Gravitational effects on grain coarsening during liquid-phase sintering
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INTRODUCTION
GRAIN coarsening during liquid phase sintering (LPS) is of both fundamental and practical interest in materials science. This coarsening process, sometimes referred to as Ostwald ripening,[1,2] is generally described as diffusion controlled growth driven by the free energy changes associated with different grain sizes. The classical theory of coarsening, widely referred as the Lifshitz–Slyozov–Wagner (LSW) theory, was developed by Greenwood,[3] Lifshitz and Slyozov,[4] and Wagner.[5] The LSW theory is based on several assumptions: (1) spherical and isotropic grains; (2) no grain contact; (3) no direct diffusional interaction between grains; and (4) essentially zero volume fraction of solid. In attempts to describe microstructure evolution in LPS, many studies have included a solid volume fraction effect.[6–15] Generally, these descriptions are modified versions of the LSW theory. Such coarsening models are incompatible with LPS systems because the grains are in contact and often exhibit nonspherical shapes, as necessitated by grain shape accommodation. In addition to problems arising from these assumptions, coalescence complicates coarsening at high solid volume fractions.[16–28] In coalescence, contacting grains fuse by grain boundary migration, rotation, or because the contact occurs without grain misorientation. Above roughly 20 vol pct solid, bonds between solid grains are unavoidable.[29] The probability of grain coalescence increases with grain contact. According to the LSW theory, growth occurs over the solid-liquid surfaces. A high degree of solid grain contact (high contiguity) shields part of the interface over which diffusion occurs and should slow grain growth. The opposite occurs, with the growth rate increasing with solid contiguity,[2,8–13,26,30–32] a factor not explained by classic models and largely attributed to coalescence. Other problems with classical coarsening theory have RANDALL M. GERMAN, Brush Chair Professor in Materials, and ANTHONY GRIFFO, Director, Materials Development, are with the Engineering Science and Mechanics Department, The Pennsylvania State University, University Park, PA 16802-6809. YIXIONG LIU, formerly Director, Theoretical Modeling, with the Engineering and Mechanics Department, The Pennsylvania State University, is Senior Engineer, Kennametal Inc., Latrobe, PA 15650-0231. Manuscript submitted February 5, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
been the subject of recent analyses.[33–36] By introducing the concept of communication neighbors to treat grain interactions, DeHoff[33] developed a geometrically general model that contrasts with classic diffusion controlled coarsening theory. The LSW theory says the growth or shrinkage of a grain depends on its size relative to the mean grain size. However, direct observations show some grains larger than average shrink and some grains smaller than average grow, indicative of local effects not embraced by existing LSW models.[37] Likewise, computer simulations based on LSW theory show a significant n
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