Equilibrium States of Liquid, Solid, and Vapor and the Configurations for Copper, Tungsten, and Pores in Liquid-Phase Si
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IQUID-PHASE sintering (LPS) is applied to the consolidation of mixed powder compacts to produce high-performance composite materials. During heating, a liquid forms, spreads, bonds, and usually densifies the solid grains.[2] In most cases, the liquid forms at temperatures far below the melting range for the solid. Once the liquid flows, the solid grains rearrange and pore space is filled with a more efficient grain arrangement accompanying liquid flow and grain shape accommodation. As a consequence, the starting powder geometry (size, shape, and spacing) transforms during LPS to give a microstructure that usually involves a liquid laced along the grain boundaries of the solid grains. Beere,[3] Wray,[4] and Kipphut et al.[5] solved for some equilibrium geometries in which the volume fraction of the solid and the dihedral angle were used to determine the grain configuration. These are two-phase solutions in which the starting conditions correspond to three phases, solid–liquid–vapor (pore), but this structure is ignored in the solid–liquid solutions just mentioned.[3–5] Consequently, some grain geometries develop outside those predicted, such as pores located inside liquid pockets that, in turn, are located inside solid grains, such as shown by Liu et al.[6] Other examples are observed in JONATHAN FIKES, Undergraduate Student, is with the Mechanical Engineering Department, Mississippi State University, Starkville, MS 39759. SEONG JIN PARK, Associate Professor, is with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea. Contact e-mail: [email protected] RANDALL M. GERMAN, Associate Dean, is with the College of Engineering, San Diego State University, San Diego, CA 92101. Manuscript submitted May 14, 2009. Article published online December 9, 2010. 202—VOLUME 42B, FEBRUARY 2011
tungsten heavy alloys, cermets, and composites in which liquid pools exist inside the solid grains. Figure 1 is a cross-section micrograph of a LPS tungsten heavy alloy in which solidified liquid pockets are evident in several single crystal tungsten grains. Trapped liquid pockets inside solid grains are evident in several LPS systems. Besides W-Ni, titanium carbide cermets with a ferrous matrix show this attribute as well as mixed carbides consisting of titanium-tungsten carbo nitrides in a cobalt matrix, such as (Ti,W)(C,N)-Co, (TiC-WC-MoC)(Ni,Co), Fe-Cu, and Mo-Ni.[2,7–11] Because systems are different in many regards, but the formation of liquid pockets inside the solid grains seems to be a reflection of grain growth and the trapping of liquid by coalescence rather than a system specific factor. These inside-out variants of liquid inside the solid grain are not included in the equilibrium geometry treatments mentioned. Thus, including the initial three phases (solid, liquid, and vapor) in solving for the lowest energy provides insight as to other metastable or minimum energy solutions, including situations in which pores or liquid pools are stable inside the solid grains. The final equi
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