A new parameter for describing the structure bifurcation in two-phase alloys containing coherent particles

Abstract

The so-called bifurcation diagrams for γ′ precipitate particles in nickel-based alloys were obtained by calculating the energy state for a pair of particles on the basis of the bifurcation theory. Based on the bifurcation diagrams, we have proposed a new parameter for describing the two-phase structure containing coherent particles. The parameter is defined as the mean particle radius at the intersection of the energy ridge and the line ofR=−0.5 orR=0.5 in the bifurcation diagram (R≡(r _α−r _β)/(r _α+r _β), wherer _α andr _β are the radii of α and β), and is symbolized by¯r ^* _±0.5. Because the energy state of the paired α and β is maximum at¯r ^* _±0.5 whenR=±0.5,¯r ^* _±0.5 is just like the watershed and hence we have termed it “structureshed”. This parameter successfully describes the effects of elastic energy as well as surface energy on the microstructural changes during coarsening of precipitate particles.