-
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:
- 电卡效应 /
- 铁电材料 /
- 热力学计算 /
- Landau-Devonshire理论
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:
- electrocaloric effect /
- ferroelectric material /
- thermodynamic calculation /
- Landau-Devonshire theory
[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 1200Google Scholar
[2] Liu G, Kong L, Hu Q, Zhang S 2020 Appl. Phys. Rev. 7 021405Google Scholar
[3] Wang J J, Su Y J, Wang B, Ouyang J, Ren Y H, Chen L Q 2020 Nano Energy 72 104665Google Scholar
[4] 邢洁, 谭智, 郑婷, 吴家刚, 肖定全, 朱建国 2020 物理学报 69 127707Google Scholar
Xing J, Tan Z, Zheng T, Wu J G, Xiao D Q, Zhu J G 2020 Acta Phys. Sin. 69 127707Google 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 物理学报 69 127701Google 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 127701Google Scholar
[6] 刘迪, 王静, 王俊升, 黄厚兵 2020 物理学报 69 127801Google Scholar
Liu D, Wang J, Wang J S, Huang H B 2020 Acta Phys. Sin. 69 127801Google Scholar
[7] Kobeco P, Kurtchatov I 1930 Z. Phys. 66 192Google Scholar
[8] Mischenko A S, Zhang Q, Scott J F, Whatmore R W, Mathur N D 2006 Science 311 1270Google Scholar
[9] Chen C, Wang S, Zhang T, Zhang C, Chi Q, Li W 2020 RSC Adv. 10 6603Google Scholar
[10] Prasad S, Hou X, Zhang J, Wu S, Wang J 2020 IEEE Trans. Electron Devices 67 1769Google Scholar
[11] Karthik J, Martin L W 2011 Appl. Phys. Lett. 99 032904Google Scholar
[12] Sun X H, Huang H B, Ma X, Wen Y, Dang Z M 2018 J. Ceram. Sci. Technol. 9 201Google 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 4811Google 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 102901Google 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 1566Google Scholar
[16] Zhou Y, Lin Q, Liub W, Wang D 2016 RSC Adv. 6 14084Google 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 6430Google Scholar
[18] Bai Y, Han X, Qiao L 2013 Appl. Phys. Lett. 102 252904Google Scholar
[19] Weyland F, Hayati R, Novak N 2019 Ceram. Int. 45 11408Google Scholar
[20] Sun X H, Huang H B, Jafri H M, Wang J S, Wen Y, Dang Z M 2019 Appl. Sci. 9 1672Google Scholar
[21] Li F, Zhai J, Shen B, Zeng H, Jian X, Lu S 2019 J. Alloys Compd. 803 185Google Scholar
[22] Zheng G P, Uddin S, Zheng X, Yang J 2016 J. Alloys Compd. 663 249Google Scholar
[23] Matsushita Y, Yoshimura T, Kiriya D, Fujimura N 2020 Appl. Phys. Express 13 041007Google Scholar
[24] Aziguli H, Liu Y, Zhang G Z, Jiang S L, Yu P, Wang Q 2019 Europhys. Lett. 125 57001Google Scholar
[25] Li J, Zhao X, Zhang T, Qian X, Hou Y, Yang L, Zhang Q M 2017 Phase Transitions 90 99Google Scholar
[26] Qian X S, Yang T N, Zhang T, Chen L Q, Zhang Q M 2016 Appl. Phys. Lett. 108 142902Google Scholar
[27] Qian J, Peng R, Shen Z, Jiang J, Xue F, Yang T, Chen L, Shen Y 2019 Adv. Mater. 31 1801949Google Scholar
[28] Zhang G, Zhang X, Yang T, Li Q, Chen L Q, Jiang S, Wang Q 2015 ACS Nano 9 7164Google 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 1907927Google Scholar
[30] Yang Y, Zhou Z, Ke X, Wang Y, Su X, Li J, Bai Y, Ren X 2020 Scr. Mater. 174 44Google Scholar
[31] Zhao C, Yang J, Huang Y, Hao X, Wu J 2019 J. Mater. Chem. A 7 25526Google Scholar
[32] Mendez-Gonzalez Y, Pelaiz-Barranco A, Guerra J D S 2019 Appl. Phys. Lett. 114 162902Google Scholar
[33] Lu B, Li P, Tang Z, Yao Y, Gao X, Kleemann W, Lu S G 2017 Sci. Rep. 7 45335Google Scholar
[34] Sun X H, Huang H B, Wang J S, Wen Y Q, Dang Z M 2019 J. Alloys Compd. 777 821Google Scholar
[35] Wu H H, Zhu J, Zhang T Y 2015 Nano Energy 16 419Google Scholar
[36] Hou X, Wu H, Li H, Chen H, Wang J 2018 J. Phys.: Condens. Matter 30 465401Google Scholar
[37] Wu H H, Zhu J, Zhang T Y 2015 RSC Adv. 5 37476Google Scholar
[38] Liu Z, Yang B, Cao W, Lookman T 2018 Phys. Status Solidi B 255 1700469Google Scholar
[39] Hou X, Li H, Shimada T, Kitamura T, Wang J 2018 J. Appl. Phys. 123 124103Google Scholar
[40] Zeng Y K, Li B, Wang J B, Zhong X L, Wang W, Wang F, Zhou Y C 2014 RSC Adv. 4 30211Google 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 8760Google Scholar
[42] Wang J J, Fortino D, Wang B, Zhao X, Chen L Q 2019 Adv. Mater. 32 1906224Google 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 16189Google Scholar
[44] Liu D, Zhao R, Jafri H M, Wang J S, Huang H B 2019 Appl. Phys. Lett. 114 112903Google Scholar
[45] Wang J J, Wu P P, Ma X Q, Chen L Q 2010 J. Appl. Phys. 108 114105Google Scholar
[46] Li Y L, Hu S Y, Liu Z K, Chen L Q 2002 Acta Mater. 50 395Google 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 13199Google Scholar
[48] Bai G, Qin X, Xie Q, Gao C 2019 Physica B 560 208Google Scholar
[49] Huang C, Yang H B, Gao C F 2018 J. Appl. Phys. 123 154102Google Scholar
[50] Qiu J H, Ding J N, Yuan N Y, Wang X Q, Yang J 2011 Eur. Phys. J. B 84 25Google Scholar
[51] Bai G, Liu D, Gao C 2019 J. Appl. Phys. 126 164105Google Scholar
-
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
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.
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$\left.\left(\dfrac{55}{523}\right)\right]$. 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.
-
[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 1200Google Scholar
[2] Liu G, Kong L, Hu Q, Zhang S 2020 Appl. Phys. Rev. 7 021405Google Scholar
[3] Wang J J, Su Y J, Wang B, Ouyang J, Ren Y H, Chen L Q 2020 Nano Energy 72 104665Google Scholar
[4] 邢洁, 谭智, 郑婷, 吴家刚, 肖定全, 朱建国 2020 物理学报 69 127707Google Scholar
Xing J, Tan Z, Zheng T, Wu J G, Xiao D Q, Zhu J G 2020 Acta Phys. Sin. 69 127707Google 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 物理学报 69 127701Google 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 127701Google Scholar
[6] 刘迪, 王静, 王俊升, 黄厚兵 2020 物理学报 69 127801Google Scholar
Liu D, Wang J, Wang J S, Huang H B 2020 Acta Phys. Sin. 69 127801Google Scholar
[7] Kobeco P, Kurtchatov I 1930 Z. Phys. 66 192Google Scholar
[8] Mischenko A S, Zhang Q, Scott J F, Whatmore R W, Mathur N D 2006 Science 311 1270Google Scholar
[9] Chen C, Wang S, Zhang T, Zhang C, Chi Q, Li W 2020 RSC Adv. 10 6603Google Scholar
[10] Prasad S, Hou X, Zhang J, Wu S, Wang J 2020 IEEE Trans. Electron Devices 67 1769Google Scholar
[11] Karthik J, Martin L W 2011 Appl. Phys. Lett. 99 032904Google Scholar
[12] Sun X H, Huang H B, Ma X, Wen Y, Dang Z M 2018 J. Ceram. Sci. Technol. 9 201Google 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 4811Google 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 102901Google 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 1566Google Scholar
[16] Zhou Y, Lin Q, Liub W, Wang D 2016 RSC Adv. 6 14084Google 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 6430Google Scholar
[18] Bai Y, Han X, Qiao L 2013 Appl. Phys. Lett. 102 252904Google Scholar
[19] Weyland F, Hayati R, Novak N 2019 Ceram. Int. 45 11408Google Scholar
[20] Sun X H, Huang H B, Jafri H M, Wang J S, Wen Y, Dang Z M 2019 Appl. Sci. 9 1672Google Scholar
[21] Li F, Zhai J, Shen B, Zeng H, Jian X, Lu S 2019 J. Alloys Compd. 803 185Google Scholar
[22] Zheng G P, Uddin S, Zheng X, Yang J 2016 J. Alloys Compd. 663 249Google Scholar
[23] Matsushita Y, Yoshimura T, Kiriya D, Fujimura N 2020 Appl. Phys. Express 13 041007Google Scholar
[24] Aziguli H, Liu Y, Zhang G Z, Jiang S L, Yu P, Wang Q 2019 Europhys. Lett. 125 57001Google Scholar
[25] Li J, Zhao X, Zhang T, Qian X, Hou Y, Yang L, Zhang Q M 2017 Phase Transitions 90 99Google Scholar
[26] Qian X S, Yang T N, Zhang T, Chen L Q, Zhang Q M 2016 Appl. Phys. Lett. 108 142902Google Scholar
[27] Qian J, Peng R, Shen Z, Jiang J, Xue F, Yang T, Chen L, Shen Y 2019 Adv. Mater. 31 1801949Google Scholar
[28] Zhang G, Zhang X, Yang T, Li Q, Chen L Q, Jiang S, Wang Q 2015 ACS Nano 9 7164Google 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 1907927Google Scholar
[30] Yang Y, Zhou Z, Ke X, Wang Y, Su X, Li J, Bai Y, Ren X 2020 Scr. Mater. 174 44Google Scholar
[31] Zhao C, Yang J, Huang Y, Hao X, Wu J 2019 J. Mater. Chem. A 7 25526Google Scholar
[32] Mendez-Gonzalez Y, Pelaiz-Barranco A, Guerra J D S 2019 Appl. Phys. Lett. 114 162902Google Scholar
[33] Lu B, Li P, Tang Z, Yao Y, Gao X, Kleemann W, Lu S G 2017 Sci. Rep. 7 45335Google Scholar
[34] Sun X H, Huang H B, Wang J S, Wen Y Q, Dang Z M 2019 J. Alloys Compd. 777 821Google Scholar
[35] Wu H H, Zhu J, Zhang T Y 2015 Nano Energy 16 419Google Scholar
[36] Hou X, Wu H, Li H, Chen H, Wang J 2018 J. Phys.: Condens. Matter 30 465401Google Scholar
[37] Wu H H, Zhu J, Zhang T Y 2015 RSC Adv. 5 37476Google Scholar
[38] Liu Z, Yang B, Cao W, Lookman T 2018 Phys. Status Solidi B 255 1700469Google Scholar
[39] Hou X, Li H, Shimada T, Kitamura T, Wang J 2018 J. Appl. Phys. 123 124103Google Scholar
[40] Zeng Y K, Li B, Wang J B, Zhong X L, Wang W, Wang F, Zhou Y C 2014 RSC Adv. 4 30211Google 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 8760Google Scholar
[42] Wang J J, Fortino D, Wang B, Zhao X, Chen L Q 2019 Adv. Mater. 32 1906224Google 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 16189Google Scholar
[44] Liu D, Zhao R, Jafri H M, Wang J S, Huang H B 2019 Appl. Phys. Lett. 114 112903Google Scholar
[45] Wang J J, Wu P P, Ma X Q, Chen L Q 2010 J. Appl. Phys. 108 114105Google Scholar
[46] Li Y L, Hu S Y, Liu Z K, Chen L Q 2002 Acta Mater. 50 395Google 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 13199Google Scholar
[48] Bai G, Qin X, Xie Q, Gao C 2019 Physica B 560 208Google Scholar
[49] Huang C, Yang H B, Gao C F 2018 J. Appl. Phys. 123 154102Google Scholar
[50] Qiu J H, Ding J N, Yuan N Y, Wang X Q, Yang J 2011 Eur. Phys. J. B 84 25Google Scholar
[51] Bai G, Liu D, Gao C 2019 J. Appl. Phys. 126 164105Google Scholar
计量
- 文章访问数: 12760
- PDF下载量: 742
- 被引次数: 0