Correlation between dielectric anisotropy and positive or zero transverse piezoelectric coefficients in perovskite ferroelectric single crystals

The transverse piezoelectric coefficient (d(31)(star)) has been calculated for tetragonal barium titanate (BT) and lead titanate (PT) cut along nonpolar axes, over a range of temperatures, using the phenomenological Landau-Ginzburg-Devonshire theory. It is shown that negative values of d(31)(star) are favored when the transverse dielectric susceptibility eta(11) and shear coefficient d(15) are large, such that polarization rotation is more significant than the collinear piezoelectric effect. This occurs in tetragonal BT close to its ferroelectric-ferroelectric phase transition to an orthorhombic phase. In PT, however, where no phase transition occurs, d(15) is small and polarization "extension" due to d(33) dominates: small or positive values of d(31)(star) become prominent. This extends a previous result found for polycrystalline modified PT ceramics. (c) 2005 American Institute of Physics.

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

Domain engineering of the transverse piezoelectric coefficient in perovskite ferroelectrics

Dragan Damjanovic, Matthew Davis, Nava Setter

The transverse piezoelectric coefficient d(31), has been calculated for the six domain-engineered structures occurring in perovskite single crystals, using data for rhombohedral PMN-33PT [0.67Pb(Mg1/3Nb2/3)O-3-0.33PbTiO(3)], orthorhombic potassium niobate (KNbO3), tetragonal barium titanate (BaTiO3), and tetragonal lead titanate (PbTiO3). Unlike the longitudinal coefficient (d(33)), d(31)* is found to be strongly dependent on the transverse (x(1)') direction of the as-cut crystal. In general, different domains in a domain-engineered structure will contribute different values of d(31)* to that measured. Predicting the global d(31), is therefore difficult since it will depend on the proportion of each domain variant in the structure. Important qualitative differences between tetragonal BaTiO3 and PbTiO3 are discussed. Whereas polarization rotation is important in BaTiO3, PbTiO3 shows a stronger collinear piezoelectric effect due the absence of a low-temperature ferroelectric-ferroelectric phase transition. This leads to low values of d(33) and even positive values of d(31)*, in the 111-poled (C: pseudocubic) domain-engineered structure. The methodology described can be usefully applied to all perovskites. (c) 2005 American Institute of Physics.

2005

Surface-stimulated phenomena in the polarization response of ferroelectrics

Guido Gerra

The integration of ferroelectrics in electronic devices requires that they be used in the form of thin films, which implies that for such systems finite-size effects related to the presence of a ferroelectric-electrode interface become important. In this thesis, a number of theoretical studies are presented on the properties of metal-ferroelectric-metal structures, focusing on the impact of the metal-ferroelectric interface on the polarization response of the system. First, a model for reverse domain nucleation in ferroelectrics is introduced, which takes into account the ferroelectric-electrode coupling in both the homogeneous and random cases. The model provides a solution to the coercivity paradox—i.e., the large discrepancy between the observed and predicted coercive fields. The possibility of non-thermally activated nucleation of reverse domains is demonstrated. It is found that small inhomogeneities in the ferroelectric-electrode interface may lead to an exponentially wide spectrum of waiting times for switching. The model predicts that switching is facilitated near morphotropic phase boundaries in perovskite-type ferroelectrics. In order to quantitatively analyze the size-effect problem in metal-ferroelectric-metal systems, an approach is developed which combines first-principles calculations and phenomenological theory. The parameters of the model can be extracted from calculations on ultrathin films, while experimentally verifiable predictions can be made on thick films. Using the developed approach, it is demonstrated how the size effect can be separated into two distinct contributions: a long-range electrostatic and a short-range "chemical" one. By considering symmetric SrRuO3/BaTiO3/SrRuO3 heterostructures with different types of termination (TiO2–TiO2 or RuO2–RuO2), it is shown that the balance between the long-range and the short-range contribution to the size effect can be essentially affected by the type of termination of the ferroelectric and by the polarization hardness of the electrode. The leading role of the long-range contribution to the size effect in SrRuO3/BaTiO3/SrRuO3 heterostructures is demonstrated. Application of the approach to the case of SrRuO3/BaTiO3/SrRuO3 heterostructures with asymmetric interfaces enables to provide a quantitative description of a number of manifestations of such asymmetry in films of technologically meaningful thickness. In particular, it is found that the asymmetry exerts a poling effect on the films, leading to a smearing of the phase transition, to an induced piezoelectric response above the transition temperature, and to the reversal of the polarization asymmetry by application of biaxial strain. Another important result of such calculations is the observation that the ionic relaxations in the metal-oxide electrode play a crucial role in stabilizing the ferroelectric phase of the films. Comparison with frozen-phonon calculations shows that the degree of softness of the SrRuO3 lattice has an essential impact on the screening of ferroelectric polarization, reducing the critical thickness for ferroelectricity of the system. These results provide a possible explanation for the observed beneficial impact of oxide electrodes on the switching and dielectric properties of ferroelectric capacitors.