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

The study addresses the mechanism and enhancement of the negative electrocaloric effect (ECE) in antiferroelectric (AFE) materials, particularly PbZrO3 (PZO), and explores how polar boundaries can modulate electrocaloric performance. With increasing heat-dissipation demands in miniaturized electronics, electrocaloric refrigeration offers advantages over traditional vapor compression systems. Positive ECE in ferroelectrics (e.g., PbTiO3, BaTiO3) is well understood, typically peaking near the Curie temperature with large polarization entropy change under strong fields. However, AFE materials like PZO can exhibit negative ECE, where an electric field induces an AFE–FE transition accompanied by cooling. The microscopic origin of negative ECE remains debated, with hypotheses including field-induced first-order endothermal AFE–FE transitions and antiparallel polarization instability. High-resolution microscopy has observed AFE–FE phase coexistence and interface evolution during field-induced transitions, but real-time observation of polarization switching under high temperature is difficult. Thermodynamic calculations have linked negative ECE changes to AFE–FE free-energy barriers, yet the coupled roles of temperature, electric field, and doping at the polarization scale need further study. This work proposes and refines an AFE phase-field model including temperature–electric field coupling to investigate how polar boundaries (from antiphase boundaries, AFE domain boundaries, and nanodomains) nucleate and facilitate AFE–FE transitions, aiming to broaden the operating temperature range and understand negative ECE enhancement. The central hypothesis is that increasing polar-boundary density transforms a transient, abrupt transition into a gradual, boundary-mediated one, thereby widening the usable temperature window while tuning the ΔT magnitude.

Prior work has established strong positive ECE near Curie temperature in ferroelectrics, supported by extensive experiments and theory. In contrast, negative ECE in PZO-based AFEs has been attributed to mechanisms such as field-induced first-order endothermal AFE–FE transitions and antiparallel polarization instabilities. Experimental studies have visualized AFE–FE phase coexistence and boundary motion under applied fields. Thermodynamic modeling linked negative ECE behavior to the free-energy barrier associated with the AFE–FE transition. Phase-field simulations have become a powerful tool for investigating both positive and negative ECE at the polarization scale, including domain-wall contributions and nanoscale geometry effects. Materials design strategies (e.g., doping, defect dipoles, compositional tuning) have been used to enhance ΔT and broaden operating ranges, and concepts combining positive and negative ECE have been proposed for wider temperature coverage. However, a clear microscopic, polarization-scale understanding of how polar boundaries nucleate and mediate AFE–FE transitions under coupled temperature–field conditions has remained incomplete, motivating the present phase-field approach with explicit temperature–field dependence and boundary engineering.

The authors develop and refine a temperature–electric field coupled antiferroelectric phase-field model for PZO-based materials to study negative ECE. The temporal evolution of the polarization vector field Pi(r,t) follows the time-dependent Ginzburg–Landau equation, with dynamics driven by the functional derivative of the total free energy. The total free energy comprises Landau, elastic, electrostatic, and gradient energy densities. A high-order gradient energy formulation captures next-nearest-neighbor interactions between antiparallel polarizations and the coupling between oxygen octahedral tilt and polarization. The gradient energy coefficients are linked to temperature via the oxygen tilt order parameter, enabling explicit temperature dependence. A linear relation between temperature and first-order gradient energy coefficients is fitted for PZO, enabling simulations across temperatures (examples provided at 450–480 K). Domain structures modeled include: AFE stripe domains (commensurate 2×2 antiparallel configuration), polymorphic domains (multiple orthorhombic variants with local incommensurate antiphase boundaries), and doping-induced AFE nanodomains. Inhomogeneous composition due to doping is emulated by introducing a spatially varying potential function, implying spatial variations in effective Curie temperature and local phase-transition barriers, which generate high densities of polar boundaries in nanodomains. Simulation setup and conditions: periodic mechanical boundary conditions; grid size typically 2564x × 2564y × 14z with 0.5 nm grid spacing (324×324×14 used for stripe domains); Landau coefficients adapted from Pb(Zr1−xTix)O3 (x ≤ 0.1); the electrostatic field includes applied, dipole–dipole, and in PTO nanodomain cases, local fields from random defect dipoles. Temperature–electric field phase diagrams are computed over 298–510 K and 0–84 kV/cm for PZO polymorphic domains. P–E loops and domain switching are simulated by ramping the field (e.g., up to 42 kV/cm at 474 K) with snapshots of domain evolution to identify nucleation and growth at polar boundaries. P–T curves are computed for stripe, polymorphic, and nanodomain cases at various fields (e.g., 21, 42, 84 kV/cm). Electrocaloric metrics are calculated by the indirect method using the Maxwell relation: isothermal entropy change from ∂P/∂T at constant field, and adiabatic temperature change ΔT from ΔS with assumed density and heat capacity of PZO. Additional validation and generality checks include: (1) temperature-induced transitions among commensurate AFE, incommensurate AFE near Tc, and PE above Tc; (2) extension to ferroelectric PbTiO3 (PTO) bulk domains versus nanodomains under 100 kV/cm across 300–700 °C, incorporating a fraction of defect dipoles to generate polar nanoregions and high-density polar boundaries. Numerical solution uses a semi-implicit Fourier spectral method.

• Polar boundaries (antiphase boundaries, AFE domain boundaries, and those associated with nanodomains) act as preferential nucleation sites for the field-induced AFE–FE transition, converting a sharp, system-wide transition into a gradual, boundary-mediated one and stabilizing mixed-phase regions near the phase boundary.
• Temperature–electric field phase diagram (298–510 K; 0–84 kV/cm) for PZO polymorphic domains shows no temperature-induced AFE–FE transition at zero field and a direct AFE→PE transition at higher temperatures; a stable mixed AFE–FE region exists near the boundary, unlike in ideal stripe domains.
• Domain-switching simulations at 474 K under a ramped field to 42 kV/cm reveal: initial linear P–E behavior; FE nucleation at AFE domain boundaries (point A); rapid growth and preferential transition at local incommensurate antiphase boundaries (point B); fully FE state (point C); upon field removal, reverse AFE nucleation at FE domain walls (point D).
• P–T behavior at 42 kV/cm: stripe domains show an abrupt transition with minimal intermediate stabilization; polymorphic domains show a broader mixed-phase region; AFE nanodomains, with higher boundary density, begin transitioning by ~453 K and still exhibit localized AFE regions at 468 K due to inhomogeneous barriers, yielding a much gentler P–T slope and extended operating range.
• Negative ECE metrics (indirect Maxwell method): • Polymorphic domains: peak ΔT increases from −5.77 K at 21 kV/cm to −9.58 K at 42 kV/cm; corresponding negative ECE strength decreases from 2.75 to 2.28 K·m/MV; operating temperature range remains around 460–480 K. • AFE nanodomains: peak ΔT increases from −1.40 K at 21 kV/cm to −13.05 K at 84 kV/cm; negative ECE strength increases from 0.67 to 1.55 K·m/MV; operating ranges are significantly wider. Notably, at 42 kV/cm, ΔT > 0.1 K is maintained over ~75 K (402–477 K).
• Temperature-induced domain evolution indicates stabilization of commensurate 2×2 AFE from room temperature up to ~450 K, emergence of incommensurate AFE near Tc, and PE phase above Tc, suggesting the possibility of sequential negative then positive ECE in PZO across AFE–FE–PE transitions.
• Extension to FE PTO: introducing nanodomains and defect-dipole-induced polar nanoregions leads to earlier domain switching (at lower temperatures) under 100 kV/cm compared to bulk domains, thereby broadening the positive ECE operating range. Increasing defect-dipole concentration (0→10%) shifts peak polarization to lower temperature and transforms the system toward relaxor-like behavior, further broadening the ECE window.

The results directly support the hypothesis that polar boundaries significantly modulate electrocaloric behavior by facilitating local nucleation and diffusion-driven growth during the AFE–FE transition, replacing an abrupt transformation with a progressive one. This mechanism stabilizes mixed phases near the AFE–FE boundary and markedly widens the operating temperature range for negative ECE, particularly in nanodomains with high boundary density. Although peak ΔT can decrease at moderate fields when boundary density is very high, the dramatically expanded temperature window is advantageous for practical refrigeration cycles. The constructed temperature–electric field phase diagram clarifies why mixed-phase stabilization occurs in polymorphic domains but not in ideal stripe domains. The observed commensurate-to-incommensurate AFE evolution near Tc and the transition to PE above Tc further imply that PZO-based systems could realize sequential negative and positive ECE, enabling broader, tunable cooling ranges. Generality is supported by PTO simulations showing that polar boundaries similarly promote domain switching at lower temperatures in ferroelectrics, broadening positive ECE operating ranges and illustrating that boundary engineering (via defect dipoles, doping, or nanostructuring) is an effective, material-agnostic strategy for ECE optimization.

This work refines a temperature–electric field coupled AFE phase-field framework for PZO-based materials and elucidates how polar boundaries control AFE–FE transition pathways and negative ECE performance. By engineering domain structures from stripe to polymorphic to nanodomain states (increasing boundary density), the operating temperature range of negative ECE is substantially widened while tuning the ΔT magnitude. Simulations yield a peak ΔT of −13.05 K at 84 kV/cm for AFE nanodomains and, notably, a broad operating range of about 75 K (402–477 K) with ΔT > 0.1 K at 42 kV/cm. In the same field, an operating window of ~75 K with a maximum ΔT ≈ −4.57 K is demonstrated. The phase diagram confirms stable mixed-phase regions near the AFE–FE boundary in polymorphic domains, and the temperature-induced evolution from commensurate to incommensurate AFE near Tc suggests potential for sequential negative–positive ECE in PZO. Extension to PTO shows boundary engineering also broadens positive ECE ranges in ferroelectrics. Future work should explore systematic boundary-density control (via doping, defect dipoles, and nanostructuring), integrate stress and electric loading into thermodynamic modeling where omitted, and develop design strategies that combine negative and positive ECE for wide-temperature-range, high-performance solid-state refrigeration.

• The study is primarily simulation-based; electrocaloric metrics are obtained via the indirect Maxwell method using simulated P–T data rather than direct calorimetry.
• In the thermodynamic (Landau) modeling used for verification, applied stress and electric field were neglected for simplification, which may limit quantitative accuracy under coupled loading.
• Doping and compositional inhomogeneity are approximated by a spatially varying potential function and random defect dipoles; this idealization may not capture all microstructural complexities of real materials.
• Periodic boundary conditions and finite simulation cell sizes may constrain domain morphology and boundary statistics relative to bulk samples.
• Material parameters (e.g., Landau coefficients and fitted temperature dependences) are specific to PZO-based systems and may require recalibration for other compositions; experimental validation of predicted ΔT and operating ranges under identical conditions would strengthen generalizability.