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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

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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

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
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  • 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.
    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.
      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
      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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  • 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.

    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.

    图 3  不同铁电材料的电卡强度ΔSE和ΔTE随温度的变化 (a), (c)一级相变材料BTO, PTO, MDABCO和P(VDF-TrFE) ΔSE和ΔTE随温度的变化; (b), (d)二级相变材料BFO, ImClO4和CIPS的ΔSE和ΔTE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 ΔSE and ΔTE from different ferroelectric materials: (a), (c) Temperature dependent ΔSE and ΔTE from first-order phase transition materials BTO, PTO, MDABCO and P(VDF-TrFE); (b), (d) temperature dependent ΔSE and ΔTE 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

    图 4  不同铁电材料在TC-5, TC-3, TC-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 TC-5, TC-3, TC-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.

    图 5  不同铁电材料在TC-5, TC-3, TC-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TC-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 TC-5, TC-3, TC-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 TC-5 (K) from different ferroelectric materials.

    表 1  不同铁电材料的Landau系数

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

    CoefficientsBaTiO3[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}$3.8 × 105×
    (T – 752)
    4.646 × 105×
    (T – 1103)
    7.533 × 107×
    (T – 373)
    4.01 × 106×
    (T – 437)
    1.76 × 107×
    (T – 315)
    1.412 × 107×
    (T – 315)
    α11/C–4·m6·N–1.154×108–0.73×1082.290×1081.5×1011–7.032×1091.38×1011–1.842×1011
    α12/C–4·m6·N6.530×1087.5×1083.064×1081.124×108
    α111/C–6·m10·N–2.106×1092.6×1085.99×1092×1012α111(T)6.81×10132.585×1013
    α112/C–6·m10·N4.091×1096.1×108–3.340×1080
    α123/C–6·m10·N–6.688×109–3.7×109–1.778×109–2.018×1010
    α1111/C–8·m14·N7.590×1010
    α1112/C–8·m14·N–2.193×1010
    α1122/C–8·m14·N–2.221×1010
    α1123/C–8·m14·N2.416× 1010
    注: α111(T): T > T0(437 K), α111 = 3×1011; TT0, α111 = –3.5085×109× 55$\left[{\rm Coth}\left(\dfrac{55}{T}\right) \right.$ –Coth$\left.\left(\dfrac{55}{523}\right)\right]$.
    下载: 导出CSV

    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.

    ParametersBaTiO3[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–36020830083461719403934051886
    C/J·m–3·K–13.05 × 1063.9 × 1062.88 × 1062.423 × 1064.039 × 1061.896 × 1062.244 × 106
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-07-24
  • 修回日期:  2020-08-06
  • 上网日期:  2020-11-13
  • 刊出日期:  2020-11-05

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