Theoretical modeling of densification during activated solid-state sintering
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I.
INTRODUCTION
ACTIVATED sintering is a powder processing technique aimed at accelerating the sintering rate by decreasing the activation energy for diffusion. A prime example is the reduction in sintering temperature that results from the addition of small amounts (less than 0.5 wt pct) of transition elements to W. Palladium, Ni, Co, Fe, and Pt are all effective activators of W, with Pd and Ni giving the greatest sintering enhancement.tL-5]The relative rankings of activator effectiveness are related to electron configurations, as first observed by Samsonov and Yakovlev. t6-n] Later, German and Munirtl.121 developed a quantitative model for activated sintering by combining electron configuration concepts with diffusional kinetics. German[131 also incorporated the diffusional activation energy into kinetic equations for the initial, intermediate, and final stages of sintering to predict densification under isothermal conditions. The resulting model underestimates shrinkage due to simplifying assumptions, but the main relations are in good agreement with experimental results. Farooq t~41 then extended German's model to include the effects of constant heating rates and successfully modeled the solid-state densification of the W-Ni-Cu system. In this article, the approach used by German and Farooq is refined to better represent the geometry of the microstructure during solidstate sintering, and the model results are applied to ele-
JOHN L. JOHNSON, formerly Director of Materials Development, P/M Lab, Department of Engineering Science and Mechanics, The Pennsylvania State University, is Injection Systems Engineer, Howmet Corp., Morristown, TN 37814. RANDALL M. GERMAN, Brush Chair Professor in Materials, is with the P/M Lab, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802-6809. Manuscript submitted April 19, 1995. METALLURGICALAND MATERIALSTRANSACTIONSA
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2
Fig. 1--Two particle geometry for predicting densification during the initial stage of solid-state sintering.
mental W as well as Co-, Ni-, Fe-, and Pd-activated samples.
II.
MATHEMATICAL MODELING
Solid-state sintering can be broken down into three stages: initial, intermediate, and final. In the initial stage, particles in contact with each other undergo neck growth, and densification occurs as the centers of the particles approach each other. The driving force for densification is the decrease in surface energy that accompanies dissipation of the curvature of the neck region. The classic two particle geometry shown in Figure 1 has been used by several researchers to analyze the initial stage sintering kinetics of single-phase materials, such as alumina, hematite, and silver,tlS-tsJ German[131also used the two particle geometry to analyze the enhanced initial stage sintering of refractory metals containing second-phase additions. After approximately 3 pct linear shrinkage, the curvature of the neck region decreases sufficiently that initial stage sintering VOLUME27A, FEBRUARY1996--441
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