Compositional behaviour of phonons in Pb(Zr1-xTix)O3 ceramics


We developed a purposely designed mathematical analysis of the Raman spectra based on their frequency derivatives: the method finds the curvature maxima in concave-down regions of the spectra (CMCD analysis), in order to count peaks and shoulders of the experimental spectra, comparing them to the results of the standard fitting with damped harmonic oscillators. The combination of the two approaches is very helpful to find “hidden” structure in the spectra of disordered materials.

In the case of PZT, the crossover from the tetragonal to the rhombohedral phase is clearly visible in the Raman spectra; however, there are no indications of a systematic splitting of the E-symmetry modes into A’–A’’ doublets related to the monoclinic symmetry in the morphotropic samples. Detailed adjustment of the response function to the spectrum requires to assume additional Raman active modes, but this holds for a much broader concentration range than that of the anticipated monoclinic phase.

The analysis of the phonons found also that the lowest frequency transverse optic mode of E-symmetry (soft mode of the ferroelectric phase transition) is split into two components, a THz frequency anharmonic (central mode-like) component and a resonant component (at frequencies ω ~ 80 cm-1). A new Raman band appearing in this frequency range at low temperatures is rather associated with the anti-phase tilt vibrations of the oxygen octahedra. These results are in perfect agreement with our previous IR studies on these ceramics [E. Buixaderas et al., Phys. Rev. B 84, 184302 (2011)].

Obr. 1: CMCD analysis of the Raman spectrum of the PZT 52/48 ceramics at 400 K together with the simulated smoothed spectrum and its derivatives up to the third order. Arrows denote frequencies of the maxima and the cross-symbols denote CMCD points, defined as negative minima of the second derivative of the spectrum.
Obr. 2: Compositional dependence of the phonon frequencies in PZT ceramics at 80 K. Black crosses correspond to the negative minima of the second derivative (peaks and shoulders). Spectra of the tetragonal sample 30/70 with labels are shown for illustration.