Quantitative determination of topological and metric properties during sintering of copper
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] . H E objective of the work reported in this paper is the quantitative description of the path of m i c r o s t r u c rural change, defined as the sequence of m i c r o s t r u c rural states, that accompanies sintering in the simple case of a unary, one phase metal. This path is described in t e r m s of geometric properties of features that exist in sintered m i c r o s t r u c t u r e s . The m i c r o structural features that may exist in such a structure are: the pore and solid phases; the pore-solid interface and grain boundaries in the solid phase; triple lines where grain boundaries intersect the pore-solid interface, and where three grain boundaries meet; and two kinds of quadruple points. The m i c r o s t r u c t u r a l state of any sintered structure is specified by applying quantitative microscopy to estimate geometric properties of some of these features. In the present paper, measurements of the following properties are reported for three series of sintered structures: 1) two topological properties, number of disconnected parts (Np) and connectivity (Gp), of the pore and solid phases, as well as the pore-solid interface; and 2) four m e t r i c properties, volume fraction (V V) of the pore network, surface a r e a per unit volume of both the pore-solid interface (Sv) and the grain boundary network in the solid phase (Syzb) , and the total curvature (Mv) of the pore-solid in-terface. E. H. AIGELTINGERis Post Doctoral Assistant, Department of Metallurgy, University of Melbourne, Melbourne, Australia. R. T. DeHOFF is Professor, Department of Materials Science and Engineering, Universityof Florida, Gainesville, FL. Manuscript submitted October 13, 1971. METALLURGICAL TRANSACTIONS A
These properties were determined for a sequence of pore volume fractions prepared by loose sintering each of two size fractions of spherical copper powder ( - 120 + 140) or 115 micron, and ( - 270 + 325) or 48 micron, and a single size fraction of dendritic copper powder ( - 270 + 325). In each case the variation of topological and metric properties with pore volume fraction delineates the path of microstructural change for the system. The three powders studied were chosen to provide quantitative comparison of the effect of particle size or scale of the system, and effects of particle shape and stacking, upon the path of m i c r o structural change. The metric properties, volume fraction, surface area and total curvature, were determined using e s tablished procedures of quantitative microscopy. 1 The topological properties were determined by applying new procedures developed specifically for this r e s e a r c h . The estimation of connectivity and number of isolated parts of a phase is based upon an analysis of a s e r i e s of closely spaced microsections through the system and involves identifying and counting specific classes of changes that can be inferred to have occurred between adjacent sections. This inspection permits the analysis of a network which r e p r e s e n t s the skeleton of the phase, called its defor
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