Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes

Abstract

The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, τ, consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log10 units of time above τ. In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; τS = ηS/G (where τS is the shear relaxation time, G is the shear modulus at infinite frequency and ηS is the zero frequency shear viscosity). The value of G known for SiO2 and several other silicate glasses. The shear modulus, G , and the bulk modulus, K , are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to ηS, G may be considered a constant (independent of composition and temperature) and the value of ηS, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.

For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from 29Si NMR studies.

Using data obtained over a range of frequencies and strain-rates we illustrate the significance of relaxed versus unrelaxed behavior in laboratory experiments on silicate melts. Similarly, using strain-rate estimates for magmatic processes we evaluate the significance of the liquid-glass transition in igneous petrogenesis.

This is a preview of subscription content, log in to check access.

References

  1. Angell CA (1984) Strong and fragile liquids. Relaxations in Complex Systems. Ngai KL and Wright GB (eds) Office of Naval Research and National Technical Information Service

  2. Angell CA, Torell LM (1983) Short time structural relaxation processes in liquids: comparison of experimental and computer simulation glass transition on picosecond timescales. J Chem Phys 78:937–945

  3. Angell CA, Cheesemen PA, Kadiyala RR (1987) Diffusivity and thermodynamic properties of diopside and Jadeite melts by computer simulation studies. Chem Geol 62:83–92

  4. Astin AV (1962) Certificate of viscosity values. Standard sample No. 710 Soda-Lime-Silica Glass. US Dept of Commerce, Natl Bur Stds. Washington DC

  5. Bansal NP, Doremus RH (1986) Handbook of glass properties. Academic Press, New York, London, pp 680

  6. Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymeric liquids Vol 1. Wiley and Sons, New York, pp 470

  7. Bucaro JA, Dardy HD (1974) High-temperature Brillouin scattering in fused quartz. J Appl Phys 45:5324–5329

  8. Brückner R (1987) Structural aspects of highly deformed melts. J Non-Cryst Sol 95–96:961–968

  9. Calas G, Hawthorne FC (1988) Introduction to spectroscopic methods. In: FC Hawthorne (ed) Spectroscopic methods in mineralogy and geology. Mineralogical Society of America Reviews in Mineralogy 18, 1–9

  10. Dingwell DB, Scarfe CM, Cronin D (1985) The effect of fluorine on viscosities in the system Na2O-Al2O3-SiO2: implications for phonolites, trachytes and rhyelites. Am Mineral 70:80–87

  11. Dunn T (1982) Oxygen diffusion in three silicate melts along the join diopside-anorthite. Geochim Cosmochim Acta 46:2293–2299

  12. Glasstone S, Laidler KJ, Eyring H (1941) The theory of rate processes. McGraw-Hill, New York, pp 611

  13. Gruber GJ, Litovitz TA (1964) Shear and structural relaxation in molten Zinc Chloride. J Chem Phys. 40:13–26

  14. Herzfeld KF, Litovitz TA (1956) Absorption and dispersion of ultrasonic waves. Academic Press, New York, pp 535

  15. Höfler S, Seifert FA (1984) Volume relaxation of compacted glass: a model for the conservation of natural diaplectic glasses. Earth Planet Sci Lett 67:433–438

  16. Hofmaier G, Urbain G (1968) The viscosity of pure silica. Sci Ceram 4:25–32

  17. Jackson I (1986) The laboratory study of seismic wave attenuation. In Mineral and rock deformation: Laboratory studies, (eds) Hobbs BE and Heard HC, 11–24, AGU

  18. Kurkjian CR (1963) Relaxation of torsional stress in the transformation range of a soda-lime-silica glass. Phys Chem Glass 4:128–136

  19. Laberge NL, Vasilescu VV, Montrose CJ, Macedo PB (1973) Equilibrium compressibilities and density fluctuations in K2O-SiO2 glasses. J Am Cer Soc 56:506–509

  20. Lambert JB, Nienhuis RJ, Keepers JW (1981) Kinetik intramolekularer Reaktionen aus Relaxationszeitmessungen. Angew Chem 93, 533–566

  21. Lange RA, Carmichael ISE (1987) Densities of Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochim Cosmochim Acta 51:2931–2946

  22. Larsen DC, Mills JJ, Sievert JL (1974) Stress relaxation behavior of soda-lime glass between the transformation and softening temperatures. J Non-Cryst Sol 14:269–279

  23. Li JH, Uhlmann DR (1970) The flow of glass at high stress levels. J Non-Cryst Sol 33:235–248

  24. Litovitz TA, Davis CM (1965) Structural and shear relaxation in liquids. In: Mason WP (ed) Physical Acoustics Vol. I IA, Academic Press, New York, 281–349

  25. Liu S-B, Stebbins JF, Schneider E, Pines A (1988) Diffusive motion in alkali silicate melts: an NMR study at high temperature. Geochim Cosmochim Acta 52:527–538

  26. Mills JJ (1974) Low frequency storage and loss moduli of soda silica glasses in the transformation range. J Non-Cryst Solids 14:255–268

  27. Muehlenbachs K, Schaeffer HA (1977) Oxygen diffusion in vitreous silica-utilization of natural isotopic abundances. Can Mineral 15:179–184

  28. Nowick AS, Berry BS (1973) Anelastic relaxation in solids. Academic Press, New York, pp 677

  29. Nye JF (1957) Physical properties of crystals. Oxford Press, Oxford, pp 322

  30. O'Connell RJ, Budiansky B (1978) Measures of dissipation in viscoelastic media. Geophys Res Lett 5:5–8

  31. Richet P (1984) Viscosity and configurational entropy of silicate melts. Geochim Cosmochim Acta 48:471–483

  32. Rigden SM, Ahrens TJ, Stolper EM (1988) Shock compression of molten silicate: results for a model basaltic composition. J Geophys Res 93:367–382

  33. Rosen SL (1982) Fundamental principles of polymeric materials. Wiley and Sons, New York, pp 346

  34. Ritland HN (1954) Density phenomena in the transformation range of a borosilicate crown glass. J Am Cer Soc 37:370–378

  35. Rai CS, Manghnani MH, Katahara KW (1981) Ultrasonic studies on a basalt melt. Geophys Res Lett 8:1215–1218

  36. Rivers ML, Carmichael ISE (1987) Ultrasonic studies of silicate melts. J Geophys Res 92:9247–9270

  37. Ryan MP, Blevins JYK (1987) The viscosity of synthetic and natural silicate melts and glasses at high temperatures and 1 bar (105 pascals) pressure and higher pressures. USGS Bull 1764, pp 563

  38. Sato H, Manghnani MH (1985) Ultrasonic measurements of VP and Qp: relaxation spectrum of complex modulus on basalt melts. Phys Earth Planet Int 41:18–33

  39. Scarfe CM, Cronin DJ, Wenzel JT, Kauffman DA (1983) Viscositytemperature relationships at 1 atm in the system diopside-anorthite. Am Mineral 68:1083–1088

  40. Scarfe CM, Mysen BO, Virgo D (1987) Pressure dependence of the viscosity of silicate melts. Magmatic Processes: Physicochemical Principles, Mysen BO (ed) 59–67

  41. Shaw HR (1972) Viscosities and magmatic silicate liquids: an empirical method of prediction. Am J Sci 272:870–893

  42. Shimizu N, Kushiro I (1984) Diffusivity of oxygen in Jadeite and diopside melts at high pressures. Geochim Cosmochim Acta 48:1295–1303

  43. Simmons JH, Mohr RK, Montrose CJ (1982) Non-Newtonian viscous flow in glass. J Appl Phys 53:4075–4080

  44. Spera FJ, Borgia A, Strimple J, Feigenson M (1988) Rheology of melts and magmatic suspensions.I. Design and calibration of concentric cylinder viscometer with application to rhyolitic magma. J Geophys Res 93:10273–10294

  45. Stebbins JF, Farnan I (1988) Spatial orientation of structural units in silicate glasses: results from NMR spectroscopy. EOS 69, 504 (abstr)

  46. Stockhorst H, Brückner R (1982) Structure sensitive measurements on E-glass fibers. J Non-Cryst Sol 49, 471–484

  47. Sucov EW (1963) Diffusion of oxygen in vitreous silica. J Am Cer Soc 46:14–20

  48. Tauke J, Litovitz TA, Macedo PB (1968) Viscous relaxation and non-Arrhenius behavior in B2O3. J Am Ceram Soc 51:158–163

  49. Tyburzcy JA, Waff HS (1983) Electrical conductivity of molten basalt and andesite to 25 kilobars pressure: geophysical significance and implications for charge transport and melt structure. J Geophys Res 88:2413–2430

  50. Weast RC (1972) Handbook of physics and chemistry, CRC Press, Cleveland, pp 2335

  51. Williams EL (1965) Diffusion of oxygen in fused silica. J Am Cer Soc 48:190–194

  52. Woodcock LV, Angell CA, Cheeseman P (1976) Molecular dynamic studies of the vitreous state: simple ionic systems and silica. J Chem Phys 65:1565–1577

Download references

Author information

Additional information

Dedicated to the memory of Chris Scarfe

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dingwell, D.B., Webb, S.L. Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes. Phys Chem Minerals 16, 508–516 (1989). https://doi.org/10.1007/BF00197020

Download citation

Keywords

  • Silicate
  • Relaxation Time
  • Shear Viscosity
  • Bulk Modulus
  • Structural Relaxation