The instability of solid-liquid interface (ISLI) during the liquid-phase sintering was studied using carbide-Ni composites. Of the various transitional metal carbides TiC of 4th period is the only carbide that exhibits a strong ISLI with negative curvatures in molten Ni. No ISLI was observed for other carbides in the 5th and 6th periods. The origin of ISLI is strain developed at the interface between the carbides and the newly formed solid solutions. The difference in the size of the atoms involved can be used to predict the formation of a carbide-Ni solid solution when the Hume-Rothery rules are applied. Aside from the size factor, other factors in the rules are not effective in predicting this phenomenon.