Parameter determination of an analytical model for phase transformation kinetics: Application to crystallization of amor
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This study used an analytical model for phase-transformation kinetics. We used different combinations of various nucleation mechanisms [mixed nucleation (site saturation plus continuous nucleation), Avrami nucleation, and site saturation plus Avrami nucleation] and growth mechanisms (volume diffusion-controlled growth and interface-controlled growth) for a single transformation. Our work incorporated the effect of impingement of the growing particles. These factors have been applied to the same experimental results to find out the prevailing mechanisms. We made a detailed analysis for the determination of the parameters of the analytical phase-transformation model, in order to determine the most reasonable nucleation and growth modes, and the values for the activation energies of nucleation and growth. We used the model to study the crystallization kinetics of Mg82Ni18 and Mg88.7Ni11.3, as measured by means of both isothermal and isochronal differential scanning calorimetry.
I. INTRODUCTION
Solid-state phase transformations are important means for the adjustment of microstructure, and thereby the tuning of the properties of materials. To exploit this tool to its full extent, much effort is spent on the modeling of phase transformations. It appears appropriate to introduce a path variable, , which depends on thermal history [i.e., the path followed in the temperature-time diagram: T(t) prescribes 1]. The transformed fraction, f, depends on the path variable  through f = F共兲 .
(1)
The dependence of the path variable  on the thermal history can be described as the integral over time of a rate constant K[T(t)], not conceived to be dependent on t other than through T =
兰K关T共t兲兴dt
(2)
,
with K as the rate constant. K(T) can be given for many applications by an Arrhenius-type equation
冉
K关T共t兲兴 = K0 exp −
Q RT共t兲
冊
,
(3)
with Q as the overall, effective activation energy, K0 as a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0341 2586
http://journals.cambridge.org
J. Mater. Res., Vol. 19, No. 9, Sep 2004 Downloaded: 14 Mar 2015
the temperature and time-independent rate constant, and R as the gas constant. The classical Johnson-MehlAvrami (JMA) equation2 is compatible with the above approach and in its most general form can be written as1 f = 1 − exp共−n兲 ,
(4)
applicable to isothermal and non-isothermal transformations; and where n is the so-called growth exponent. However, the JMA equation only holds if extreme cases of nucleation mechanisms occur: site saturation and continuous nucleation (Refs. 3–6). Recently, a more general kinetic, numerical model3–6 has been proposed. This modular model recognizes the three mechanisms: nucleation, growth, and impingement of growing new phase particles. The model is applicable to both isothermal and non-isothermal transformations. The kinetic parameters of the JMA model (n, Q, and K0) depend on the choice of the nucleation and growth mode. The occurrence of changes in the values of n and Q, in particular, has oft
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