Interfacial criterion of spontaneous and forced engulfment of reinforcing particles by an advancing solid/liquid interface

Abstract

The sign of the interfacial force acting between a ceramic particle and a solidification front through the thin layer of a liquid metal is determined by the sign of the quantity Δσ cls. A new, generally valid equation has been developed for this parameter: Δσ cls = 2σ cs− σ cl− σ sl(where σ cs, σ cl, and σ slare the interfacial energies in the ceramic/solid metal, in the ceramic/liquid metal, and in the solid metal/liquid metal systems, respectively). The interfacial force is attractive, i.e., spontaneous engulfment of reinforcing particles by the front is expected, if Δσ cls < 0. A new estimation method has also been developed for the quantity σ cs. Combining this equation with the new equation for Δσ cls, the approximated expressions with easily available parameters for the parameter Δσ cls have been obtained for normal metals (Δσ cls = σ cv− σ lv· (0.08 + 1.22 · cos Θclv)) and for Si and Ge (Δσ cls = σ cv− σ lv· (0.57 + 1.66 · cos Θclv), where σ cvand σ lvare the surface energy of the ceramic and the surface tension of the liquid metal, respectively, while Θclv is the contact angle of the liquid metal on the ceramics). Calculations performed with these equations are in good qualitative agreement with all known pushing/engulfment experiments for metal/ceramic systems. Particularly, it has been theoretically predicted that, while in the majority of normal metal/ceramic and Ge/ceramic systems pushing (and, at higher solidification rates, forced engulfment) is expected, primary Si crystals (crystallizing from hypereutectic Al-Si and other alloys) will spontaneously engulf the majority of ceramic phases. The so-called “pushing/spontaneous engulfment” (PSE) diagrams have been constructed to help make a quick judgement as to whether spontaneous engulfment or pushing is expected in a given metalceramic system. For systems with Δσ cls > 0, a new equation (similar to that derived earlier by Chernov et al.) has been derived to estimate the critical velocity of the pushing-engulfment transition (PET). Calculations with this equation show excellent quantitative agreement with the critical interface velocity of the PET in the Al/ZrO2 (250 µm) system, measured recently under microgravity conditions by Stefanescu et al.