Log in

Modeling the relaxation of fluctuations in glass during the Ritland crossover experiment

  • Computational Approaches for Materials Discovery and Development Research Letter
  • Published:
MRS Communications Aims and scope Submit manuscript

Abstract

A knowledge of fluctuations is crucial for understanding the long-term kinetics of glasses. However, current approaches for modeling relaxation rely on an order parameter that only approximates the physics of relaxation. In this work, we compare a standard relaxation model with a newly proposed model in terms of their ability to capture the evolution of the glass. The results reveal that the concept of fictive temperature is unable to account for relaxation behavior of fluctuations. The newly proposed method, called the toy landscape model, can capture fluctuations but at a loss of simplicity.

Graphical abstract

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3

Data availability

Please email the authors for full access to the data.

References

  1. H.N. Ritland, Limitations of the fictive temperature concept. J. Am. Ceram. Soc. 39, 403–406 (1956). https://doi.org/10.1111/j.1151-2916.1956.tb15613.x

    Article  CAS  Google Scholar 

  2. C.J. Wilkinson, Y.Z. Mauro, J.C. Mauro, RelaxPy: python code for modeling of glass relaxation behavior. SoftwareX. 7, 255–258 (2018). https://doi.org/10.1016/j.softx.2018.07.008

    Article  Google Scholar 

  3. P.K. Gupta, J.C. Mauro, The laboratory glass transition. J. Chem. Phys. 126, 2240504 (2007). https://doi.org/10.1063/1.2738471

    Article  CAS  Google Scholar 

  4. A. Takada, R. Conradt, P. Richet, Partition function and configurational entropy in non-equilibrium states: a new theoretical model. Entropy 20, 1–15 (2018). https://doi.org/10.3390/e20040218

    Article  Google Scholar 

  5. R.G. Palmer, Broken ergodicity. Adv. Phys. 31, 669–735 (1982). https://doi.org/10.1080/00018738200101438

    Article  Google Scholar 

  6. A.K. Varshneya, J.C. Mauro, Fundamentals of inorganic glasses, 3rd edn. (Elsevier, Amsterdam, 2019)

    Google Scholar 

  7. J.C. Mauro, P.K. Gupta, R.J. Loucks, Continuously broken ergodicity. J. Chem. Phys. 126, 184511 (2007). https://doi.org/10.1063/1.2731774

    Article  CAS  Google Scholar 

  8. R.S. Welch, C.J. Wilkinson, J.C. Mauro, C.B. Bragatto, Charge carrier mobility of alkali silicate glasses calculated by molecular dynamics. Front. Mater. 6, 121 (2019). https://doi.org/10.3389/fmats.2019.00121

    Article  Google Scholar 

  9. J.C. Mauro, M.M. Smedskjaer, Statistical mechanics of glass. J. Non Cryst. Solids. 396–397, 41–53 (2014). https://doi.org/10.1016/j.jnoncrysol.2014.04.009

    Article  CAS  Google Scholar 

  10. A.Q. Tool, C.G. Eichlin, Variations caused in the heating curves of glass caused by heat treatment. J. Am. Ceram. Soc. 14, 276–308 (1931)

    Article  CAS  Google Scholar 

  11. A.Q. Tool, Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29, 240–253 (1946). https://doi.org/10.1111/j.1151-2916.1946.tb11592.x

    Article  CAS  Google Scholar 

  12. O.S. Narayanaswamy, A model of structural relaxation in glass. J. Am. Ceram. Soc. 54, 491–498 (1971). https://doi.org/10.1111/j.1151-2916.1971.tb12186.x

    Article  CAS  Google Scholar 

  13. J.C. Mauro, D.C. Allan, M. Potuzak, Nonequilibrium viscosity of glass. Phys. Rev. B 80, 094204 (2009). https://doi.org/10.1103/PhysRevB.80.094204

    Article  CAS  Google Scholar 

  14. J.C. Mauro, R.J. Loucks, P.K. Gupta, Fictive temperature and the glassy state. J. Am. Ceram. Soc. 92, 75–86 (2009). https://doi.org/10.1111/j.1551-2916.2008.02851.x

    Article  CAS  Google Scholar 

  15. K.D. Vargheese, A. Tandia, J.C. Mauro, Origin of dynamical heterogeneities in calcium aluminosilicate liquids. J. Chem. Phys. 132, 194501 (2010). https://doi.org/10.1063/1.3429880

    Article  CAS  Google Scholar 

  16. K.A. Kirchner, S.H. Kim, J.C. Mauro, Statistical mechanics of topological fluctuations in glass-forming liquids. Physica A 510, 787–801 (2018). https://doi.org/10.1016/j.physa.2018.07.028

    Article  CAS  Google Scholar 

  17. C.J. Wilkinson, J.C. Mauro, Modeling the relaxation and crystallization kinetics of glass without fictive temperature: toy landscape approach. J. Am. Ceram. Soc. 105, 245–256 (2022). https://doi.org/10.1111/jace.18078

    Article  CAS  Google Scholar 

  18. C.J. Wilkinson, C. Trivelpiece, R. Hust, R.S. Welch, S.A. Feller, J.C. Mauro, Hybrid machine learning/physics-based approach for predicting oxide glass-forming ability. Acta Mater. 222, 117432 (2022). https://doi.org/10.1016/j.actamat.2021.117432

    Article  CAS  Google Scholar 

  19. J.F. Stanzione, K.E. Strawhecker, R.P. Wool, Observing the twinkling fractal nature of the glass transition. J. Non Cryst. Solids. 357, 311–319 (2011). https://doi.org/10.1016/j.jnoncrysol.2010.06.041

    Article  CAS  Google Scholar 

  20. M.I. Ojovan, Configurons: thermodynamic parameters and symmetry changes at glass transition. Entropy 10, 334–364 (2008). https://doi.org/10.3390/e10030334

    Article  CAS  Google Scholar 

  21. H. Ritland, Relation between refractive index and density of a glass at constant temperature. J. Am. Ceram. Soc. 38, 86–88 (1955). https://doi.org/10.1111/j.1151-2916.1955.tb14581.x

    Article  CAS  Google Scholar 

  22. J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, D.C. Allan, Viscosity of glass-forming liquids. Proc. Natl. Acad. Sci. 106, 19780–19784 (2009). https://doi.org/10.1073/pnas.0911705106

    Article  Google Scholar 

  23. 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). https://doi.org/10.1103/PhysRevB.83.212202

    Article  CAS  Google Scholar 

  24. M.M. Smedskjaer, J.C. Mauro, S. Sen, Y. Yue, Quantitative design of glassy materials using temperature-dependent constraint theory. Chem. Mater. 22, 5358–5365 (2010). https://doi.org/10.1021/cm1016799

    Article  CAS  Google Scholar 

  25. Y.Z. Mauro, C.J. Wilkinson, J.C. Mauro, KineticPy: A tool to calculate long-time kinetics in energy landscapes with broken ergodicity. SoftwareX 11, 100393 (2020). https://doi.org/10.1016/j.softx.2019.100393

    Article  Google Scholar 

  26. C.J. Wilkinson, K. Doss, O. Gulbiten, D.C. Allan, J.C. Mauro, Fragility and temperature dependence of stretched exponential relaxation in glass-forming systems. J. Am. Ceram. Soc. 104, 4559–4567 (2021)

    Article  CAS  Google Scholar 

  27. M.D. Ediger, Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem. 51, 99–128 (2000). https://doi.org/10.1146/annurev.physchem.51.1.99

    Article  CAS  Google Scholar 

  28. J.C. Mauro, S.S. Uzun, W. Bras, S. Sen, Nonmonotonic evolution of density fluctuations during glass relaxation. Phys. Rev. Lett. 102, 155506 (2009). https://doi.org/10.1103/PhysRevLett.102.155506

    Article  CAS  Google Scholar 

  29. O. Gulbiten, J.C. Mauro, P. Lucas, Relaxation of enthalpy fluctuations during sub-Tg annealing of glassy selenium. J. Chem. Phys. 138, 244504 (2013). https://doi.org/10.1063/1.4811488

    Article  CAS  Google Scholar 

  30. J.C. Mauro, R.J. Loucks, S. Sen, Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems. J. Chem. Phys. 133, 164503 (2010). https://doi.org/10.1063/1.3499326

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Karan Doss for his critical comments on this manuscript.

Funding

The authors did not receive funding for this work.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Collin J. Wilkinson or John C. Mauro.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wilkinson, C.J., Lee, KH., Yin, D. et al. Modeling the relaxation of fluctuations in glass during the Ritland crossover experiment. MRS Communications 12, 1060–1066 (2022). https://doi.org/10.1557/s43579-022-00195-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43579-022-00195-4

Keywords

Navigation