Viscosity of Glass and Glass-Forming Melts

  • Ulrich FotheringhamEmail author
Part of the Springer Handbooks book series (SHB)


Beginning with a selection of commercial glasses, the typical temperature course of the shear viscosity of inorganic glasses is discussed. The significance of the different temperature ranges for the different production steps (melting, hotforming, annealing) is explained. The viscosity-based typology of glasses as long or short is introduced and discussed with respect to glass composition.

The glass viscosity measurement methods conforming to ISO 7884 1-7 are described. This includes the individual rules for the determination of the shear viscosity fix points. Special shear viscosity measurement techniques applying to extremely high or low viscosity values are also described.

Concerning viscosity theory and modeling, Adams–Gibbs theory, Angell's fragility concept, and the semiempirical models after Vogel–Fulcher–Tammann (), Avramov–Milchev (), and Waterton–Mauro–Yue–Ellison–Gupta–Allan () are presented, applied to different glasses, and compared.

Viscoelastic behavior is discussed with respect both to shear and bulk deformation, including Boltzmann's superposition principle, the particular effect of delayed elasticity, the special viscoelastic models after Maxwell, Kelvin–Voigt, Burger etc. as well as special mathematics, i. e., the stretched exponential or Kohlrausch(–Williams–Watts) function. Viscoelastic characterization by dynamic mechanical analysis and by reversible compression in a quasi-isostatic device are discussed considering experimental data.


  1. D.L. Landau, E.M. Lifshitz: Fluid Mechanics, Course on Theoretical Physics, Vol. 6, 2nd edn. (Pergamon, Oxford 1987)Google Scholar
  2. F. Irgens: Rheology and Non-Newtonian Fluids (Springer, Cham 2014)CrossRefGoogle Scholar
  3. G.J. Janz: Molten salts data as reference standards for density, surface tension, viscosity, and electrical conductance: KNO3 and NaCl, J. Phys. Chem. Ref. Data 9, 791 (1980)CrossRefGoogle Scholar
  4. K.H. Sun: Fundamental condition of glass formation, J. Am. Ceram. Soc. 30, 277–281 (1947)CrossRefGoogle Scholar
  5. A. Dietzel: Die Kationenfeldstärken und ihre Beziehungen zu Entglasungsvorgängen, zur Verbindungsbildung und zu den Schmelzpunkten von Silikaten, Z. Elektrochem. 48, 9–23 (1942)Google Scholar
  6. ISO 7884-1: Glass – Viscosity and Viscosimetric Fix Points – Part 1: Principle for Determining Viscosity and Viscosimetric Fix Points (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  7. M. Kuhr: Analytische Methoden zur Untersuchung von Schmelzaggregaten. In: Chemische, Physikalische und Emissionsrelevante Analytik für die Glasindustrie, HVG-Fortbildungskurs, (Verlag der Deutschen Glastechnischen Gesellschaft, Offenbach 2015)Google Scholar
  8. U. Fotheringham, W. Kob, K. Binder, U. Buchenau, A. Wischnewski, R. Sprengard, S. Reinsch, R. Müller: Dynamics of the Glass Structure. In: Analysis of the Composition and Structure of Glass and Glass Ceramics, Schott Series on Glass and Glass Ceramics, ed. by H. Bach, D. Krause (Springer, Berlin 1999)Google Scholar
  9. SCHOTT AG: Technical Glasses Handbook, 18.11.15_final_schott_technical_glasses_row.pdf, available from (2014)
  10. C.A. Angell: Strong and fragile liquids. In: Relaxations in Complex Systems, ed. by K.L. Ngai, G.B. Write (National Technical Information Service, US Department of Commerce, Springeld 1985)Google Scholar
  11. ISO 7884-2 Glass – Viscosity and Viscosimetric Fix Points – Part 2: Determination of Viscosity by Means of Rotation Viscosimeters (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  12. ISO 7884-5: Glass – Viscosity and Viscosimetric Fix Points – Part 5: Determination of Viscosity by Sinking Bar Viscosimeter (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  13. ISO 7884-3: Glass – Viscosity and Viscosimetric Fix Points – Part 3: Determination of Viscosity by Fibre Elongation Viscosimeter (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  14. ISO 7884-6: Glass – Viscosity and Viscosimetric Fix Points – Part 6: Determination of Softening Point (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  15. ISO 7884-4: Glass – Viscosity and Viscosimetric Fix Points – Part 4: Determination of Viscosity by Beam Bending (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  16. G.W. Scherer: Relaxation in Glass and Composites (Krieger, Malabar 1992)Google Scholar
  17. ISO 7884-7: Glass – Viscosity and Viscosimetric Fix Points – Part 7: Determination of Annealing Point and Strain Point by Beam Bending (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  18. V.P. Klyuev, A.S. Totesh: Metody i Apparatura Dlya Kontrolya Vyazkosti Stekla (Methods and Instruments for Testing the Viscosity of Glasses) (VNIIESM, Moscow 1975), cited after: S.M. Rekhson: Viscosity and stress relaxation in commercial glasses in the glass transition region, J. Non-Cryst. Solids 38-39, 457–462 (1980)Google Scholar
  19. H. Kadali: Experimental Characterization of Stress Relaxation in Glass, Ph.D. Thesis (Clemson University, Clemson 2009)Google Scholar
  20. L.S. Negi: Strength of Materials (Tata McGraw-Hill, New Delhi 2008)Google Scholar
  21. G.J. Dienes, H.F. Klemm: Theory and application of the parallel plate plastometer, J. Appl. Phys. 17(6), 458–471 (1946)CrossRefGoogle Scholar
  22. A.N. Gent: Theory of the parallel plate viscometer, Br. J. Appl. Phys. 11, 85–87 (1960)CrossRefGoogle Scholar
  23. D. Joshi, P.F. Joseph: Parallel plate viscometry for glass at high viscosity, J. Am. Ceram. Soc. 97, 354–357 (2014)CrossRefGoogle Scholar
  24. L. Shartsis, S. Spinner: Viscosity and density of molten optical glasses, J. Res. Natl. Bur. Stand. 46(3), 176–194 (1951)CrossRefGoogle Scholar
  25. J. de Bast, P. Gilard: Rheologie du verre sous constraint dans l'intervalle de transformation, No. 32 (L'Institute pour l'Encouragement de la Recherche Scientifique dans l'Industrie et l'Agriculture (IRSIA), Colfontaine 1965) 23Google Scholar
  26. W. Beitz, K.-H. Küttner (Eds.): Dubbel, Taschenbuch für den Maschinenbau, 18th edn. (Springer, Berlin 1998) pp. C8–C26Google Scholar
  27. H. Serizawa, C.A. Lewinsohn, H. Murakawa: FEM evaluation of asymmetrical four-point bending test of SiC/SiC composite joints, Transactions JWRI 30(1), 119–125 (2001)Google Scholar
  28. U. Fotheringham: Dynamic mechanical analysis with an asymmetric 4-point bending mode. In: The American Ceramic Society Spring 2006 Glass & Optical Materials Division Meeting, Greenville (2006)Google Scholar
  29. S.P. Jaccani, L. Huang: A simple and convenient set-up for high-temperature Brillouin light scattering, J. Phys. D: Appl. Phys. 45, 275302 (2012)CrossRefGoogle Scholar
  30. M. Guerette, L. Huang: Understanding sodium borate glasses and melts from their elastic response to temperature, Int. J. of Appl. Glass Sci. 7(4), 452–463 (2016)CrossRefGoogle Scholar
  31. R.E. Wetton, R.D.L. Marsh, J.G. Van-de-Velde: Theory and application of dynamic mechanical thermal analysis, Thermochim. Acta 175, 1–11 (1991)CrossRefGoogle Scholar
  32. U. Fotheringham, R. Wurth, C. Rüssel: Thermal analyses to assess diffusion kinetics in the nano-sized interspaces between the growing crystals of a glass ceramics, Thermochim. Acta 522, 144–150 (2011)CrossRefGoogle Scholar
  33. G.C. Berry, D.J. Plazek: On the use of stretched-exponential functions for both linear viscoelastic creep and stress relaxation, Rheol. Acta 36, 320–329 (1997)CrossRefGoogle Scholar
  34. R.-G. Duan, G. Roebben, O. Van der Biest: Glass microstructure evaluations using high temperature mechanical spectroscopy measurements, J. Non-Cryst. Solids 316, 138–145 (2003)CrossRefGoogle Scholar
  35. A. Granato: The shear modulus of liquids, J. Phys. IV Colloq. 06(C8), C8-1–C8-9 (1996)Google Scholar
  36. P. Tordjeman, J.M. Felio, L. Gazagnes: Thermal effects on viscoelastic properties of silicate glass melts, J. Chem. Phys. 119(24), 13129–13134 (2003)CrossRefGoogle Scholar
  37. Y. Yue, R. Brückner: A new description and interpretation of the flow behaviour of glass forming melts, J. Non-Cryst. Solids 180, 66–79 (1994)CrossRefGoogle Scholar
  38. G. Adam, J. Gibbs: On the temperature dependence of cooperative relaxation properties in glass-forming liquids, J. Chem. Phys. 43, 139–146 (1965)CrossRefGoogle Scholar
  39. C.A. Angell: Relaxation in liquids, polymers and plastic crystals – Strong/fragile patterns and problems, J. Non-Cryst. Solids 131–133, 13–31 (1991)CrossRefGoogle Scholar
  40. U. Fotheringham, A. Baltes, R. Müller, R. Conradt: The residual configurational entropy below the glass transition: Determination for two commercial optical glasses, J. Non-Cryst. Solids 355, 642–652 (2009)CrossRefGoogle Scholar
  41. U. Fotheringham, R. Müller, K. Erb, A. Baltes, F. Siebers, E. Weiß, R. Dudek: Evaluation of the calorimetric glass transition of glasses and glass ceramics with respect to structural relaxation and dimensional stability, Thermochim. Acta 461, 72–81 (2007)CrossRefGoogle Scholar
  42. C.A. Angell, W. Sichina: Thermodynamics of the glass transition: Empirical aspects, Ann. N.Y. Acad. Sci. 279, 53–67 (1976)CrossRefGoogle Scholar
  43. C.A. Angell: Spectroscopy simulation and scattering, and the medium range order problem in glass, J. Non-Cryst. Solids 73, 1–17 (1985)CrossRefGoogle Scholar
  44. C.A. Angell: Formation of glasses from liquids and biopolymers, Science 267, 1924–1935 (1995)CrossRefGoogle Scholar
  45. C.A. Angell: Structural instability and relaxation in liquid and glassy phases near the fragile liquid limit, J. Non-Cryst. Solids 102, 205–221 (1988)CrossRefGoogle Scholar
  46. A.L. Greer, K.F. Kelton, S. Sastry (Eds.): Proc. Symp. Frag. Glass-Form. Liq. TRIPS Series, Vol. 13 (Hindustan Book Agency, Gurgaon 2014)Google Scholar
  47. S.N. Glasstone, K. Laidler, H. Eyring: The Theory of Rate Processes (McGraw-Hill, New York 1941)Google Scholar
  48. O.V. Mazurin, Y.K. Startsev, S.V. Stoljar: Temperature dependences of viscosity of glass-forming substances at constant fictive temperatures, J. Non-Cryst. Solids 52, 105–114 (1982)CrossRefGoogle Scholar
  49. Q. Zheng, J.C. Mauro, A.J. Ellison, M. Potuzak, Y. Yue: Universality of the high-temperature viscosity limit of silicate liquids, Phys. Rev. B 83, 212202 (2011)CrossRefGoogle Scholar
  50. ISO 7884-1: Glass – Viscosity and Viscosimetric Fix Points – Part 1: Principles for Determining Viscosity and Viscometric Fixed Points (International Organization for Standardization ISO Central Secretariat, Geneva 1987)Google Scholar
  51. H. Vogel: Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten, Phys Z. 22, 645–646 (1921)Google Scholar
  52. G.S. Fulcher: Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8, 339–355 (1925)CrossRefGoogle Scholar
  53. G. Tammann, W. Hesse: Die Abhängigkeit der Viskosität von der Temperatur bei unterkühlten Flüssigkeiten, Z. Anorg. Allg. Chem. 156, 245–257 (1926)CrossRefGoogle Scholar
  54. I.M. Hodge: Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 6. Adam-Gibbs formulation of nonlinearity, Macromolecules 20, 2897–2908 (1987)CrossRefGoogle Scholar
  55. U. Fotheringham, F.-T. Lentes, D.B. Dingwell: The Predictive power of three parameter viscosity models. In: Proc. 2011 Glass Opt. Mater. Div. Annu. Meet (American Ceramic Society, Savannah 2011)Google Scholar
  56. J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, D.C. Allan: Viscosity of glass-forming liquids, Proc. Natl. Acad. Sci. 106(47), 19780–19784 (2009)CrossRefGoogle Scholar
  57. I. Avramov, A. Milchev: Effect of disorder on diffusion and viscosity in condensed systems, J. Non-Cryst. Solids 104, 253–260 (1988)CrossRefGoogle Scholar
  58. I. Avramov: Viscosity of glassforming melts, J. Non-Cryst. Solids 238, 6–10 (1998)CrossRefGoogle Scholar
  59. H. Bässler: Viscous flow in supercooled liquids analyzed in terms of transport theory for random media with energetic disorder, Phys. Rev. Lett. 58, 767 (1987)CrossRefGoogle Scholar
  60. S.C. Waterton: The viscosity-temperature relationship and some inferences on the nature of molten and of plastic glass, J. Soc. Technol. 16, 244–249 (1932)Google Scholar
  61. A.L. Zijlstra: The viscosity of some silicate glasses in connection with the thermal history, Phys. Chem. Glasses 4, 143–151 (1963)Google Scholar
  62. G. Meerlender: Die erweiterte Jenckel-Gleichung, eine leistungsfähige Viskositäts-Temperatur-Formel, I. Eigenschaften und Anwendbarkeit auf die numerische Interpolation, Rheol. Acta 6(4), 143–151 (1967)CrossRefGoogle Scholar
  63. P.K. Gupta, J.C. Mauro: Composition dependence of glass transition temperature and fragility. I. A topological model incorporating temperature-dependent constraints, J. Chem. Phys. 130, 094503 (2009)CrossRefGoogle Scholar
  64. I.S. Gutzow, J. Schmelzer: The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization (Springer, Berlin 2013)CrossRefGoogle Scholar
  65. C. Alba-Simionesco: Isothermal glass transitions in supercooled and overcompressed liquids, J. Chem. Phys. 100, 2250–2257 (1994)CrossRefGoogle Scholar
  66. SCHOTT AG: Material Safety Data Sheets (SCHOTT AG, Mainz 2005)Google Scholar
  67. C. Bienert: Measurement of the Dimensional Relaxation Effect in Optical Glasses, Diploma Thesis (University of Erlangen-Nürnberg, Erlangen 2007)Google Scholar
  68. U. Fotheringham, O. Sohr, P. Fischer, G. Westenberger, D. Frost, C. Bienert, R. Weißmann, K. Richardson: Optische und volumetrische Messungen an Gigapascal-verdichteten optischen Gläsern, dgg journal 9(2), 32–33 (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of Materials DevelopmentSCHOTT AGMainzGermany

Personalised recommendations