Many-electron calculations of the phase stability of ${\mathrm{ZrO}}_2$ polymorphs

Zirconia $\left({\mathrm{ZrO}}_2\right)$ has been well studied experimentally for decades, but still poses a severe challenge for computational approaches. We present thorough many-electron benchmark calculations within the random-phase approximation framework of the phase stabilities of the most common ${\mathrm{ZrO}}_2$ phases and assess the performance of various density functional theory (DFT) and beyond-DFT methods. We find that the commonly used DFT and hybrid functionals strongly overestimate both the energetic differences of the common phases and the stability of two metastable phases. The many-electron calculations offer a significantly improved description of the predicted bulk properties, especially of the bulk modulus $B_0$. On the DFT level, the van der Waals corrected meta-generalized-gradient approximation (SCAN-rVV10) provides much better agreement with the experimental values than other (semi)local and hybrid approaches.

Figure 1

(a)–(e) Cubic, tetragonal, metamonoclinic, monoclinic, and anatase phases. Zr and O atoms are colored green and red, respectively. (f) Total energy differences per formula unit of the five phases calculated with selected functionals.

Figure 2

Helmholtz free energy $F\left(T\right)$ in the harmonic approximation calculated with the (a) PBE, (b) SCAN, and (c) SCAN-rVV10 functionals. The crossing points highlighted by horizontal lines indicate the predicted monoclinic-tetragonal and tetragonal-cubic phase transition temperatures.