Degree of pore-grain boundary contact during sintering
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I.
INTRODUCTION
INHIBITION of grain growth through pinning by a second phase is a well-known phenomenon. Precipitates and inclusions often inhibit grain boundary migration, and the relationship between the matrix grain size and the size and amount of second-phase particles has been modeled by the classical Zener relationship m and others, tz,3m During sintering of powdered metals or ceramics also, pores pin grain boundaries and inhibit grain growth until at approximately 90 pct of full density, more rapid grain growth occurs. Since grain boundaries would be observed to be in contact with second-phase particles or pores by random intersection, even if no pinning effect occurred, the pinning effect can be quantified by the amount of excess contact beyond random between grain boundaries and the second phase. Aigeltinger and Exner I5] proposed a measure of this excess contact as the ratio of the length of triple line marking the intersection between pore surfaces and grain boundaries in a material to the length of intersection expected for random contact. Ratios larger than unity indicate a strong pinning effect, a ratio of unity indicates no pinning tendency, a ratio less than unity would indicate an unstable interaction between surfaces. In their derivation, Aigeltinger and Exner rSl determined the grain boundary surface area per unit volume in the extended structure, i.e., that which would exist if pores were not present, as Sgv~/(1 - Wv), where S~vb is the grain boundary surface per unit volume in the real structure and VPvis the volume fraction of porosity. The resulting extended quantity is actually biased toward smaller values, since the grain boundaries intersect a greater fraction of porosity than V~ due to the pinning effect itself. In the current paper, the degree of excess contact is rederived using the a p p a r e n t volume fraction of porosity intersected by grain boundary rather than V~,. The application of this modified measure of excess pore-grain boundary contact to new data for sintered tungsten is described below. B.R. PATTERSON, Associate Professor, and Y. LIU, Graduate Student, are with the Department of Materials Science and Engineering, University of Alabama at Birmingham, Birmingham, AL 35294. J.A. GRIFFIN, formerly Graduate Student, Department of Materials Science and Engineering, University of Alabama at Birmingham, is Associate Engineer, Southern Research Institute, Birmingham, AL 35255. Manuscript submitted November 28, 1989. METALLURGICAL TRANSACTIONS A
II.
DERIVATION
Aigeltinger and Exner's tSj analysis involved plotting the measured length of intersection between grain boundary and pore surface per unit volume, L ~ , vs the amount of that triple line expected for random intersections of the two surfaces per unit volume, L~. In computing this random value, they employed the amount of grain boundary surface in the extended structure, i.e., that which would be present if the porosity was not present. In computing this by their Eq. [6], gb (sv)e,
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1 -
v~
11]
in which S{,b i
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