Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-20T02:51:03.379Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical solution for the Kissinger equation

Published online by Cambridge University Press:  31 January 2011

Pere Roura  and
Jordi Farjas
Pere Roura*
Affiliation:
GRMT, Department of Physics, University of Girona, Campus Montilivi, E17071 Girona, Catalonia, Spain
Jordi Farjas
Affiliation:
GRMT, Department of Physics, University of Girona, Campus Montilivi, E17071 Girona, Catalonia, Spain
*
a) Address all correspondence to this author. e-mail: pere.roura@udg.es
Get access

Abstract

An analytical solution for the Kissinger equation relating the activation energy, E, with the peak temperature of the reaction rate, Tm, has been found. It is accurate (relative error below 2%) for a large range of E/RTm values (from 15 to above 60) that cover most experimental situations. The possibilities opened by this solution are outlined by applying it to the analysis of some particular problems encountered in structural relaxation of amorphous materials and in kinetic analysis.

Keywords

KineticsPhase transformationSimulation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 10 , October 2009 , pp. 3095 - 3098
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Henderson, D.W.: Thermal-analysis of nonisothermal crystallization kinetics in glass forming liquids. J. Non-Cryst. Solids 30, 301 (1979).CrossRefGoogle Scholar
2.Farjas, J. and Roura, P.: Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution. Acta Mater. 54, 5573 (2006).CrossRefGoogle Scholar
3.Farjas, J. and Roura, P.: Simple approximate analytical solution for nonisothermal single-step transformations: Kinetic analysis. AIChE J. 54, 2145 (2008).Google Scholar
4.Kissinger, H.E.: Reaction kinetics in thermal analysis. Anal. Chem. 29, 1702 (1957).Google Scholar
5.Lee, J.W., Kim, H.S., Lee, J.Y., and Kang, J.K.: Hydrogen storage and desorption properties of Ni-dispersed carbon nanotubes. Appl. Phys. Lett. 88, 143126 (2006).CrossRefGoogle Scholar
6.Jona, E., Simon, P., Nemcekova, K., Pavlik, V., Rudinska, G., and Rudinska, E.: Thermal properties of oxide glasses. Part II. Activation energy as a criterion of thermal stability of Li2O°2SiO2°nTiO°2 glass systems against crystallization. J. Therm. Anal. Calorim. 84, 673 (2006).Google Scholar
7.Srivastava, A.P., Srivastava, D., and Dey, G.K.: A study on microstructure, magnetic properties and kinetics of the nanocrystallization of Fe40Ni38B18Mo4 metglass. J. Magn. Magn. Mater. 306, 147 (2006).CrossRefGoogle Scholar
8.Ladbrook, B.D. and Chapman, D.: Thermal analysis of lipids, proteins and biological membranes. A review and summary of some recent studies. Chem. Phys. Lipids 3, 304 (1969).Google Scholar
9.Budrugeac, P. and Segal, E.: Applicability of the Kissinger equation in thermal analysis revisited. J. Therm. Anal. Calorim. 88, 703 (2007).CrossRefGoogle Scholar
10.Yinnon, H. and Uhlmann, D.R.: Applications of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liquids. 1. Theory. J. Non-Cryst. Solids 54, 253 (1983).CrossRefGoogle Scholar
11.Vyazovkin, S. and Sbirrazzuoli, N.: Isoconversional kinetic analysis of thermally stimulated processes in polymers. Macromol. Rapid Commun. 27, 1515 (2006).CrossRefGoogle Scholar
12.Padhi, S.K.: Solid-state kinetics of thermal release of pyridine and morphological study of [Ni(ampy)2(NO3)2]; ampy = 2-picolylamine. Thermochim. Acta 448, 1 (2006).CrossRefGoogle Scholar
13.Roura, P. and Farjas, J.: Structural relaxation kinetics for first and second-order processes: Application to pure amorphous silicon. Acta Mater. 57, 2098 (2009).CrossRefGoogle Scholar
14.Khonik, V.A., Kitagawa, K., and Morii, H.: On the determination of the crystallization activation energy of metallic glasses. J. Appl. Phys. 87, 8440 (2000).CrossRefGoogle Scholar
15.Gibbs, M.R.J., Evetts, J.E., and Leake, J.A.: Activation-energy spectra and relaxation in amorphous materials. J. Mater. Sci. 18, 278 (1983).CrossRefGoogle Scholar
16.Shin, J.H. and Atwater, H.A.: Activation-energy spectrum and structural relaxation dynamics of amorphous-silicon. Phys. Rev. B 48, 5964 (1993).Google Scholar
17.Deceuninck, W., Knuyt, G., Stulens, H., Deschepper, L., and Stals, L.M.: Determination of the attempt frequency for relaxation phenomena in amorphous metals. Mater. Sci. Eng., A 133, 337 (1991).CrossRefGoogle Scholar
18.Mercure, J-F., Karmouch, R., Anahory, Y., Roorda, S., and Schiettekatte, F.: Dependence of the structural relaxation of amorphous silicon on implantation temperature. Phys. Rev. B 71, 134205 (2005).CrossRefGoogle Scholar
19.Popescu, C. and Segal, E.: Variation of the maximum rate of conversion and temperature with heating rate in non-isothermal kinetics. 2. Thermochim. Acta 82, 387 (1984).CrossRefGoogle Scholar