We present a critical review that encompasses the fundamentals and state-of-the-art knowledge of barium titanate-based piezoelectrics. First, the essential crystallography, thermodynamic relations, and concepts necessary to understand piezoelectricity and ferroelectricity in barium titanate are discussed. Strategies to optimize piezoelectric properties through microstructure control and chemical modification are also introduced. Thereafter, we systematically review the synthesis, microstructure, and phase diagrams of barium titanate-based piezoelectrics and provide a detailed compilation of their functional and mechanical properties. The most salient materials treated include the (Ba,Ca)(Zr,Ti)O3, (Ba,Ca)(Sn,Ti)O3, and (Ba,Ca)(Hf,Ti)O3 solid solution systems. The technological relevance of barium titanate-based piezoelectrics is also discussed and some potential market indicators are outlined. Finally, perspectives on productive lines of future research and promising areas for the applications of these materials are presented.

The question of whether one can systematically identify (previously unknown) ferroelectric phases of a given material is addressed, taking hafnia (HfO2) as an example. Low free energy phases at various pressures and temperatures are identified using a first-principles based structure search algorithm. Ferroelectric phases are then recognized by exploiting group theoretical principles for the symmetry-allowed displacive transitions between non-polar and polar phases. Two orthorhombic polar phases occurring in space groups P ca21 and P mn21 are singled out as the most viable ferroelectric phases of hafnia, as they display low free energies (relative to known non-polar phases), and substantial switchable spontaneous electric polarization. These results provide an explanation for the recently observed surprising ferroelectric behavior of hafnia, and reveal pathways for stabilizing ferroelectric phases of hafnia as well as other compounds.Commonly known structural phases of hafnia (HfO 2 ) are centrosymmetric, and thus, non-polar. Hence, recent observations of ferroelectric behavior of hafnia thin films (when doped with Si, Zr, Y, Al or Gd) [1][2][3][4][5][6][7] are rather surprising as ferroelectricity requires the presence of switchable spontaneous electrical polarization. The emergence of non-polar hafnia-as a linear high dielectric constant (or high-κ) successor to SiO 2 -for use in modern electronic devices (e.g., field-effect transistors) is now well-established [8,9]. If the origins of its unexpected ferroelectricity can be understood and appropriately harnessed, hafnia-based materials may find applications in nonvolatile memories and ferroelectric field effect transistors as well.A broader question that arises within this context, and also the one that will be addressed directly in this contribution, is whether one can systematically identify ferroelectric phases of a given material system. We show that this can indeed be accomplished and ascertained, for the example of hafnia, in two steps. First, a computationbased structure search method, e.g., the minima-hopping method [10][11][12], is used to identify low-energy phases at various pressures and temperatures. Then, ferroelectric phases are singled out by applying the group theoretical symmetry reduction principles, established by Shuvalov for ferroelectricity [13]. These principles allow for the systematic identification of all possible lower symmetry proper ferroelectric phases that can result from highersymmetry non-polar prototype (parent) phases.Using this approach, we find two ferroelectric phases of hafnia, belonging to the P ca2 1 and P mn2 1 orthorhombic space groups, which are close in free energy with the known non-polar equilibrium phases of hafnia over a wide temperature and pressure range. Figure 1(a) displays the computed equilibrium phase diagram of hafnia indicating the regimes at which the known non-polar phases are stable. This includes the low-temperature lowpressure P 2 1 /c monoclinic phase, high-pressure P bca and P nma orthorhombic p...

The surprising ferroelectricity displayed by hafnia thin films has been attributed to a metastable polar orthorhombic (Pca2 1 ) phase. Nevertheless, the conditions under which this (or another competing) ferroelectric phase may be stabilized remain unresolved. It has been hypothesized that a variety of factors, including strain, grain size, electric field, impurities and dopants, may contribute to the observed ferroelectricity. Here, we use first-principles computations to examine the influence of mechanical and electrical boundary conditions (i.e., strain and electric field) on the relative stability of a variety of relevant nonpolar and polar phases of hafnia. We find that although strain or electric field, independently, do not lead to a ferroelectric phase, the combined influence of in-plane equibiaxial deformation and electric field results in the emergence of the polar Pca2 1 structure as the equilibrium phase. The results provide insights for better controlling the ferroelectric characteristics of hafnia thin films by adjusting the growth conditions and electrical history.

The generic case of a ferroelectric solid solution is considered wherein different symmetry phases located at opposing ends of the diffusionless phase diagram are separated by a morphotropic boundary (MB). It is shown that the Landau theory of weak first-order phase transformations automatically predicts vanishing of the anisotropy of polarization, continuity of thermodynamic properties, and a drastic decrease in domain wall energy near the MB line that results in the formation of adaptive ferroelectric nanodomain states. Low-resolution diffraction from these adaptive states acquired at the coherence lengths of elastic x-ray or neutron scattering probes will produce the same diffraction pattern as attributed to monoclinic (MA,MB,MC) phases. It is further shown that the electric- or stress-field-induced reconfiguration of these adaptive nanodomain states results in a softening of the piezoelectric, elastic, and dielectric properties near the MB line. In addition, the spherical degeneration of the polarization direction, reflecting the decoupling of the polarization from the crystal lattice at the MB, also predicts the formation of a polar glass state whose properties should be similar to the special properties of amorphous ferromagnets. In particular, the vanishing of the polarization anisotropy at the MB should result in ferroelectric domains with irregular shapes exhibiting high configurational sensitivity to external forces. The theory further predicts that two tricritical points will occur on the line of paraelectric→ferroelectric transitions and it is shown that all two-phase equilibrium lines of the diffusionless phase diagram—including the MB line—must be replaced by two-phase fields. Within these two-phase fields, the adjacent ferroelectric-ferroelectric and paraelectric-ferroelectric phases coexist. Possible topologies of the equilibrium MB phase diagram illustrating these two-phase equilibrium fields are computed and discussed.

A thermodynamic analysis is presented for the diffusionless phase diagrams of ferroelectric solid solutions that display a morphotropic phase boundary (MPB) separating adjacent tetragonal and rhombohedral phases. Equations are developed for the shape of the MPB, the locations of triple and tricritical points, and for the line along which the anisotropy of polarization vanishes. The appearance of lower symmetry orthorhombic and monoclinic phases is considered and the topologies of energy surfaces in the region of the phase diagram where these phases may stabilize are illustrated. The theory is applied to the solid solution of lead zirconate with lead titanate (PZT) and relationships between polar anisotropy and the transformation strain, dielectric susceptibility and piezoelectric properties, are discussed. The analysis is used to reproduce phase boundary lines for solid solutions of lead titanate with lead magnesium niobate (PMN‐PT) and lead zinc niobate (PZN‐PT) and composition–temperature diagrams along isopleths in the ternary system PMN‐PZT are estimated. The anisotropies of polarization in solid solutions based on lead titanate and barium titanate are contrasted. The results provide a thermodynamic framework useful for guiding experimental investigations of ferroelectric solid solutions and for generating energy functions used in constitutive modeling and phase field simulations of microstructure and properties.

Although dopants have been extensively employed to promote ferroelectricity in hafnia films, their role in stabilizing the responsible ferroelectric non-equilibrium P ca2 1 phase is not well understood. In this work, using first principles computations, we investigate the influence of nearly 40 dopants on the phase stability in bulk hafnia to identify dopants that can favor formation of the polar P ca2 1 phase. Although no dopant was found to stabilize this polar phase as the ground state, suggesting that dopants alone cannot induce ferroelectricity in hafnia, Ca, Sr, Ba, La, Y and Gd were found to significantly lower the energy of the polar phase with respect to the equilibrium monoclinic phase. These results are consistent with the empirical measurements of large remnant polarization in hafnia films doped with these elements. Additionally, clear chemical trends of dopants with larger ionic radii and lower electronegativity favoring the polar P ca2 1 phase in hafnia were identified. For this polar phase, an additional bond between the dopant cation and the 2nd nearest oxygen neighbor was identified as the root-cause of these trends. Further, trivalent dopants (Y, La, and Gd) were revealed to stabilize the polar P ca2 1 phase at lower strains when compared to divalent dopants (Sr and Ba). Based on these insights, we predict that the lanthanide series metals, the lower half of alkaline earth metals (Ca, Sr and Ba) and Y as the most suitable dopants to promote ferroelectricity in hafnia.2

A 50 °C shift in Curie temperature has been observed for c-axis oriented PbTiO3 thin films using x-ray diffraction. An analysis of the electrostrictive strain based on the Devonshire thermodynamic formalism showed that the shift in the Curie point for these films can be plausibly explained by an effective two-dimensional compressive stress of ≊400 MPa. The single-domain, single-crystal dielectric susceptibility (η33) and piezoelectric coefficient (d33) were calculated and found to be relatively unaffected, at room temperature, by a compressive stress of this magnitude.

A thermodynamic analysis of the electrocaloric ͑EC͒ effect in BaTiO 3 ferroelectric thin films has been carried out under differing mechanical boundary conditions. It is shown that both the magnitude of the electrocaloric effect and temperature at which it is maximized depend not only on the extent of the applied field change but also on the value of the initial field. For initial fields smaller than a critical value the EC effect is largest at the phase transition temperature but the effect is a strong function of temperature. For external electrical fields larger than this value, conversely, the EC effect is the largest at a higher temperature and is a weak function of temperature. Perfect lateral clamping transforms the first-order phase transition into a second-order transition, lowering the magnitude of the electrocaloric effect and dependence on temperature. Compressive and tensile misfit strains also alter the nature of the phase transition and affect the electrocaloric properties in an analogous way. A compressive misfit strain shifts the maximum in the EC effect to higher temperatures, reduces its magnitude, and reduces its dependence on temperature, while tensile misfit strain results in the opposite effects. Control of the misfit strain by appropriate choice of substrate provides potential means to vary both the magnitude and the temperature sensitivity of the EC effect for use in cooling or thermodielectric power conversion devices.