Soft antiferroelectric fluctuations in morphotropic PbZr${}_{1-x}$Ti${}_x$O${}_3$ single crystals as evidenced by inelastic x-ray scattering

Lattice dynamics of a PbZr${}_{1-x}$Ti${}_x$O${}_3$ single crystal with composition close to the morphotropic phase boundary has been investigated by inelastic x-ray scattering. Dispersion curves of the lowest frequency transverse optic and the transverse acoustic phonon modes propagating along the [100] direction have been determined in the high-temperature paraelectric phase as well as in the room-temperature monoclinic phase. The measurement also reveals that upon cooling from the paraelectric to monoclinic phase, the spectral response of the $M_{5^{\prime }}$ zone boundary phonon mode associated with antiferroelectric vibrations of lead ions is progressively transforming to a broad central mode. This indicates a crossover from vibrational to relaxational-type dynamics. The existence of this phenomenon previously observed in relaxor materials is a striking result for PZT and it is believed to arise from the nanoscale structural inhomogeneity of these materials.

Figure 1

Room-temperature inelastic x-ray spectrum of transverse acoustic (TA) and transverse optic (TO) modes propagating along the pseudocubic [010] direction in the PZT single crystal.

Figure 2

Low-frequency phonon dispersion curves of PZT single crystal with $x~0.475$ determined from the IXS measurements. Full symbols are phonon frequencies measured at room temperature (high-temperature monoclinic phase), open symbols were taken at 740 K (cubic phase). Data shown in (a), (b), and (c), were determined from measurements with momentum transfers $(\xi ,0.5,3.5)$, $(\xi ,\xi ,3-\xi )$, and $(3,\xi ,0)$, respectively. Open triangle stands for the room-temperature soft-mode frequency determined by Raman scattering in Ref. 16, continuous lines are guides to the eye.

Figure 3

Inelastic x-ray spectra showing (a) $M_{2^{\prime }}$ and (b) $M_{5^{\prime }}$ zone boundary modes as a function of temperature. Lines are guides to the eye.

Figure 4

Eigenmodes of the $M$-point [$\mathbf{q}=(0.5,0.5,0)$] phonons associated with lead ion motions. (a) $M_{2^{\prime }}$ singlet mode; (b) $x$ component of the $M_{5^{\prime }}$ doublet. Pb${}^{2+}$ ions are represented by spheres, oxygen octahedra are shown schematically.