Journal of Thermal Analysis and Calorimetry

, Volume 118, Issue 3, pp 1715–1720 | Cite as

Generalized kinetics of overall phase transition explicit to crystallization

  • Isak Avramov
  • Jaroslav Šesták


Modeling of process for reaction kinetics is a fashionable subject of publications. This paper tests various phenomenological models starting with the Verhulst logistic functions, Kolmogorov adaptation up to the renowned KJMA and SB variants. The meaning of both the mortality (α) and fertility (1 − α) terms are mathematically analyzed in detail involving variation of their power exponents, their characteristic points, and shape examination of the rate curves. Kolmogorov derivation of nucleation-growth process is revised.


Phase transition Nucleation-growth Crystallization Logistic function Epidemic model 



The results were developed within the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088 that is co-funded from the ERDF within the OP RDI program of the Ministry of Education, Youth and Sports.


  1. 1.
    Avramov I. Kinetics of distribution of infections in network. Phys A. 2007;379:615.CrossRefGoogle Scholar
  2. 2.
    White PS. Pattern, process, and natural disturbance in vegetation. Bot Rev. 1979;45:229.CrossRefGoogle Scholar
  3. 3.
    Mooney HA, Godron M, editors. Disturbance and ecosystems. New York: Springer; 1983.Google Scholar
  4. 4.
    Romme WH, Knight DH. Landscape diversity: the concept applied to Yellowstone Park. Bioscience. 1982;32:664.CrossRefGoogle Scholar
  5. 5.
    Pickett STA, White PS, editors. Ecology of natural disturbance and patch dynamics. New York: Academic Press; 1985.Google Scholar
  6. 6.
    Turner MG, editor. Landscape heterogeneity and disturbance. New York: Springer; 1987.Google Scholar
  7. 7.
    Verhulst PF. Notice sur la loi que la population poursuit dans son accroissement. Correspondancemathématiqueet physique 1838; X: 113–121.Google Scholar
  8. 8.
    Verhulst PF. Recherches mathématiques sur la loi d’accroisement de la population.Mem.Acad. R. Bruxelles, 1844;18:1.Google Scholar
  9. 9.
    West B, Rrigolini PG. Complex webs. Cambridge: Cambridge University Press; 2011.Google Scholar
  10. 10.
    Young DA. Decomposition of solids. Oxford: Pergamon Press; 1966.Google Scholar
  11. 11.
    Šesták J. Modelling of reaction mechanism: use of Euclidian and fractal geometry, Chap. 10. In: Science of heat and thermophysical studies: a generalized approach to thermal analysis. pp. 276-314, Elsevier, Amsterdam 2005.Google Scholar
  12. 12.
    Prout EG, Tompkins FC. The thermal decomposition of potassium permanganate. Trans Faraday Soc. 1944;40:488–98.CrossRefGoogle Scholar
  13. 13.
    Kolmogorov A. statistical theory for the recrystallization of metals. Akad. Nauk SSSR. Izv. Ser. Matem. 1937;1:355 (in Russian).Google Scholar
  14. 14.
    Šesták J, Berggren G. Study of the kinetics of the mechanism of solid-state reactions at increasing temperature. Thermochim Acta. 1971;3:1–12.CrossRefGoogle Scholar
  15. 15.
    Gorbachev VM. Some aspects of Šesták’s generalized kinetic equation in thermal analysis. J Therm Anal. 1980;18:193–7.CrossRefGoogle Scholar
  16. 16.
    Šimon P. Fourty years of the Šesták-Berggren equation. Thermochim Acta. 2011;520:15–156.Google Scholar
  17. 17.
    Šesták J. Diagnostic limits of phenomenological kinetic models when introducing an accommodation function. J Therm Anal. 1991;36:1997.Google Scholar
  18. 18.
    Johnson W, Mehl R. Reaction kinetics in processes of nucleation and growth. Trans AIME. 1939;135:416–62.Google Scholar
  19. 19.
    Avrami M. Kinetics of phase change I—general theory. J Chem Phys. 1939;7:1103.CrossRefGoogle Scholar
  20. 20.
    Avrami M. Kinetics of phase change II—granulation, phase change and microstructure. J Chem Phys. 1940;8:212.CrossRefGoogle Scholar
  21. 21.
    Bagchi TP, Sen PK. Combined differential and integral method for analysis of non-isothermal kinetic data. Thermochim Acta. 1981;51:175.CrossRefGoogle Scholar
  22. 22.
    Yinnon H, Uhlmann D. Application of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liquids, Part I: Theory. J Non-Cryst Solids. 1983;54:253–75.CrossRefGoogle Scholar
  23. 23.
    Koga N, Šesták J, Málek J. Distortion of the Arrhenius parameters by the inappropriate kinetic model function. Thermochim Acta. 1991;188:333–6.CrossRefGoogle Scholar
  24. 24.
    Weinberg MC, Birnie DP III. Avrami exponents for transformations producing anisotropic particles. J Non-Cryst Solids. 1996;202:290–6.CrossRefGoogle Scholar
  25. 25.
    Málek J. Applicability of KJMA model in the thermal analysis of crystallization kinetics of glasses. Thermochim Acta. 1995;267:61–73.CrossRefGoogle Scholar
  26. 26.
    Koga N. Physico-geometric kinetics of solid-state reactions by thermal analysis. J Therm Anal. 1997;49:45–56.CrossRefGoogle Scholar
  27. 27.
    Mamleev V, Bourbigot S, LeBras M, Duquesne S, Šesták J. Thermogravimeric analysis models of multistage decomposition of materials. Phys Chem Chem Phys. 2000;2:4796–803.CrossRefGoogle Scholar
  28. 28.
    Illeková E, Šesták J. Crystallization kinetics of metallic micro-, nano- and non-crystalline glasses, chap. 13. In: Šesták J, Šimon P, editors. Thermal analysis of micro-, nano- and non-crystalline materials. Berlin: Springer; 2013. p. 257–90.Google Scholar
  29. 29.
    Koga N, Šimon P, Šesták J. Some fundamental and historical aspects of phenomenological kinetics in solid-state studied by thermal analysis, chap. 1. In: Šesták J, Šimon P, editors. Thermal analysis of micro-, nano- and non-crystalline materials. Berlin: Springer; 2013. p. 1–28.Google Scholar
  30. 30.
    Šesták J. Rationale and fallacy of thermoanalytical kinetic patterns: how we model subject matter. J Thermal Anal Calor. 2012;110:5–16.CrossRefGoogle Scholar
  31. 31.
    Kemeny T, Šesták J. Comparison of crystallization kinetics determined by isothermal and nonisothermal methods Thermochim. Acta. 1987;110:113–29.Google Scholar
  32. 32.
    Šesták J. On applicability of p(x) function to the determination of kinetic parameters at increasing temperature. Thermochim Acta. 1971;3:1.CrossRefGoogle Scholar
  33. 33.
    Šesták J, Holba P. Heat inertia and temperature gradient in the treatment of DTA peaks: Existing on every occasion of real measurements but until now omitted. J Thermal Anal Calor, 2013;113:1633–43.Google Scholar
  34. 34.
    Kissinger HE. Reaction kinetics in differential thermal analysis. Anal Chem. 1957;29:1702–6.CrossRefGoogle Scholar
  35. 35.
    Šesták J. Is the original Kissinger equation obsolete today—not obsolete the entire non-isothermal kinetics? J Thermal Anal Calor. 2014;117:3–7.CrossRefGoogle Scholar
  36. 36.
    Šesták J, Holba P, Živkovič Ž. Doubts on Kissinger´s method of kinetic evaluation based on several conceptual models showing the difference between the maximum of reaction rate and the extreme of DTA peak. J Min Metall Sect B. 2014;50:77–81.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Institute of Physical ChemistryBulgarian Academy of SciencesSofiaBulgaria
  2. 2.New Technologies - Research Centre of the Westbohemian RegionUniversity of West BohemiaPlzeňCzech Republic

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