Piezoelectric anisotropy-phase transition relations in perovskite single crystals

The orientation dependence of the longitudinal piezoelectric coefficient, d(33)(), is investigated as a function of temperature in BaTiO3 and PbTiO3 crystals using the Landau-Ginsburg-Devonshire theory. We show that a presence of the ferroelectric-ferroelectric phase transitions in BaTiO3 leads to enhanced d(33)() along nonpolar directions. The reason for this is that in the vicinity of a phase transition temperature at which a polarization vector changes its direction (tetragonal-orthorhombic/monoclinic, orthorhombic/monoclinic-rhombohedral), the shear piezoelectric coefficients become high. It is shown for all ferroelectric phases of BaTiO3 that the shear stress deforms the crystal cell and changes the polarization direction in a similar way as the corresponding temperature-induced phase transition. The influence of the piezoelectric shear effect on the anisotropy of d(33)() is particularly pronounced in the orthorhombic/monoclinic phase where the piezoelectric shear coefficients are determined by the presence of both the high-temperature tetragonal and the low-temperature rhombohedral phases. In PbTiO3, which does not exhibit ferroelectric-ferroelectric phase transitions, the shear piezoelectric effect is weak and d(33)() has its maximum along the polar axis at all temperatures. These results can be generalized to include phase transitions induced by electric-field and composition variations and are valid for all perovskite materials, including complex relaxor-ferroelectric perovskites that have recently attracted attention for their exceptionally large piezoelectric properties. (C) 2003 American Institute of Physics.

Piezoelectric anisotropy and free energy instability in classic perovskites

Marko Budimir

Several members of the perovskite family are investigated: the temperature dependence of dielectric, elastic, piezoelectric and coupling coefficients of KNbO3 in its orthorhombic ferroelectric phase is determined experimentally; the values of dielectric stiffness coefficients at constant stress, α, are estimated for the 6th order Landau-Ginzburg-Devonshire phenomenological description of KNbO3; the origins of the enhanced piezoelectric responses along non polar directions in perovskites are investigated by studying phenomenologically the temperature evolution of the piezoelectric anisotropy in a material with a sequence of ferroelectric-ferroelectric phase transitions (BaTiO3) and in a material with only one ferroelectric phase (PbTiO3); the influence of external bias fields on piezoelectric response and its anisotropy in ferroelectric perovskites is discussed phenomenologically by studying tetragonal BaTiO3, PbTiO3 and Pb(Zr,Ti)O3 under electric bias field applied anti-parallel to the spontaneous polarization and uniaxial compressive bias stress along the polarization direction; a discussion about a common underlying thermodynamic process able to generally describe the enhancement of the piezoelectric response and its anisotropy is given by investigating the Gibbs free energy flattening in tetragonal BaTiO3, PbTiO3 and Pb(Zr,Ti)O3 upon changes of temperature, bias fields and composition. The main conclusions resulting from this work are: a comparison of the results of electromechanical properties measurements on KNbO3 obtained in this work, the ones found in the literature, and estimates using LGD phenomenology from this work gives discrepancies that suggest that published measurements should be redone; in the absence of bias fields, the intrinsic origin of the enhanced piezoelectric responses in perovskites is the anticipation of a phase transition, no matter what is the cause of that transition (temperature, composition); in the presence of sufficiently high bias fields, an enhanced piezoelectric response along non-polar direction can be predicted in some materials (PbTiO3 under high uniaxial compressive stress along the polar direction); the influence of the external bias fields on electromechanical properties of perovskites may generally be of significant importance: if the electric fields applied anti-parallel to the spontaneous polarization or the uniaxial compressive bias stresses applied along the polarization axis are high enough, the perovskite system can be strongly dielectrically softened (metastable state), increasing the values of dielectric permittivities and piezoelectric coefficients; in the vicinity of a coercive field or a phase transition these electromechanical coefficients can increase by several orders of magnitude; the flattening of the Gibbs free energy profile of each of examined perovskite systems, regardless of whether this flattening is caused by temperature or composition variation, or by applying compressive pressure or antiparellel electric field bias, leads to enhancements of dielectric susceptibilities and of the piezoelectric response; the anisotropy of the free energy flattening is the origin of the anisotropic enhancement of the piezoelectric response, which can occur either by polarization rotation or by polarization contraction.

EPFL2006

Pulsed laser deposition of (SrBa)Nb2O6 thin films and their properties

Anna Infortuna

Strontium barium niobate (SrxBa1-xNb2O6, shortly SBN) is a solid solution system with tetragonal tungsten bronze crystal structure. It exhibits a ferroelectric phase with only one polar axis and a transition temperature depending on the Sr/Ba ratio. This thesis studies the growth of SBN thin films, in order to obtain a ferroelectric thin film model system for the study of 180° domain switching close to the ferroelectric phase transition. SBN has been chosen not only because uniaxial, but because it is possible to tune the temperature of phase transition varying the Sr/Ba ratio. It is thus possible to study electric properties of the phase transition close to room temperature, where conduction phenomena related to defects are normally lower. Thin films of SBN were grown by Pulsed Laser Deposition in a vacuum system constructed during this thesis work. For the formulation of a model it is desirable to have a system as close as possible to a single crystal. Therefore deposition parameters have been optimized to grow SBN thin films with the polar axis oriented perpendicular to the film plane. The films are integrated in parallel plate capacitor structures, in order to measure dielectric properties. The stability of the ferroelectric phase is found to be sensitive to impurities; contaminants with concentration below 1% induce a lowering of the transition temperature of about 100°C. Strain as well has influence on the phase transition; in the case of substrate with thermal expansion coefficients different from the SBN ones, the SBN film is under stress. A 0.6% tensile strain induces a lowering of the transition temperature of about 100°C, this is the case of silicon single crystal substrate. Grown on strontium titanate single crystals (STO), whose thermo-mechanical properties are close to the one of SBN, the films exhibit a phase transition temperature compatible with the one measured on single crystals. The obtained films suffer from leakage that is reduced by thermal treatment in oxygen rich atmosphere. The oxygen vacancies, created during the deposition process, are considered to be responsible of leakage. Vacancies recovery upon annealing does not eliminate the problem, and measurement of polarization at room temperature is difficult. However, piezoelectric measurements performed on individual grains, with atomic force microscope, prove that these have ferroelectric properties; by these experiment has been proved that it is possible to switch the polarization. Films with a disordered structure of grains are much less leaky than the ones with columnar grains spanning the whole cross section. These observations lead to the conclusion that conduction goes trough the grain boundaries. On STO single crystals, SBN grows epitaxial in Volmer-Weber mode. With a suitable preparation of the substrate surface, it is possible to induce the growth of films with different orientations of the polar axis: in the film plane, perpendicular to it or inclined of 45°. A model is proposed, explaining the epitaxial relation with the substrate on the basis of the perovskite kernel contained in the unit cell of the tetragonal tungsten bronze structure. The film grows from the nucleation of the perovskite structure that rules the orientation of the film; the high temperature at which the substrate is kept during the deposition, assure the necessary mobility for the arriving atoms to organize in the SBN structure around these nuclei. The study of literature data allows to state that such a model is valid not only for substrates with perovskite structure, but can be extended to substrates with a cubic crystal structure, like magnesium oxide.

EPFL2005

Phase transitions, anisotropy and domain engineering

Matthew Davis

Relaxor-ferroelectric single crystals PZN-xPT [(1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3] and PMN-xPT [(1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3] continue to attract much interest due to their anomalously large piezoelectric properties (d33 > 2000 pm/V; k33 > 90%) when poled ("domain-engineered") along a non-polar [001]C direction. In this thesis, the bulk dielectric, pyroelectric, ferroelectric and piezoelectric properties of single crystal PMN-xPT and PZN-xPT with morphotropic phase boundary (MPB) compositions are investigated. The concept of "pseudo-rhombohedral" ("R") and "pseudoorthorhombic" ("O") phases is introduced to encompass the rhombohedral, orthorhombic, and monoclinic (MA, MB and MC) ferroelectric phases occurring in poled crystals; all bulk measurements are rationalized in this way. Poling in different orientations affects the thermal stabilities of the "R", "O" and tetragonal (T) phases, likely due to the presence of residual bias fields. Phase diagrams are constructed for [001]C-poled crystals based on bulk electrical measurements, which agree well with those derived elsewhere from diffraction experiments. Large pyroelectric coefficients (< 1000 µCm-2K-1) are evidenced in [111]C-poled PMN-28PT; these might be exploitable in heat sensing and thermal imaging applications. A "R" phase is induced metastably in otherwise pseudo-orthorhombic PZN-8PT by poling along the [111]C direction at sub-zero temperatures. The related electric field induced ("O" - "R") phase transition is evidenced in strain-field measurements and, in situ, by polarized light microscopy. Hysteresis, and discontinuities in polarization and strain, are due to nucleation and growth of the induced phase; this first-order phase transition corresponds to a discontinuous "jump" of the polar vector within the MB plane. Further electric-field induced phase transitions are evidenced in unipolar strain-field loops for [001]C-poled PZN-xPT and PMN-xPT, with various MPB compositions, at temperatures between 25°C and 100°C. In PZN-6.5PT, PMN-30PT and PMN-30.5PT, the polarization rotation path "R" - "O" - T is evidenced by two first-order "jumps" in strains, one between the MA and MC monoclinic planes, and one within the MC plane to the tetragonal phase. Electric field-temperature (E-T) phase diagrams are constructed from the experimental data; trends for the electrical stabilities of the "R", "O" and T phases are shown. The (direct) piezoelectric response of [001]C-poled PZN-4.5PT, PZN-6.5PT, PZN-8PT and PMN-31PT is investigated under compressive stresses both along and perpendicular to the poling direction (longitudinal d33 and transverse d31 modes, respectively). Dynamic measurements are made in a Berlincourt-type press, over a range of stresses (< 20 MPa) and temperatures (25 to 200°C). In the longitudinal mode, Rayleigh-law hysteresis and nonlinearity indicates a significant extrinsic contribution from the irreversible (pinned) motion of interfaces, and likely ferroelastic domain walls; however, domain switching is not generally expected in domain engineered, pseudo-rhombohedral crystals. It is postulated that domain wall motion is driven by a local stress-induced phase transition, clearly evidenced in quasi-static, charge-stress loops and in situ X-ray diffraction at larger stresses (< 100 MPa). The reversible contribution to the response is always found to be larger than the irreversible (extrinsic) contribution in the "R" and "O" phases, the latter accounting for around 20% of d33 in PZN-8PT, at room temperature, and 5% in PZN-4.5PT. Both contributions are shown to increase upon heating towards the tetragonal phase; the increase in extrinsic contribution is likely due to increased domain wall mobility as the ferroelectric-ferroelectric phase transition temperature is approached. In contrast, the transverse response of PMN-31PT and PZN-4.5PT is anhysteretic ("non-lossy") and linear at low stresses (< 10 MPa). This might be exploitable in sensing applications. The difference between the behaviors is likely related to differing directions of polarization rotation. In the transverse mode, rotation is towards the [001]C poling direction and the domain engineered structure is retained during the stress-induced phase transition. Lastly, published monodomain properties are used to calculate the piezoelectric (d33* and d31* ) coefficients of domain-engineered 3m PMN-33PT and mm2 PZN-9PT; both positive and negative transverse coefficients can be application tailored by domain-engineering. According to such calculations, intrinsic crystal anisotropy accounts for at least 50% of the "giant" piezoelectric response of polydomain, [001]C-poled, PMN-33PT and PZN-9PT. Both compositions show inherently strong piezoelectric anisotropy (d15/d33 ≫ 1) in accordance with an "easy" polarization rotation. This is related to a high dielectric anisotropy (ε11/ε33) and the degeneracy of the "R", "O" and T phases near the MPB. Similar effects are observed in all ferroelectric perovskites, although the effect is uncommonly large in PMN-xPT and PZN-xPT: it is noted that all monodomain compliances, piezoelectric coefficients and permittivities are around an order of magnitude larger in PMN-xPT and PZN-xPT compared to their simpler perovskite relatives. This is likely a result of their background "relaxor" nature. Finally, it is suggested that the presence of zero-field monoclinic phases in PMN-xPT and PZN-xPT is related to their inherently large piezoelectric response in the presence of residual stresses and bias fields, not the other way round as is commonly accepted.

EPFL2006

Pulsed laser deposition of (SrBa)Nb2O6 thin films and their properties

Anna Infortuna

EPFL2005

Piezoelectric anisotropy and free energy instability in classic perovskites

Marko Budimir

EPFL2006

Phase transitions, anisotropy and domain engineering

Matthew Davis

EPFL2006