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.

Key words： electrocaloric effect; effective Hamiltonian; phase-field modeling; different theoretical models

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.

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