Skip to main content
SpringerLink
Log in

Isoconversional analysis of solid-state transformations

A critical review. Part III. Isothermal and non isothermal predictions

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

A key issue in kinetic analysis is the "prediction" of the evolution of a solid state transformation for a particular temperature program. Many methods have been proposed to calculate this evolution from kinetic parameters determined from non-isothermal isoconversional methods. In this study, we will review and compare the most accurate methods. We will then introduce a new method that provides an accurate prediction for an arbitrary temperature program.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. Like Sbirrazzuoli et al. [26], we have not observed significant differences when using the integral method in place of the differential or advanced methods and vice versa.

References

  1. Flynn JH. The isoconversional method for determination of energy of activation at constant heating rates. J Therm Anal Calorim. 1983;27:95–102.

    Article  CAS  Google Scholar 

  2. Sbirrazzuoli N, Girault Y, Elégant L. Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 3—Peak maximum evolution methods and isoconversional methods. Thermochim Acta. 1997;293:25–37.

    Article  CAS  Google Scholar 

  3. Vyazovkin S, Wight CA. Kinetics in solids. Annu Rev Phys Chem. 1997;48:125–49.

    Article  CAS  Google Scholar 

  4. Vyazovkin S, Wight CA. Isothermal and nonisothermal reaction kinetics in solids: in search of ways toward consensus. J Phys Chem A. 1997;101:8279–84.

    Article  CAS  Google Scholar 

  5. Starink MJ. The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods. Thermochim Acta. 2003;404:163–76.

    Article  CAS  Google Scholar 

  6. Brown ME, et al. Computational aspects of kinetic analysis: Part A: The ICTAC kinetics project-data, methods and results. Thermochim Acta. 2000;355:125–43.

    Article  CAS  Google Scholar 

  7. Roduit B, Dermaut W, Lunghi A, Folly P, Berger B, Sarbach A. Advanced kinetics-based simulation of time to maximum rate under adiabatic conditions. J Therm Anal Calorim. 2008;93:163–73.

    Article  CAS  Google Scholar 

  8. Vyazovkin S. Computational aspects of kinetic analysis.: Part C. The ICTAC kinetics project—the light at the end of the tunnel? Thermochim Acta. 2000;355:155–63.

    Article  CAS  Google Scholar 

  9. Vyazovkin S, Linert W. Reliability of conversion-time dependencies as predicted from thermal analysis data. Anal Chim Acta. 1994;295:101–7.

    Article  CAS  Google Scholar 

  10. Vyazovkin S, Wight CA. Model-free and model-fitting approaches to kinetic analysis of isothermal and nonisothermal data. Thermochim Acta. 1999;340–341:53–68.

    Article  Google Scholar 

  11. Vyazovkin S. Kinetic concepts of thermally stimulated reactions in solids: a view from a historical perspective. Int Rev Phys Chem. 2000;19:45.

    Article  CAS  Google Scholar 

  12. Roduit B, Folly P, Berger B, Mathieu J, Sarbach A, Andres H, Ramin M, Vogelsanger B. Evaluating SADT by advanced kinetics-based simulation approach. J Therm Anal Calorim. 2008;93:153–61.

    Article  CAS  Google Scholar 

  13. Farjas J, Roura P. Isoconversional analysis of solid state transformations: a critical review. I Single step transformations with constant activation energy. J Therm Anal Calorim. doi:10.1007/s10973-011-1446-4.

  14. Farjas J, Roura P. Isoconversional analysis of solid state transformations: a critical review. II complex transformations. J Therm Anal Calorim. doi:10.1007/s10973-011-1447-3.

  15. Brown M, Dollimore D, Galwey A. Comprehensive chemical kinetics. In: Bamford C, Tipper CFH, editors. Reactions in the solid state, vol. 22. Amsterdam: Elsevier; 1980. p. 41–113.

    Chapter  Google Scholar 

  16. Sesták J. Thermophysical properties of solids, their measurements and theoretical analysis, vol. 12D. Amsterdam: Elsevier; 1984.

    Google Scholar 

  17. Farjas J, Roura P. Simple approximate analytical solution for nonisothermal single-step transformations: kinetic analysis. AICHE J. 2008;54:2145–54.

    Article  CAS  Google Scholar 

  18. Coats AW, Redfern JP. Kinetic parameters from thermogravimetric data. Nature. 1964;201:68–9.

    Article  CAS  Google Scholar 

  19. Vyazovkin S. Modification of the integral isoconversional method to account for variation in the activation energy. J Comput Chem. 2001;22:178–83.

    Article  CAS  Google Scholar 

  20. Vyazovkin S, Dranca I. Isoconversional analysis of combined melt and glass crystallization data. Macromol Chem Phys. 2006;207:20–5.

    Article  CAS  Google Scholar 

  21. Chen K, Vyazovkin S. Temperature dependence of sol-gel conversion kinetics in gelatin-water system. Macromol Biosci. 2009;9:383–92.

    Article  CAS  Google Scholar 

  22. Sbirrazzuoli N, Vincent L, Bouillard J, Elégant L. Isothermal and non-isothermal kinetics when mechanistic information available. J Therm Anal Calorim. 1999;56:783–92.

    Article  CAS  Google Scholar 

  23. Li C, Tang TB. Dynamic thermal analysis of solid-state reactions. J Therm Anal Calorim. 1997;49:1243–8.

    Article  CAS  Google Scholar 

  24. Sbirrazzuoli N. Is the Friedman method applicable to transformations with temperature dependent reaction heat? Macromol Chem Phys. 2007;208:1592–7.

    Article  CAS  Google Scholar 

  25. Vyazovkin S. A unified approach to kinetic processing of nonisothermal data. Int J Chem Kinet. 1996;28:95–101.

    Article  CAS  Google Scholar 

  26. Sbirrazzuoli N, Vincent L, Mija A, Guigo N. Integral, differential and advanced isoconversional methods: complex mechanisms and isothermal predicted conversion–time curves. Chemom Intell Lab Syst. 2009;96:219–26.

    Article  CAS  Google Scholar 

  27. Vyazovkin S, Dranca I, Fan X, Advincula R. Kinetics of the thermal and thermo-oxidative degradation of a polystyrene-clay nanocomposite. Macromol Rapid Commun. 2004;25:498–503.

    Article  CAS  Google Scholar 

  28. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes in C: the art of scientific computing. Cambridge: Cambridge University Press; 1994.

    Google Scholar 

  29. Friedman HL. Kinetics of thermal degradation of char-forming plastics from thermogravimetry. Application to a phenolic plastic. J Polym Sci C. 1964;6:183–95.

    Google Scholar 

  30. Galwey AK, Brown ME. Chapter 3 Kinetic background to thermal analysis and calorimetry. In: Brown ME, editor. Handbook of thermal analysis and calorimetry, vol. 1. Amsterdam: Elsevier Science B.V.; 1998. p. 147–224.

    Google Scholar 

  31. Roduit B, et al. The simulation of the thermal behavior of energetic materials based on DSC and HFC signals. J Therm Anal Calorim. 2008;93:143–52.

    Article  CAS  Google Scholar 

  32. Vyazovkin S. Evaluation of activation energy of thermally stimulated solid-state reactions under arbitrary variation of temperature. J Comput Chem. 1997;18:393–402.

    Article  CAS  Google Scholar 

  33. Vyazovkin S. Advanced isoconversional method. J Therm Anal Calorim. 1997;49:1493–9.

    Article  CAS  Google Scholar 

  34. Vyazovkin S, Dollimore D. Linear and nonlinear procedures in isoconversional computations of the activation energy of nonisothermal reactions in solids. J Chem Inf Comput Sci. 1996;36:42–5.

    Article  CAS  Google Scholar 

  35. Spinella C, Lombardo S, Priolo F. Crystal grain nucleation in amorphous silicon. J Appl Phys. 1998;84:5383–414.

    Article  CAS  Google Scholar 

  36. Farjas J, Roura P, Cabarrocas P. Grain size control by means of solid phase crystallization of amorphous silicon. In: Chu V, Miyazaki P, Nathan A, Yang J, Zan H, editors. Amorphous and polycrystalline thin-film silicon science and technology, vol. 989. Warrendale: Materials Research Society; 2007. p. 139–44.

    Google Scholar 

  37. Kumomi H, Yonehara T. Transient nucleation and manipulation of nucleation sites in solid-state crystallization of a-Si films. J Appl Phys. 1994;75:2884–901.

    Article  CAS  Google Scholar 

  38. Kempen ATW, Sommer F, Mittemeijer EJ. Determination and interpretation of isothermal and non-isothermal transformation kinetics; the effective activation energies in terms of nucleation and growth. J Mater Sci. 2002;37:1321–32.

    Article  CAS  Google Scholar 

  39. Tkatch VI, Limanovskii AI, Kameneva VY. Studies of crystallization kinetics of Fe40Ni40P14B6 and Fe80B20 metallic glasses under non-isothermal conditions. J Mater Sci. 1997;32:5669–77.

    Article  CAS  Google Scholar 

  40. Liu F, Sommer F, Bos C, Mittemeijer EJ. Analysis of solid state phase transformation kinetics: models and recipes. Int Mater Rev. 2007;52:193–212.

    Article  CAS  Google Scholar 

  41. Avrami M. Kinetics of phase change I—general theory. J Chem Phys. 1939;7:1103–12.

    Article  CAS  Google Scholar 

  42. Avrami M. Kinetics of phase change. II Transformation-time relations for random distribution of nuclei. J Chem Phys. 1940;8:212.

    Article  CAS  Google Scholar 

  43. Avrami M. Granulation, phase change, and microstructure—kinetics of phase change. III. J Chem Phys. 1941;9:177–84.

    Article  CAS  Google Scholar 

  44. Johnson W, Mehl R. Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Eng. 1939;135:416–42.

    Google Scholar 

  45. Kolmogorov A. On the static theory of metal crystallization. Izv Akad Nauk SSSR Ser Fiz. 1937;3:355–9.

    Google Scholar 

  46. Farjas J, Roura P. Numerical model of solid phase transformations governed by nucleation and growth: microstructure development during isothermal crystallization. Phys Rev B. 2007;75:184112.

    Article  Google Scholar 

  47. Farjas J, Rath C, Roura P, Roca i Cabarrocas P. Crystallization kinetics of hydrogenated amorphous silicon thick films grown by plasma-enhanced chemical vapour deposition. Appl Surf Sci. 2004;238:165–8.

    Article  CAS  Google Scholar 

  48. Farjas J, Butchosa N,Roura P. A simple kinetic method for the determination of the reaction model from non-isothermal experiments. J Therm Anal Calorim. 2010;102:615–25.

    Google Scholar 

Download references

Acknowledgements

This study was funded by the Spanish Programa Nacional de Materiales under contract No. MAT2009-08385 and by the Generalitat de Catalunya contract No. 2009SGR-185.

Author information

Authors and Affiliations

  1. GRMT, Department of Physics, University of Girona, Campus Montilivi, 17071, Girona, Catalonia, Spain

    J. Farjas & P. Roura

Authors
  1. J. Farjas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Roura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Farjas.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 244 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farjas, J., Roura, P. Isoconversional analysis of solid-state transformations. J Therm Anal Calorim 109, 183–191 (2012). https://doi.org/10.1007/s10973-011-1642-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-011-1642-2

Keywords

Search

Navigation