A Phase Diagram for Epitaxial PbZr_1−xTi_xO₃ Thin Films at the Bulk Morphotropic Boundary Composition

Abstract

A phase diagram of temperature versus strain was constructed for a (001)‐oriented PbZr1−xTixO3 epitaxial single crystal thin film near the bulk morphotropic boundary composition (x=0.47) on an (001)‐oriented cubic substrate. The phase‐field approach is employed. It is shown that a mixture of distorted rhombohedral, orthorhombic, and tetragonal phases exists under small values of strain, i.e., close to the in‐plane clamped boundary condition. This result contradicts thermodynamic calculations assuming a single‐domain state that predicted a single distorted rhombohedral phase under similar strains. Furthermore, it is demonstrated that under a large tensile strain current phase‐field simulations showed a tetragonal phase with a1/a2 twin structures as the stable state whereas thermodynamic calculations predicted an orthorhombic phase.

Development of residual stress in sol-gel derived Pb(Zr,Ti)O3 films: An experimental study

“…The phase field simulations for epitaxial PZT 52/ 48 films show that the phase formation in PZT 52/ 48 takes place gradually during cooling. 53 At first the tetragonal phase is being formed which can partly transform to a rhombohedral phase. Thus the total TEC of the ͑100͒ oriented PZT 52/ 48 films is the sum of the TEC of a-and c-oriented tetragonal domains and the ͑100͒ oriented rhombohedral phase.…”

Fabrication and mechanical reinforcement of piezoelectric nanocomposites with ZrO2 nanoparticles embedded in situ

“…The amount of residual stress around the secondary phase particle was proportional to the differences in the thermal expansion coefficients between the matrix and the secondary particle phase (˛m and˛p), and nanocomposites made good use of these residual stresses [22,28,29]. For the PZT/ZrO 2 system, p /˛m > 1, the stress state in the matrix of PZT, was expressed as the hydrostatic compressive pressure that could enhance the ferroelectricity and reduce the Curie temperature of ferroelectrical ceramics [30][31][32], and the stresses inside the particle were hydrostatic tensile, which might promote the transformation of ZrO 2 from the tetragonal phase to the monoclinic phase in the cooling stage of sintering. The residual stresses model, proposed by Timoshenko and Goodier [33], was used to calculate the stresses along the PZT/ZrO 2 nanocomposite boundary, and the values were listed in Table 2.…”

Theoretical Methods of Domain Structures in Ultrathin Ferroelectric Films: A Review

“…Phase diagrams of PbTiO 3 [124,274], SrTiO 3 [306], BST [307,308], and PZT [309,310,311,312,313] have also been constructed based on the numerical approaches. In particular, for the solid solution PZT thin film, phase field simulations have shown that the tetragonal phase remains stable at a high mole fraction of Ti for compressive, tensile, and stress-free substrate constraint, while the orthorhombic phase is stable at low mole fraction of Ti for tensile constraint [309].…”

“…It is noteworthy that, misfit strain effect for (001)-oriented PZT thin films at the morphotropic phase boundary (MPB) composition, which exhibits strong electromechanical coupling, is of keen interest. Figure 11a shows a misfit strain-temperature phase diagrams for (001)-oriented PbZr 0.53 Ti 0.47 O 3 thin films constructed by Choudhury et al [310] based on phase field method, with two selected domain structures depicted in Figure 11b. According to the phase diagram in Figure 11, there are narrow regions where different domain states coexist, and large tensile misfit strain is found to favor tetragonal a 1 / a 2 -domain structure.…”