Low-temperature structure and the ferroelectric phase transitions in the $\mathrm{CdTi}{\mathrm{O}}_3$ perovskite

The paraelectric-ferroelectric transition in $\mathrm{CdTi}{\mathrm{O}}_3$ has been monitored using high-resolution neutron diffraction data. This necessitated preparing a sample enriched in ${}^{114}\mathrm{Cd}$. A subtle, but significant, anisotropy in the thermal expansion of the lattice parameters for $\mathrm{CdTi}{\mathrm{O}}_3$ associated with the transition to the polar structure was observed. First-principles calculations are presented to understand energies, phonon dispersion, and structures of possible phases with different symmetries.

Figure 1

The total energy versus f.u. volume for $\mathrm{CdTi}{\mathrm{O}}_3$ with different space groups. From the 12 structures in panel (a) the four low-energy phases are highlighted in panel (b).

Figure 2

Phonon dispersion curves for the (a) $Pnma$ phase, (b) $Pnma$ phase with $1\%$ expansion of volume, (c) $Pn{2}_{1}a$ phase and (d) $R\overline{3}$ phase of $\mathrm{CdTi}{\mathrm{O}}_3$.

Figure 3

Observed, calculated and difference neutron diffraction profile for $\mathrm{CdTi}{\mathrm{O}}_3$. The data were recorded at 300 K and fit is in space group $Pnma$ to the parameters listed in Table 2.

Figure 4

Representation of the corner-sharing $\mathrm{Ti}{\mathrm{O}}_6$ arrangement in $\mathrm{CdTi}{\mathrm{O}}_3$. The Ti cations are represented by gray spheres at the center of the octahedra. The oxygen atoms are represented by the small red spheres and the Cd cations by the green spheres.

Figure 5

Temperature dependence of the pseudocubic lattice parameters of $\mathrm{CdTi}{\mathrm{O}}_3$ between 7 and 300 K (transformation from orthorhombic to pseudocubic cell 1/2 0 1/2/0 1/2 0/−1/2 0 1/2). The estimated standard deviations are less than the size of the symbols. The pseudocubic volume is simply $\frac{1}{2}$ of the unit-cell volume which is illustrated in Fig. 6.

Figure 6

Temperature dependence of the normalized cell volume [Volume ($T$)/Volume (0 K)] of $\mathrm{CdTi}{\mathrm{O}}_3$ (closed symbols) and $\mathrm{CaTi}{\mathrm{O}}_3$ (open symbols). Estimated standard deviations for the unit-cell volumes are substantially smaller than the plotting symbols for both phases at all temperatures. The data for $\mathrm{CaTi}{\mathrm{O}}_3$ are taken from Knight [43].

Figure 7

Temperature dependence of the normaliszed lattice parameters of $\mathrm{CdTi}{\mathrm{O}}_3$ (closed symbols) and $\mathrm{CaTi}{\mathrm{O}}_3$ (open symbols). The values for $\mathrm{CaTi}{\mathrm{O}}_3$ have been offset for clarity. The data for $\mathrm{CaTi}{\mathrm{O}}_3$ are taken from Knight [43] transformed to $Pnma$. Estimated standard deviations for the unit-cell volumes are substantially smaller than the plotting symbols for both phases at all temperatures.