Microstructure of the gravitationally settled region in a liquid-phase sintered dilute tungsten heavy alloy
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INTRODUCTION
LIQUID
phase sintering (LPS) is widely employed for the fabrication of both metallic and ceramic materials, j~,2~ During the sintering cycle, the microstructure consists of solid grains in a liquid matrix, in which the liquid provides both a capillary force and transport medium that promotes densification. Because there are few systems where the solid and liquid densities are equal, LPS is generally restricted to compositions that have high solid volume fractions in which structural connectivity inhibits gross solid-liquid separation. However, density gradients are evident after sintering even with high solid contents.13] For tungsten-nickel-iron alloys (termed tungsten heavy alloys or WHAs), the large density difference between the solid and liquid phases (near 9 g / c m 3) limits LPS to tungsten contents above approximately 80 wt pct (about 60 vol pct solid). At 78 wt pct tungsten, there is solidliquid separation in sintering, t41 Even with higher solid contents, there is progressive compact distortion with solid-liquid gradients after sintering for long times or at high temperatures. Identification of the critical lower-limit solids content is an easy task for LPS systems with a zero dihedral angle. Under Earth-based conditions, monosized spherical particles typically form random loose packings with a coordination number between 6 and 7. This corresponds to a density near 60 vol pct solid, the limit for random loose packing of smooth, dense spheres. 15,6~During liquid-phase sintering, a spherical grain shape is expected for the solid grains when the interfacial energy is isotropic. Usually, the grain-size distribution is relatively narrow in LPS, so a monosized grain approximation is reasonable. If the dihedral angle is not zero, then the grains will form bonds that give rigidity to the structure. Depending on the rate of bond formation, the grains can agglomerate with a restricted packing density. RANDALL M. GERMAN, Brush Chair Professor in Materials, is with the Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802-6809. Manuscript submitted September 20, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
Even so, the solid skeleton should densify over time through solid-skeleton densification. Mechanical stability of spherical grains requires at least a tetrahedral packing structure with a coordination number of 4 to avoid collapse under the action of gravity, tSJ Recent computer simulations determined that about 4.5 contacts per grain gives stability, trl and experimental measurements estimate the limiting coordination number at 4.75 contacts per grain. 171From prior calculations, it is possible to relate the grain coordination number Nc, dihedral angle ~, and solid volume fraction Vs as follows: 181 vs = -0.83
+ 0.81Nc - 0.056N~
+ 0.0018N3c - 0.36A + 0.008A 2
[1]
where A = Nc cos (dp/2). This equation was generated for monosized grains and may slightly underestimate the solid content for liquid-phase sintered microstructures that
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