Phonon anharmonicity of monoclinic zirconia and yttrium-stabilized zirconia

Inelastic neutron scattering measurements on monoclinic zirconia $({\mathrm{ZrO}}_{\text{2}})$ and 8 mol% yttrium-stabilized zirconia were performed at temperatures from 300 to $1373w\mathrm{K}$. Temperature-dependent phonon densities of states (DOS) are reported, as are Raman spectra obtained at elevated temperatures. First-principles lattice dynamics calculations with density functional theory gave total and partial phonon DOS curves and mode Grüneisen parameters. These mode Grüneisen parameters were used to predict the experimental temperature dependence of the phonon DOS with partial success. However, substantial anharmonicity was found at elevated temperatures, especially for phonon modes dominated by the motions of oxygen atoms. Yttrium-stabilized zirconia (YSZ) was somewhat more anharmonic and had a broader phonon spectrum at low temperatures, owing in part to defects in its structure. YSZ also has a larger vibrational entropy than monoclinic zirconia.

Figure 1

Intensity of ${\chi }^{\prime \prime }(Q,E)$ for (a) zirconia and (b) 8 mol% YSZ at 300 K from the time-of-flight inelastic neutron scattering measurements with background subtracted. The color scales are in log scale and with the same range. YSZ shows fewer features at low energy transfers.

Figure 2

Comparison of the Raman spectra of zirconia [red, top (773 K) and bottom (300 K)] and YSZ (black) at temperatures as labeled.

Figure 3

Temperature dependencies of fit parameters for Raman peaks, numbered as in Fig. 2. Solid black lines are for YSZ, and dashed red for ${\mathrm{ZrO}}_2$. (a) Center energy. (b) Full width at half maximum.

Figure 4

Normalized neutron-weighted phonon DOS curves of (a) zirconia, and (b) 8 mol% YSZ from inelastic neutron scattering with 163 or 175 meV incident energies at temperatures from 300 to 1373 K with background subtracted. The solid lines are the results from the MICAS furnace, dashed lines from the stick furnace. The vertical lines are aligned with peaks at 300 K.

Figure 5

Neutron-weighted phonon DOS curves of (a) zirconia, and (b) 8 mol% YSZ from inelastic neutron scattering with 90 meV incident energies at temperatures from 300 to 1373 K in the MICAS furnace with background subtracted. The lower incident energy gives better resolution than the results of Fig. 4.

Figure 6

Total and partial phonon DOS curves of (a) monoclinic, (c) tetragonal phases from first principles DFT calculations. The thick gray lines are the phonon DOS with proper neutron weighting and ARCS instrument resolution at 163 meV incident energy. They are compared with the results from neutron experiments on monoclinic zirconia (b), on YSZ (d) at 300 K on the right.

Figure 7

Grüneisen parameters for monoclinic and tetragonal phases calculated from first-principles and finite displacement methods. The energy-dependent averages are shown as solid lines.

Figure 8

Experimental phonon DOS curves of (a) monoclinic zirconia and (b) tetragonal YSZ compared with the QHA model calculations described in the text. Predictions with mode Grüneisen parameters for both the monoclinic and tetragonal materials are shown in panel b.

Figure 9

The approximate difference between phonon entropies of YSZ and monoclinic zirconia, $\Delta S=S_{\mathrm{YSZ}}-S_{\mathrm{mono}}$, corrected approximately for neutron weighting.