Design of polar boundaries enhancing negative electrocaloric performance by antiferroelectric phase-field simulations

The miniaturization and performance enhancements of electronic devices in the 5G era have highlighted the critical need for efficient heat dissipation. Traditional vapor compression refrigeration systems, however, suffer from low efficiency and large size limitations. Electrocaloric refrigeration (ECR), a novel technology, offers advantages such as high efficiency, controllable size, and environmental friendliness, making it a promising alternative. However, existing ECR materials based on PbTiO3 (PTO) and BaTiO3 (BTO) systems face challenges of small adiabatic temperature change (ΔT) and narrow operating temperature ranges. Doping and material structure design strategies have shown potential for improvement. Recently, approaches combining positive and negative ECEs have been proposed to broaden operating ranges and increase ΔT. While the positive ECE in ferroelectric (FE) materials is well-understood, the negative ECE in antiferroelectric (AFE) materials like PbZrO3 (PZO) requires further investigation. The microscopic mechanism of the negative ECE remains debated, with suggestions attributing it to field-induced first-order endothermal transitions between AFE and FE phases or antiparallel polarization instability. High-resolution electron microscopy has revealed AFE-FE phase coexistence and phase interface evolution, but real-time observation of polarization switching during field-induced AFE-FE transitions under high temperatures remains challenging. Therefore, understanding the electric field-induced AFE phase nucleation and interface motion at the polarization scale is crucial for clarifying the mechanism and improving the negative ECE performance. Thermodynamic calculations have linked negative ECE changes to the free energy barrier of the AFE-FE phase transition, but the influence of temperature, electric field, and doping on the phase transition at the polarization scale requires further study. Phase-field simulations provide a powerful tool to investigate these effects at the polarization scale. This research focuses on investigating the AFE-FE phase transition and domain switching process in prototype PZO, including AFE stripe domains, polymorphic domains, and AFE nanodomains, under various temperatures and electric field conditions via phase-field simulations to calculate the negative ECE properties using the Maxwell relation.

Previous research extensively explored the positive electrocaloric effect (ECE) in ferroelectric (FE) materials, demonstrating that ultra-high peaks in positive ECE occur near the Curie temperature (Tc), where a large external electric field induces an FE-paraelectric (PE) phase transition, accompanied by a large polarization entropy change. However, the understanding of the negative ECE in antiferroelectric (AFE) materials, exemplified by PbZrO3 (PZO), is less developed. Studies have suggested that the negative ECE might arise from a field-induced first-order endothermal transition between AFE and FE phases or from antiparallel polarization instability. High-resolution electron microscopy has provided visual evidence of AFE-FE phase coexistence and phase interface evolution during electric field-induced phase transitions. However, real-time observation of polarization switching at high temperatures remains difficult, highlighting the need for theoretical modeling to elucidate the underlying mechanisms. Existing phase-field models have been used to explain the negative ECE of PZO-based ceramics, linking the effect to the free energy barrier of the AFE-FE phase transition. However, a comprehensive understanding of the effects of temperature, electric field, and doping on the AFE-FE phase transition at the polarization scale remains incomplete, prompting the need for further investigation using advanced simulation techniques.

This study employs an improved antiferroelectric phase-field model to simulate the temperature and electric field-induced antiferroelectric-ferroelectric phase transition in PbZrO3-based materials. The model incorporates two order parameters (p and q) to describe the antiparallel polarization in two sublattices, along with a high-order gradient energy term to account for next-nearest-neighbor interactions between antiparallel polarizations. The model is further refined by quantitatively incorporating temperature and electric field factors into the time-dependent Ginzburg-Landau (TDGL) equation, which governs the temporal evolution of the polarization vector field. The total free energy of the system is expressed as a functional including Landau free energy, elastic energy, electrostatic energy, and gradient energy. The gradient energy density incorporates terms describing polar-polar interactions and the coupling between oxygen tilt and polarizations, along with a high-order gradient energy term to drive the AFE-FE phase transition. The gradient energy coefficients are normalized for numerical solution convergence, and the oxygen tilt is correlated with temperature. The first-order gradient energy term is simplified based on its negative value in AFE materials, resulting in a linear relationship between temperature and the gradient energy coefficients. Experimental data is used to fit this linear relationship for PbZrO3. The improved model simulates the AFE-FE phase transition domain switching process in prototype PZO bulk materials, including AFE stripe domains, polymorphic domains, and AFE nanodomains, under various temperature and electric field conditions. The negative ECE properties are then calculated from the simulated polarization response using the Maxwell relation. To simulate the effect of doping, a spatial rise and fall of the potential function is introduced in the phase-field model to approximate the inhomogeneous composition distribution. The P-E loops under different temperatures and electric field strengths are simulated to understand the domain switching process, and the P-T curves of different domain structures (stripe domains, polymorphic domains, and AFE nanodomains) are compared. The negative ECE properties (ΔT-T curves, entropy change) are calculated using the Maxwell relation. The model is validated by comparing the simulated temperature-electric field phase diagram with experimental data. To verify the generality of the polar boundary mechanism, the simulations are extended to the PbTiO3 system, simulating the positive ECE properties under different conditions. A detailed equation for the volume energy density is given for the PbTiO3 nanodomains, considering a 10% volume fraction of defect dipoles. The influence of defect dipole concentration on the P-T curves of PbTiO3 is also simulated.

The phase-field simulations reveal that polar boundaries, generated by AFE domain boundaries, local incommensurate antiphase boundaries, and AFE nanodomains, serve as nucleation sites for the AFE-FE phase transition. These boundaries facilitate a stepwise, rather than transient, phase transition process, broadening the operating temperature range of the negative ECE. The simulations show that increasing the density of polar boundaries significantly increases the operating temperature range, although it might slightly reduce the peak ΔT. In antiferroelectric nanodomains, a peak ΔT of -13.05 K is achieved at 84 kV/cm, with a wide temperature range of approximately 75 K realized at 42 kV/cm. The simulations show the temperature-electric field phase diagram for the prototype PZO polymorphic domains, revealing the stable coexistence of mixed AFE-FE phases near the phase boundary. The P-E loops for the polymorphic domains illustrate the gradual nature of the phase transition, with nucleation of the FE phase near the AFE domain boundaries and preferential phase transition at the local incommensurate antiphase boundaries. The comparison of P-T curves for stripe domains, polymorphic domains, and AFE nanodomains shows that AFE nanodomains exhibit a much lower slope, indicating the initiation of the AFE-FE phase transition at lower temperatures. The simulations of the negative ECE properties (ΔT-T curves) show that polymorphic domains exhibit a high negative ΔT at low electric fields, while AFE nanodomains, although exhibiting a somewhat lower peak ΔT, demonstrate a significantly wider operating temperature range. Under an electric field of 42 kV/cm, a wide operating temperature range of about 75 K (402–477 K) is achieved with ΔT > 0.1 K. The results are compared with experimental data of PZO-based ceramics, highlighting the superior performance of AFE nanodomains in terms of both negative ECE strength and operating temperature range. The simulations also confirm that the mechanism of polar boundaries enhancing the operating temperature range applies to ferroelectric materials as well, as demonstrated by the PbTiO3 system, where nanodomains show a wider operating temperature range due to the presence of a high density of polar boundaries.

The findings of this study significantly advance the understanding of the negative electrocaloric effect in antiferroelectric materials. The demonstration of enhanced negative ECE performance by manipulating polar boundary density provides a crucial design principle for next-generation electrocaloric refrigeration devices. The observed stepwise phase transition mechanism contrasts with the transient transitions observed in materials lacking dense polar boundaries, highlighting the importance of microstructural control in optimizing ECE performance. The broader operating temperature range achieved in AFE nanodomains offers substantial practical advantages for refrigeration applications, extending the usability of these materials. The validation of the polar boundary mechanism in both AFE and FE materials suggests its general applicability across a range of electrocaloric materials, opening new avenues for materials design and optimization. The use of phase-field simulations allows for detailed insights into the complex domain switching processes and provides valuable guidance for experimental efforts in material synthesis and characterization.

This research presents a comprehensive phase-field simulation study demonstrating the enhancement of negative electrocaloric effect (ECE) in antiferroelectric materials through the design of polar boundaries. The simulations reveal a mechanism where polar boundaries act as preferential nucleation sites for the antiferroelectric-ferroelectric phase transition, leading to a stepwise transition and a broadened operating temperature range. The study demonstrates that AFE nanodomains offer significantly improved performance compared to other structures. Future research could focus on exploring different doping strategies to further optimize polar boundary density and explore the combined positive and negative ECE for even broader operating temperature ranges and larger ΔT values. Experimental validation of the findings is also crucial to confirm the theoretical predictions.

The simulations rely on a simplified phase-field model and may not fully capture all aspects of the complex physical phenomena involved in the AFE-FE phase transition. The model parameters were fitted to experimental data, and slight variations in these parameters could affect the simulation results. The simulations focus on specific AFE and FE materials (PbZrO3 and PbTiO3), and the results may not be directly generalizable to all AFE and FE systems. Further studies are needed to investigate the influence of other factors, such as grain size, defects, and interfaces on the ECE.