It is known that the chemistries of hafnium and zirconium are more nearly identical than for any other two congeneric elements. Thus, both zirconia and hafnia, with the dielectric constant K > 20, have emerged as potential replacements for silica (K = 3.9) as a gate dielectric. We report an important difference between the zirconia/Si and hafnia/Si interfaces based on density functional theory calculations with the Perdew-Wang 91 exchange-correlation functional on the oxides, silicides, and silicates of Zr and Hf. The zirconia/Si interface has been found to be unstable with respect to formation of silicides whereas the hafnia/Si interface is stable. The difference between the two interfaces results from the fact that HfO2 is more stable than ZrO2 (i.e. has a larger heat of formation from its constituent elements) by more than 53 kJ/mol. The hafnium silicides, on the other hand, are less stable than zirconium silicides by ca. 20 kJ/mol.