Si diffusion across the liquid/solid interface of capillary driven (Al–Si)-K_xAl_yF_z micro-layers

Abstract

Diffusion is an important phenomenon involved in thermal processing, e.g., a Si diffusion in an (Al–Si)-K_xAl_yF_z clad alloy during aluminum (Al–Mn) brazing, to be considered in this study. Specifically, the Si migration affects the amount of liquid metal available to form a mating surfaces’ bond and further influences the solid substrate dissolution at the liquid–solid interface between (Al–Si)-K_xAl_yF_z and Al–Mn. These events greatly impact the performance (e.g., joint formation) of the materials involved. To quantify theoretically the available liquid metal contributing to the subsequent joint formation, the diffusion process is in the first approximation divided into two evolving time segments, both before the onset of resolidification: 1. the solid-state Si diffusion prior the clad melting and 2. the liquid state Si diffusion after the clad melting. Of the two segments, the later has not been addressed in the available literature. The analysis of the sequence of the solid and liquid diffusion segments has been facilitated by performing a series of experimental benchmark studies. The Si solid diffusion across the clad–core interface has been monitored at 150 °C, 250 °C, 350 °C, 450 °C and 550 °C peak temperatures. Each dwell at the peak lasted for 10 min. For the study of the impact of liquid diffusion on the solid substrate, the experiments have been performed at the peak temperature of 600 °C with different heating rates, ranging from 1 to 60 °C/min. The joint formation process evolution has been modeled, and an excellent agreement with empirical data has been established.

Graphical abstract

Appendices

Appendix A

Mean liquid diffusion coefficient

The mean liquid diffusion coefficient $\overline{{D_{liquid} }} = { 3}.{63 } \times { 1}0^{{ - {11}}}$ m²/s is calculated based on the following conditions: (1) the liquid diffusion range’s starting temperature is 590 °C; (2) the silicon solid solubility in aluminum, ${c}_{s}$, used in Eq. (4) is 1.1 wt%, which is evaluated at 600 °C. Alternative conditions may also be taken into consideration. For example, the liquid diffusion may already take place at the solidus line at 577 °C, which will affect both the solid and liquid diffusion time and as a result, influence the value of the liquid diffusion coefficient; In addition, the silicon solid solubility in aluminum, ${c}_{s}$, is changing with temperature. Thus, the boundary condition involved in Eq. (4) may also change. The current GDOES or EDS measurement is not sensitive enough to tell the difference. This also affects the calculation of the liquid diffusion coefficient. Table 5 illustrates the average liquid diffusion coefficient of Si at around 600 °C. The values vary from 1.00 × 10^–11 to 3.63 × 10^–11 m²/s, depending on different liquid diffusion starting temperature and silicon solubilities. These numbers are an order of magnitude larger than that of the pure solid diffusion coefficient of Si, which is 1.47 × 10^–12 m²/s as indicated in Table 3.

Table 5 Average liquid diffusion coefficient of Si at around 600 °C calculated depending on different conditions