Diffusion-based model for isothermal solidification kinetics during transient liquid-phase sintering
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I. INTRODUCTION
TRANSIENT liquid phase sintering (TLPS) offers a number of processing advantages over solid-state sintering, including rapid densification during sintering, lower sintering temperatures, use of less-expensive elemental powders vs alloyed powders, and reduced microstructural coarsening.[1] Despite its importance as an advanced powder processing method, a fundamental understanding of the process, and the important variables controlling it, is incomplete.[2] During TLPS, a liquid phase forms, which spreads throughout the powder compact under capillary forces, causing particle rearrangement, enhanced mass transport, and densification.[2,3] This liquid phase is produced by the addition of an additive phase (constituent A), which melts at low temperatures and/or forms a low-melting-point eutectic with the base metal (constituent B). Eventually, the liquid must be readsorbed into the base metal, such that solidification occurs at the processing temperature.[4] Successful completion of the process requires that the volume of the liquid and its duration be sufficient to cause the required degree of densification. In addition, resolidification (liquid-phase readsorption) kinetics must be rapid enough so that the desired transient liquid affect is produced under the processing conditions used. The degree to which these requirements are met is determined by the interaction between the base and additive powders during processing, both before and after liquid is present. These interactions are primarily diffusion based, such as the solid-state diffusion of solute from the low-melting-point A phase into the highermelting-point B-phase powders.[2,4–6] The formation of intermediate (intermetallic) compounds can also form between the two constituents.[1,7–10] Base-additive interactions are most importantly determined by the choice of materials, but also by the processing variables, including powder size, green-powder packing density, heating rate, and sintering temperature.[1–11] The importance of the time for which the transient liquid is present is widely acknowledged.[2,5] However, the resolidification kinetics of the transient liquid is not well understood and has been described only on a qualitative basis. S.F. CORBIN, Assistant Professor, is with Department of Mechanical Engineering, University of Waterloo, ON, Canada N2L 3G1. Manuscript submitted January 3, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
The purpose of this study was to develop a simple, diffusion-based model to describe and quantify the rate of isothermal solidification during TLPS. The model was used to elucidate the important parameters, such as base-metal particle size and compact composition, that control the TLPS process. II. THE MODEL Modeling was restricted to a TLPS mixture consisting of an array of mixed powders from a binary alloy system with a eutectic phase diagram (Figure 1). A high-melting-point powder with a pure composition (i.e., XBo ⫽ 0, where X refers to the compositional weight fraction of solute in the phase) was consi
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