Phase field simulation of misfit strain manipulating domain structure and ferroelectric properties in PbZr(1–x)TixO3 thin films

Liu Di; Wang Jing; Wang Jun-Sheng; Huang Hou-Bing

doi:10.7498/aps.69.20200310

Abstract

Ferroelectric domain structures and ferroelectric properties in the hetero-epitaxially constrained ferroelectric thin films can be manipulated by substrate misfit strain. In this work, three kinds of phase structures of PbZr_(1–x)Ti_xO₃ thin films, including tetragonal, tetragonal- rhombohedral-mixed and rhombohedral phases, are investigated. Firstly, the ferroelectric domain structures at different substrate misfit biaxial strains are obtained by the phase-field simulation. Then we calculate the polarization-electric field hysteresis loops at different misfit strains, and obtain the coercive field, saturation polarization, and remnant polarization. In the tetragonal PbZr_(1–x)Ti_xO₃ (x = 0.8) thin film, compressive strain contributes to the formation of out-of-plane c1/c2 domain, and tensile strain favors in-plane a1/a2 domain formation. With the increase of compressive strain, the tetragonal phase and the rhombohedral phase coexist in PbZr_(1–x)Ti_xO₃ (x = 0.48) film near the morphotropic phase boundary, while the tensile strain reduces the rhombohedral domain size. In the rhombohedral PbZr_(1–x)Ti_xO₃ (x = 0.2) film, the rhombohedral domains are steady states under compressive strain and tensile strain. As the misfit strain changes from –1.0% to 1.0%, the value of the coercive field, saturation polarization and remnant polarization decrease. Among them, for tetragonal-rhombohedral mixed phase, the reductions of saturation field and remnant polarization are larger than for tetragonal phase and rhombohedral phase. The coercive field of mixed phase decreases rapidly under the compressive strain, but deceases slowly under the tensile strain. It is worth noting that the remnant polarization decreases faster than the saturation polarization in three components of ferroelectric thin film. Due to the electromechanical coupling, when x = 0.48 at the morphotropic phase boundary it is shown that the remnant polarization reduction is faster than those of the other two types of ferroelectric thin films, and the small coercive field is obtained in the case of large tensile strain. Therefore, tensile strain can effectively improve the energy storage efficiency in ferroelectric thin films, and the efficiency of x = 0.48 thin film increases significantly compared with that of x = 0.8 or 0.2 thin film. Both the ratio of rhombohedral/tetragonal phase and the domain size will play a significant role in ferroelectric performance. Therefore, our results contribute to the understanding of the electromechanical coupling mechanism of PbZr_(1–x)Ti_xO₃, and provide guidance for the experimental design of ferroelectric functional thin film materials.

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

FullText HTML : translate this paragraph

References

[1]	Xu F, Trolier-McKinstry S, Ren W, Xu B, Xie Z L, Hemker K J 2001 J. Appl. Phys. 89 1336 Google Scholar
[2]	Kim D J, Maria J P, Kingon A I, Streiffer S K 2003 J. Appl. Phys. 93 5568 Google Scholar
[3]	Karthik J, Martin L 2011 Phys. Rev. B 84 024102 Google Scholar
[4]	Karthik J, Damodaran A R, Martin L W 2012 Phys. Rev. Lett. 108 167601 Google Scholar
[5]	赵晓英, 刘世建, 褚君浩, 戴宁, 胡古今 2008 物理学报 57 5968 Google Scholar Zhao X Y, Liu S J, Chu J H, Dai N, Hu G J 2008 Acta Phys. Sin. 57 5968 Google Scholar
[6]	Arimoto Y, Ishiwara H 2004 MRS Bull. 29 823 Google Scholar
[7]	Ganapathi K L, Rath M, Rao M S R 2019 Semicond. Sci. Technol. 34 055016 Google Scholar
[8]	Won S S, Seo H, Kawahara M, Glinsek S, Lee J, Kim Y, Jeong C K, Kingon A I, Kim S H 2019 Nano Energy 55 182 Google Scholar
[9]	Hoshyarmanesh H, Ebrahimi N, Jafari A, Hoshyarmanesh P, Kim M, Park H H 2019 Sensors 19 13 Google Scholar
[10]	Gupta R, Gupta V, Tomar M 2020 Mater. Sci. Semicond. Process. 105 104723 Google Scholar
[11]	Rath M, Varadarajan E, Premkumar S, Shinde S, Natarajan V, Rao M S R 2019 Ferroelectrics 551 17 Google Scholar
[12]	Yao Z H, Song Z, Hao H, Yu Z Y, Cao M H, Zhang S J, Lanagan M T, Liu H X 2017 Adv. Mater. 29 1601727 Google Scholar
[13]	Pan H, Li F, Liu Y, Zhang Q, Wang M, Lan S, Zheng Y, Ma J, Gu L, Shen Y, Yu P, Zhang S, Chen L Q, Lin Y H, Nan C W 2019 Science 365 578 Google Scholar
[14]	Wang J J, Su Y J, Wang B, Ouyang J, Ren Y, Chen L Q 2020 Nano Energy 72 104665 Google Scholar
[15]	Li A D, Mak C L, Wong K H, Shao Q Y, Wang Y J, Wu D, Ming N B 2002 J. Cryst. Growth 235 307 Google Scholar
[16]	Ehara Y, Shimizu T, Yasui S, Oikawa T, Shiraishi T, Tanaka H, Kanenko N, Maran R, Yamada T, Imai Y Sakata O, Valanoor N, Funakubo H 2019 Phys. Rev. B 100 104116 Google Scholar
[17]	Izyumskaya N, Alivov Y I, Cho S J, Morkoç H, Lee H, Kang Y S 2007 Crit. Rev. Solid. State Mater. Sci. 32 111 Google Scholar
[18]	Choi K J, Biegalski M, Li Y L, Sharan A, Schubert J, Uecker R, Reiche P, Chen Y B, Pan X Q, Gopalan V, Chen L Q, Schlom D G, Eom C B 2004 Science 306 1005 Google Scholar
[19]	Noguchi Y, Maki H, Kitanaka Y, Matsuo H, Miyayama M 2018 Appl. Phys. Lett. 113 012903 Google Scholar
[20]	Li Y L, Chen L Q 2006 Appl. Phys. Lett. 88 072905 Google Scholar
[21]	Pertsev N A, Tagantsev A K, Setter N 2000 Phys. Rev. B 61 R825 Google Scholar
[22]	Haeni J H, Irvin P, Chang W, Uecker R, Reiche P, Li Y L, Choudhury S, Tian W, Hawley M E, Craigo B, Tagantsev A K, Pan X Q, Streiffer S K, Chen L Q, Kirchoefer S W, Levy J, Schlom D G 2004 Nature 430 758 Google Scholar
[23]	Zhang J X, Li Y L, Choudhury S, Chen L Q, Chu Y H, Zavaliche F, Cruz M P, Ramesh R, Jia Q X 2008 J. Appl. Phys. 103 094111 Google Scholar
[24]	Ren W, Yang Y, Diéguez O, Íñiguez J, Choudhury N, Bellaiche L 2013 Phys. Rev. Lett. 110 187601 Google Scholar
[25]	Zhang Y, Xue F, Chen Z H, Liu J M, Chen L Q 2020 Acta Mater. 183 110 Google Scholar
[26]	Li Y L, Hu S Y, Liu Z K, Chen L Q 2002 Acta Mater. 50 395 Google Scholar
[27]	Li Y L, Hu S Y, Chen L Q 2005 J. Appl. Phys. 97 034112 Google Scholar
[28]	Yu Q, Li J, Zhu F, Li J 2014 J. Mater. Chem. C 2 5836 Google Scholar
[29]	Lu X Y, Chen Z H, Cao Y, Tang Y L, Xu R J, Saremi S, Zhang Z, You L, Dong Y Q, Das S, Zhang H B, Zheng L M, Wu H P, Lv W M, Xie G Q, Liu X J, Li J Y, Chen L, Chen L Q, Cao W W, Martin L W 2019 Nat. Commun. 10 3951 Google Scholar
[30]	Nguyen M D, Dekkers M, Houwman E, Steenwelle R, Wan X, Roelofs A, Schmitz-Kempen T, Rijnders G 2011 Appl. Phys. Lett. 99 252904 Google Scholar
[31]	Xue F, Wang J J, Sheng G, Huang E, Cao Y, Huang H-H, Munroe P, Mahjoub R, Li Y, Valanoor N, Chen L 2013 Acta Mater. 61 2909 Google Scholar
[32]	Lin F Y, Cheng X, Chen L Q, Sinnott S B 2018 J. Am. Ceram. Soc. 101 4783 Google Scholar
[33]	Devonshire A F 1949 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 40 1040 Google Scholar
[34]	Chen L Q 2008 J. Am. Ceram. Soc. 91 1835 Google Scholar
[35]	Chen L Q 2002 Ann. Rev. Mater. Res. 32 113 Google Scholar
[36]	Li Y L, Hu S Y, Liu Z K, Chen L Q 2001 Appl. Phys. Lett. 78 3878 Google Scholar
[37]	Li Y L, Choudhury S, Liu Z K, Chen L Q 2003 Appl. Phys. Lett. 83 1608 Google Scholar
[38]	Shu W L, Wang J, Zhang T Y 2012 J. Appl. Phys. 112 064108 Google Scholar
[39]	Wang J J, Wang B, Chen L Q 2019 Ann. Rev. Mater. Res. 49 127 Google Scholar
[40]	Li Y L, Chen L Q, Asayama G, Schlom D G, Zurbuchen M A, Streiffer S K 2004 J. Appl. Phys. 95 6332 Google Scholar
[41]	Chen L Q, Shen J 1998 Comput. Phys. Commun. 108 147 Google Scholar
[42]	Haun M J, Zhuang Z Q, Furman E, Jang S J, Cross L E 1989 Ferroelectrics 99 45 Google Scholar
[43]	Hu H L, Chen L Q 1998 J. Am. Ceram. Soc. 81 492
[44]	Damjanovic D 2005 J. Am. Ceram. Soc. 88 2663 Google Scholar
[45]	Liu W F, Ren X B 2009 Phys. Rev. Lett. 103 257602 Google Scholar
[46]	Li F, Lin D B, Chen Z B, Cheng Z X, Wang J L, Li C C, Xu Z, Huang Q W, Liao X Z, Chen L Q, Shrout T R, Zhang S J 2018 Nat. Mater. 17 349 Google Scholar
[47]	Liao Z Y, Xue F, Sun W, Song D S, Zhang Q Q, Li J F, Chen L Q, Zhu J 2017 Phys. Rev. B 95 214101 Google Scholar
[48]	Liu H, Chen J, Huang H B, Fan L L, Ren Y, Pan Z, Deng J X, Chen L Q, Xing X R 2018 Phys. Rev. Lett. 120 055501 Google Scholar
[49]	Ma Z, Ma Y, Chen Z, Zheng F, Gao H, Liu H, Chen H 2018 Ceram. Int. 44 4338 Google Scholar

Cited By

图 1 PZT铁电材料的晶体结构示意图　(a)立方顺电相结构; (b)四方铁电相结构; (c)正交铁电相结构; (d)菱方铁电相结构

Figure 1. Schematic of PZT ferroelectric structure: (a) Paraelectric cubic phase; (b) ferroelectric tetragonal phase; (c) ferroelectric orthorhombic phase; (d) ferroelectric rhombohedral phase.

DownLoad: Full-Size Img PowerPoint

图 2 (a)−(f)室温下随Ti成分降低(x = 0.8—0.2) PZT的三维自由能曲面, 蓝色代表最小值, 红色代表最大值; (g)−(i) T相、R/T混合相及R相二维自由能双势阱示意图

Figure 2. (a)−(f) Free energy surface of PZT with the decrease of Ti composition (x = 0.8–0.2) at room temperature. Blue and red color represents the minimum and maximum value respectively; (g)−(i) Schematic of double well potential of tetragonal phase (g), mixed phase (h) and rhombohedral phase (i).

DownLoad: Full-Size Img PowerPoint

图 3 相场模拟PZT薄膜在不同基底失配应变下的畴结构　(a)—(c)分别对应于PZT (x = 0.8)薄膜ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%; (d)—(f)分别对应于PZT (x = 0.48)薄膜ε_sub = 0, ε_sub = –0. 5%, ε_sub = 0.5%; (g)—(h)分别对应于PZT (x = 0.2)薄膜ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%

Figure 3. Domain structures of PZT (x = 0.8, x = 0.48, x = 0.2) thin film with different substrate biaxial misfit strain (ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%): (a)−(c) Domain structures of PZT (x = 0.8) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%; (d)−(f) domain structures of PZT (x = 0.48) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%; (g)−(h) domain structures of PZT (x = 0.2) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%.

DownLoad: Full-Size Img PowerPoint

图 4 室温下PZT铁电薄膜四方相(x = 0.8), 混合相(x = 0.48)以及菱方相(x = 0.2)在不同的基底失配应变下(ε_sub = ± 0.1%, ± 0.5%, ± 1.0%)的电滞回线, 其中P^*和E^*表示归一化后的极化强度和电场强度值　(a)−(c)分别表示压应变下四方相、混合相和菱方相的电滞回线; (d)−(f)分别表示拉应变下四方相、混合相和菱方相的电滞回线

Figure 4. Hysteresis loops of PZT thin films with three Ti components at different substrate biaxial misfit strains (ε_sub = ± 0.1%, ± 0.5%, ± 1.0%), and P^* and E^* are normalized polarization and electric field: (a)−(c) The case of compressive strains; (d)−(f) the case of tensile strains.

DownLoad: Full-Size Img PowerPoint

图 5 三种相PZT铁电薄膜的矫顽场、饱和极化和剩余极化值与基底应变的关系　(a) 矫顽场E_c^*; (b) 饱和极化值P_s^*; (c) 剩余极化值P_r^*

Figure 5. Normalized coercive field (E_c^*), saturation polarization (P_r^*), and remnant polarization (P_s^*) as a function of substrate misfit strain (ε_sub), where three PZT ferroelectric thin films with x = 0.8, 0.48 and 0.2 Ti component are considered: (a) Coercive field vs. strain; (b) saturation polarization vs. strain; (c) remnant polarization vs. strain.

DownLoad: Full-Size Img PowerPoint

图 6 (a)电滞回线中充放电过程中储能示意图; (b) 三种PZT薄膜材料能量存储效率与基底应变之间的关系

Figure 6. (a) Schematic of P-E loop used for energy storage; (b) the energy storage efficiency as a function of substrate misfit strain.

DownLoad: Full-Size Img PowerPoint

表 1 三种成分PZT铁电薄膜介电刚度系数和电致伸缩常数

Table 1. Corresponding material constants for the Landau free energy, the electrostrictive coefficients of three components PZT thin films.

Coefficients	PbZr_0.2Ti_0.8O₃	PbZr_0.52Ti_0.48O₃	PbZr_0.8Ti_0.2O₃
$ {a}_{1} $/C^–2·m²·N	3.44 × 10⁵(T – 456.38)	1.45 × 10⁵(T – 387.06)	2.71 × 10⁵(T – 300.57)
$ {a}_{11} $/C^–4·m⁶·N	–3.05 × 10⁷	5.83 × 10⁷	3.13 × 10⁸
$ {a}_{12} $/C^–4·m⁶·N	6.32 × 10⁸	1.82 × 10⁸	–3.45 × 10⁶
$ {a}_{111} $/C^–6·m¹⁰·N	2.47 × 10⁸	1.50 × 10⁸	4.29 × 10⁸
$ {a}_{112} $/C^–6·m¹⁰·N	9.68 × 10⁸	6.88 × 10⁸	1.81 × 10⁹
$ {a}_{123} $/C^–6·m¹⁰·N	–4.90 × 10⁹	–3.24 × 10⁹	–7.54 × 10⁹
$ {Q}_{11} $/C^–2·m⁴	0.081	0.094	0.056
$ {Q}_{12} $/C^–2·m⁴	–0.024	–0.044	–0.017
$ {Q}_{44} $/C^–2·m⁴	0.032	0.040	0.026

DownLoad: CSV

表 2 三种PZT薄膜材料在不同应变下的储能效率值η

Table 2. Energy storage efficiency values of the PZT thin films under different strains.

Strain/%	Energy storage efficienc η/%
Strain/%	PbZr_0.2Ti_0.8O₃	PbZr_0.52Ti_0.48O₃	PbZr_0.8Ti_0.2O₃
–1.0	8.0	7.8	11.2
–0.5	12.0	17.4	18.7
–0.1	16.8	31.0	23.4
0.1	20.0	40.6	27.4
0.5	30.7	61.0	34.7
1.0	43.9	73.6	55.8

DownLoad: CSV

[1]	Xu F, Trolier-McKinstry S, Ren W, Xu B, Xie Z L, Hemker K J 2001 J. Appl. Phys. 89 1336 Google Scholar
[2]	Kim D J, Maria J P, Kingon A I, Streiffer S K 2003 J. Appl. Phys. 93 5568 Google Scholar
[3]	Karthik J, Martin L 2011 Phys. Rev. B 84 024102 Google Scholar
[4]	Karthik J, Damodaran A R, Martin L W 2012 Phys. Rev. Lett. 108 167601 Google Scholar
[5]	赵晓英, 刘世建, 褚君浩, 戴宁, 胡古今 2008 物理学报 57 5968 Google Scholar Zhao X Y, Liu S J, Chu J H, Dai N, Hu G J 2008 Acta Phys. Sin. 57 5968 Google Scholar
[6]	Arimoto Y, Ishiwara H 2004 MRS Bull. 29 823 Google Scholar
[7]	Ganapathi K L, Rath M, Rao M S R 2019 Semicond. Sci. Technol. 34 055016 Google Scholar
[8]	Won S S, Seo H, Kawahara M, Glinsek S, Lee J, Kim Y, Jeong C K, Kingon A I, Kim S H 2019 Nano Energy 55 182 Google Scholar
[9]	Hoshyarmanesh H, Ebrahimi N, Jafari A, Hoshyarmanesh P, Kim M, Park H H 2019 Sensors 19 13 Google Scholar
[10]	Gupta R, Gupta V, Tomar M 2020 Mater. Sci. Semicond. Process. 105 104723 Google Scholar
[11]	Rath M, Varadarajan E, Premkumar S, Shinde S, Natarajan V, Rao M S R 2019 Ferroelectrics 551 17 Google Scholar
[12]	Yao Z H, Song Z, Hao H, Yu Z Y, Cao M H, Zhang S J, Lanagan M T, Liu H X 2017 Adv. Mater. 29 1601727 Google Scholar
[13]	Pan H, Li F, Liu Y, Zhang Q, Wang M, Lan S, Zheng Y, Ma J, Gu L, Shen Y, Yu P, Zhang S, Chen L Q, Lin Y H, Nan C W 2019 Science 365 578 Google Scholar
[14]	Wang J J, Su Y J, Wang B, Ouyang J, Ren Y, Chen L Q 2020 Nano Energy 72 104665 Google Scholar
[15]	Li A D, Mak C L, Wong K H, Shao Q Y, Wang Y J, Wu D, Ming N B 2002 J. Cryst. Growth 235 307 Google Scholar
[16]	Ehara Y, Shimizu T, Yasui S, Oikawa T, Shiraishi T, Tanaka H, Kanenko N, Maran R, Yamada T, Imai Y Sakata O, Valanoor N, Funakubo H 2019 Phys. Rev. B 100 104116 Google Scholar
[17]	Izyumskaya N, Alivov Y I, Cho S J, Morkoç H, Lee H, Kang Y S 2007 Crit. Rev. Solid. State Mater. Sci. 32 111 Google Scholar
[18]	Choi K J, Biegalski M, Li Y L, Sharan A, Schubert J, Uecker R, Reiche P, Chen Y B, Pan X Q, Gopalan V, Chen L Q, Schlom D G, Eom C B 2004 Science 306 1005 Google Scholar
[19]	Noguchi Y, Maki H, Kitanaka Y, Matsuo H, Miyayama M 2018 Appl. Phys. Lett. 113 012903 Google Scholar
[20]	Li Y L, Chen L Q 2006 Appl. Phys. Lett. 88 072905 Google Scholar
[21]	Pertsev N A, Tagantsev A K, Setter N 2000 Phys. Rev. B 61 R825 Google Scholar
[22]	Haeni J H, Irvin P, Chang W, Uecker R, Reiche P, Li Y L, Choudhury S, Tian W, Hawley M E, Craigo B, Tagantsev A K, Pan X Q, Streiffer S K, Chen L Q, Kirchoefer S W, Levy J, Schlom D G 2004 Nature 430 758 Google Scholar
[23]	Zhang J X, Li Y L, Choudhury S, Chen L Q, Chu Y H, Zavaliche F, Cruz M P, Ramesh R, Jia Q X 2008 J. Appl. Phys. 103 094111 Google Scholar
[24]	Ren W, Yang Y, Diéguez O, Íñiguez J, Choudhury N, Bellaiche L 2013 Phys. Rev. Lett. 110 187601 Google Scholar
[25]	Zhang Y, Xue F, Chen Z H, Liu J M, Chen L Q 2020 Acta Mater. 183 110 Google Scholar
[26]	Li Y L, Hu S Y, Liu Z K, Chen L Q 2002 Acta Mater. 50 395 Google Scholar
[27]	Li Y L, Hu S Y, Chen L Q 2005 J. Appl. Phys. 97 034112 Google Scholar
[28]	Yu Q, Li J, Zhu F, Li J 2014 J. Mater. Chem. C 2 5836 Google Scholar
[29]	Lu X Y, Chen Z H, Cao Y, Tang Y L, Xu R J, Saremi S, Zhang Z, You L, Dong Y Q, Das S, Zhang H B, Zheng L M, Wu H P, Lv W M, Xie G Q, Liu X J, Li J Y, Chen L, Chen L Q, Cao W W, Martin L W 2019 Nat. Commun. 10 3951 Google Scholar
[30]	Nguyen M D, Dekkers M, Houwman E, Steenwelle R, Wan X, Roelofs A, Schmitz-Kempen T, Rijnders G 2011 Appl. Phys. Lett. 99 252904 Google Scholar
[31]	Xue F, Wang J J, Sheng G, Huang E, Cao Y, Huang H-H, Munroe P, Mahjoub R, Li Y, Valanoor N, Chen L 2013 Acta Mater. 61 2909 Google Scholar
[32]	Lin F Y, Cheng X, Chen L Q, Sinnott S B 2018 J. Am. Ceram. Soc. 101 4783 Google Scholar
[33]	Devonshire A F 1949 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 40 1040 Google Scholar
[34]	Chen L Q 2008 J. Am. Ceram. Soc. 91 1835 Google Scholar
[35]	Chen L Q 2002 Ann. Rev. Mater. Res. 32 113 Google Scholar
[36]	Li Y L, Hu S Y, Liu Z K, Chen L Q 2001 Appl. Phys. Lett. 78 3878 Google Scholar
[37]	Li Y L, Choudhury S, Liu Z K, Chen L Q 2003 Appl. Phys. Lett. 83 1608 Google Scholar
[38]	Shu W L, Wang J, Zhang T Y 2012 J. Appl. Phys. 112 064108 Google Scholar
[39]	Wang J J, Wang B, Chen L Q 2019 Ann. Rev. Mater. Res. 49 127 Google Scholar
[40]	Li Y L, Chen L Q, Asayama G, Schlom D G, Zurbuchen M A, Streiffer S K 2004 J. Appl. Phys. 95 6332 Google Scholar
[41]	Chen L Q, Shen J 1998 Comput. Phys. Commun. 108 147 Google Scholar
[42]	Haun M J, Zhuang Z Q, Furman E, Jang S J, Cross L E 1989 Ferroelectrics 99 45 Google Scholar
[43]	Hu H L, Chen L Q 1998 J. Am. Ceram. Soc. 81 492
[44]	Damjanovic D 2005 J. Am. Ceram. Soc. 88 2663 Google Scholar
[45]	Liu W F, Ren X B 2009 Phys. Rev. Lett. 103 257602 Google Scholar
[46]	Li F, Lin D B, Chen Z B, Cheng Z X, Wang J L, Li C C, Xu Z, Huang Q W, Liao X Z, Chen L Q, Shrout T R, Zhang S J 2018 Nat. Mater. 17 349 Google Scholar
[47]	Liao Z Y, Xue F, Sun W, Song D S, Zhang Q Q, Li J F, Chen L Q, Zhu J 2017 Phys. Rev. B 95 214101 Google Scholar
[48]	Liu H, Chen J, Huang H B, Fan L L, Ren Y, Pan Z, Deng J X, Chen L Q, Xing X R 2018 Phys. Rev. Lett. 120 055501 Google Scholar
[49]	Ma Z, Ma Y, Chen Z, Zheng F, Gao H, Liu H, Chen H 2018 Ceram. Int. 44 4338 Google Scholar

[1]	Tian Guo, Fan Zhen, Chen De-Yang, Hou Zhi-Peng, Liu Jun-Ming, Gao Xing-Sen. Laboratory experiments based on tip probe － Scanning probe detection and regulation of ferroelectric domains and their microscopic physical properties. Acta Physica Sinica, 2023, 72(20): 207501. doi: 10.7498/aps.72.20230954
[2]	Jiang Yan-Bo, Liu Wen-Bo, Sun Zhi-Peng, La Yong-Xiao, Yun Di. Phase-field simulation of void evolution in UO₂ under applied stress. Acta Physica Sinica, 2022, 71(2): 026103. doi: 10.7498/aps.71.20211440
[3]	Li Ling, Pan Tian-Ze, Ma Jia-Jun, Zhang Shan-Tao, Wang Yao-Jin. Mechanism of local stress field enhanced pyroelectric performance of PNZST:AlN composite ceramics. Acta Physica Sinica, 2022, 71(21): 217701. doi: 10.7498/aps.71.20221250
[4]	Lin Cui, Bai Gang, Li Wei, Gao Cun-Fa. Strain tuning of negative capacitance in epitaxial PbZr_0.2Ti_0.8O₃ thin films. Acta Physica Sinica, 2021, 70(18): 187701. doi: 10.7498/aps.70.20210810
[5]	Yang Zhao-Xi, Liu Wen-Bo, Zhang Cong-Yu, He Xin-Fu, Sun Zheng-Yang, Jia Li-Xia, Shi Tian-Tian, Yun Di. Phase field simulation of grain boundary segregation and radiation-enhanced segregation in Fe-Cr alloys. Acta Physica Sinica, 2021, 70(11): 116101. doi: 10.7498/aps.70.20201840
[6]	Yang Wen-Da, Chen Hong-Ying, Chen Yan, Tian Guo, Gao Xing-Sen. Recent progress in exotic polar topological states in ferroelectric nanostructures. Acta Physica Sinica, 2020, 69(21): 217501. doi: 10.7498/aps.69.20201063
[7]	Tan Cong-Bing, Zhong Xiang-Li, Wang Jin-Bin. Polar topological structures in ferroelectric materials. Acta Physica Sinica, 2020, 69(12): 127702. doi: 10.7498/aps.69.20200311
[8]	Duan Pei-Pei, Xing Hui, Chen Zhi, Hao Guan-Hua, Wang Bi-Han, Jin Ke-Xin. Phase-field modeling of free dendritic growth of magnesium based alloy. Acta Physica Sinica, 2015, 64(6): 060201. doi: 10.7498/aps.64.060201
[9]	Du Li-Fei, Zhang Rong, Xing Hui, Zhang Li-Min, Zhang Yang, Liu Lin. Phase-field simulation of solidified microstructure evolution in the presence of lateral constraint. Acta Physica Sinica, 2013, 62(10): 106401. doi: 10.7498/aps.62.106401
[10]	Wang Jing, Feng Lu, Hao Yi, Zhao Yang, Chen Zhen-Fei. Strain effect on the morphological instability of a circular island in heteroepitaxy. Acta Physica Sinica, 2013, 62(23): 238102. doi: 10.7498/aps.62.238102
[11]	Pan Shi-Yan, Zhu Ming-Fang. Quantitative phase-field model for dendritic growth with two-sided diffusion. Acta Physica Sinica, 2012, 61(22): 228102. doi: 10.7498/aps.61.228102
[12]	Yu Gang, Dong Xian-Lin, Wang Gen-Shui, Chen Xue-Feng, Cao Fei. Ferroelectric polarization reversal behavior in 63PbTiO3-37BiScO3 bulk ceramics. Acta Physica Sinica, 2010, 59(12): 8890-8896. doi: 10.7498/aps.59.8890
[13]	Liang Xiao-Lin, Gong Yue-Qiu, Liu Zhi-Zhuang, Lü Ye-Gang, Zheng Xue-Jun. Effect of external electric field on phase transitions of ferroelectric thin films. Acta Physica Sinica, 2010, 59(11): 8167-8171. doi: 10.7498/aps.59.8167
[14]	Zhou Bo, Chen Yun-Lin, Liu Gang, Zhan He. Improvement on the classical model for new domain nucleation in ferroelectrics. Acta Physica Sinica, 2009, 58(4): 2762-2767. doi: 10.7498/aps.58.2762
[15]	Wang Gang, Xu Dong-Sheng, Yang Rui. Phase field simulation on sideplates formation in Ti-6Al-4V alloy. Acta Physica Sinica, 2009, 58(13): 343-S348. doi: 10.7498/aps.58.343
[16]	Chen Xue-Feng, Li Hua-Mei, Li Dong-Jie, Cao Fei, Dong Xian-Lin. Study on slim-loop ferroelectric ceramics for high-power pulse capacitors. Acta Physica Sinica, 2008, 57(11): 7298-7304. doi: 10.7498/aps.57.7298
[17]	Wang Ying-Long, Wei Tong-Ru, Liu Bao-Ting, Deng Ze_Chao. Effect of thickness of epitaxial PbZr0.4Ti0.6O3 film on the physical properties. Acta Physica Sinica, 2007, 56(5): 2931-2936. doi: 10.7498/aps.56.2931
[18]	Zeng Hua-Rong, Yu Han-Feng, Chu Rui-Qing, Li Guo-Rong, Yin Qing-Rui, Tang Xin-Gui. Field-induced displacement properties of nanoscale domain structure in PZT thin film. Acta Physica Sinica, 2005, 54(3): 1437-1441. doi: 10.7498/aps.54.1437
[19]	Li Bao-Shan, Zhu Zhi-Gang, Li Guo-Rong, Yin Qing-Rui, Ding Ai-Li. Frequency and temperature dependence of the hysteresis loop in PMnN-PZT ceramics. Acta Physica Sinica, 2005, 54(2): 939-943. doi: 10.7498/aps.54.939
[20]	Wang Long-Hai, Yu Jun, Wang Yun-Bo, Peng Gang, Liu Feng, Gao Jun-Xiong. A model of ferroelectric capacitors based on hysteresis loop. Acta Physica Sinica, 2005, 54(2): 949-954. doi: 10.7498/aps.54.949

Catalog

Vol. 69, Issue 12 - 2020-06-20

Metrics

Abstract views: 9200
PDF Downloads: 432
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Phase field simulation of misfit strain manipulating domain structure and ferroelectric properties in PbZr_(1–x)Ti_xO₃ thin films

Abstract

Authors and contacts

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

FullText HTML : translate this paragraph

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板