Influence of variable diffusion coefficient on solid-liquid interface migration kinetics during transient liquid phase bonding

ABSTRACT

A new finite difference numerical model with variable diffusion coefficient is developed by using an explicit-fully-implicit hybrid method and Landau transformation with adaptable spatial discretization to study the solid–liquid interface migration kinetics during transient liquid phase bonding. It is found that notwithstanding the fact that diffusion coefficient varies with concentration, the kinetics of the solid–liquid interface displacement can still be represented by a constant parameter, known as isothermal solidification rate constant. Nevertheless, the results of the numerical model, which are verified with experimental data, reveal a key reason why the extent of diffusion-controlled isothermal solidification during TLP bonding deviates from a linear relationship with$\sqrt{t}$, i.e. deviation from parabolic law behaviour. The deviation occurs when the concentration dependency of diffusivity changes with time. This key finding constitutes a new explanation for the occurrence of deviation from the parabolic law behaviour and it can explicate the deviation occurrence in systems where prior suggested reasons in the literature do not apply.

KEYWORDS:

• Brazing
• transient liquid phase bonding
• joining

Acknowledgment

The authors gratefully acknowledge financial support by NSERC of Canada.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada.