A review on different theoretical models of electrocaloric effect for refrigeration

Abstract

The performance parameters for characterizing the electrocaloric effect are isothermal entropy change and the adiabatic temperature change, respectively. This paper reviews the electrocaloric effect of ferroelectric materials based on different theoretical models. First, it provides four different calculation scales (the first-principle-based effective Hamiltonian, the Landau-Devonshire thermodynamic theory, phase-field simulation, and finite element analysis) to explain the basic theory of calculating the electrocaloric effect. Then, it comprehensively reviews the recent progress of these methods in regulating the electrocaloric effect and the generation mechanism of the electrocaloric effect. Finally, it summarizes and anticipates the exploration of more novel electrocaloric materials based on the framework constructed by the different computational methods.

Graphical abstract

Keywords

electrocaloric effect / effective Hamiltonian / phase-field modeling / different theoretical models

References

[1] Wang J J, Wang B, Chen L Q. Understanding, predicting, and designing ferroelectric domain structures and switching guided by the phase-field method. Annual Review of Materials Research, 2019, 49(1): 127–152

[2] KutnjakZRožič BPircR, . Electrocaloric effect: Theory, measurements, and applications. In: Webster J G, ed. Wiley Encyclopedia of Electrical and Electronics Engineering. John Wiley & Sons, Inc., 2015

[3] Shi J, Han D, Li Z. . Electrocaloric cooling materials and devices for zero-global-warming-potential, high-efficiency refrigeration. Joule, 2019, 3(5): 1200–1225

[4] CorreiaTZhang Q. Electrocaloric effect: An introduction. In: Correia T, Zhang Q, eds. Electrocaloric Materials. Engineering Materials. Berlin, Springer, 2014

[5] GunnarSOleg PGeraldG. Electrocaloric cooling. In: Orhan E, ed. Refrigeration. IntechOpen, 2017

[6] Lu S G, Zhang Q M. Electrocaloric materials for solid-state refrigeration. Advanced Materials, 2009, 21(19): 1983–1987

[7] GranicherH. Induzierte Ferroelektrizitat von SrTiO₃ bei sehr tiefen temperatur und uber dieKalterzeugung durch adiabatic Entpolarisierung. 1956

[8] Hegenbarth E. Studies of the electrocaloric effect of ferroelectric ceramics at low temperatures. Cryogenics, 1961, 1(4): 242–243

[9] KobekoPKurtschatov J. Dielektrische Eigenschaften der Seignettesalzkristalle. 1930

[10] Wiseman G G, Kuebler J K. Electrocaloric effect in ferroelectric rochelle salt. Physical Review, 1963, 131(5): 2023–2027

[11] Scott J F. Electrocaloric materials. Annual Review of Materials Research, 2011, 41(1): 229–240

[12] Mischenko A S, Zhang Q, Scott J F. . Giant electrocaloric effect in thin-film PbZr_0.95Ti_0.05O₃. Science, 2010, 37(23): 1270–1271

[13] Neese B, Chu B, Lu S G. . Large electrocaloric effect in ferroelectric polymers near room temperature. Science, 2008, 321(5890): 821–823

[14] Moya X, Stern-Taulats E, Crossley S. . Giant electrocaloric strength in single-crystal BaTiO₃. Advanced Materials, 2013, 25(9): 1360–1365

[15] Torelló A, Lheritier P, Usui T. . Giant temperature span in electrocaloric regenerator. Science, 2020, 370(6512): 125–129

[16] SuchaneckGGerlach G. Thin films for electrocaloric cooling devices. In: Kumar S, Aswal D, eds. Recent Advances in Thin Films. Materials Horizons: From Nature to Nanomaterials. Singapore: Springer, 2020

[17] Aziguli H, Chen X, Liu Y. . Enhanced electrocaloric effect in lead-free organic and inorganic relaxor ferroelectric composites near room temperature. Applied Physics Letters, 2018, 112(19): 193902

[18] CuiHHeW PeiQ B, . Electrocaloric effects in ferroelectric polymers. In: Kamal A, ed. Organic Ferroelectric Materials and Applications. Woodhead Publishing, 2022

[19] Ožbolt M, Kitanovski A, Tušek J. . Electrocaloric refrigeration: Thermodynamics, state of the art and future perspectives. International Journal of Refrigeration, 2014, 40: 174–188

[20] Honmi H, Hashizume Y, Nakajima T. . Thermodynamic analysis of a cooling system using electrocaloric effect. Japanese Journal of Applied Physics, 2017, 56(S10): 10PC09

[21] Greco A, Masselli C. Electrocaloric cooling: A review of the thermodynamic cycles, materials, models, and devices. Magnetochemistry (Basel, Switzerland), 2020, 6(4): 67

[22] MaY BAlbe KXuB X. Monte Carlo simulations of the electrocaloric effect in relaxor ferroelectrics. In: Joint IEEE International Symposium on the Applications of Ferroelectric (ISAF), International Symposium on Integrated Functionalities (ISIF), and Piezoelectric Force Microscopy Workshop (PFM), Singapore, 2015

[23] Ma Y B, Albe K, Xu B X. Lattice-based Monte Carlo simulations of the electrocaloric effect in ferroelectrics and relaxor ferroelectrics. Physical Review B: Condensed Matter and Materials Physics, 2015, 91(18): 184108

[24] Beckman S P, Wan L F, Barr J A. . Effective Hamiltonian methods for predicting the electrocaloric behavior of BaTiO₃. Materials Letters, 2012, 89(25): 254–257

[25] Tarnaoui M, Zaim M, Kerouad M. . First-principles effective Hamiltonian calculations of the electrocaloric effect in ferroelectric Ba_xSr_1–xTiO₃. Physics Letters, 2020, 384(4): 126093

[26] Barr J A, Beckman S P. Electrocaloric response of KNbO₃ from a first-principles effective Hamiltonian. Materials Science and Engineering B, 2015, 196: 40–43

[27] Ghosez P, Junquera J. Modeling of ferroelectric oxide perovskites: From first to second principles. Annual Review of Condensed Matter Physics, 2022, 13(1): 325–364

[28] Lee J Y, Soh A K, Chen H T. . Phase-field modeling of the influence of domain structures on the electrocaloric effects in PbTiO₃ thin films. Journal of Materials Science, 2015, 50(3): 1382–1393

[29] Zhu J, Chen H, Hou X. . Phase-field simulations on the electrocaloric properties of ferroelectric nanocylinders with the consideration of surface polarization effect. Journal of Applied Physics, 2019, 125(23): 234101

[30] Gao R Z, Shi X M, Wang J. . Understanding electrocaloric cooling of ferroelectrics guided by phase-field modeling. Journal of the American Ceramic Society, 2022, 105(6): 3689–3714

[31] Guo D, Gao J, Yu Y J. . Design and modeling of a fluid-based micro-scale electrocaloric refrigeration system. International Journal of Heat and Mass Transfer, 2014, 72: 559–564

[32] Liebschner R, Gerlad G. 3D-FEM simulation of a MEMS-based electrocaloric Ba(Zr_0.2Ti_0.8)O₃ thin-film microfluidic refrigeration device. Energy Technology: Generation, Conversion, Storage, Distribution, 2018, 6(8): 1553–1559

[33] Shi J, Li Q, Gao T. . Numerical evaluation of a kilowatt-level rotary electrocaloric refrigeration system. International Journal of Refrigeration, 2020, 121: 279–288

[34] Torelló A, Defay E. Electrocaloric coolers: A review. Advanced Electronic Materials, 2022, 8(6): 2101031

[35] Kumar A, Thakre A, Jeong D Y. . Prospects and challenges of the electrocaloric phenomenon in ferroelectric ceramics. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 2019, 7(23): 6836–6859

[36] Moya X, Kar-Narayan S, Mathur N. Caloric materials near ferroic phase transitions. Nature Materials, 2014, 13(5): 439–450

[37] He H, Lu X, Hanc E. . Advances in lead-free pyroelectric materials: A comprehensive review. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 2020, 8(5): 1494–1516

[38] Valant M. Electrocaloric materials for future solid-state refrigeration technologies. Progress in Materials Science, 2012, 57(6): 980–1009

[39] Aprea C, Greco A, Masselli C. . A review of the state of the art of the solid-state caloric cooling processes at room-temperature before. International Journal of Refrigeration, 2019, 106: 66–88

[40] Meng Y, Pu J H, Pei Q B. Electrocaloric cooling over high device temperature span. Joule, 2021, 5(4): 780–793

[41] Völker B, Marton P, Elsässer C. . Multiscale modeling for ferroelectric materials: A transition from the atomic level to phase-field modeling. Continuum Mechanics and Thermodynamics, 2011, 23(5): 435–451

[42] Völker B, Landis C M, Kamlah M. Multiscale modeling for ferroelectric materials: Identification of the phase-field model’s free energy for PZT from atomistic simulations. Smart Materials and Structures, 2012, 21(3): 035025

[43] Zhang J, Hou X, Zhang Y. . Electrocaloric effect in ferroelectric materials: From phase field to first-principles based effective Hamiltonian modeling. Materials Reports: Energy, 2021, 1(3): 100050

[44] KohnWSham L. Self-consistent equations including exchange and correlation effects. Physical Review, 1965, 140(4A): A1133

[45] Hohenberg P, Kohn W. Inhomogeneous electron gas. Physical Review, 1964, 136(3B): B864–B871

[46] Zhong W, Vanderbilt D, Rabe K M. First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO₃. Ferroelectrics, 1998, 206(9): 181–204

[47] Zhong W, Vanderbilt D, Rabe K M. Phase transitions in BaTiO₃ from first principles. Physical Review Letters, 1994, 73(13): 1861–1864

[48] Tinte S, Stachiotti M G, Sepliarsky M. . Atomistic modeling of BaTiO₃ based on first-principles calculations. Journal of Physics Condensed Matter, 1999, 11(48): 9679–9690

[49] Migoni R. Lattice dynamics of BaTiO₃ in the cubic phase. Journal of Physics Condensed Matter, 2010, 405(19): 4226–4230

[50] Dick B G, Overhauser A W. Theory of the dielectric constants of alkali halide crystals. Physical Review, 1958, 112(1): 90–103

[51] Thomas N W. A bond-valence approach to one-dimensional ferroelectrics. Ferroelectrics, 1989, 100(1): 77–100

[52] Brown I D. Recent developments in the methods and applications of the bond valence model. Chemical Reviews, 2009, 109(12): 6858–6919

[53] Bellaiche L, García A, Vanderbilt D. Finite-temperature properties of Pb(Zr_1–xTi_x)O₃ alloys from first principles. Physical Review Letters, 2000, 84(23): 5427–5430

[54] Walizer L, Lisenkov S, Bellaiche L. Finite-temperature properties of (Ba, Sr)TiO₃ systems from atomistic simulations. Physical Review. B, 2006, 299(14): G1128–G1138

[55] Bellaiche L, García A, Vanderbilt D. Low-temperature properties of Pb(Zr_1−xTi_x)O₃ solid solutions near the morphotropic phase boundary. Ferroelectrics, 2002, 266(1): 41–56

[56] King-Smith R D, Vanderbilt D. First-principles investigation of ferroelectricity in perovskite compounds. Physical Review B: Condensed Matter, 1994, 49(9): 5828–5844

[57] Kornev I A, Bellaiche L, Janolin P E. . Phase diagram of Pb(Zr,Ti)O₃ solid solutions from first-principles. Physical Review Letters, 2006, 97(15): 157601

[58] Kornev I A, Lisenkov S, Haumont R. . Finite-temperature properties of multiferroic BiFeO₃. Physical Review Letters, 2007, 99(22): 227602

[59] Bhattacharjee S, Rahmedov D, Wang D W. . Ultrafast switching of the electric polarization and magnetic chirality in BiFeO₃ by an electric field. Physical Review Letters, 2014, 112(14): 147601

[60] Íñiguez J, Vanderbilt D. First-principle study of the temperature-pressure phase diagram of BaTiO₃. Physical Review Letters, 2002, 89(11): 115503

[61] Kornev I A, Lisenkov S, Haumont R. . Finite-temperature properties of multiferroic BiFeO₃. Physical Review Letters, 2007, 99(22): 227602

[62] Lines M E, Glass A M, Burns G. Principles and applications of ferroelectrics and related materials. Physics Today, 1978, 31(9): 56–58

[63] Zhong S, Ban Z G, Alpay S P. . Large piezoelectric strains from polarization graded ferroelectrics. Applied Physics Letters, 2006, 89(14): 142913

[64] Mani B K, Lisenkov S, Ponomareva I. Finite-temperature properties of antiferroelectric PbZrO₃ from atomistic simulations. Physical Review B: Condensed Matter and Materials Physics, 2015, 91(13): 134112

[65] Yang Y, Xu B, Xu C S. . Understanding and revisiting the most complex perovskite system via atomistic simulations. Physical Review. B, 2018, 97(17): 174106

[66] Bellaiche L, Vanderbilt D. Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites. Physical Review B, 2000, 61: 7877

[67] Ramer N J, Rappe A M. Application of a new virtual crystal approach for the study of disordered perovskites. Journal of Physics and Chemistry of Solids, 2000, 61(2): 315–320

[68] Rapaport D C. The art of molecular dynamics simulation. Computers in Physics, 1995, 10: 456

[69] Mani B K, Chang C M, Ponomareva I. Atomistic study of soft-mode dynamics in PbTiO₃. Physical Review B: Condensed Matter and Materials Physics, 2013, 88(6): 064306

[70] Prosandeev S, Ponomareva I, Naumov I. . Original properties of dipole vortices in zero-dimensional ferroelectrics. Journal of Physics Condensed Matter, 2008, 20(19): 193201

[71] Devonshire A F. Theory of ferroelectrics. Advances in Physics, 1954, 3(10): 85–130

[72] Thomson W. On the thermoelastic, thermomagnetic, and pyroelectric properties of matter. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 1878, 5(28): 4–27

[73] Rožič B, Kosec M, Uršič H. . Influence of the critical point on the electrocaloric response of relaxor ferroelectrics. Journal of Applied Physics, 2011, 110(6): 519

[74] Liu Y, Wei J, Janolin P E. . Prediction of giant elastocaloric strength and stress-mediated electrocaloric effect in BaTiO₃ single crystals. Physical Review B: Condensed Matter and Materials Physics, 2014, 90(10): 104107

[75] Wu H H, Zhu J M, Zhang T Y. Double hysteresis loops and large negative and positive electrocaloric effects in tetragonal ferroelectrics. Physical Chemistry Chemical Physics, 2015, 17(37): 23897–23908

[76] Wu H H, Zhu J, Zhang T Y. Pseudo-first-order phase transition for ultrahigh positive/negative electrocaloric effects in perovskite ferroelectrics. Nano Energy, 2015, 16: 419–427

[77] Peräntie J, Hagberg J, Uusimäki A. . Electric-field-induced dielectric and temperature changes in a ⟨011⟩-oriented Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ single crystal. Physical Review B: Condensed Matter and Materials Physics, 2010, 82(13): 134119

[78] Geng W P, Yang L, Bellaiche L. . Giant negative electrocaloric effect in antiferroelectric La-doped Pb(ZrTi)O₃ thin films near room temperature. Advanced Materials (Deerfield Beach, Fla.), 2015, 27(20): 3165–3169

[79] Lu S G, Tang X G, Wu S H. . Large electrocaloric effect in ferroelectric materials. Journal of Inorganic Materials, 2014, 29(1): 6–12

[80] Lu S G, Rozic B, Zhang Q M. . Electrocaloric effect in ferroelectric polymers. Applied Physics. A, Materials Science & Processing, 2012, 107(3): 559–566

[81] Pirc R, Kutnjak Z, Blinc R. . Electrocaloric effect in relaxor ferroelectrics. Journal of Applied Physics, 2011, 110(7): 074113

[82] Colla E V, Jurik N, Liu Y. . Kinetics and thermodynamics of the ferroelectric transitions in PbMg_1/3Nb_2/3O₃ and PbMg_1/3Nb_2/3O₃-12% PbTiO₃ crystals. Journal of Applied Physics, 2013, 113(18): 184104

[83] Luo L, Dietze M, Solterbeck C H. . Orientation and phase transition dependence of the electrocaloric effect in 0.71PbMg_1/3Nb_2/3O₃-0.29PbTiO₃ single crystal. Applied Physics Letters, 2012, 101(6): 062907

[84] Peng B L, Zhang Q, Gang B. . Phase-transition induced giant negative electrocaloric effect in a lead-free relaxor ferroelectric thin film. Energy & Environmental Science, 2019, 12(5): 1708–1717

[85] Chen L Q, Zhao Y H. From classical thermodynamics to phase-field method. Progress in Materials Science, 2022, 124: 100868

[86] Chen L Q. Phase-field models for microstructure evolution. Annual Review of Materials Research, 2002, 32(1): 113–140

[87] Wu S, Sheng J, Yang C. . Phase-field model of hydride blister growth kinetics on zirconium surface. Frontiers in Materials, 2022, 9: 916593

[88] Liu M, Wang J. Giant electrocaloric effect in ferroelectric nanotubes near room temperature. Scientific Reports, 2015, 5(1): 7728

[89] Haun M J, Furman E, Jang S J. . Thermodynamic theory of PbTiO₃. Journal of Applied Physics, 1987, 62(8): 3331–3338

[90] Chen X, Li S, Jian X. . Maxwell relation, giant (negative) electrocaloric effect, and polarization hysteresis. Applied Physics Letters, 2021, 118(12): 122904

[91] Gao R Z, Shi X M, Wang J. . Designed giant room-temperature electrocaloric effects in metal-free organic perovskite [MDABCO](NH₄)I₃ by phase-field simulations. Advanced Functional Materials, 2021, 31(38): 2104393

[92] Sebald G, Seveyrat L, Capsal J F. . Differential scanning calorimeter and infrared imaging for electrocaloric characterization of poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) terpolymer. Applied Physics Letters, 2012, 101(2): 022907

[93] Li X, Qian X S, Lu S G. . Tunable temperature dependence of electrocaloric effect in ferroelectric relaxor poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene terpolymer. Applied Physics Letters, 2011, 99(5): 052907

[94] Li Y L, Chen L Q. Temperature-strain phase diagram for BaTiO₃ thin films. Applied Physics Letters, 2006, 88(7): 072905

[95] Bai Y, Ding K, Zheng G P. . Entropy-change measurement of electrocaloric effect of BaTiO₃ single crystal. Physica Status Solidi. A, Applications and Materials Science, 2012, 209(5): 941–944

[96] Qian X S, Ye H J, Zhang Y T. . Giant electrocaloric response over a broad temperature range in modified BaTiO₃ ceramics. Advanced Functional Materials, 2014, 24(9): 1300–1305

[97] Akcay G, Alpay S P, Mantese J V. . Magnitude of the intrinsic electrocaloric effect in ferroelectric perovskite thin films at high electric fields. Applied Physics Letters, 2007, 90(25): 252909

[98] Li Z, Li J, Wu H H. . Effect of electric field orientation on ferroelectric phase transition and electrocaloric effect. Acta Materialia, 2020, 191: 13–23

[99] Okazaki A, Kawaminami M. Lattice constant of strontium titanate at low temperatures. Materials Research Bulletin, 1973, 8(5): 545–550

[100] Nishimatsu T, Iwamoto M, Kawazoe Y. . First-principles accurate total-energy surfaces for polar structural distortions of BaTiO₃, PbTiO₃, and SrTiO₃: Consequences to structural transition temperatures. Physical Review B: Condensed Matter and Materials Physics, 2010, 82(13): 134106

[101] Liu C H, Si W, Wu C. . The ignored effects of vibrational entropy and electrocaloric effect in PbTiO₃ and PbZr_0.5Ti_0.5O₃ as studied through first-principles calculation. Acta Materialia, 2020, 191(1): 221–229

[102] Lisenkov S, Mani B K, Chang C M. . Multicaloric effect in ferroelectric PbTiO₃ from first principles. Physical Review B: Condensed Matter and Materials Physics, 2013, 87(22): 224101

[103] Mikhaleva E A, Flerov I N, Gorev M V. . Caloric characteristics of PbTiO₃ in the temperature range of the ferroelectric phase transition. Physics of the Solid State, 2012, 54(9): 1832–1840

[104] Zeng X W, Cohen R E. Thermo-electromechanical response of a ferroelectric perovskite from molecular dynamics simulations. Applied Physics Letters, 2011, 99(14): 142902

[105] Sai N, Rabe K M, Vanderbilt D. Theory of structural response to macroscopic electric fields in ferroelectric systems. Physical Review B: Condensed Matter, 2002, 66(10): 104108

[106] Pan Z, Wang P, Hou X. . Fatigue-free aurivillius phase ferroelectric thin films with ultrahigh energy storage performance. Advanced Energy Materials, 2020, 10: 2001536

[107] Wang S, Yi M, Xu B X. A phase-field model of relaxor ferroelectrics based on random field theory. International Journal of Solids and Structures, 2016, 83: 142–153

[108] Lisenkov S, Mani B, Glazkova E. . Scaling law for electrocaloric temperature change in antiferroelectrics. Scientific Reports, 2016, 6(1): 19590

[109] Glazkova-Swedberg E, Cuozzo J, Lisenkov S. . Electrocaloric effect in PbZrO₃ thin films with antiferroelectric-ferroelectric phase competition. Computational Materials Science, 2017, 129: 44–48

[110] Kingsland M, Lisenkov S, Ponomareva I. Unveiling electrocaloric potential of antiferroelectrics with phase competition. Advanced Theory and Simulations, 2018, 1(11): 1800096

[111] Xu K, Shi X M, Dong S Z. . Antiferroelectric phase diagram enhancing energy-storage performance by phase-field simulations. ACS Applied Materials & Interfaces, 2022, 14(22): 25770–25780

[112] Tan X, Ma C, Frederick J. . The antiferroelectric ↔ ferroelectric phase transition in lead-containing and lead-free perovskite ceramics. Journal of the American Ceramic Society, 2011, 94(12): 4091–4107

[113] Liu N T, Liang R H, Zhang G Z. . Colossal negative electrocaloric effects in lead-free bismuth ferrite-based bulk ferroelectric perovskite for solid-state refrigeration. Journal of Materials Chemistry. C, 2018, 6: 10415–10421

[114] Ayyub P, Chattopadhyay S, Pinto R. . Ferroelectric behavior in thin films of antiferroelectric materials. Physical Review B: Condensed Matter, 1998, 57(10): R5559–R5562

[115] Nishimatsu T, Barr J A, Beckman S P. Direct molecular dynamics simulation of electrocaloric effect in BaTiO₃. Journal of the Physical Society of Japan, 2013, 82(11): 114605

[116] Rožič B, Malič B, Uršič H. . Direct measurements of the giant electrocaloric effect in soft and solid ferroelectric materials. Ferroelectrics, 2010, 405(1): 26–31

[117] Zhang J T, Hou X, Wang J. Direct and indirect methods based on effective Hamilton for electrocaloric effect of BaTiO₃ nanoparticle. Journal of Physics: Condensed Matter, 2019, 31: 255402

[118] Marathe M, Grünebohm A, Nishimatsu T. . First principles-based calculation of the electrocaloric effect in BaTiO₃: A comparison of direct and indirect methods. Physical Review. B, 2016, 93(5): 054110

[119] Joffé A F. Mechanical and electrical strength and cohesion. Transactions of the Faraday Society, 1928, 24: 65–72

[120] Junquera J, Ghosez P. Critical thickness for ferroelectricity in perovskite ultrathin films. Nature, 2003, 422(6931): 506–509

[121] Glazkova E, Chang C M, Lisenkov S. . Depolarizing field in ultrathin electrocalorics. Physical Review B: Condensed Matter and Materials Physics, 2015, 92(6): 064101

[122] Bin-Omran S, Kornev I, Ponomareva I. . Diffuse phase transition in ferroelectric ultrathin films from first principles. Physical Review B: Condensed Matter and Materials Physics, 2010, 81(9): 094119

[123] Mani B K, Chang C M, Lisenkov S. . Critical thickness for antiferroelectricity in PbZrO₃. Physical Review Letters, 2015, 115(9): 097601

[124] Ponomareva I, Naumov I I, Kornev I. . Atomistic treatment of depolarizing energy and field in ferroelectric nanostructures. Physical Review B: Condensed Matter and Materials Physics, 2005, 72(14): 140102

[125] Fu H, Bellaiche L. Ferroelectricity in barium titanate quantum dots and wires. Physical Review Letters, 2003, 91(25): 257601

[126] Liu D, Wang J, Jafri H M. . Phase-field simulations of vortex chirality manipulation in ferroelectric thin films. npj Quantum Materials, 2022, 7: 34

[127] Zhu W X, Shi X M, Gao R Z. . Enhancing the elastocaloric strength by combining positive and negative elastocaloric effects. Physica Status Solidi. Rapid Research Letters, 2022, 16(8): 2200183

[128] Bin-Omran S. The influence of mechanical and electrical boundary conditions on electrocaloric response in (Ba_0.50Sr_0.50)TiO₃ thin films. Materials Research Bulletin, 2017, 95: 334–338

[129] Wang J, Kamlah M. Effect of electrical boundary conditions on the polarization distribution around a crack embedded in a ferroelectric single domain. Engineering Fracture Mechanics, 2010, 77(18): 3658–3669

[130] Li Y L, Hu S Y, Liu Z K. . Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Applied Physics Letters, 2002, 81(3): 427–429

[131] Marathe M, Ederer C. Electrocaloric effect in BaTiO₃: A first-principles-based study on the effect of misfit strain. Applied Physics Letters, 2014, 104(21): 212902

[132] Akcay G, Alpay S P, Rossetti G A Jr. . Influence of mechanical boundary conditions on the electrocaloric properties of ferroelectric thin films. Journal of Applied Physics, 2008, 103(2): 024104

[133] Wang J, Ma J, Huang H B. . Ferroelectric domain-wall logic units. Nature Communications, 2022, 13(1): 3255

[134] Zhang J, Heitmann A A, Alpay S P. . Electrothermal properties of perovskite ferroelectric films. Journal of Materials Science, 2009, 44(19): 5263–5273

[135] Qiu J, Jiang Q. Effect of misfit strain on the electrocaloric effect in epitaxial SrTiO₃ thin films. European Physical Journal B, 2009, 71(1): 15–19

[136] Karthik J, Martin L W. Effect of domain walls on the electrocaloric properties of Pb(Zr_1–xTi_x)O₃ thin films. Applied Physics Letters, 2011, 99(3): 032904

[137] Wang J J, Fortino D, Wang B. . Extraordinarily large electrocaloric strength of metal-free perovskites. Advanced Materials, 2020, 32(7): 1906224

[138] Li B, Wang J B, Zhong X L. . Room temperature electrocaloric effect on PbZr_0.8Ti_0.2O₃ thin film. Journal of Applied Physics, 2010, 107(1): 014109

[139] Wang F, Li B, Ou Y. . Multicaloric effects in PbZr_0.2Ti_0.8O₃ thin films with 90° domain structure. Europhysics Letters, 2017, 118(1): 17005

[140] Li B, Wang J B, Zhong X L. . The coexistence of the negative and positive electrocaloric effect in ferroelectric thin films for solid-state refrigeration. Europhysics Letters, 2013, 102(4): 47004

[141] Wang F, Li B, Ou Y. . A stress-mediated negative/positive electrocaloric effect in Bi₄Ti₃O₁₂ nanoparticles. Materials Letters, 2017, 196: 179–182

[142] Huang C, Yang H B, Gao C F. Giant electrocaloric effect in a cracked ferroelectric. Journal of Applied Physics, 2018, 123(15): 154102

[143] Van Lich L, Hou X, Phan M H. . Electrocaloric effect enhancement in compositionally graded ferroelectric thin films driven by a needle-to-vortex domain structure transition. Journal of Physics. D, Applied Physics, 2021, 54(25): 255307

[144] Ji Y, Chen W J, Zheng Y. The emergence of tunable negative electrocaloric effect in ferroelectric/paraelectric superlattices. Journal of Physics. D, Applied Physics, 2020, 53(50): 505302

[145] Huang D, Wang J B, Li B. . Influence of 90° charged domain walls on the electrocaloric effect in PbTiO₃ ferroelectric thin films. Journal of Applied Physics, 2016, 120(21): 214105

[146] Wang J, Liu M, Zhang Y. . Large electrocaloric effect induced by the multi-domain to mono-domain transition in ferroelectrics. Journal of Applied Physics, 2014, 115(16): 164102

[147] Hou X, Wu H P, Li H Y. . Giant negative electrocaloric effect induced by domain transition in the strained ferroelectric thin film. Journal of Physics: Condensed Matter, 2018, 30(46): 465401

[148] Li B, Wang J B, Zhong X L. . Giant electrocaloric effects in ferroelectric nanostructures with vortex domain structures. RSC Advances, 2013, 3: 7928–7932

[149] Zeng Y K, Li B, Wang J B. . Influence of vortex domain switching on the electrocaloric property of a ferroelectric nanoparticle. RSC Advances, 2014, 4(57): 30211–30214

[150] Ye C, Wang J B, Li B. . Giant electrocaloric effect in a wide temperature range in PbTiO₃ nanoparticle with double-vortex domain structure. Scientific Reports, 2018, 8(1): 293

[151] Van Lich L, Vu N L, Ha M T. . Enhancement of electrocaloric effect in compositionally graded ferroelectric nanowires. Journal of Applied Physics, 2020, 127(21): 214103

[152] Li B, Wang J B, Zhong X L. . Domain wall contribution to the electrocaloric effect in BaTiO₃ nanoparticle: A phase-field investigation. Journal of Nanoparticle Research, 2013, 15(2): 1427

[153] Sluka T, Tagantsev A, Damjanovic D. . Enhanced electromechanical response of ferroelectrics due to charged domain walls. Nature Communications, 2012, 3(1): 748

[154] Ondrejkovic P, Marton P, Guennou M. . Piezoelectric properties of twinned ferroelectric perovskites with head-to-head and tail-to-tail domain walls. Physical Review B: Condensed Matter and Materials Physics, 2013, 88(2): 024114

[155] Hou X, Li X, Zhang J. . Effect of grain size on the electrocaloric properties of polycrystalline ferroelectrics. Physical Review Applied, 2021, 15(5): 054019

[156] Chen X, Fang C. Study of electrocaloric effect in barium titanate nanoparticle with core-shell model. Physica B: Condensed Matter, 2013, 415: 14–17

[157] Qiu J H, Jiang Q. Grain size effect on the electrocaloric effect of dense BaTiO₃ nanoceramics. Journal of Applied Physics, 2009, 105(3): 034110

[158] Morozovska A N, Eliseev E A, Glinchuk M D. . Analytical description of the size effect on pyroelectric and electrocaloric properties of ferroelectric nanoparticles. Physical Review Materials, 2019, 3(10): 104414

[159] Patel S, Kumar M. Influence of grain size on the electrocaloric and pyroelectric properties in non-reducible BaTiO₃ ceramics. AIP Advances, 2020, 10(8): 085302

[160] Das S, Tang Y L, Hong Z. . Observation of room-temperature polar skyrmions. Nature, 2019, 568(7752): 368–372

[161] Li Q, Stoica V A, Paściak M. . Subterahertz collective dynamics of polar vortices. Nature, 2021, 592(7854): 376–380

[162] Wang Y J, Feng Y P, Zhu Y L. . Polar meron lattice in strained oxide ferroelectrics. Nature Materials, 2020, 19(8): 881–886

[163] Abid A Y, Sun Y, Hou X. . Creating polar antivortex in PbTiO₃/SrTiO₃ superlattice. Nature Communications, 2021, 12(1): 2054

[164] Huang H, Zhang G, Ma X. . Size effects of electrocaloric cooling in ferroelectric nanowires. Journal of the American Ceramic Society, 2018, 101(4): 1566–1575

[165] Ishidate T, Abe S, Takahashi H. . Phase diagram of BaTiO₃. Physical Review Letters, 1997, 78(12): 2397–2400

[166] Wang J J, Wu P P, Ma X Q. . Temperature-pressure phase diagram and ferroelectric properties of BaTiO₃ single crystal based on a modified Landau potential. Journal of Applied Physics, 2010, 108(11): 114105

[167] Yu H, Wang J, Kozinov S. . Phase field analysis of crack tip parameters in ferroelectric polycrystals under large-scale switching. Acta Materialia, 2018, 154: 334–342

[168] Huang Y H, Wang J J, Yang T N. . A thermodynamic potential, energy storage performances, and electrocaloric effects of Ba_1–xSr_xTiO₃ single crystals. Applied Physics Letters, 2018, 112(10): 102901

[169] Cao G P, Huang H B, Liang D S. . A phenomenological potential and ferroelectric properties of BaTiO₃-CaTiO₃ solid solution. Ceramics International, 2017, 43(9): 6671–6676

[170] Zhang G Z, Zhang X S, Yang T N. . Colossal room-temperature electrocaloric effect in ferroelectric polymer nanocomposites using nanostructured barium strontium titanates. ACS Nano, 2015, 9(7): 7164–7174

[171] Qian J F, Peng R C, Shen Z H. . Interfacial coupling boosts giant electrocaloric effects in relaxor polymer nanocomposites: In situ characterization and phase-field simulation. Advanced Materials, 2019, 31(5): 1801949

[172] Shi X M, Wang J, Xu J W. . Quantitative investigation of polar nanoregion size effects in relaxor ferroelectrics. Acta Materialia, 2022, 237: 118147

[173] Xu S Q, Shi X M, Pan H. . Strain engineering of energy storage performance in relaxor ferroelectric thin film capacitors. Advanced Theory and Simulations, 2022, 5(6): 2100324

[174] Liu Y, Yang T, Zhang B. . Structural insight in the interfacial effect in ferroelectric polymer nanocomposites. Advanced Materials, 2020, 32(49): 2005431

[175] Gao R Z, Wang J, Wang J S. . Investigation into electrocaloric effect of different types of ferroelectric materials by Landau-Devonshire theory. Acta Physica Sinica, 2020, 69(21): 217801

[176] Wang J, Zhu R X, Ma J. . Photoenhanced electroresistance at dislocation-mediated phase boundary. ACS Applied Materials & Interfaces, 2022, 14(16): 18662–18670

[177] Wang J, Fan Y Y, Song Y. . Microscopic physical origin of polarization induced large tunneling electroresis-tance in tetragonal-phase BiFeO₃. Acta Materialia, 2022, 225: 117564

[178] Gu H, Qian X, Li X. . A chip scale electrocaloric effect based cooling device. Applied Physics Letters, 2013, 102(12): 122904

[179] Plaznik U, Vrabelj M, Kutnjak Z. . Electrocaloric cooling: The importance of electric-energy recovery and heat regeneration. Europhysics Letters, 2015, 111(5): 57009

[180] Qian X S, Yang T N, Zhang T. . Anomalous negative electrocaloric effect in a relaxor/normal ferroelectric polymer blend with controlled nano- and meso-dipolar couplings. Applied Physics Letters, 2016, 108(14): 142902

[181] Akamatsu H, Yuan Y, Stoica V A. . Light-activated gigahertz ferroelectric domain dynamics. Physical Review Letters, 2018, 120(9): 096101

[182] Yang T, Wang B, Hu J M. . Domain dynamics under ultrafast electric-field pulses. Physical Review Letters, 2020, 124(10): 107601

[183] Shao C C, Shi X M, Wang J. . Designing ultrafast cooling rate for room temperature electrocaloric effects by phase-field simulations. Advanced Theory and Simulations, 2022, 5(10): 2200406

[184] Li Q, Shi J, Han D. . Concept design and numerical evaluation of a highly efficient rotary electrocaloric refrigeration device. Applied Thermal Engineering, 2021, 190: 116806

[185] Aprea C, Greco A, Maiorino A. . A comparison between different materials in an active electrocaloric regenerative cycle with a 2D numerical model. International Journal of Refrigeration, 2016, 69: 369–382

[186] Aprea C, Greco A, Maiorino A. . A two-dimensional model of a solid-state regenerator based on combined electrocaloric-elastocaloric effect. Energy Procedia, 2017, 126: 337–344

[187] ApreaCGreco AMaiorinoA, . Solid-state refrigeration: A comparison of the energy performances of caloric materials operating in an active caloric regenerator. Energy, 2018, 165(Part A): 439–455

[188] Aprea C, Greco A, Maiorino A. . The employment of caloric-effect materials for solid-state heat pumping. International Journal of Refrigeration, 2019, 109: 1–11

[189] Aprea C, Greco A, Maiorino A. . A numerical investigation on a caloric heat pump employing nanofluids. International Journal of Heat and Technology, 2019, 37(3): 675–681

[190] Gu H, Qian X S, Ye H J. . An electrocaloric refrigerator without external regenerator. Applied Physics Letters, 2014, 105(16): 162905

[191] Zhang T, Qian X S, Gu H M. . An electrocaloric refrigerator with direct solid to solid regeneration. Applied Physics Letters, 2017, 110(24): 243503

[192] Smullin S J, Wang Y, Schwartz D E. System optimization of a heat-switch-based electrocaloric heat pump. Applied Physics Letters, 2015, 107(9): 093903

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 51972028) and the State Key Development Program for Basic Research of China (Grant No. 2019YFA0307900).

Competing interests

The authors declare that they have no competing interests.

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