ABSTRACT

The occurrence of the anomalous behaviour of increased isothermal solidification completion time, $t_f$ with increasing temperature in transient liquid phase (TLP) bonding, is investigated for cases of one-dimensional and multi-dimensional migration of solid–liquid boundary, using a numerical model. The analysis shows that the anomalous behaviour is not restricted to the generally reported one-dimensional case but also occurs during multi-dimensional displacements of the solid–liquid interface. It is found that it is possible for isothermal solidification rate constant $(\mathrm{\varnothing })$ to increase with increasing temperature and yet $t_f$ increase. Instead of a mere increase in $\mathrm{\varnothing }$ with temperature, it is the extent of the increase that determines if $t_f$ will reduce with an increase in bonding temperature. Increase in $t_f$ with temperature occurs when the increase in $\mathrm{\varnothing }$ is inadequate to overcome the concomitant increase in the volume of liquid produced at a higher bonding temperature. Additionally, the study shows that in contrast to general expectation, an increase in temperature can cause the diffusion-controlled $\mathrm{\varnothing }$ to decrease, notwithstanding a concomitant increase in the solute diffusion coefficient. This unique condition also causes$t_f$ to increase with an increase in bonding temperature. The theoretical findings in this work are corroborated by experimental observations reported in the literature.

摘要

等温凝固完成时间增加的异常行为的发生， ${Ť}_F$使用数值模型，研究了瞬态液相（TLP）键中温度升高的情况，研究了固液边界一维和多维迁移的情况。分析表明，异常行为不仅限于通常报道的一维情况，而且还发生在固液界面的多维位移过程中。发现等温凝固速率常数是可能的$（\mathrm{\varnothing }）$ 随温度升高而增加 ${Ť}_F$增加。而不是仅仅增加$\mathrm{\varnothing }$ 随着温度的升高，决定是否 ${Ť}_F$会随着粘合温度的升高而降低。增加${Ť}_F$ 随着温度的升高 $\mathrm{\varnothing }$不足以克服在较高的结合温度下随之产生的液体体积的增加。此外，研究表明，与一般预期相反，温度升高会导致扩散控制$\mathrm{\varnothing }$尽管溶质扩散系数会随之增加，但仍会降低。这种独特的情况也导致${Ť}_F$随着接合温度的升高而增加。这项工作的理论发现得到了文献报道的实验观察的证实。