Determination of pore mobility during sintering
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I.
INTRODUCTION
THE importance of the interaction between grain boundaries and pores with regard to microstructural evolution during sintering has long been recognized, t~,2,31 Theoretical models previously have been developedt4,Sj for grain growth in porous compacts where the rate of grain-boundary migration is controlled by the movement of pores. Pore velocity is conventionally treated as the product of driving force and pore mobility, and for a particular grain size, the pore mobility is the decisive factor in controlling the pore velocity, which in turn controis the velocity of the moving grain boundary. Although the concept of pore mobility is imperative in developing models of pore-controlled grain growth, few models, if any, have been tested experimentally due to the lack of means for experimentally determining pore mobility. Shewmon t6] developed theoretical expressions for the mobilities of individual spherical particles or pores, Mp, moving by surface, lattice, or vapor transport, and these expressions have been employed in numerous models of pore-controlled grain growth. Since these expressions are based upon the driving force per pore, these models must include ad hoc assumptions concerning the number of spherical monosized pores per grain boundary. Defining mobility in terms of individual pores also results in different units than conventionally used for grainboundary mobility, creating problems in modeling)4,71 Recently, simpler, more realistic models of inhibited grain growth have been derived, tTl employing more general descriptions of the amount of porosity in contact with grain boundaries, independent of pore morphology, connectivity, and size distribution. Models such as these, based upon measurable stereological parameters, have the benefit of being easily tested experimentally. It is desirable that pore mobility also be expressed in general terms, allowing experimental evaluation from direct Y. LIU, Postdoctoral Researcher, and B.R. PATTERSON, Professor, are with the Department of Materials Science and Engineering, University of Alabama at Birmingham, Birmingham, AL 35294. Manuscript submitted October 9, 1992. METALLURGICAL AND MATERIALS TRANSACTIONS A
microstructural measurements. Such general expressions for pore mobility are especially desirable in light of the changes in pore morphology that occur during sintering, with the porosity in the form of interconnected sheets at low-sintered densities, changing to interconnected channels and finally to separate spheres at the highest densities. A credible method for determining pore mobility must also consider these morphological changes in the pore phase. The present article develops a new expression of pore mobility based on stereologically measurable microstructural parameters, following Shewmon's t61 methodology, but avoiding geometric assumptions. The present model of pore mobility can be readily employed using experimentally accessible microstructural experimental data, as illustrated here for sintered copper and tungsten.
II.
DERIVATIO
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