Landau-Devonshire理论探究不同类型铁电材料的电卡效应

高荣贞; 王静; 王俊升; 黄厚兵

doi:10.7498/aps.69.20201195

摘要

近年来, 低成本、高效、环保的电卡效应制冷材料得到了广泛研究, 其中包括无机钙钛矿、有机钙钛矿、有机聚合物、分子铁电材料和二维铁电材料等. 这些不同铁电材料的相变类型和电卡性能各异, 而造成其差异的物理起源尚不明确. 本文选择传统无机钙钛矿BaTiO₃, PbTiO₃和BiFeO₃, 有机钙钛矿[MDABCO](NH₄)I₃, 有机聚合物P(VDF-TrFE), 分子铁电体ImClO₄和二维铁电体CuInP₂S₆这七种材料, 利用Landau-Devonshire理论, 研究并对比了其温变、熵变和电卡强度. 通过分析自由能与极化之间的关系发现, 在相变点附近, 铁电材料的自由能势垒高度随温度的变化率越大, 造成的极化随温度的变化率越高, 而材料的电卡性能也越优异. 本文揭示了不同类型铁电材料电卡性能差异的物理起源, 为进一步开发具有高电卡性能的铁电材料提供理论指导.

关键词:

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:

作者及机构信息

1.
北京理工大学材料学院, 北京　100081

2.
北京理工大学前沿交叉科学研究院, 北京　100081

通信作者: 黄厚兵, hbhuang@bit.edu.cn

基金项目: 国家自然科学基金(批准号: 51972028)和国家重点研发计划(批准号: 2019YFA0307900)资助的课题

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).

文章全文 : translate this paragraph

参考文献

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施引文献

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

Fig. 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

Fig. 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])

Fig. 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

Fig. 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

Fig. 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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map

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