The contiguity of liquid phase sintered microstructures
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INTRODUCTION
CONTIGUITY is a quantitative measure of interphase contact. It is defined as the fraction of internal surface area of a phase shared with grains of the same phase in a two phase microstructure. J Liquid phase sintered microstructures exhibit a dispersion of one phase (the solid phase during sintering) in a matrix (the liquid). A certain degree of contact occurs in such materials depending on gravity, surface energy, volume fraction solid, and grain shape. In liquid phase sintering, these contacts serve a useful role in providing rigidity to a compact, thereby controlling shape distortion. The importance of the solid phase contiguity in materials formed by liquid phase sintering is recognized. 2'3 This is especially true in cemented carbides where links have been created between contiguity and properties like hardness, fracture toughness, and strength. 4'5'6 Other studies have shown contiguity to be important to properties like thermal conductivity, 7 electrical conductivity, 8'9'J~ ductility,H and wear erosion. 12 The contiguity has been measured vs processing parameters in several systemsJ -22 It has been observed that contiguity initially varies with sintering time. This is attributed to a change in the solid-liquid surface energy as the liquid changes composition during dissolution, spreading, and penetration of grain boundaries. After prolonged sintering, the contiguity approaches a constant value, independent of grain growth.16 19Changes in the sintering temperature will alter the solubility and interfacial energies and likewise cause a variation in the contiguity. 18'19 Additionally, it is expected that a decreasing solubility with temperature will lead to a contiguity dependence on cooling rate after the sintering cycle. Accordingly, there is a contiguity dependence on the post-sintering heat treatment. 22 Underlying these processing effects is a fundamental contiguity variation with the basic material characteristics like volume fraction solid and interfacial energies. In general, the contiguity increases with the volume fraction of solid phase. The upper limit is a contiguity of unity for a single phase, dense material. However, the models presented to date for the contiguity variation with volume fraction solid and dihedral angle have been simple empirical correlations, s'16-18 For example, Warren and Waldron 16 suggest the contiguity R.M. GERMAN is Professor, Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12181. Manuscript submitted January 17, 1984.
METALLURGICALTRANSACTIONSA
is linearly dependent on the dihedral angle at a volume fraction solid of 0.8. Close examination of such models shows them to be useful only over narrow ranges. In addition, the effect of a grain size distribution is unknown. The present calculations model the contiguity variation with dihedral angle, volume fraction solid, and grain size. It is assumed that the grain shape is spherical with isotropic interfacial energies. Although this represents an ideal condition, such assumption
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