Strain Tuning of Domain Structure in BaTiO3 Polycrystalline Nanofilms

doi:10.16553/j.cnki.issn1000-985x.2026.0069

Abstract

Abstract: BaTiO₃ ferroelectric nanofilms demonstrate intricate domain structures and distinct nonlinear electromechanical behaviors as a result of the constraints imposed by diverse substrates. This work utilized a phase field model grounded in the framework of continuum thermodynamics to investigated the novel characteristics imparted to ferroelectric polycrystalline nanofilm systems by the rapid polarization reversal process under different tensile and compressive strain conditions. In contrast to existing studies focusing on single-crystal epitaxial films， this paper comprehensively examined factors including grain boundary effects and grain orientation. It further simulated the impact of in-plane strain on the microstructural domain structure and electromechanical characteristics of ferroelectric polycrystalline nanofilms， considering two distinct grain sizes， 60 and 10 nm. The results indicate that for a grain size of 60 nm， both the coercive field and remnant polarization decrease monotonically， suggesting that increased compressive strain effectively enhances the ferroelectric properties of the nanofilm. Conversely， at a grain size of 10 nm， excessive compressive strain results in a sudden reduction in both remnant polarization and coercive field. Furthermore， in contrast to single-crystal films， due to the existence of grain boundaries in polycrystalline films， the domain structures （90° domains， 180° domains and vortex domain structures） of the films under different tensile and compressive strains show diversity， even if the polycrystalline films produce a variety of complex electromechanical characteristics. This study explores the micro-mechanisms of ferroelectric materials by examining their internal microstructure， with the aim of facilitating the application and regulation of the macroscopic properties of ferroelectric nanofilms. The findings provide theoretical guidance for the design of high-performance ferroelectric nanofilms microelectronic devices.

Key words: BaTiO₃; ferroelectric polycrystalline nanofilm; phase-field method; domain structure; strain tuning; in-plane strain; size effect

CLC Number:

TB383.2

ZHANG Mingran, MA Rui, ZHANG Yuanxiang. Strain Tuning of Domain Structure in BaTiO₃ Polycrystalline Nanofilms[J]. Journal of Synthetic Crystals, 2026, 55(9): 1448-1459.

Figures/Tables 9

Fig.1 2D representative unit of BaTiO3 polycrystalline nanofilm

Table 1 Twenty-two grains and corresponding orientation angles in BaTiO3 polycrystalline nanofilm

No.	$φ$ /（°）	No.	$φ$ /（°）
1	0	12	45.00
2	4.09	13	49.09
3	8.18	14	53.18
4	12.27	15	57.27
5	16.36	16	61.36
6	20.45	17	64.45
7	24.54	18	69.54
8	28.63	19	73.63
9	32.72	20	77.72
10	36.81	21	81.18
11	40.90	22	85.90

Table 1 Twenty-two grains and corresponding orientation angles in BaTiO3 polycrystalline nanofilm

No.	$φ$ /（°）	No.	$φ$ /（°）
1	0	12	45.00
2	4.09	13	49.09
3	8.18	14	53.18
4	12.27	15	57.27
5	16.36	16	61.36
6	20.45	17	64.45
7	24.54	18	69.54
8	28.63	19	73.63
9	32.72	20	77.72
10	36.81	21	81.18
11	40.90	22	85.90

Fig.2 Hysteresis loops （a） and butterfly loops（b） of BaTiO3 polycrystalline nanofilm with an average grain size of 60 nm under different tensile and compressive strains

Fig.3 Hysteresis loops （a） and butterfly loops （b） of BaTiO3 polycrystalline nanofilm with an average grain size of 10 nm under different tensile and compressive strains

Fig.4 Variation of remnant polarization and coercive field （a）， and dielectric constant and piezoelectric constant （κ0=P0/E0，d330=ε0/E0）（b） as a function of in-plane strain in BaTiO3 polycrystalline nanofilm

Fig.5 Variation of remnant polarization （a） and coercive field （b） as a function of in-plane strain in different studies

Fig.6 Polarization distribution of BaTiO3 polycrystalline nanofilm with grain size of 60 nm. （a） Remnant polarization state；（b） coercive field state

Fig.7 Polarization distribution of BaTiO3 polycrystalline nanofilm with grain size of 10 nm. （a） Remnant polarization state；（b） coercive field state

Fig.8 Microstructure distribution of BaTiO3 polycrystalline nanofilm at remnant polarization state under in-plane strain of -1.00% with different grain sizes. （a） 60 nm；（b） 10 nm

References 56

[1]	BAUMGARTEN L， SZYJKA T， MITTMANN T， et al. Smart design of Fermi level pinning in HfO₂-based ferroelectric memories［J］. Advanced Functional Materials， 2024， 34（3）： 2307120. DOI URL
[2]	JAYAKRISHNAN A R， KUMAR A， DRUVAKUMAR S， et al. Inorganic ferroelectric thin films and their composites for flexible electronic and energy device applications： current progress and perspectives［J］. Journal of Materials Chemistry C， 2023， 11（3）： 827-858. DOI URL
[3]	戚佳斌，谢欣瑜，李忠贤. 柔性无机铁电薄膜的制备及其在存储器领域应用研究进展［J］. 人工晶体学报， 2023， 52（3）： 380-393.
	QI J B， XIE X Y， LEE C H. Research progress on preparation of flexible inorganic ferroelectric thin film and its application in memory field［J］. Journal of Synthetic Crystals， 2023， 52（3）： 380-393 （in Chinese）.
[4]	FERNANDEZ A， ACHARYA M， LEE H G， et al. Thin-film ferroelectrics［J］. Advanced Materials， 2022， 34（30）： 2108841. DOI URL
[5]	FAN L， REDER M， SCHNEIDER D， et al. Multiphase-field modeling of domain structure evolution in ferroelectric thin film［J］. Journal of the European Ceramic Society， 2025， 45（1）： 116875. DOI URL
[6]	CHOI K J， BIEGALSKI M， LI Y L， et al. Enhancement of ferroelectricity in strained BaTiO₃ thin films［J］. Science， 2004， 306（5698）： 1005-1009. DOI URL
[7]	NOGUCHI Y， MAKI H， KITANAKA Y， et al. Control of misfit strain in ferroelectric BaTiO₃ thin-film capacitors with SrRuO₃-based electrodes on （Ba， Sr）TiO₃-buffered SrTiO₃ substrates［J］. Applied Physics Letters， 2018， 113： 012903.
[8]	LIU C， WANG J. Strain engineering of ferroelectric negative capacitance in PbZr_（1- _x_）TiO₃ thin films［J］. Acta Materialia， 2021， 206： 116607. DOI URL
[9]	ZHAO Z， BUSCAGLIA V， VIVIANI M， et al. Grain-size effects on the ferroelectric behavior of dense nanocrystalline BaTiO₃ ceramics［J］. Physical Review B， 2004， 70（2）： 024107.
[10]	BUSCAGLIA M T， VIVIANI M， BUSCAGLIA V， et al. High dielectric constant and frozen macroscopic polarization in dense nanocrystalline BaTiO₃ ceramics［J］. Physical Review B， 2006， 73（6）： 064114.
[11]	BHATTACHARYA K， JAMES R D. A theory of thin films of martensitic materials withapplications to microactuators［J］. Journal of the Mechanics and Physics of Solids， 1999， 47（3）： 531-576. DOI URL
[12]	SHAW T M， TROLIER-MCKINSTRY S， MCINTYRE P C. The properties of ferroelectric films at small dimensions［J］. Annual Review of Materials Science， 2000， 30： 263-298. DOI URL
[13]	QIAO L， BI X F. Epitaxial integration of ferroelectric BaTiO₃with semiconductor Si： from a structure-property correlation point of view［M］//LALLART M. Ferroelectrics-Material Aspects. InTech. 2011： 365-388.
[14]	SUN L， CHEN Y F， MA W H， et al. Evidence of ferroelectricity weakening in the polycrystalline PbTiO₃ thin films［J］. Applied Physics Letters， 1996， 68（26）： 3728-3730. DOI URL
[15]	岳文锋，俞　亮，郭全胜，等. 多铁性材料的应变调控［J］. 人工晶体学报， 2022， 51（1）： 154-169.
	YUE W F， YU L， GUO Q S， et al. Strain tuning of multiferroic materials［J］. Journal of Synthetic Crystals， 2022， 51（1）： 154-169 （in Chinese）.
[16]	HAENI J H， IRVIN P， CHANG W， et al. Room-temperature ferroelectricity in strained SrTiO₃ ［J］. Nature， 2004， 430（7001）： 758-761. DOI
[17]	KIM J， TAKENAKA H， QI Y B， et al. Epitaxial strain control of relaxor ferroelectric phase evolution［J］. Advanced Materials， 2019， 31（21）： 1901060. DOI URL
[18]	GAO L J， CHEN X F， QI J S. Strain engineering of ferroelectric polarization and domain in the two-dimensional multiferroic semiconductor［J］. Applied Physics Letters， 2024， 125（21）： 212903. DOI URL
[19]	夏雨虹，杨振清，周露露，等. 新型热电材料Y₂Te₃热电性能应变调控研究［J］. 人工晶体学报， 2023， 52（8）： 1422-1431.
	XIA Y H， YANG Z Q， ZHOU L L， et al. Thermoelectric properties of the novel thermoelectric material Y₂Te₃ through strain modulation［J］. Journal of Synthetic Crystals， 2023， 52（8）： 1422-1431 （in Chinese）.
[20]	SÁNCHEZ-SANTOLINO G， ROUCO V， PUEBLA S， et al. A 2D ferroelectric vortex pattern in twisted BaTiO₃ freestanding layers［J］. Nature， 2024， 626（7999）： 529-534. DOI
[21]	ZHANG Q N， XIA X D， WANG J， et al. Effects of epitaxial strain， film thickness and electric-field frequency on the ferroelectric behavior of BaTiO₃ nano films［J］. International Journal of Solids and Structures， 2018， 144/145： 32-45. DOI URL
[22]	李昊晴，苏　煜. BaTiO₃纳米单晶薄膜在外加电场作用下畴结构演化的相场研究［J］. 人工晶体学报， 2024， 53（7）： 1136-1149.
	LI H Q， SU Y. Phase field study on domain structure evolution of BaTiO₃ nano single crystal thin films under applied electric field［J］. Journal of Synthetic Crystals， 2024， 53（7）： 1136-1149 （in Chinese）.
[23]	GUO C Q， WANG J， HUANG H B. Effects of shear and bending strains on domain structures in freestanding ferroelectric thin films from phase-field simulations［J］. Applied Physics Letters， 2024， 125（6）： 062903.
[24]	GUO C Q， DONG S Z， WANG J， et al. Strain-induced toroidal polar states in wrinkled ferroelectric polymer by phase-field simulations［J］. Advanced Electronic Materials， 2023， 9（11）： 2300193. DOI URL
[25]	SCHLOM D G， CHEN L Q， EOM C B， et al. Strain tuning of ferroelectric thin films［J］. Annual Review of Materials Research， 2007， 37： 589-626. DOI URL
[26]	ESTANDÍA S， DIX N， GAZQUEZ J， et al. Engineering ferroelectric Hf_0.5Zr_0.5O₂ thin films by epitaxial stress［J］. ACS Applied Electronic Materials， 2019， 1（8）： 1449-1457. DOI URL
[27]	XU S Q， SHI X M， PAN H， et al. Strain engineering of energy storage performance in relaxor ferroelectric thin film capacitors［J］. Advanced Theory and Simulations， 2022， 5（6）： 2100324. DOI URL
[28]	WANG J J， SU Y J， WANG B， et al. Strain engineering of dischargeable energy density of ferroelectric thin-film capacitors［J］. Nano Energy， 2020， 72： 104665. DOI URL
[29]	ZHU H F， ZHAO Y Y， OUYANG J， et al. Achieving a record-high capacitive energy density on Si with columnar nanograined ferroelectric films［J］. ACS Applied Materials & Interfaces， 2022， 14（6）： 7805-7813.
[30]	ZHAO Y Y， OUYANG J， WANG K， et al. Achieving an ultra-high capacitive energy density in ferroelectric films consisting of superfine columnar nanograins［J］. Energy Storage Materials， 2021， 39： 81-88. DOI URL
[31]	QIAN J， YU Z Y， GE G L， et al. Topological vortex domain engineering for high dielectric energy storage performance［J］. Advanced Energy Materials， 2024， 14（8）： 2303409. DOI URL
[32]	POTNIS P R， TSOU N T， HUBER J E. A review of domain modelling and domain imaging techniques in ferroelectric crystals［J］. Materials， 2011， 4（2）： 417-447. DOI PMID
[33]	SU Y， LANDIS C M. Continuum thermodynamics of ferroelectric domain evolution： theory， finite element implementation， and application to domain wall pinning［J］. Journal of the Mechanics and Physics of Solids， 2007， 55（2）： 280-305. DOI URL
[34]	ZHANG W， BHATTACHARYA K. A computational model of ferroelectric domains. Part I： model formulation and domain switching［J］. Acta Materialia， 2005， 53（1）： 185-198. DOI URL
[35]	SINNAMON L J， SAAD M M， BOWMAN R M， et al. Exploring grain size as a cause for “dead-layer” effects in thin film capacitors［J］. Applied Physics Letters， 2002， 81（4）： 703-705. DOI URL
[36]	SCHIØTZ J， DI TOLLA F D， JACOBSEN K W. Softening of nanocrystalline metals at very small grain sizes［J］. Nature， 1998， 391（6667）： 561-563. DOI URL
[37]	CHOUDHURY S， LI Y L， KRILL C， et al. Effect of grain orientation and grain size on ferroelectric domain switching and evolution： phase field simulations［J］. Acta Materialia， 2007， 55（4）： 1415-1426. DOI URL
[38]	ABDOLLAHI A， ARIAS I. Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions［J］. Journal of the Mechanics and Physics of Solids， 2012， 60（12）： 2100-2126. DOI URL
[39]	FAN L， WERNER W， SUBOTIĆ S， et al. Multigrain phase-field simulation in ferroelectrics with phase coexistences： an improved phase-field model［J］. Computational Materials Science， 2022， 203： 111056. DOI URL
[40]	HOU X， LI X K， ZHANG J T， et al. Effect of grain size on the electrocaloric properties of polycrystalline ferroelectrics［J］. Physical Review Applied， 2021， 15（5）： 054019.
[41]	INDERGAND R， VIDYASAGAR A， NADKARNI N， et al. A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT［J］. Journal of the Mechanics and Physics of Solids， 2020， 144： 104098. DOI URL
[42]	YU H J， WANG J， KOZINOV S， et al. Phase field analysis of crack tip parameters in ferroelectric polycrystals under large-scale switching［J］. Acta Materialia， 2018， 154： 334-342. DOI URL
[43]	GARCIA V， FUSIL S， BOUZEHOUANE K， et al. Giant tunnel electroresistance for non-destructive readout of ferroelectric states［J］. Nature， 2009， 460（7251）： 81-84. DOI
[44]	LIU Y， WEI J， LOU X J， et al. Influence of epitaxial strain on elastocaloric effect in ferroelectric thin films［J］. Applied Physics Letters， 2015， 106（3）： 032901
[45]	EDERER C， SPALDIN N A. Effect of epitaxial strain on the spontaneous polarization of thin film ferroelectrics［J］. Physical Review Letters， 2005， 95（25）： 257601. DOI URL
[46]	刘永广，康爱国，张少飞，等. 钛酸钡纳米颗粒铁电性临界尺寸的理论分析［J］. 物理学报， 2015， 64（17）： 177702.
	LIU Y G， KANG A G， ZHANG S F， et al. Theoretical analysis on ferroelectricity critical dimension of BaTiO₃ nanoparticles［J］. Acta Physica Sinica， 2015， 64（17）： 177702 （in Chinese）. DOI URL
[47]	MANGERI J， ESPINAL Y， JOKISAARI A， et al. Topological phase transformations and intrinsic size effects in ferroelectric nanoparticles［J］. Nanoscale， 2017， 9（4）： 1616-1624. DOI PMID
[48]	SU Y， KANG H， WANG Y， et al. Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics［J］. Physical Review B， 2017， 95（5）： 054121.
[49]	吕烨同，覃业霞，王　梅，等. 晶粒尺寸对多层陶瓷电容器可靠性能的影响与机理［J］. 华南师范大学学报（自然科学版）， 2024， 56（3）： 1-8.
	LÜ Y T， QIN Y X， WANG M， et al. The influence and mechanism of grain size on the reliability of multilayer ceramic capacitors［J］. Journal of South China Normal University （Natural Science Edition）， 2024， 56（3）： 1-8 （in Chinese）.
[50]	ZHANG W， BHATTACHARYA K. A computational model of ferroelectric domains. Part Ⅱ： grain boundaries and defect pinning［J］. Acta Materialia， 2005， 53（1）： 199-209. DOI URL
[51]	CHOUDHURY S， LI Y L， CHEN L Q， et al. Strain effect on coercive field of epitaxial barium titanate thin films［J］. Applied Physics Letters， 2008， 92（14）： 142907. DOI URL
[52]	SANG Y L， LIU B， FANG D N. The size and strain effects on the electric-field-induced domain evolution and hysteresis loop in ferroelectric BaTiO₃ nanofilms［J］. Computational Materials Science， 2008， 44（2）： 404-410. DOI URL
[53]	FEDELI P， CUNEO F， MAGAGNIN L， et al. On the simulation of the hysteresis loop of polycrystalline PZT thin films［J］. Smart Materials and Structures， 2020， 29（9）： 095007.
[54]	PERTSEV N A， CONTRERAS J R， KUKHAR V G， et al. Coercive field of ultrathin Pb（Zr_0.52Ti_0.48）O₃ epitaxial films［J］. Applied Physics Letters， 2003， 83（16）： 3356-3358. DOI URL
[55]	刘　迪，王　静，王俊升，等. 相场模拟应变调控PbZr_（1- _x_）Ti _x O₃薄膜微观畴结构和宏观铁电性能［J］. 物理学报， 2020， 69（12）： 127801.
	LIU D， WANG J， WANG J S， et al. Phase field simulation of misfit strain manipulating domain structure and ferroelectric properties in PbZr_（1- _x_）Ti _x O₃ thin films［J］. Acta Physica Sinica， 2020， 69（12）： 127801 （in Chinese）. DOI URL
[56]	LI Y L， CHEN L Q. Temperature-strain phase diagram for BaTiO₃ thin films［J］. Applied Physics Letters， 2006， 88（7）： 072905.

Strain Tuning of Domain Structure in BaTiO₃ Polycrystalline Nanofilms

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 56

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	LI Haoqing, SU Yu. Phase Field Study on Domain Structure Evolution of BaTiO₃ Nano Single Crystal Thin Films under Applied Electric Field [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2024, 53(7): 1136-1149.
[2]	SHI Yufeng, WANG Pengfei, MU Honghe, SU Liangbi. Numerical Simulation Investigation of Size Effect on Calcium Fluoride Crystals Grown by Vertical Bridgman Method [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2024, 53(6): 973-981.
[3]	WANG Yaqi, FU Dashi, WANG Yanan, QIN Yalin, ZHANG Yongcheng. Preparation and Opto-Electric Properties of Lead-Free 0.96KNNTS_x-0.04BNKZ Transparent Piezoelectric Ceramics [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2024, 53(11): 1964-1971.
[4]	REN Yijing, MA Xinguo, ZHANG Feng, LU Jingjing, ZHANG Li, WANG Han. Preparation of BaTiO₃ Thin Film and Its Application in Electro-Optic Modulator [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2023, 52(4): 688-700.
[5]	HUANG Jiangfeng, WANG Tao, WANG Fenghua, HE Zhixing, CHEN Zhe, HUANG Yinbo, WU Wenjuan. Properties of Novel Ternary Relaxor Ferroelectrics Modified by Bismuth Series Compounds [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(3): 411-418.
[6]	LEI Lei, WU Jian, DONG Zihan, LU Lin, LI Xu, WANG Liang, WAN Hao. Novel BT-BMT-xBNT Lead-Free Ceramics with High Energy Storage Density [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(11): 1967-1972.
[7]	HUANG Zhiqiang, HE Xiujiang, HE Xinhua, FU Xiaoyi, WANG Xin, LU Zhenya. Structure and Electrical Properties of Sb₂O₃-Doped BiFeO₃-BaTiO₃ Piezoelectric Ceramics [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2021, 50(3): 565-571.
[8]	WEI Ye;ZHOU Bing;SANG Sheng-bo;DENG Xiao;CHAI Jing;CHEN Ze-hua;ZHANG Wen-dong. Mechanism Study on Size Effects of Cluster Implantation on Silicon [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2017, 46(6): 1064-1071.
[9]	LIU Wen-bin;KANG Ai-guo;LIU Yong-guang;ZHANG Shao-fei;LI Liang-hui. Study on the Size Effect of Resistivity and Leakage Current of Fine Grained BaTiO3 Ceramics [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2016, 45(8): 2097-2100.
[10]	WANG Ben;YIN Wen-dian;WANG Ming-hai;LIU Dong-xi. Study of Hardness Reverse Indentation Size Effect of Isotropic Pyrolytic Graphite [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2016, 45(2): 509-514.
[11]	WANG Ben;WANG Ming-hai;LIU Dong-xi;ZHENG Yao-hui;LI Xiao-peng. Size Effect of Isotropic Pyrolytic Graphite during Indentation Experiment [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2015, 44(1): 127-132.
[12]	FENG De-sheng;LIU Xi-tao;WANG Jing;YI Zhi-guo. Growth and Properties of BiVO4 Crystal by Bridgman Method [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2014, 43(12): 3104-3107.
[13]	LI Yan;KANG Ren-ke;GAO Hang;WU Dong-jiang;WANG Jing-he. Analysis on the Nanomechanical Properties of CdZnTe(211) Face [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2009, 38(6): 1442-1445.
[14]	NI You-bao;WU Hai-xin;GENG Lei;WANG Zhen-you;MAO Ming-sheng;CHENG Gan-chao;HUANG Fei. Preliminary Exploration on the Dielectric Properties of AgGaGeS_4 Crystal [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2009, 38(5): 1055-1058.
[15]	XU Tao;XU Yan-ping;CAO Yong-ge;LAN Yu-cheng;LI Jian-ye;ZHANG Yue;YANG Zhi;CHEN Xiao-long. Synthesis and Raman Scattering of GaN Nanocrystallite Solids [J]. JOURNAL OF SYNTHETIC CRYSTALS, 2001, 30(2): 154-158.