Paper 5.1

The Kinetics of Precipitate-Nucleation in the Edge of Miscibility Gap.

Miyazaki Toru¹, Kozakai Takao¹ and Schoen Claudio G.²

¹Nagoya Institute of Technology, Nagoya, Japan

²Universidade de Sao Paulo, Sao Paulo, Brazil 

The nucleation is a process critically dependent on the chemical driving force and the interfacial energy. Therefore, to understand the nucleation process, it is important to know experimentally how the nucleation process varies with a systematic change in the driving force of the alloy, particularly in the very vicinity of a phase boundary.

In the present, the critical size of nucleus and the time to nucleation in the vicinity of miscibility edge were determined for several binary alloy systems such as Ni-Si, Ni-Al, Cu-Ti and Cu-Co by utilizing the macroscopic composition gradient method recently proposed by us[1], where the solute composition macroscopically changes continuously so as to step over the phase boundary.

The critical nucleus size shows a rapid increase up to several hundreds of nanometer in a very narrow composition range less than 0.3at% from the solubility limit. The diameter of nucleus size can reach over 500 nm in the composition very close to the solubility limit. Such big nuclei are statistically rationalized by the conventional nucleation theory such as the Gibbs-Thomson relation.

However, the kinetics of the nucleus formation is never justified by any conventional nucleation theories. The kinetic equation shown below must give a largely bend curve in the edge of miscibility gap because of a strong influence of the second term.  However, the experimental log-log plot of the nucleation rate  and the super saturation showed a straight line for all alloy systems.

This clearly demonstrates that the 1st term of equation is only effective, and even in a typical N-G region near the solubility limit the 2nd term resulting from the energy barrier for nucleation has not contributed at all.  This clearly shows that the spinodal decomposition has arisen also in such a low concentration alloy. This phenomenon is never rationalized by the Boltzmann-Gibbs free energy.  The experimental results obtained here are considered to be only rationalized by Tsallis's free energy[2] where non-extensive entropy is taken into consideration.

(1) Metallurgical and Materials Transactions A, 30A(1999), 2783

(2) C.Tsallis:Nonextensive Statistical Mechanics and Its Application, ed.by S.Abe and Y.Okamoto, Springer (2000), 3