Transition and equilibrium processes in metal-ceramic particle systems
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I.
INTRODUCTION
THE theoretical study of particle behavior at the solidliquid interfacd u occasioned an approach to certain practical matters, such as the formation of spheroidal graphite in cast iron, the behavior of inclusions in steel, the in situ processing of composites, and particularly, the processing of metal composite materials.t2.3,4] As a rule, when the solidification front in motion intercepts the particle, it either incorporates or expels it. tS] The incorporation is carried out by the growth of the solid on the particle followed by the incorporation of the particle in the solid. If, for certain reasons, the solidification front is divided into cells, dendrites, or equiaxed grains, two or more solidification fronts may converge on the particle. In this case, if the particle is not incorporated by one of the fronts, it will be caught between the fronts and, finally, included in the solid at the end of the solidification process. The behavior of particles at the solid-liquid interface differs, depending on how the solidification process develops: in the case of unidirectional solidification, the particles may be engulfed or pushed, and in the case of multidirectional solidification, the particles may be engulfed, pushed, or entrapped. In the case of unidirectional solidification, the liquidsolid transfer depends on the morphology of the interface, which may be planar, cellular, or dendritic. Thermodynamically, at the transmission of the particle from liquid to solid, there occurs a variation of the total free energy AF,, so that supposing the solid interface remains planar and neglecting the upward forces, we distinguish t61 AF, < 0 AF, > 0
the particle is incorporated the particle is expelled
Kinetically, the transition of the particle from liquid to solid requires analysis of the following issues: (1) the nature of the repulsive forces between the interface and the particle; (2) the mechanism involved in the mass transfer; and
IOAN CARCEA and MARICEL AGOP, Professors, are with the Departments of Materials Science and Physics, respectively, "Gh. Asachi" Technical University, Iasi 6600, Romania. Manuscript submitted October 12, 1994.
METALLURGICALAND MATERIALS TRANSACTIONS A
(3) the influence of the particle on the shape of the interface. Finding a solution to these issues offered the possibility to build up certain analytical models; the purpose of these models was to calculate the critical interfacial speed. Thus, in the model suggested by Uhlmann et aL,m the following relation is established between Vcr and radius r of the particle:
Vcr" r 2 = const
[1]
On the basis of the same hypothesis as in Reference 1 but paying more attention to the roughness of the particle, Boiling and Cisse t71 find the relation vcr" r" = const
[2]
with n between 1.5 and 4. Similar relations are given in References 1 and 8. A more complex analytical model, which also takes into account the role of the upward forces, was suggested by Stef'anescu et aL t91 In the case of ionic crystals, they obtained the following e
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