A model for coupled growth of reaction layers in reactive brazing of ZrO 2 -toughened Al 2 O 3
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INTRODUCTION
BRAZING of ceramics is normally done by the use of active filler metals in order to promote wetting and subsequent bonding of the materials.[1] The expression ‘‘reactive brazing’’ refers to a situation where strong oxide and nitride formers such as titanium or zirconium are added to the filler metal. Their role is mainly to facilitate the formation of a reaction layer at the interface between the braze metal and the ceramic, which, in turn, can help to ensure intimate interfacial contact and hence a high bond strength.[2–5] When an interfacial reaction takes place between a ceramic and a reactive metal, different reaction layer products may form, depending on the nature of the diffusion couple. Whereas diffusion in binary systems can be subjected to an exact analytical treatment,[6,7] diffusion in multicomponent systems cannot be treated with the same degree of mathematical precision because of the complexity of the rate phenomena involved.[8,9] Additional problems result from the lack of adequate thermodynamic data and the fact that some of the constituent elements may diffuse up their own concentration gradient as opposed to the binary case where both the concentration and activity gradients usually have the same direction.[8] In spite of these difficulties, several models have been developed over the years to describe reaction layer growth during brazing and solid-state diffusion bonding.[6,8–12] The most thorough analysis is probably that of van Loo,[8] who have presented generic solutions for ternary diffusion couples. A different modeling approach has recently been launched by Torvund et al.,[13,14] on the basis of the classical solution for parabolic growth of transformation products. Here, the microstructure evolution is captured mathematically in terms of differential variation of the primary state variable with time to allow for transient effects during heating and cooling as well as changes in the growth kinetics T. TORVUND, formerly graduate Student, Department of Metallurgy, Norwegian University of Science and Technology, is Research ˚ rdal, Norway. Metallurgist with Hydro Aluminium, N-5870 Øvre A Ø. GRONG, Professor, is with the Department of Metallurgy, Norwegian University of Science and Technology, N-7034 Trondheim, Norway. O.M. AKSELSEN, Research Manager, and J.H. ULVENSØEN, Group Leader, are with SINTEF-Materials Technology, N-7034 Trondheim, Norway. Manuscript submitted January 15, 1996. 3630—VOLUME 27A, NOVEMBER 1996
due to consumption of the reactive element. Although this method involves many simplifications and assumptions, it has proved to work well for many ceramic-braze metal combinations where the growth process can be described by a single diffusion mechanism.[13] Problems arise, however, when different diffusion mechanisms are operating in succession at the same time as the primary reactions become masked by subsequent solid-state transformations. In such cases, each step must be modeled separately and then coupled in a manner that enforces continuity and equilibrium.
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