A critique of activation energies for nucleation growth and overall transformation kinetics

Berkenpas, Michael B.; Barnard, J. A.; Ramanujan, R.V.; Aaronson, H.I.

doi:10.1016/0036-9748(86)90151-1

Cited by 38 publications

(8 citation statements)

References 4 publications

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“…All methods presume that the equilibrium state is constant. In some cases this assumption may not hold and this introduces deviations in the measured activation energies [23,50]. The different sources of inaccuracies for various methods are gathered in Table 1. The deviations introduced by factors v and vi are analysed in some detail elsewhere [5,23,37], and to assess the relative importance of the other factors the following analysis is applied.…”

Section: Accuracies Of Isoconversion Methodsmentioning

confidence: 99%

The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods

2003

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Model-free isoconversion methods are the most reliable methods for the calculation of activation energies of thermally activated reactions. A large number of these isoconversion methods have been proposed in the literature. A classification of these methods is proposed. Type A methods such as Friedman methods make no mathematical approximations, and Type B methods, such as the generalised Kissinger equation, apply a range of approximations for the temperature integral. The accuracy of these methods is investigated, by deriving expressions for the main sources of error which includes the inaccuracy in reaction rate measurement, approximations for the temperature integral and inaccuracies in determination of temperature for equivalent fraction transformed. Both highly inaccurate and highly accurate Type B methods are identified. In cases where some uncertainty over baselines of the thermal analysis data exists or where accuracy of determination of transformation rates is limited, type B methods will often be more accurate than type A methods.

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Section: Accuracies Of Isoconversion Methodsmentioning

confidence: 99%

The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods

2003

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“…As pointed out in Ref. 49, at these temperatures the activation energy for this process is not exactly that for growth Q in equation (23). Nevertheless, as the temperature decreases, the activation energy for the process tends towards the value for growth, as can be seen from Table 2 and as would be expected from the mathematics of equation (23).…”

Section: Hy~a~tmentioning

confidence: 94%

Theoretical calculations of kinetics of equiaxed ferrite transformations in Fe, Fe–Ni, and Fe–Cr alloys

Wilson¹

1991

Materials Science and Technology

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The kinetics of the equiaxedferrite massive transformation in Fe and Fe alloys has been examined theoretically. The basis of the analysis is that the plateau temperature in a plot of transformation temperature versus cooling rate corresponds to the maximum rate of transformation.An approximate approach for the geometry of grain corner and grain edge nuclei having one or more coherent interfaces has been used. Neither Russell's treatment of incubation periods nor Cahn's analysis of overall reaction involving nucleation and growth predict the observed transformation plateaux temperatures. Instead, calculations assuming that growth kinetics is the rate controlling factor give good agreement for the plateaux temperatures in Fe, Fe-Ni, and Fe-Cr alloys. The theoretical calculations also show the existence of a plateau within ±10 K over a range of cooling rates. The marked hardenability of Fe-Ni alloys is also discussed. MST/1393 List of symbols ay lattice parameter of austenite (Ref. 1) ae dimensionless parameter (Ref. 2) representing variation of number of grain corner nuclei with time t (equation (17)) ar 2 austenite grain boundary area occupied by embryo of spherical surface radius r (Refs. 3, 4) be dimensionless parameter (Ref. 2) relating nucleation rate of grain corners Ie, growth rate G, and grain size d (equation (16)) br 2 area of a/y interface of embryo of a of spherical surface radius r (Refs. 3, 4) C number of grain corners/unit volume in tetrakaidecahedra of equal size cr 3 volume of embryo of a of spherical surface radius r (Ref. 3) d austenite grain size D diffusion constant for movement of incoherent boundary Do diffusion coefficient for movement of incoherent boundary (taken as 3·4 cm 2 S-1 from Ref. 5) F effective surface energy term for nucleation of a g constant relating grain geometry of austenite and sites for nucleation of a G rate of growth of equiaxed a L1Gy-+a chemical driving force/mole of a for y~a transformation i\Gv chemical driving force/unit volume of a for y~a transformation (=L1Gy-+a/N A Qa) i\Go overall Gibbs free energy for embryo of a above its surroundings (Refs. 3,4) i\G* activation energy for nucelation of a i\Hy-+a enthalpy/mole of a for y~a transformation I nucleation rate of a for y~a transformation Ie grain corner nucleation rate of a for y~a transformation (Ref. 2) k Boltzmann's constant (= 1·381 x 10-23 J K -1) m number of coherent interfaces/embryo of a Ms martensite start temperature n number of atoms/embryo of a n* number of atoms in critical nucleus of a N A Avogadro's number (= 6·022 x 10 23 mol-1 ) p maximum number of possible coherent interfaces/embryo of a Q activation energy for movement of incoherent a/y boundary; taken as 39 kcal mol-1 (~163 kJ mol-1 ) from Ref. 5 r radius of spherical surface of embryo of a (Refs. 3,4) r* radius of spherical surface of critical nucleus of a (Refs. 3, 4) R* radius of equivalent sphere of critical nucleus of a R gas constant (= 1·987 cal mol-1~8 ·314 J mol-1 K-1 ) t time t(b) time of growth of a to fraction y te start time for tr...

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“…According to the literature, this value is equal to the activation energy for the diffusion of vacancy-Mg atom pairs (Berkenpas et al, 1986). So, it can be easily verified that this mechanism controls the aging kinetics.…”

Section: Fig 3 One Obtains Thatmentioning

confidence: 95%

“…So, it can be easily verified that this mechanism controls the aging kinetics. It is discussed by Berkenpas et al (1986), the apparent activation energy from the slope of the plot of ln(t c ) versus 1000/T is the sum of the Fig. 3 -ln(t c ) versus 1000/RT and the degree of fitting (R 2 ).…”

Section: Fig 3 One Obtains Thatmentioning

confidence: 99%

Modeling age hardening kinetics of an Al–Mg–Si–Cu aluminum alloy

Eivani

Taheri

2008

Journal of Materials Processing Technology

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A critique of activation energies for nucleation growth and overall transformation kinetics

Cited by 38 publications

References 4 publications

The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods

The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods

Theoretical calculations of kinetics of equiaxed ferrite transformations in Fe, Fe–Ni, and Fe–Cr alloys

Modeling age hardening kinetics of an Al–Mg–Si–Cu aluminum alloy

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