glass is constant and inde- pendent of temperature (because the temperature dependences of the relaxation time and the viscosityare very similar to each other), that is, The investigation of the stress relaxation can be essentially simplified using a preliminary stabilization of the samples, i.e., such heat treatment which results in almost completion of the structural relaxation. Indeed, the study of the mechanical relaxation against the back- where Kσ is the constant numerically equal to such a ground of the structural relaxation involves additional viscosity of the glass at which the time τσ is equal to 1 s.
problems [13]. With the aim of overcoming these prob- The smaller the constant Kσ at a certain fixed viscosity, lems, experimenters should preliminarily determine the the lower the relaxation process rate. This circumstance parameters characterizing the kinetics of the structural permits one to represent the data obtained on the stress relaxation at different temperatures in the same plot in The mechanical relaxation in the stabilized samples can be studied by performing the following three addi- 0– log t , which is termed the mus- ter curve in the English-language literature [9].
tional operations: (1) the preliminary measurement of Therefore, the investigation into the kinetics of the temperature dependence of the viscosity, (2) the stress relaxation amounts to determining the parame- determination of the structural stabilization time at a chosen experimental temperature (for example, accord- ing to the procedure recommended in [14]), and (3) the In our relaxometer, the system of experimental data stabilization of the sample at the chosen temperature.
collection consists of the following components: an In a number of works (see, for example, [5, 13]), IBM PC AT 286 computer, a CAMAC or unibus data analysis of the experimental data with the use of Eq. (1) converter, a small-displacement transducer on the basis was reduced to the linearization of this equation by tak- of a mechanotron (a vacuum-tube twin diode with an ing the double logarithm and the determination of the elastic diaphragm) or an inductive transducer, a mea- suring instrument [a V7-28 digital voltmeter (for σ and bσ by the least-squares tech- CAMAC) or a V7-34 digital voltmeter (for unibus)], thermoelectric transducers (reference and controlling It follows from Eq. (1) and the results obtained by thermocouples), a temperature controller of the PTR- Kurkjian [8] that, when processing the experimental 105 type (AO Thermex), and a resistance furnace.
data on stress relaxation, the stress σ0 should be deter- GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002 SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES included the possibility of choosing the initial instant of time and the stress at this instant by a researcher.2 The concentration dependences of the glass transi- tion temperature calculated from the dilatometric curves obtained upon cooling of the glasses studied are plotted in Fig. 1. This figure also shows the concentra- tion dependences of the structural thermal expansion coefficient αs, which is equal to the difference between the thermal expansion coefficients determined at tem- peratures above and below the glass transition range(α s = αl – αg ). The lines in Fig. 1 are represented by the polynomials of best approximation to the experimental The glass transition temperatures of glasses in all three series are characterized by the negative deviation from the additivity. This agrees with the behavior observed for the concentration dependences of the vis- The replacement of smaller sized cations by larger sized cations leads to an increase in the structural ther- mal expansion coefficient. Note that this increase is largest for lithium potassium series and reflects the ten- dency to a change in the amount of fourfold-coordi- nated boron in the glass structure [15]. No deviations from the additivity are found in the concentration dependences of the structural thermal expansion coeffi- Figure 2 displays the concentration dependences of the kinetic parameters of the structural (bs) and mechanical (bσ) relaxations and the dependences of the Kohlrausch relaxation times τs and τσ. These times were calculated by the relationship Kj = η/ τj, where Kj are the moduli derived by processing the data on the structural (j ≡ s) and mechanical (j ≡ σ) relaxations.
The relaxation times for lithium sodium, sodium potas- sium, and lithium potassium glasses are given at 420, 400, and 410°C, respectively. The solid lines in Fig. 2are represented by the polynomials of best approxima- Fig. 1. Concentration dependences of (1) the glass transi-
tion to the experimental data on the parameters τj tion temperature Tg and (2) the structural thermal expansion coefficient αs for (a) lithium sodium, (b) sodium potassium,and (c) lithium potassium glasses.
As can be seen from Fig. 2, the behavior of the con- centration dependences of the relaxation times forglasses in all series reflects the behavior of the concen- mined as precisely as possible; i.e., it is necessary to tration dependences of the viscosity. It should be noted account for the noninstantaneous character of deforma- that the structural relaxation times are somewhat longer tion. The influence of this factor resides in the fact that than the mechanical relaxation times. This is in agree- the first reliable measurement of relaxing stresses can ment with a similar difference previously found for be carried out only beginning with a certain instant of commercial multicomponent silicate glasses [5, 7, 9, time when the relaxation can proceed in part, and, hence, processes described by shorter relaxation times As one alkali oxide is replaced by another alkali will be completed. For this reason, the zeroth instant of time should be chosen between the last measurement s and bσ have a certain tendency to increase; however, this increase is within the limits of before the starting of deformation and the first mea-surement after its completion. The algorithm used in 2 The computer code for this algorithm was developed by our work for determining the parameters τσ and bσ A.I. Priven (AO Thermex, St. Petersburg).
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002 Fig. 2. Concentration dependences of the kinetic parameters of the structural (bs and τs) and mechanical (bσ and τσ) relaxations for
(a) lithium sodium, (b) sodium potassium, and (c) lithium potassium glasses: (1) bs, (2) τs, (3) bσ, and (4) τσ.
their computational error. The dependences of the to their number calculated from the additivity principle parameters bs and bσ do not deviate from the additive Our investigation of the thermal expansion and the structural and mechanical relaxations in alkali borate glasses with a total alkali oxide content of 15 mol %revealed that the mixed alkali effect manifesting itself Zhong and Bray [16] studied mixed alkali borate in the deviation from the additivity is not observed in glasses at a total alkali oxide content of 40 mol % anddrew the inference that the manifestation of the the concentration dependences of these properties. The mixed alkali effect in the properties of these glasses found linear dependences of the properties allow us to is associated with a decrease in the number of boron assume that the content of fourfold-coordinated boron atoms in the fourfold-coordinated state as compared obeys the additivity principle upon replacement of one GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002 SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES glasses, the intensities of the absorption bands with a groups are close to each other, whereas the absorption bands with a maximum at 3.5 µm have different inten-sities. According to the data obtained in different works [17, 18], the latter absorption band is assigned to the so-called bound hydroxyl groups linked by hydrogen bonds to the nonbridging oxygen atoms that are formed upon introduction of alkali oxides into the glass struc-ture. As can be seen from Fig. 3, the intensity of the absorption band associated with the bound hydroxyl groups for mixed alkali glasses of all the series studiedis lower than that for the corresponding binary glasses.
This can indicate that a smaller number of hydrogen bonds are formed in the structure of alkali borate glasses containing two alkali oxides.
The replacement of smaller sized alkali cations by larger sized cations results in a decrease in the number of hydrogen bonds and a linear decrease in the numberof fourfold-coordinated boron atoms in mixed alkali glasses. This favors the viscous flow and leads to a neg- ative deviation from the additivity in the concentrationdependences of the viscosity without deviations from the additivity in the concentration dependences of thethermal expansion coefficient and the relaxation Moreover, in our previous work [2], we noted that no mixed alkali effect is observed for anhydrous glasses. This fact can also be explained by the possibleinfluence of two alkali oxides in the glass composition The results of the above investigation into the con- centration dependences of the thermal expansion coef-ficient and the structural and mechanical relaxationparameters for mixed alkali borate glasses with a total Fig. 3. Comparison of the IR absorption spectra of (a) lith-
ium sodium, (b) sodium potassium, and (c) lithium potas-
alkali oxide content of 15 mol % can be summarized as sium glasses: (1) L15B, (2) LN7.5, (3) N15B, (4) NK7.5, (5) K15B, and (6) LK7.5 (see table).
(1) No deviation from the additivity is found for the structural thermal expansion coefficient and the struc- alkali oxide by another alkali oxide in the glasses of the tural and mechanical relaxation parameters upon replacement of one alkali oxide by another alkali oxidein the glass composition.
On the other hand, in our earlier work [2], we showed that the concentration dependences of the vis- (2) The mixed alkali effect in the concentration cosity for the same glasses are characterized by the dependences of the glass transition temperature and the mixed alkali affect manifesting itself in negative devia- structural and mechanical relaxation times manifests itself in negative deviations from the additivity. Thisagrees with the behavior observed for the concentration The IR absorption spectra K(λ) (where K is the absorption coefficient in terms of cm–1 and λ is thewavelength in terms of µm) of mixed alkali borate (3) The replacement of one alkali oxide by another glasses with the same contents of alkali oxides for three oxide leads to a change in the parameter bs characteriz- studied series and the spectra of the corresponding ing the structural relaxation and does not noticeably binary alkali borate glasses are compared in Fig. 3. It is affect the parameter bσ characterizing the stress relax- seen from this figure that, for binary and mixed alkali GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002 (4) The content of residual structural water in mixed 9. Mills, J.J. and Sievert, J.L., Stress Relaxation Modulus alkali borate glasses likely affects the manifestation of of a Commercial Glass, J. Am. Ceram. Soc., 1973, the mixed alkali effect in the properties of these glasses.
10. Kohlrausch, F., Ueber die elastische Nachwirkung bei der Torsion, Ann. Phys. Chem., 1863, vol. 119, pp. 337– 1. Startsev, Yu.K. and Golubeva, O.Yu., Specific Features 11. Cunat, Ch., The Distribution of Non-Linear Relaxations of Changes in the Properties of One- and Two-Alkali (DNLR) Approach and Relaxation Phenomena: Part I.
Borate Glasses Containing Water: I. Viscosity, Thermal Historical Account and DNLR Formalism, Mech. Time- Expansion, and Kinetics of Structural Relaxation in Depend. Mater., 2001, vol. 5, no. 1, pp. 39–65.
Binary Alkali Borate Glasses, Fiz. Khim. Stekla, 2002,vol. 28, no. 3, pp. 230–245 [Glass Phys. Chem. (Engl.
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GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002

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