The recent and ongoing refinements of the phase diagrams of the PZT and NBT-BT solid solutions from anelastic and dielectric measurements1-3 are used to demonstrate the type of information that the two techniques can provide. The emphasis is put on the anelasticity experiments, which probe the stress-strain response and are only indirectly affected by the polar dynamics of ferroelectrics. This fact is advantageous, for example, in studying the non polar modes like octahedral tilting, but also allows additional information to be extracted on the nature of the phase transitions. As a first example, the morphotropic phase boundary (MPB) between rhombohedral (R) and tetragonal (T) phases is discussed. A major issue is whether the high electromechanical response near this border is due to the presence of a genuine monoclinic (M) intermediate phase4 or instead to nanotwinning of R or mixed R/T phases.5 The two alternatives are not easily distinguished with diffraction experiments, but PZT presents also a peak of the elastic compliance without frequency dispersion and whose amplitude is maximum at the middle of the MPB.1,3 Analysing this fact in terms of the Landau theory of phase transitions, it is shown that this peak in the compliance indicates that shear strain is linearly coupled to a continuous rotation of the polarisation direction, indicating that the transition is between T and M phases. Next, the octahedral tilting instability, omnipresent in perovskites, is discussed in the usual terms of mismatch between the equilibrium bond lengths of the octahedra and of the Pb-O sublattice, and in this view is expected to enclose the low T and low x region of the phase diagram of PbZr1 xTixO3. The onset of tilting below TT is most clearly seen in the anelastic than in the dielectric spectra, since the latter are dominated by the polar dynamics. The line TT(x) separating tilted and untilted R phases in PZT is shown to prosecute toward high x its decrease into the T phase, as expected. On the other hand, below x ~ 0.2 it splits into two distinct transitions. One is the usual border to the low-temperature R phase with octahedra rotated in antiphase along the <111> direction, which unexpectedly starts a ripid decrease for x < 0.2; instead, the path expected for TT is followed by the new transition, which therefore is interpreted as disordered or partial octahedral tilting. The (Na1/2Bi1/2)1-xBaxTiO3 solid solution is more difficult to study than PZT, due to the much stronger disorder: in fact there is coexistence of differently charged Na+, Bi3+ and Ba2+ ions, while in PZT Ti and Zr differ only in size. Yet, the anelastic spectra allow the border between the cubic paraelectric and tetragonal ferrielectric phase to be followed up to x ~ 0.06. Around this composition, the high disorder shortens the correlation lengths so much to give rise to diffuse or relaxor-like transitions. There is also a maximum in the compliance, less defined than that at the MPB of PZT, which by analogy may indicate the presence of M phase with very small correlation length also at the MPB of NBT-BT. [1] F. Cordero, F. Craciun and C. Galassi, Phys. Rev. Lett. 98, 255701 (2007). [2] F. Cordero, F. Craciun, F. Trequattrini, E. Mercadelli and C. Galassi, Phys. Rev. B 81, 144124 (2010). [3] F. Cordero, F. Trequattrini, F. Craciun and C. Galassi, J. Phys.: Condens. Matter 23, 415901 (2011). [4] B. Noheda and D.E. Cox, Phase Transit. 79 5 (2006). [5] A.G. Khachaturyan, Phil. Mag. 90 37 (2010).
Contributions from anelastic and dielectric spectroscopies to the definition of the phase diagrams of ferroelectric perovskites
F Cordero
2012
Abstract
The recent and ongoing refinements of the phase diagrams of the PZT and NBT-BT solid solutions from anelastic and dielectric measurements1-3 are used to demonstrate the type of information that the two techniques can provide. The emphasis is put on the anelasticity experiments, which probe the stress-strain response and are only indirectly affected by the polar dynamics of ferroelectrics. This fact is advantageous, for example, in studying the non polar modes like octahedral tilting, but also allows additional information to be extracted on the nature of the phase transitions. As a first example, the morphotropic phase boundary (MPB) between rhombohedral (R) and tetragonal (T) phases is discussed. A major issue is whether the high electromechanical response near this border is due to the presence of a genuine monoclinic (M) intermediate phase4 or instead to nanotwinning of R or mixed R/T phases.5 The two alternatives are not easily distinguished with diffraction experiments, but PZT presents also a peak of the elastic compliance without frequency dispersion and whose amplitude is maximum at the middle of the MPB.1,3 Analysing this fact in terms of the Landau theory of phase transitions, it is shown that this peak in the compliance indicates that shear strain is linearly coupled to a continuous rotation of the polarisation direction, indicating that the transition is between T and M phases. Next, the octahedral tilting instability, omnipresent in perovskites, is discussed in the usual terms of mismatch between the equilibrium bond lengths of the octahedra and of the Pb-O sublattice, and in this view is expected to enclose the low T and low x region of the phase diagram of PbZr1 xTixO3. The onset of tilting below TT is most clearly seen in the anelastic than in the dielectric spectra, since the latter are dominated by the polar dynamics. The line TT(x) separating tilted and untilted R phases in PZT is shown to prosecute toward high x its decrease into the T phase, as expected. On the other hand, below x ~ 0.2 it splits into two distinct transitions. One is the usual border to the low-temperature R phase with octahedra rotated in antiphase along the <111> direction, which unexpectedly starts a ripid decrease for x < 0.2; instead, the path expected for TT is followed by the new transition, which therefore is interpreted as disordered or partial octahedral tilting. The (Na1/2Bi1/2)1-xBaxTiO3 solid solution is more difficult to study than PZT, due to the much stronger disorder: in fact there is coexistence of differently charged Na+, Bi3+ and Ba2+ ions, while in PZT Ti and Zr differ only in size. Yet, the anelastic spectra allow the border between the cubic paraelectric and tetragonal ferrielectric phase to be followed up to x ~ 0.06. Around this composition, the high disorder shortens the correlation lengths so much to give rise to diffuse or relaxor-like transitions. There is also a maximum in the compliance, less defined than that at the MPB of PZT, which by analogy may indicate the presence of M phase with very small correlation length also at the MPB of NBT-BT. [1] F. Cordero, F. Craciun and C. Galassi, Phys. Rev. Lett. 98, 255701 (2007). [2] F. Cordero, F. Craciun, F. Trequattrini, E. Mercadelli and C. Galassi, Phys. Rev. B 81, 144124 (2010). [3] F. Cordero, F. Trequattrini, F. Craciun and C. Galassi, J. Phys.: Condens. Matter 23, 415901 (2011). [4] B. Noheda and D.E. Cox, Phase Transit. 79 5 (2006). [5] A.G. Khachaturyan, Phil. Mag. 90 37 (2010).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
