  Zirconia (zirconium dioxide) and hafnia (hafnium dioxide) are binary oxides
used in a range of applications. Because zirconium and hafnium are chemically
equivalent, they have three similar polymorphs, and it is important to
understand the properties and energetics of these polymorphs. However, while
density functional theory calculations can get the correct energetic ordering,
the energy differences between polymorphs depend very much on the specific
density functional theory approach, as do other quantities such as lattice
constants and bulk modulus. We have used highly accurate quantum Monte Carlo
simulations to model the three zirconia and hafnia polymorphs. We compare our
results for structural parameters, bulk modulus, and cohesive energy with
results obtained from density functional theory calculations. We also discuss
comparisons of our results with existing experimental data, in particular for
structural parameters where extrapolation to zero temperature can be attempted.
We hope our results of structural parameters as well as for cohesive energy and
bulk modulus can serve as benchmarks for density-functional theory based
calculations and as a guidance for future experiments.
