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 s olidification front through the thin layer of a liquid metal is determined by the sign of the quantity Delta sigma (cls). A new, generally valid equat ion has been developed for this parameter: Delta sigma (cls) = 2 sigma (cs) - sigma (cl) - sigma (sl) (where sigma (cs), sigma (cl), and sigma (sl) ar e the interfacial energies in the ceramic/solid metal, in the ceramic/liqui d metal, and in the solid metal/ liquid metal systems, respectively). The i nterfacial force is attractive, i.e., spontaneous engulfment of reinforcing particles by the front is expected, if Delta sigma (cls) < 0. A new estima tion method has also been developed for the quantity <sigma>(cs). Combining this equation with the new equation for Delta sigma (cls),, the approximat ed expressions with easily available parameters for the parameter Delta sig ma (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 (Delt a 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 perfo rmed 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 meta l/ceramic and Ge/ceramic systems pushing land, at higher solidification rat es, forced engulfment) is expected, primary Si crystals (crystallizing from hypereutectic Al-Si and other alloys) will spontaneously engulf the majori ty 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 sys tem. For systems with Delta sigma (cls) > 0, a new equation (similar to tha t derived earlier by Chernov er al.) has been derived to estimate the criti cal velocity of the pushing-engulfment transition (PET). Calculations with this equation show excellent quantitative agreement with the critical inter face velocity of the PET in the Al/ZrO2 (250 mum) system, measured recently under microgravity conditions by Stefanescu et al.