Structure and thermodynamic properties of hafnia–silica glasses with low hafnia content

• We study HfO2–SiO2 glass with low hafnia content (2.8–10.0 mol%).
• Our models show formation of HfOx clusters and Hf–O–Hf linkages.
• Solubility of HfO2 in SiO2 is 1.9 [− 0.3/+ 11.6] mol% at 1873 K.
• Heat capacities of hafnia–silica glass follow a simple rule of mixture.
• Adding hafnia to silica depletes low frequency modes that relate to floppy modes.

Using density functional calculations we study structural, elastic, vibrational and thermo-chemical properties of hafnia–silica glasses with low hafnia content (≤ 10 mol%). Melt-quench-generated models show a preference for Hf–O–Hf linkages and early formation of HfOx-clusters. We compute an enthalpy of mixing of HfO2 in SiO2 of (0.8 ± 0.3) eV/HfO2, and estimate a solubility of HfO2 in SiO2 of 1.9 [− 0.3/+ 11.6] mol% at 1873 K. Elastic moduli of hafnia–silica glasses are comparable to those of pure silica for the range of compositions addressed here. Heat capacities of mixed glasses follow a simple rule of mixture. Addition of hafnia to silica glass shifts high-frequency modes to lower wave numbers. Our data suggests that Hf atoms and small HfOx-clusters pin floppy modes in silica glass, visible in a depletion of low-frequency vibrational modes.