Modeling of Intermetallic Compounds Growth Between Dissimilar Metals
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RMETALLIC compounds (IMCs) are often formed at the interface between dissimilar metals during diffusion bonding, welding, and mechanical milling, etc.[1–5] The IMCs usually have properties that are very different from the base metals and thus have a critical effect in controlling overall joint performance. Diffusion bonding is a widely used technique to study the growth kinetics of IMC phases between dissimilar metals. In a diffusion-bonded couple, two different metals are brought into intimate contact and then annealed at an appropriate temperature below the eutectic melting temperature. Solid-state diffusion occurs between the two metals and leads to the formation of one or more IMC phases at the interface between the two metal substrates once a critical level of enrichment is reached. Once the IMC has formed a continuous layer at the interface, further growth is only possible by diffusion through the IMC itself, and an abrupt change in kinetics is often observed. To produce a bond with good mechanical properties, it is usually essential to maintain the IMC layer thickness below a critical value, since IMC phases are typically brittle and can lead to a marked loss in joint toughness if allowed to become too thick.[5–8] Therefore, many researchers have studied reactive diffusion in a large number of binary alloy diffusion couples and there have also been several attempts to model the evolution of the IMC layer.[1–5] It is widely accepted that reactive diffusion is mainly LI WANG, Engineer, formerly with the Grosvenor Street, Manchester M13 9PL, UK, is now with the Jaguar Land Rover Company, Coventry, UK. Contact e-mails: lwang9@jaguarlandrover. com; [email protected] YIN WANG, Ph.D. Student, PHILIP PRANGNELL, Professor, and JOSEPH ROBSON, Reader, are with the University of Manchester. Manuscript submitted March 8, 2015. Article published online July 8, 2015 4106—VOLUME 46A, SEPTEMBER 2015
governed by volume diffusion,[1–3,9,10] and the thickness of an IMC phase generally follows a parabolic relationship with annealing time.[3,5,9,10] It is common in analyzing reactive interdiffusion to measure the thickness of the IMC layer as a function of time under isothermal conditions and then fit the data to a parabolic law of the form: l2 ¼ kt;
½1
where l is the layer thickness, k the parabolic coefficient, and t is time. By performing such experiments at a range of temperatures, an effective activation energy Q and the pre-exponent factor k0 for the thickening kinetics are obtained from the Arrhenius equation.[1–3,10] According to Kidson,[11] the parabolic coefficient is a mixture of many different parameters, and the simple Arrhenius dependence on temperature is not strictly correct. It is found that the values of activation energy that are derived from such experiments show a large variation even for the same system between studies, e.g., the activation energy for thickening of the Al3Mg2 phase, which is the main IMC phase in the Al-Mg binary diffusion system, is reported in a range from 65 to 86 kJ/mol, which is a very significan
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