Transient liquid-phase bonding in two-phase ternary systems
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INTRODUCTION
THE problem of transient liquid-phase (TLP) bonding (along with the allied one of liquid-phase sintering) has received considerable attention in recent years. The joining process holds high promise for the controlled bonding of base materials; it involves the isothermal disappearance of a liquid phase at a rate determined primarily by solid-state diffusion. The liquid results from the placement at the joint of a thin layer (interlayer) with a melting point lower than that of the material to be joined. In the simplest case, the base material is a pure component, and the interlayer a binary alloy containing the base material as a solvent and a solute that lowers its melting point. In a more general case, the base material and the interlayer will be made up of more than two components. For the most part, the literature makes only passing reference to the possible effect of a third component (a second solute) on the process of isothermal solidification.[1] This contribution builds on a previous communication dealing with the extension to the three-component problem.[2] The experimental situation is reviewed, along with the analysis of the binary problem in a recent article by Zhou et al.[3] The process is considered as a sequence of distinct stages: heating to the joining temperature, isothermal solidification, and homogenization. The usual treatment of the isothermal solidification stage is relatively simple, as illustrated in Figure 1, for the case of bonding a pure element using an interlayer containing a solute,[1] which lowers the melting point of the solvent. For a given temperature, the compositions of the liquid and solid in equilibrium are fixed. Once the interlayer material melts, it is assumed rapidly to come to equilibrium with the solid base material. (This equilibration process will generally involve the growth of the liquid phase from its initial volume.) In the subsequent solidification stage, the solute is taken from the liquid by solid-state diffusion; consequently, the interlayer shrinks, and eventually disappears. Under the reasonable assumptions of local equilibrium at the solid-liquid interface, planar solid-liquid interfaces, complete mixing in the thin liquid C.W. SINCLAIR, Graduate Student, and G.R. PURDY, Professor, are with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada L8S 4L7. J.E. MORRAL, Professor, is with the Metallurgy and Materials Engineering Department, Institute of Materials Science, University of Connecticut, Storrs, CT 06269-3136. Manuscript submitted July 20, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
layer, and constant diffusion coefficient in the solid, the binary solidification problem lends itself to a straightforward analytical treatment. For the isothermal solidification stage, the result is a parabolic time dependence of the liquid-layer thickness w on the diffusion length (!Dt) of solute 1 in the solid a phase[3]: w } !D1a t
[1]
If we consider the ternary extension of this most elementary analysis, we
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