Investigation into electrocaloric effect of different types of ferroelectric materials by Landau-Devonshire theory

Gao Rong-Zhen; Wang Jing; Wang Jun-Sheng; Huang Hou-Bing

doi:10.7498/aps.69.20201195

Abstract

The electrocaloric effects in various types of materials, including inorganic perovskites, organic perovskites, organic polymers, molecular ferroelectrics and two-dimensional ferroelectric materials, possess great potential in realizing solid-state cooling devices due to the advantages of low-cost, high-efficiency and environmental friendly. Different ferroelectric materials have distinct characteristics in terms of phase transition and electrocaloric response. The mechanism for enhancing the electrocaloric effect currently remains elusive. Here, typical inorganic perovskite BaTiO₃, PbTiO₃ and BiFeO₃, organic perovskite [MDABCO](NH₄)I₃, organic polymer P(VDF-TrFE), molecular ferroelectric ImClO₄ and two-dimensional ferroelectric CuInP₂S₆ are selected to analyze the origins of their electrocaloric effects based on the Landau-Devonshire theory. The temperature-dependent pyroelectric coefficients and electrocaloric performances of different ferroelectric materials indicate that the first-order phase transition material MDABCO and the second-order phase transition material ImClO₄ have excellent performances for electrocaloric refrigeration. The predicted results also strongly suggest that near the phase transition point of the ferroelectric material, the variation rate of free energy barrier height with temperature contributes to the polarizability change with temperature, resulting in enhanced electrocaloric effect. This present work provides a theoretical basis and a new insight into the further development of ferroelectric materials with high electrocaloric response.

Keywords:

Authors and contacts

1.
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
2.
Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Huang Hou-Bing, hbhuang@bit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51972028) and the National Key R&D Program of China (Grant No. 2019YFA0307900).

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References

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图 1 不同铁电材料的极化及热释电系数随温度的变化　(a), (b) BTO, PTO, BFO, ImClO₄, MDABCO, CIPS, P(VDF-TrFE)在电场为0 (a) 和5 MV/m (b) 时极化随温度的变化; (c)一级相变材料BTO, PTO, MDABCO, P(VDF-TrFE)在电场为5 MV/m时热释电系数随温度的变化; (d)二级相变材料BFO, ImClO₄, CIPS在电场为5 MV/m时热释电系数随温度的变化

Figure 1. Temperature dependent polarization and pyroelectric coefficients obtained in different ferroelectric materials: (a), (b) Temperature-dependent polarization for BTO, PTO, BFO, ImClO₄, MDABCO, CIPS, and P(VDF-TrFE) with the electric field of 0 and 5 MV/m, respectively; (c) temperature dependent pyroelectric coefficients for the first-order phase transition materials BTO, PTO, MDABCO and P(VDF-TrFE) with the electric field of 5 MV/m; (d) temperature dependent pyroelectric coefficients for the second-order phase transition materials BFO, ImClO₄ and CIPS with the electric field of 5 MV/m.

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图 2 不同铁电材料的等温熵变和绝热温变在电场为5 MV·m^–1时随温度的变化　(a), (c)一级相变材料BTO, PTO, MDABCO和P(VDF-TrFE)等温熵变和绝热温变随温度的变化; (b), (d)二级相变材料BFO, ImClO₄和CIPS等温熵变和绝热温变随温度的变化

Figure 2. Temperature dependent ΔS and ΔT from different ferroelectric materials when the applied electric field is 5 MV/m: (a), (c) Temperature dependent ΔS and ΔT from the first-order phase transition materials BTO, PTO, MDABCO and P(VDF-TrFE), respectively; (b), (d) temperature dependent ΔS and ΔT from the second-order phase transition materials BFO, ImClO₄ and CIPS, respectively.

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图 3 不同铁电材料的电卡强度ΔS/ΔE和ΔT/ΔE随温度的变化　(a), (c)一级相变材料BTO, PTO, MDABCO和P(VDF-TrFE) ΔS/ΔE和ΔT/ΔE随温度的变化; (b), (d)二级相变材料BFO, ImClO₄和CIPS的ΔS/ΔE和ΔT/ΔE随温度的变化(图中实线代表在电场为5 MV/m时的计算结果, 带符号的虚线代表P(VDF-TrFE)在较大电场(40 MV/m)的计算结果, 符号代表参考文献中数据. Ref.a, Ref.b, Ref.c, Ref.d分别对应参考文献[42]、文献[24]、文献[43]、文献[41])

Figure 3. Temperature dependent EC strength ΔS/ΔE and ΔT/ΔE from different ferroelectric materials: (a), (c) Temperature dependent ΔS/ΔE and ΔT/ΔE from first-order phase transition materials BTO, PTO, MDABCO and P(VDF-TrFE); (b), (d) temperature dependent ΔS/ΔE and ΔT/ΔE from the second-order phase change materials BFO, ImClO₄ and CIPS. The solid lines in the figure indicate the calculation results when the electric field is 5 MV/m, and the dotted lines with symbols indicate the calculation results of P(VDF-TrFE) in a larger electric field (40 MV/m). The symbols indicate the data in the references, Ref.a, Ref.b, Ref. c, Ref.d correspond to Ref. [42], Ref. [24], Ref. [43], Ref. [41] respectively

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图 4 不同铁电材料在T_C－5, T_C－3, T_C－1 (K)温度下的电滞回线　(a), (c)一级相变材料MDABCO和BTO极化随电场的变化; (b), (d)二级相变材料ImClO₄和CIPS极化随电场的变化

Figure 4. Hysteresis loops of different ferroelectric materials at temperature of T_C－5, T_C－3, T_C－1 (K): (a), (c) Electric-field dependent of polarization from the first-order phase transition materials MDABCO and BTO; (b), (d) electric-field dependent of polarization from the second-order phase transition materials ImClO₄ and CIPS.

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图 5 不同铁电材料在T_C－5, T_C－3, T_C－1 (K)温度下自由能随极化的变化　(a), (c)一级相变材料MDABCO和BTO自由能随极化的变化; (b), (d)二级相变材料ImClO₄和CIPS自由能随极化的变化; 图中三维彩色插入图为不同铁电材料在T_C－5 (K)温度下的三维自由能曲面图

Figure 5. Free energy as a function of polarization from different ferroelectric materials at the temperature of T_C－5, T_C－3, T_C－1 (K): (a), (c) Free energy curves as a function of polarization from first-order phase transition materials MDABCO and BTO; (b), (d) free energy curves as a function of polarization from second-order phase transition materials ImClO₄ and CIPS. Three-dimensional inset figures show three-dimensional free energy surface at T_C－5 (K) from different ferroelectric materials.

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表 1 不同铁电材料的Landau系数

Table 1. Landau coefficients of different kinds of ferroelectric materials.

Coefficients	BaTiO₃^[45]	PbTiO₃^[46]	BiFeO₃^[47]	ImClO₄^[43]	[MDABCO] (NH₄)I₃^[42]	CuInP₂S₆^[41]	P(VDF-TrFE)^[26]
α₁/C^–2·m²·N	$\begin{array}{cc} & 5.0 \times 10^5 \times 160 \times\\& \Big[{\rm Coth}\Big(\dfrac{160}{T} \Big)–{\rm Coth} \Big(\dfrac{160}{390}\Big)\Big] \end{array}$	3.8 × 10⁵× (T – 752)	4.646 × 10⁵× (T – 1103)	7.533 × 10⁷× (T – 373)	4.01 × 10⁶× (T – 437)	1.76 × 10⁷× (T – 315)	1.412 × 10⁷× (T – 315)
α₁₁/C^–4·m⁶·N	–1.154×10⁸	–0.73×10⁸	2.290×10⁸	1.5×10¹¹	–7.032×10⁹	1.38×10¹¹	–1.842×10¹¹
α₁₂/C^–4·m⁶·N	6.530×10⁸	7.5×10⁸	3.064×10⁸		1.124×10⁸
α₁₁₁/C^–6·m¹⁰·N	–2.106×10⁹	2.6×10⁸	5.99×10⁹	2×10¹²	α₁₁₁(T)	6.81×10¹³	2.585×10¹³
α₁₁₂/C^–6·m¹⁰·N	4.091×10⁹	6.1×10⁸	–3.340×10⁸		0
α₁₂₃/C^–6·m¹⁰·N	–6.688×10⁹	–3.7×10⁹	–1.778×10⁹		–2.018×10¹⁰
α₁₁₁₁/C^–8·m¹⁴·N	7.590×10¹⁰
α₁₁₁₂/C^–8·m¹⁴·N	–2.193×10¹⁰
α₁₁₂₂/C^–8·m¹⁴·N	–2.221×10¹⁰
α₁₁₂₃/C^–8·m¹⁴·N	2.416× 10¹⁰
注: α₁₁₁(T): T > T₀(437 K), α₁₁₁ = 3×10¹¹; T ≤ T₀, α₁₁₁ = –3.5085×10⁹× 55$\left[{\rm Coth}\left(\dfrac{55}{T}\right) \right.$ –Coth$\left.\left(\dfrac{55}{523}\right)\right]$.

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表 2 不同铁电材料的比热容和密度

Table 2. Specific heat capacity and density of different ferroelectric materials.

Parameters	BaTiO₃^[35,37,42]	PbTiO₃^[36,48,49]	BiFeO₃^[20]	ImClO₄^[43]	[MDABCO](NH₄)I₃^[42]	CuInP₂S₆^[41]	P(VDF-TrFE)^[50,51]
ρ/kg·m^–3	6020	8300	8346	1719	4039	3405	1886
C/J·m^–3·K^–1	3.05 × 10⁶	3.9 × 10⁶	2.88 × 10⁶	2.423 × 10⁶	4.039 × 10⁶	1.896 × 10⁶	2.244 × 10⁶

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[1]	Shi J Y, Han D L, Li Z C, Yang L, Lu S G, Zhong Z F, Chen J P, Zhang Q M, Qian X S 2019 Joule 3 1200 Google Scholar
[2]	Liu G, Kong L, Hu Q, Zhang S 2020 Appl. Phys. Rev. 7 021405 Google Scholar
[3]	Wang J J, Su Y J, Wang B, Ouyang J, Ren Y H, Chen L Q 2020 Nano Energy 72 104665 Google Scholar
[4]	邢洁, 谭智, 郑婷, 吴家刚, 肖定全, 朱建国 2020 69 127707 Google Scholar Xing J, Tan Z, Zheng T, Wu J G, Xiao D Q, Zhu J G 2020 Acta Phys. Sin. 69 127707 Google Scholar
[5]	鲁圣国, 李丹丹, 林雄威, 简晓东, 赵小波, 姚英邦, 陶涛, 梁波 2020 69 127701 Google Scholar Lu S G, Li D D, Lin X W, Jian X D, Zhao X B, Yao Y B, Tao T, Liang B 2020 Acta Phys. Sin. 69 127701 Google Scholar
[6]	刘迪, 王静, 王俊升, 黄厚兵 2020 69 127801 Google Scholar Liu D, Wang J, Wang J S, Huang H B 2020 Acta Phys. Sin. 69 127801 Google Scholar
[7]	Kobeco P, Kurtchatov I 1930 Z. Phys. 66 192 Google Scholar
[8]	Mischenko A S, Zhang Q, Scott J F, Whatmore R W, Mathur N D 2006 Science 311 1270 Google Scholar
[9]	Chen C, Wang S, Zhang T, Zhang C, Chi Q, Li W 2020 RSC Adv. 10 6603 Google Scholar
[10]	Prasad S, Hou X, Zhang J, Wu S, Wang J 2020 IEEE Trans. Electron Devices 67 1769 Google Scholar
[11]	Karthik J, Martin L W 2011 Appl. Phys. Lett. 99 032904 Google Scholar
[12]	Sun X H, Huang H B, Ma X, Wen Y, Dang Z M 2018 J. Ceram. Sci. Technol. 9 201 Google Scholar
[13]	Zhang G Z, Zhang X S, Huang H B, Wang J J, Li Q, Chen L Q, Wang Q 2016 Adv. Mater. 28 4811 Google Scholar
[14]	Huang Y H, Wang J J, Yang T N, Wu Y J, Chen X M, Chen L Q 2018 Appl. Phys. Lett. 112 102901 Google Scholar
[15]	Huang H B, Zhang G Z, Ma X Q, Liang D S, Wang J S, Liu Y, Wang Q, Chen L Q 2018 J. Am. Ceram. Soc. 101 1566 Google Scholar
[16]	Zhou Y, Lin Q, Liub W, Wang D 2016 RSC Adv. 6 14084 Google Scholar
[17]	Hanani Z, Mezzane D, Amjoud M, Razumnaya A G, Fourcade S, Gagou Y, Hoummada K, El Marssi M, Goune M 2019 J. Mater. Sci.: Mater. Electron. 30 6430 Google Scholar
[18]	Bai Y, Han X, Qiao L 2013 Appl. Phys. Lett. 102 252904 Google Scholar
[19]	Weyland F, Hayati R, Novak N 2019 Ceram. Int. 45 11408 Google Scholar
[20]	Sun X H, Huang H B, Jafri H M, Wang J S, Wen Y, Dang Z M 2019 Appl. Sci. 9 1672 Google Scholar
[21]	Li F, Zhai J, Shen B, Zeng H, Jian X, Lu S 2019 J. Alloys Compd. 803 185 Google Scholar
[22]	Zheng G P, Uddin S, Zheng X, Yang J 2016 J. Alloys Compd. 663 249 Google Scholar
[23]	Matsushita Y, Yoshimura T, Kiriya D, Fujimura N 2020 Appl. Phys. Express 13 041007 Google Scholar
[24]	Aziguli H, Liu Y, Zhang G Z, Jiang S L, Yu P, Wang Q 2019 Europhys. Lett. 125 57001 Google Scholar
[25]	Li J, Zhao X, Zhang T, Qian X, Hou Y, Yang L, Zhang Q M 2017 Phase Transitions 90 99 Google Scholar
[26]	Qian X S, Yang T N, Zhang T, Chen L Q, Zhang Q M 2016 Appl. Phys. Lett. 108 142902 Google Scholar
[27]	Qian J, Peng R, Shen Z, Jiang J, Xue F, Yang T, Chen L, Shen Y 2019 Adv. Mater. 31 1801949 Google Scholar
[28]	Zhang G, Zhang X, Yang T, Li Q, Chen L Q, Jiang S, Wang Q 2015 ACS Nano 9 7164 Google Scholar
[29]	Chen Y, Qian J, Yu J, Guo M, Zhang Q, Jiang J, Shen Z, Chen L Q, Shen Y 2020 Adv. Mater. 32 1907927 Google Scholar
[30]	Yang Y, Zhou Z, Ke X, Wang Y, Su X, Li J, Bai Y, Ren X 2020 Scr. Mater. 174 44 Google Scholar
[31]	Zhao C, Yang J, Huang Y, Hao X, Wu J 2019 J. Mater. Chem. A 7 25526 Google Scholar
[32]	Mendez-Gonzalez Y, Pelaiz-Barranco A, Guerra J D S 2019 Appl. Phys. Lett. 114 162902 Google Scholar
[33]	Lu B, Li P, Tang Z, Yao Y, Gao X, Kleemann W, Lu S G 2017 Sci. Rep. 7 45335 Google Scholar
[34]	Sun X H, Huang H B, Wang J S, Wen Y Q, Dang Z M 2019 J. Alloys Compd. 777 821 Google Scholar
[35]	Wu H H, Zhu J, Zhang T Y 2015 Nano Energy 16 419 Google Scholar
[36]	Hou X, Wu H, Li H, Chen H, Wang J 2018 J. Phys.: Condens. Matter 30 465401 Google Scholar
[37]	Wu H H, Zhu J, Zhang T Y 2015 RSC Adv. 5 37476 Google Scholar
[38]	Liu Z, Yang B, Cao W, Lookman T 2018 Phys. Status Solidi B 255 1700469 Google Scholar
[39]	Hou X, Li H, Shimada T, Kitamura T, Wang J 2018 J. Appl. Phys. 123 124103 Google Scholar
[40]	Zeng Y K, Li B, Wang J B, Zhong X L, Wang W, Wang F, Zhou Y C 2014 RSC Adv. 4 30211 Google Scholar
[41]	Si M W, Saha A K, Liao P Y, Gao S J, Neumayer S M, Jian J, Qin J K, Wisinger N B, Wang H Y, Maksymovych P, Wu W Z, Gupta S K, Ye P D 2019 ACS Nano 13 8760 Google Scholar
[42]	Wang J J, Fortino D, Wang B, Zhao X, Chen L Q 2019 Adv. Mater. 32 1906224 Google Scholar
[43]	Li W R, Jafri H M, Zhang C, Zhang Y J, Zhang H B, Huang H B, Jiang S L, Zhang G Z 2020 J. Mater. Chem. A 8 16189 Google Scholar
[44]	Liu D, Zhao R, Jafri H M, Wang J S, Huang H B 2019 Appl. Phys. Lett. 114 112903 Google Scholar
[45]	Wang J J, Wu P P, Ma X Q, Chen L Q 2010 J. Appl. Phys. 108 114105 Google Scholar
[46]	Li Y L, Hu S Y, Liu Z K, Chen L Q 2002 Acta Mater. 50 395 Google Scholar
[47]	Hsieh Y H, Xue F, Yang T N, Liu H J, Zhu Y M, Chen Y C, Zhan Q, Duan C G, Chen L Q, He Q, Chu Y H 2016 Nat. Commun. 7 13199 Google Scholar
[48]	Bai G, Qin X, Xie Q, Gao C 2019 Physica B 560 208 Google Scholar
[49]	Huang C, Yang H B, Gao C F 2018 J. Appl. Phys. 123 154102 Google Scholar
[50]	Qiu J H, Ding J N, Yuan N Y, Wang X Q, Yang J 2011 Eur. Phys. J. B 84 25 Google Scholar
[51]	Bai G, Liu D, Gao C 2019 J. Appl. Phys. 126 164105 Google Scholar

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Vol. 69, Issue 21 - 2020-11-05

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