Combined Stage Sintering Model: Review and Applications
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COMBINED STAGE SINTERING MODEL: REVIEW AND APPLICATIONS R.P. RUSIN*, J.D. HANSEN**, M.-H. TENG* AND D. LYNN JOHNSON* *Northwestern University, Dept. of Materials Science & Engineering, 2145 Sheridan Road, Evanston, IL Corp., 60208.2724 S. Peck Road, Monrovia, CA 91016-7118 **3M Unitek
ABSTRACT In the combined stage sintering model previously introduced[l], a single equation was derived that quantifies sintering as a continuous phenomenon from beginning to end. The microstructure is characterized by two separate parameters representing the geometry (1') and the scale (G). Calculations of r from experimental data show the effect of surface diffusion and microstructural geometry on r. The model is reviewed and discussed with respect to the sintering of alumina and spherical nickel powder. INTRODUCTION Sintering is traditionally viewed in terms of three distinct stages. Existing single-stage sintering models[2-6] assume idealized geometries, thus limiting their applicability; moreover, they do not allow consideration of the entire sintering process. A diffusion sintering model has been developed[l] that overcomes these limitations and describes sintering as a continuous process from beginning to end. Several such models have been proposed. A cell geometry has been used to describe microstructural evolution during sintering[7], but the effect of microstructural geometry on densification kinetics was not explored. A generalized sintering equation, stated without derivation or discussion, was employed in a study of sintering activation energies[8]. Recently, a general model was proposed in terms of a sintering stress[9]. In none of these was the evolution of geometry considered in any detail. The present model was obtained first by inspection of the traditional single stage models[1012] and later derived rigorously[l]. In this work we describe the features of this model and some examples of its use. lrain Boundary Pore THE MODEL The fundamental twodimensional section of a microstructure sintering under capillary forces is shown in Figure 1. This basic geometric element is common to all microstructures from the green stage to near theoretical density[l]. This element can be envisioned as the neck between two
Edge of Diffusion
Pore - Boundary Intersection
Figure 1. Fundamental sintering geometry. (From Ref. [1]. Used with permission.)
Mat. Res. Soc. Symp. Proc. Vol. 249. ©1992 Materials Research Society
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sintering particles in the initial stage, as grains with open serpentine pores at the grain boundaries in the intermediate stage, and as grains with closed pores on the grain boundaries in the final stage. Recognition of this fundamental geometry is essential to the derivation of a combined stage sintering model. In all stages of sintering, the chemical potential gradient between grain boundaries and the curved pore surfaces induces a diffusional flow of atoms to the pores. The model relates the linear shrinkage rate to this chemical potential gradient and the geometrical features of the microstructure through th
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