Calorimetric Measurements of Surface Energy of Amorphous HfO₂ Nanoparticles Produced by Gas Phase Condensation

Thermodynamics of nanomaterials is strongly influenced by the energetic contribution from atoms located at the interfaces. Therefore, accurately assessing the surface energy of nanomaterials is essential for calculating and predicting thermodynamic properties. In the present work, surface energy of amorphous hafnium oxide (am-HfO₂) nanoparticles was measured using independent calorimetric techniques. am-HfO₂ nanoparticles were synthesized by condensation from a gas phase generated through laser evaporation of bulk HfO₂ targets at 0.1 Torr oxygen pressure. Their surface energy was directly measured using high-temperature oxide melt solution calorimetry, differential scanning calorimetry, and water adsorption calorimetry. The measured surface energies using the above techniques, respectively, are 0.76 ± 0.12, 0.47 ± 0.2, and 0.59 ± 0.1 J/m². The differences among the surface energy values are about 0.3 J/m², which is generally within the experimental uncertainties and different assumptions for each technique. The surface energy of the amorphous phase is substantially smaller than that of crystalline phases, as seen previously for other oxides. Thus, the amorphous phase may be thermodynamically favored when small particles are produced and retained.