An analysis of the surface menisci in a mixture of liquid and deformable grains
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I.
INTRODUCTION
IF soap water is slowly poured into a glass beaker containing a soap froth, the soap bubbles become more spherical momentarily in the regions where the water content is high during its downward flow. If there were no effect of gravity, one would expect all bubbles to become more spherical with an increasing liquid content. The bubble shape is determined by the balance between the tendency of the bubbles to become spherical and the negative pressure due to the menisci at the saddle points between the bubbles at the surface. A similar situation arises in certain grain-liquid mixtures. In W-Ni-Fe heavy alloy and others which have been fully densified by liquid phase sintering, the grains are nearly spherical if the liquid volume fraction is high, and are anhedral (contact flattened) if the liquid volume fraction is low, as shown, for example, by Kang and Yoon ~ and in Figure l(a). 2 If the dihedral angle at the junction of liquid and grains is small and the liquid content can be freely varied, there is a tendency of the grains to become spherical in order to minimize the solid-liquid interface area. This "sphering force" of the grains is manifested as a force acting outward on the specimen surface. 3 It is effective in determining the grain shape because the grain surfaces relax readily by a rapid diffusion through liquid matrix. In a previous work, 3 the equilibrium shape of grains surrounded by a matrix was analyzed for various matrix volume fractions and dihedral angles, and from the result could be calculated the sphering force. In order to stabilize the morphology of liquid phase sintered alloys, it is then necessary to counterbalance the sphering force by another force which holds the grains together and presses one against the other. Such a force arises from the liquid menisci at the specimen surface shown in Figure l(b). 4 (Since liquid is expected to recede somewhat from the specimen surface during solidification, the actual HYO-HOON PARK, Postdoctoral Research Associate, SUK-JOONG L. KANG, Associate Professor, and DUK N. YOON, Professor, are with the Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, P.O. Box 131 Cheongryang, Seoul, Korea. Manuscript submitted November 27, 1984. METALLURGICAL TRANSACTIONS A
(a)
(b) Fig. 1 - - T h e scanning electron micrographs of (a) the fracture surface of a 98W-INi-IFe (wt pct) alloy sintered for 10 min, 2 and (b) the surface of a 95W-3.5Ni-I.5Fe (wt pct) alloy sintered for 1 h at 1460 ~ VOLUMt" 17A, FEBRUARY 1986--325
menisci shape at the liquid phase sintering temperature may not be accurately displayed here.) When the capillary forces due to the liquid menisci at the specimen surface counterbalance the sphering force, the structure of the system becomes stable as in a soap froth. The purpose of this study is to develop geometrical models for the grains and the menisci at the specimen surface in order to analyze quantitatively the balance between the capillary force and the sphering force in grain-l
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