High-pressure phases of ${\text{ZrO}}_2$: An ab initio constant-pressure study

The high-pressure behavior of ${\text{ZrO}}_2$ is studied using an ab initio constant-pressure technique up to 140 GPa. Two high-pressure phases of ${\text{ZrO}}_2$ are predicted through constant-pressure simulations. ${\text{ZrO}}_2$ undergoes a first-order phase transformation from the baddeleyite structure to an orthorhombic structure with space group $Pbcm$ at 35–40 GPa. The coordination number of Zr atoms unexpectedly changes from sevenfold to sixfold owing to this phase transformation. Further increase in pressure leads to another first-order phase transformation from the $Pbcm$ structure to a tetragonal one with the space group $P4/nmm$ at 70–80 GPa. In this structure, Zr atoms are ninefold coordinated. These phase transformations should occur around 11 and 38 GPa from enthalpy calculations, respectively.

Figure 1

(Color online) Crystal structures of ${\text{ZrO}}_2$: baddeleyite (top panel) at zero pressure, $Pbcm$ (middle panel) at 40 GPa, and $P4/nmm$ (bottom panel) at 80 GPa. All phases are viewed along [010] direction.

Figure 2

(Color online) Changes in the simulation cell lengths and angles as functions of pressure. The simulation cell vectors $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ are initially along the [100], [010], and $\left[\overline{1}01\right]$ directions, respectively. The magnitudes of these vectors are plotted in the figure. The $\beta$ is the angle between $\mathbf{A}$ and $\mathbf{C}$ vectors.

Figure 3

Pressure-volume curve.

Figure 4

(Color online) The computed energies of ${\text{ZrO}}_2$ phases as functions of volume.

Figure 5

The calculated enthalpies of ${\text{ZrO}}_2$ structures as functions of pressure: (a) $\Delta H=H_{\text{baddeleyite}}-H_{Pbca}$; (b) $\Delta H=H_{\text{baddeleyite}}-H_{Pbcm}$; (c) $\Delta H=H_{Pbca}-H_{Pnma}$; (d) $\Delta H=H_{Pbcm}-H_{P4/nmm}$.