Phase Transformations in Fe-Cu-Alloys -SANS-Experiments and Theory

Abstract

A precipitation reaction in a supersaturated metastable alloy starts with the formation of stable nuclei, then proceeds to a more or less marked growth regime and finally ends in a coarsening reaction. According to the classical nucleation theory,the nucleation rate J is mainly governed by the work of formation ΔF* of a critical nucleus with radius R^* [1]:

$$ J\,\infty \,\exp [ - \,\Delta {F^{ * }}/kT]\,and\,\Delta {F^{ * }}\, = \,4\pi \,{R^{{ * 2}}}\bullet \sigma /3 $$

((1))

(σ: specific interfacial energy). A nucleated spherical particle of radius R and solute concentration C_p embedded in a supersaturated matrix of mean solute concentration c(t) will grow at a rate [2] (D: diffusion coefficient):

$$ \frac{{dR}}{{dt}}\, = \,v(t)\, = \,\frac{{\overline c (t)\, - \,{c_{R}}}}{{{c_{{P\, - \,}}}{c_{R}}}}\,\frac{D}{R} $$

((2))