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

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 Delta sigma (cls). A new, generally valid equation has been developed for this parameter: Delta sigma (cls) = 2 sigma (cs) - sigma (cl) - sigma (sl) (where sigma (cs), sigma (cl), and sigma (sl) are 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 Delta sigma (cls) < 0. A new estimation method has also been developed for the quantity (cs). Combining this equation with the new equation for Delta sigma (cls),, the approximated expressions with easily available parameters for the parameter Delta sigma (cls), have been obtained for normal metals (Delta sigma (cls) = sigma (cv) - sigma (lv) . (0.08 + 1.22 . cos Theta (clv))) and for Si and Ge (Delta sigma (cls), = sigma (cv) - sigma (lv) . (0.57 + 1.66 . cos Theta (clv)), where sigma (cv) and sigma (lv) are the surface energy of the ceramic and the surface tension of the liquid metal, respectively, while Theta (clv) 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 land, 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 metal/ceramic system. For systems with Delta sigma (cls) > 0, a new equation (similar to that derived earlier by Chernov er 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 mum) system, measured recently under microgravity conditions by Stefanescu et al.