Pore filling process in liquid phase sintering
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I.
INTRODUCTION
IN liquid phase sintering of fine powder mixtures for producing alloys such as W-Ni-Fe heavy metal, a significant shrinkage occurs even in the solid state during heating to the sintering temperature. When liquid appears, it can flow rapidly into fine capillaries and the pores can be mostly isolated even at the beginning of liquid phase sintering. Kwon and Yoon j'2 studied densification of large spherical pores produced by melting Ni spheres embedded in fine W powder. The liquid was observed to flow into the pores after an apparent incubation time which increased with the pore size, and this observation led to the speculation that the grains had to grow to a critical size to fill the pores. This work is an attempt to provide a theoretical basis for describing this newly observed pore filling phenomenon in view of its obvious importance in liquid phase sintering. Based on geometrical models for the grains and the menisci of the liquid which surrounds them, the dependence of the menisci radius on grain size, liquid volume fraction, dihedral angle, and wetting angle are analyzed. The need for a critical grain size to fill a pore then arises quite naturally, and the driving force for liquid flow into the pore can also be described readily. Since the entire treatment is rather long and complex, this report focuses mainly on the basic physical concepts and the analysis of the simplest models. The details of the mathematical treatments and analysis of different models will be presented in a separate series of papers. 3,4 II.
THEORETICAL MODEL
liquid4 as illustrated in Figure 1. Assuming that the grains have a uniform size and are close packed, each grain may be represented by a rhombic dodecahedron with its edges truncated to form curved surfaces in contact with bulk liquid as shown in Figure 2. If the dihedral angle at the junction of the two grains and liquid is zero, the total interfacial energy per grain, E, is given by, E = %t(AI + ac)
[1]
where A/is the flat surface area in contact with neighboring grains across thin liquid films, Ac is the curved surface area along the grain edges in contact with bulk liquid, and ~/$tis
Fig. 1 - - A model of solid grains immersed in liquid matrix with menisci at the specimen surface.
A theoretical description of pore filling can begin with an analysis of forces which determines the grain shape in a system without any pores. If the liquid content in the specimen is small, the grains become anhedral with flat contact areas between them and curved surfaces in contact with bulk HYO-HOON PARK and SEONG-JAI CHO are Graduate Students, and DUK N. YOON is a Professor in the Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, P.O. Box 131 Cheongryang, Seoul, Korea. This paper is based on a presentation delivered at the symposium "Activated and Liquid Phase Sintering of Refractory Metals and Their Compounds" held at the annual meeting of the AIME in Atlanta, Georgia on March 9, 1983, under the sponsorship of the TMS Refra
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