Abstract
The relaxation parameter K sthat is equal to the ratio of the viscosity η to the Kohlrausch volume relaxation time τ s is analyzed. It is shown that this parameter can be evaluated from the temperature T 13(corresponding to a viscosity of 1013P) and the glass transition temperature T 8 +determined from the dilatometric heating curve. The maximum error of the estimate with due regard for experimental errors is equal to ± (0.4–0.5) log K sfor “strong” glasses and ±( 0.6–0.8) log K sfor “fragile” glasses, which, in both cases, corresponds to a change in the relaxation times with a change in the temperature by ±( 8–10) K. It is revealed that the viscosity, the Kohlrausch volume relaxation time τ s , and the shear modulus Gof glass-forming materials in silicate, borate, and germanate systems satisfy the relationship log(τ s G/η) ≈ 1. The procedure for calculating the temperature dependences of the viscosity and the relaxation times in the glass transition range from the chemical composition and the T 8 +temperature for glass-forming melts in the above systems is proposed. The root-mean-square deviations between the calculated and experimental temperatures T 11and T 13are equal to ±( 6–8) K for all the studied (silicate, borate, germanate, and mixed) oxide glass-forming systems. The proposed relationships can be useful for evaluating the boundaries of the annealing range and changes in the properties and their temperature coefficients upon cooling of glass-forming melts.
Similar content being viewed by others
REFERENCES
Priven, A.I., Calculation of the Viscosity of Glass-Forming Melts: IV. A Unified Method for Calculating the Viscosity of Silicate and Aluminate Melts, Fiz. Khim. Stekla, 1998, vol. 24, no. 1, pp. 48-62 [Glass Phys. Chem. (Engl. transl.), 1998, vol. 24, no. 1, pp. 31-40].
Priven, A.I., Calculation of the Viscosity of Glass-Forming Melts: V. Binary Borate Systems, Fiz. Khim. Stekla, 2000, vol. 26, no. 6, pp. 783-812 [Glass Phys. Chem. (Engl. transl.), 2000, vol. 26, no. 6, pp. 541-558].
Priven, A.I., Calculation of the Viscosity of Glass-Forming Melts: VI. The R2O-B2O3-SiO2 and RO-B2O3-SiO2 Ternary Borosilicate Systems, Fiz. Khim. Stekla, 2001, vol. 27, no. 4, pp. 536-552 [Glass Phys. Chem. (Engl. transl.), 2001, vol. 27, no. 4, pp. 360-370].
SciGlass (Glass Property Information System), Version 4.0, Lexington: SciVision, 2000.
Mazurin, O.V., Steklovanie (Glass Transition), Leningrad: Nauka, 1986.
Startsev, Yu.K., Livshits, V.Ya., Nakhapetyan, R.A., and Novotny, V., Properties of Glasses Synthesized by Batch Melting and Ion Exchange, Proceedings of the XV International Congress on Glass, Leningrad, 1989, vol. 2b, pp. 85-91.
Startsev, Yu.K., Klyuev, V.P., and Vostrikova, M.S., Determination of Glass Transition Temperatures from Simultaneously Recorded Dependences of the Expansion and Electrical Conductivity, Fiz. Khim. Stekla, 1978, vol. 4, no. 3, pp. 278-288.
Klyuev, V.P. and Bulaeva, A.V., Viscosity and Thermal Expansion of Lead Borate Glasses in the Glass Transition Range, Fiz. Khim. Stekla, 1980, vol. 6, no. 6, pp. 674-678.
Klyuev, V.P. and Mazurin, O.V., Structural Temperature Coefficients of Specific Volume and Viscosity of Lead Borate Glass Forming Melts, J. Non-Cryst. Solids, 1980, vols. 38-39,part 1, pp. 117-122.
Klyuev, V.P. and Pevzner, B.Z., Influence of Aluminum and Gallium Oxides on the Thermal Expansion and Viscosity of Barium Borate Melts, Fiz. Khim. Stekla, 1998, vol. 24, no. 4, pp. 532-545 [Glass Phys. Chem. (Engl. transl.), 1998, vol. 24, no. 4, pp. 372-381].
Mazurin, O.V., Streltsina, M.V., and Shvaiko-Shvaikovskaya, T.P., Svoistva stekol i stekloobrazuyushchikh rasplavov. Spravochnik. Tom 1. Stekloobraznyi kremnezem i dvukhkomponentnye silikatnye sistemy, Leningrad: Nauka, 1973. Handbook of Glass Data: Part A. Silica Glass and Binary Silicate Glasses: Physical Science Data 15, Amsterdam: Elsevier, 1983.
Romanova, N.V. and Nemilov, S.V., A Study of the Viscosity of Glasses in the BaO-B2O3, BaO-B2O3-La2O3, and CdO-B2O3-La2O3 Systems in the Softening Range, Izv. Akad. Nauk SSSR, Neorg. Mater., 1970, vol. 6, no. 7, pp. 1322-1326.
Klyuev, V.P. and Chernousov, M.A., An Automated Dilatometer with a Low Measuring Load, III Vsesoyuznoe soveshchanie “Metody i pribory dlya tochnykh dilatometricheskikh issledovanii materialov v shirokom diapazone temperatur,” Tezisy dokladov (III All-Union Conference Methods and Instruments for Precision Dilatometric Investigations of Materials over a Wide Range of Temperatures, Abstracts of Papers), Leningrad: VNIIM, 1984, pp. 53-54.
Priven', A.I., Volume Relaxation in 5Na2O · 95B2O3 Glass, Fiz. Khim. Stekla, 1994, vol. 20, no. 6, pp. 735-747 [Glass Phys. Chem. (Engl. transl.), 1994, vol. 20, no. 6, pp. 507-514].
Mazurin, O.V., Relaxation Phenomena in Glass, “Glass-77,” Prague, 1977, vol. 1, pp. 129-169.
Ducroux, J.-P., Rekhson, S.M., and Merat, F.L., Structural Relaxation in Thermorheologically Complex Materials, J. Non-Cryst. Solids, 1994, vols. 172-174, pp. 541-553.
Priven, A.I., Calculation of the Viscosity of Glass-Forming Melts: I. The Li2O-Na2O-K2O-SiO2 System, Fiz. Khim. Stekla, 1997, vol. 23, no. 5, pp. 491-505 [Glass Phys. Chem. (Engl. transl.), 1997, vol. 23, no. 5, pp. 344-353].
Priven, A.I., Calculation of the Temperature Coefficient of Viscosity Logarithm log / logT for Oxide Melts in the Glass Transition Range from Their Composition, Fiz. Khim. Stekla, 2000, vol. 26, no. 5, pp. 653-677 [Glass Phys. Chem. (Engl. transl.), 2000, vol. 26, no. 5, pp. 455-469].
Shelby, J.E., Properties and Structure of B2O3-GeO2 Glasses, J. Appl. Phys., 1974, vol. 45, no. 12, pp. 5272-5277.
Nemilov, S.V., A Systematic Investigation into the Influence of Sodium Oxide Additives on the Viscosity of Vitreous Germanium Dioxide, Zh. Prikl. Khim. (Leningrad), 1972, vol. 45, no. 2, pp. 256-262.
Rekhson, S.M., Structural and Shear Stress Relaxation in the Glass Transition Range, Fiz. Khim. Stekla, 1975, vol. 1, no. 5, pp. 443-446.
Nemilov, S.V. and Komarova, N.V., The Viscosity, Elastic Properties, and Structure of Glasses in the GeO2-B2O3 and GeO2-B2O3-La2O3 Systems, Fiz. Khim. Stekla, 1976, vol. 2, no. 3, pp. 262-267.
Shaw, R.R. and Uhlmann, D.R., Effect of Phase Separation on the Properties of Simple Glasses: II. Elastic Properties, J. Non-Cryst. Solids, 1971, vol. 5, no. 3, pp. 237-263.
Matusita, K., Yokota, R., Kimijima, T., Komatsu, T., and Ihara, C., Compositional Trends in Photoelastic Constants of Borate Glasses, J. Am. Ceram. Soc., 1984, vol. 67, no. 4, pp. 261-265.
Osaka, A., Soga, N., and Kunugi, M., Elastic Constants and Vickers Hardness of Lead Borate Glasses, J. Soc. Mater. Sci. Jpn., 1974, vol. 23, no. 245, pp. 128-131.
Mazurin, O.V., Klyuev, V.P., and Stolyar, S.V., Temperature Dependences of Structural Relaxation Times at Constant Fictive Temperatures in Oxide Glasses, Glastech. Ber., 1983, vol. 56, no. 2, pp. 1148-1153.
Shelby, J.E., Thermal Expansion of Mixed-Alkali Silicate Glasses, J. Appl. Phys., 1976, vol. 47, no. 10, pp. 4489-4496.
Rekhson, S.M. and Mazurin, O.V., Stress and Structural Relaxation in Na2O-CaO-SiO2 Glass, J. Am. Ceram. Soc., 1974, vol. 57, no. 7, pp. 327-328.
Priven', A.I. and Startsev, Yu.K., Calculation of Constants for the Relaxation Model of Glass Transition, Fiz. Khim. Stekla, 1993, vol. 19, no. 2, pp. 316-328 [Glass Phys. Chem. (Engl. transl.), 1993, vol. 19, no. 2, pp. 157-163].
Mazurin, O.V., Tret'yakova, N.I., and Shvaiko-Shvaikovskaya, T.P., Metod rascheta vyazkosti silikatnykh stekol (A Method for Calculating the Viscosity of Silicate Glasses), Available from VINITI, 1969, Moscow, no. 1091-69dep.
Lyon, K.C., Prediction of the Viscosities of “Soda-Lime” Silica Glasses, J. Res. Natl. Bur. Stand. (U.S.), 1974, vol. 78A, no. 4, pp. 497-503.
Mazurin, O.V. and Tret'yakova, N.I., On the Interrelation between the Viscosity and Phase Diagram of Glasses in the Na2O-BaO-SiO2 System, Neorg. Mater., 1970, vol. 6, no. 11, pp. 2022-2026.
Appen, A.A., Khimiya stekla (The Chemistry of Glasses), Leningrad: Khimiya, 1970.
Gan Fuxi, A New System of Calculating the Properties of Inorganic Oxide Glasses, Sci. Sin. (Engl. Ed.), 1974, vol. 17, no. 4, pp. 533-551.
Alekseenko, M.P. and Shchavelev, O.S., Thermal and Thermooptical Properties of Glasses, in Fizikokhimicheskie osnovy proizvodstva opticheskogo stekla (Physicochemical Principles of Manufacturing of Optical Glass), Demkina, L.I., Ed., Leningrad: Khimiya, 1976, pp. 117-134.
Takahashi, K., Thermal Expansion Coefficients and Structure of Glass, J. Soc. Glass Technol., 1953, vol. 37, no. 175, pp. 3N-7N.
Mazurin, O.V., Rekhson, S.M., and Startsev, Yu.K., On the Role of the Viscosity in Calculation of Glass Properties in Glass Transition Range, Fiz. Khim. Stekla, 1975, vol. 1, no. 5, pp. 438-442.
Moynihan, C.T., Easteal, A.J., DeBolt, M.A., and Tucker, J., Dependence of the Fictive Temperature of Glass on Cooling Rate, J. Am. Ceram. Soc., 1976, vol. 59, nos. 1-2, pp. 12-16.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Priven, A.I. Calculation of Temperature Dependences of the Viscosity and Volume Relaxation Time for Oxide Glass-Forming Melts from Chemical Composition and Dilatometric Glass Transition Temperature. Glass Physics and Chemistry 27, 527–542 (2001). https://doi.org/10.1023/A:1013298225368
Issue Date:
DOI: https://doi.org/10.1023/A:1013298225368