Size driven thermodynamic crossovers in phase stability in zirconia and hafnia

Hafnia (HfO₂) and zirconia (ZrO₂) are of great interest in the quest for replacing silicon oxide in semiconductor field effect transistors because of their high permittivity. Both exhibit extensive polymorphism and understanding the energetics of their transitions is of major fundamental and practical importance. In this study, we present a systematic thermodynamic summary of the influence of particle size on thermodynamic phase stability in hafnia and zirconia using recently measured enthalpy data from the literature. The amorphous phase is found to be the most energetically stable above 165 and 363 m²/g of surface area for HfO₂ and ZrO₂, respectively. Below 16 and 20.3 m²/g of surface area, respectively, the monoclinic phase is the most energetically stable for HfO₂ and ZrO₂. At intermediate sizes there are closely balanced energetics among monoclinic, tetragonal, and cubic phases. The energy crossovers reflect decreasing surface enthalpy in the order monoclinic, tetragonal, cubic and amorphous for both hafnia and zirconia.