First principles study on polarization and piezoelectric properties of group substitution regulated lead-free organic perovskite ferroelectrics

Zheng Peng-Fei; Liu Zhi-Xu; Wang Chao; Liu Wei-Fang

doi:10.7498/aps.73.20240385

Abstract

Organic ferroelectrics are desirable for the applications in the field of wearable electronics due to their eco-friendly process-ability, mechanical flexibility, low processing temperatures, and lightweight. In this work, we use five organic groups as substitution for organic cation and study the effects of organic cations on the structural stability, electronic structure, mechanical properties and spontaneous polarization of metal-free perovskite A-NH₄-(PF₆)₃ (A = MDABCO, CNDABCO, ODABCO, NODABCO, SHDABCO) through first-principles calculations. Firstly, the stabilities of the five materials are calculated by molecular dynamics simulations, and the energy values of all systems are negative and stable after 500 fs, which demonstrates the stabilities of the five materials at 300 K. The electronic structure calculation shows that the organic perovskite materials have wide band gap with a value of about 7.05 eV. The valence band maximum (VBM) and Cconduction band minimum (CBM) are occupied by different elements, which is conductive to the separation of electrons and holes. We find that organic cations have an important contribution to the spontaneous polarization of materials, with a contribution rate over 50%. The presence of hydrogen atoms in the substituting groups (MDABCO, ODABCO) enhances the hydrogen bond interaction between the organic cations and ${\rm PF}_6^- $ and increases the displacement of the organic cation, resulting in an increase in the contribution of the polarization of the organic cation to the total polarization. In addition, we observe large piezoelectric strain components, the calculated value of d₃₃ is 36.5 pC/N for CNDABCO-NH₄-(PF₆)₃, 32.3 pC/N for SHNDABCO-NH₄-(PF₆)₃, which is larger than the known value of d₃₃ of MDABCO-NH₄-I₃(14pC/N). The calculated value of d₁₄ is 57.5 pC/N for ODABCO-NH₄-(PF₆)₃, 27.5 pC/N for NODABCO-NH₄-(PF₆)₃. These components are at a high level among known organic perovskite materials and comparable to many known inorganic crystals. The large value of d₁₄ is found to be closely related to the large value of elastic compliance tensor s₄₄. The analysis of Young’s modulus and bulk’s modulus shows that these organic perovskite materials have good ductility. These results indicate that these organic materials are excellent candidates for future environmentally friendly piezoelectric materials.

Keywords:

Authors and contacts

1.
Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, School of Science, Tianjin University, Tianjin 300072, China
2.
School of Science, Tianjin Chengjian University, Tianjin 300192, China

Corresponding author: Liu Wei-Fang, wfliu@tju.edu.cn

Funds: Project support by the National Natural Science Foundation of China (Grant No. 51572193).

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References

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Cited By

图 1 甲基替换H原子打破阳离子对称性

Figure 1. Replacing H atoms with methyl groups to break cation symmetry.

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图 2 (a) MDABCO²⁺, ${\mathrm{NH}}_4^+ $, ${\text{PF}}_6^ - $结构示意图; (b) 沿a轴观察的MDABCO-NP₃的原胞; (c) 不同基团取代之后的阳离子; (d) MDABCO-NP₃的原胞; (e)沿着[111]方向观察到的MDABCO-NP₃的原胞; (f) 沿a轴观察的MDABCO-NP₃的晶胞

Figure 2. (a) Structures of MDABCO²⁺, ${\mathrm{NH}}_4^+ $, ${\text{PF}}_6^ - $ components; (b) the primitive cell of MDABCO-NP₃ viewed along the a-axis; (c) cations substituted with different functionalities; (d) the primitive cell of MDABCO-NP₃; (e) the primitive cell of MDABCO-NP₃ viewed along [111] direction; (f) the unit cell of MDABCO-NP₃ viewed along a-axis.

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图 3 (a) A-NP₃的结合能; (b) A-NP₃在300 K条件下的分子动力学模拟

Figure 3. (a) Binding energy of A-NP₃; (b) molecular dynamics simulation of A-NP₃ under 300 K conditions.

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图 4 (a) 5种材料的总态密度; (b)—(f)分别为NODABCO-NP₃, SHDABCO-NP₃, ODABCO-NP₃, CNDABCO-NP₃, MDABCO-NP₃的投影态密度 ; 费米能级设置为0 eV

Figure 4. (a) Total density of states for A-NP₃; (b)–(f) projected density of states of (b) NODABCO-NP₃, (c) SHDABCO-NP₃, (d) ODABCO-NP₃, (e) CNDABCO-NP₃, (f) MDABCO-NP₃. Fermi level is set to zero.

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图 5 –R3到+R3结构的转变过程　(a) –R3铁电相 (λ = –1)结构; (b)中间相变结构(λ =0); (c) +R3铁电相(λ = 1)结构; (d) 类反铁电($ {\lambda }' = -1$)结构

Figure 5. Transformation of –R3 to +R3 structure: (a) –R3 ferroelectric phase (λ = –1) structure; (b) intermediate phase transition structure (λ = 0); (c) +R3 ferroelectric phase (λ = 1) structure; (d) quasi-antiferroelectric phase structure ($ {\lambda }' =-1$).

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图 6 计算的(a) MDABCO-NP₃, (b) SHDABCO-NP₃, (c) NODABCO-NP₃, (d) ODABCO- NP₃, (e) CNDABCO-NP₃的经极化量子数修正的和未修正的极化值; (f) 5种材料总的极化值

Figure 6. Calculated polarization value of (a) MDABCO-NP₃, (b) SHDABCO-NP₃, (c) NODABCO-NP₃, (d) ODABCO-NP₃, (e) CNDABCO-NP₃ with and without correction for polarization quantum; (f) the total polarization values of five materials.

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图 7 体系的差分电荷密度　(a) MDABCO-NP₃; (b) SHDABCO-NP₃; (c) NODABCO-NP₃; (d) OHDABCO-NP₃; (e) CNDABCO-NP₃

Figure 7. Differential charge density distribution of differ systems: (a) MDABCO-NP₃; (b) SHDABCO-NP₃; (c) NODABCO-NP₃; (d) OHDABCO-NP₃; (e) CNDABCO-NP₃.

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图 8 计算的 A-NP₃的(a) 压电应变张量和(b) 压电应力张量

Figure 8. Calculated piezoelectric strain (a) and stress (b) tensor of A-NP₃.

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表 1 采用PBE和PBE+D3方法优化后的A-NP₃的晶格结构参数

Table 1. Structural optimization of A-NP₃ by using PBE and PBE+D3 methods.

Material	Method	a/Å	α/(°)	V/Å³
MDABCO-NP₃	PBE	7.89(0.57%)	84.91(0.06%)	485.51
	PBE+D3	7.73(–1.46%)	84.55(–0.36%)	478.25
	Exp	7.84	84.86	496.46
SHDABCO-NP₃	PBE	7.93	83.84	489.86
SHDABCO-NP₃	PBE+D3	7.74	83.18	483.46
NODABCO-NP₃	PBE	7.95	83.74	493.15
NODABCO-NP₃	PBE+D3	7.84	81.25	485.65
ODABCO-NP₃	PBE	7.85	85.2	478.75
ODABCO-NP₃	PBE+D3	7.75	83.65	475.21
CNDABCO-NP₃	PBE	10.58	85.21	477.19
CNDABCO-NP₃	PBE+D3	9.28	83.48	486.48

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表 2 A位阳离子的极化P_A(μC/cm²)和材料的总极化P_S(μC/cm²)及阳离子的极化对总极化的贡献P_A/P_S

Table 2. Polarization of A-site cations (P_A) and total polarization of materials (P_S) and the contribution of cation polarization to total polarization (P_A/P_S).

Materials	P_A	P_S	P_A/P_S
SHDABCO-NP₃	2.4	3.8	0.64
NODABCO-NP₃	2.6	4.2	0.63
ODABCO-NP₃	4.3	6.0	0.71
MDABCO-NP₃	4.3	6.3	0.68
CNDABCO-NP₃	5.7	9.4	0.61

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表 3 计算的A-NP₃的弹性刚度张量C_ij、体积模量B、剪切模量G、杨氏模量E (GPa)、皮尤比(B/G)和泊松比$ \nu $

Table 3. Calculated elastic tensor coefficients C_ij , bulk modulu B, shear modulu G, Young’s modulu E(GPa), Pugh’s and Poisson’s ratios of A-NP₃.

Materials	C₁₁	C₃₃	C₄₄	C₁₂	C₁₃	C₁₄	C₂₅	B	G	E	B/G	ν
MDABCO-NP₃	32.9	15.9	8.2	15.9	16.3	0.8	0.1	21.4	8.2	21.8	2.6	0.3
ODABCO-NP₃	21.9	7.2	6.7	7.2	14.4	0.2	0.4	18.4	3.6	10.2	2.8	0.3
CNDABCO-NP₃	35.2	19.4	6.6	19.4	22.8	0.6	1.3	25.7	6.7	18.4	4.0	0.4
SHDABCO-NP₃	32.4	21.8	8.6	21.8	24.1	4.8	4.4	25.9	7.3	20.1	4.1	0.4
NODABCO-NP₃	36.2	19.7	4.4	19.7	19.7	0.3	0.4	25.0	5.9	16.5	4.5	0.4

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表 7 代表性无机、有机压电体对CNDABCO-NP₃和SHDABCO-NP₃的压电分量d₃₃的对比.

Table 7. Comparison of piezoelectric component d₃₃ of representative inorganic, organic piezoelectrics to CNDABCO-NP₃ and SHDABCO-NP₃.

Materials	d₃₃/(pC·N^–1)
ZnS^[41]	3.2
LiNbO₃, LN^[42]	6.0
CdS^[43]	10.3
ZnO^[44]	12.4
MDABCO-NI₃^[19]	14.4
CNDABCO-NP₃	36.5
SHDABCO-NP₃	32.3

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表 8 代表性无机、有机压电体对MDABCO-NP₃, NODABCO-NP₃ 和ODABCO-NP₃的压电分量d₁₄的对比

Table 8. Comparison of piezoelectric component d₁₄ of representative inorganic, organic piezoelectrics to MDABCO-NP₃, NODABCO-NP₃ and ODABCO-NP₃.

Materials	d₁₄/(pC·N^–1)
NaClO₃^[45]	1.7
La₃Ga_5.5Ta_0.5O₁₄, LGT^[46]	5.0
GaN^[47]	6.4
AlN^[47]	9.7
Ca₃TaGa₃Si₂O₁₄, CTGS^[48]	24.3
MDABCO-NP₃	6.3
NODABCO-NP₃	27.5
ODABCO-NP₃	57.5

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表 4 A-NP₃的压电应变张量d_ij(pC/N)

Table 4. Piezoelectric strain tensor d_ij of A-NP₃ (pC/N).

Materials	d₁₁	d₂₂	d₃₃	d₁₄	d₁₅	d₃₁
MDABCO-NP₃	–2.9	–2.6	2.0	–6.3	–1.0	3.0
ODABCO-NP₃	–5.5	–0.9	7.4	–57.5	–28.9	0.9
CNDABCO-NP₃	–1.3	–2.7	36.5	–7.9	–1.6	17.0
SHDABCO-NP₃	–18.2	–20.9	32.3	–10.6	–41.6	27.2
NODABCO-NP₃	–0.8	–0.4	7.1	27.5	–21.8	6.18

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表 5 A-NP₃的压电应力张量e_ij(C/m²)

Table 5. Piezoelectric stress tensor e_ij of A-NP₃ (C/m²).

Materials	e₁₁	e₂₂	e₃₃	e₁₄	e₁₅	e₃₁
MDABCO-NP₃	–3.5	–3.0	2.4	4.5	–0.6	4.9
ODABCO-NP₃	–2.1	–0.5	3.5	8.1	–1.7	9.9
CNDABCO-NP₃	–1.9	–4.7	34.7	4.7	–0.8	9.7
SHDABCO-NP₃	–5.2	–6.6	7.3	4.3	–21.9	6.5
NODABCO-NP₃	–1.6	–0.5	10.5	8.9	–10.7	16.8

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表 6 A-NP₃的柔性刚度张量s_ij(10^–12 m/N).

Table 6. Elastic compliance tensor s_ij of A-NP₃ (10^–12 m/N).

Materials	s₁₁	s₃₃	s₄₄	s₁₂	s₁₃	s₁₄	s₂₅
MDABCO-NP₃	48.8	49.8	130.3	–16.8	–16.7	3.2	0.6
ODABCO-NP₃	38.4	57.2	247.3	–9.0	–17.6	18	45.5
CNDABCO-NP₃	56.9	85.4	157.3	–8.8	–35.7	–5.5	13.3
SHDABCO-NP₃	124.7	142.4	218.9	–37.0	–79.2	–60.1	5.0
NODABCO-NP₃	46.8	51.2	199.0	–16.6	–17.2	17.1	19.9

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[1]	Kieslich G, Sun S J, Cheetham A K 2014 Chem. Sci. 5 4712 Google Scholar
[2]	Sessolo M, Bolink H J 2011 Adv. Mater. 23 1829 Google Scholar
[3]	Bechmann R 2005 J. Acoust. Soc. Am. 28 347 Google Scholar
[4]	Haertling G H 1999 J. Am. Cera. Soc. 82 797 Google Scholar
[5]	Zhao Y X, Zhu K 2016 Chem. Soc. Rev. 45 655 Google Scholar
[6]	Mischenko A S, Zhang Q, Scott J F, Whatmore R W, Mathur N D 2006 Science 311 1270 Google Scholar
[7]	Peña M A, Fierro J 2001 Chem. Rev. 101 1981 Google Scholar
[8]	郑隆立, 齐世超, 王春明, 石磊, 2019 物理学报 68 147701 Google Scholar Zheng L L, Qi S C, Wang C M, Shi L 2019 Acta Phys. Sin. 68 147701 Google Scholar
[9]	Neaten J B, Ederer C, Waghmare U V, Spaldin N A, Rabe K M 2005 Phys. Rev. B 71 14111 Google Scholar
[10]	Lebeugle D, Colson D, Forget A, Viret M 2007 Appl. Phys. Lett. 91 22907 Google Scholar
[11]	Palkar V R, Kundaliya D C, Malik S K 2003 J. Appl. Phys. 93 4337 Google Scholar
[12]	Gao W X, Chang L, Ma H, You L, Yin J, Liu J M, Liu Z G, Wang J L, Yuan G L 2015 NPG Asia Mater. 7 e189 Google Scholar
[13]	Xu W J, Kopyl S, Kholkin A, Rocha J 2019 Coordin. Chem. Rev. 387 398 Google Scholar
[14]	Nandi P, Topwal D, Park N G, Shin H 2020 J. Phys. D: Appl. Phys. 53 493002 Google Scholar
[15]	Köhnen E, Jost M, Morales-Vilches A B, Tockhorn P, Al-Ashouri A, Macco B, Kegelmann L, Korte L, Rech B, Schlatmann R, Stannowski B, Albrecht S 2019 Sustain. Energ. Fuels 3 1995 Google Scholar
[16]	Sahli F, Werner J, Kamino B A, Bräuninger M, Monnard R, Paviet-Salomon B, Barraud L, Ding L, Diaz Leon J J, Sacchetto D, Cattaneo G, Despeisse M, Boccard M, Nicolay S, Jeangros Q, Niesen B, Ballif C 2018 Nat. Mater. 17 820 Google Scholar
[17]	Yang W S, Park B, Jung E H, Jeon N J, Kim Y C, Lee D U, Shin S S, Seo J, Kim E K, Noh J H, Seok S I 2017 Science 356 1376 Google Scholar
[18]	Yun J S, Park C K, Jeong Y H, Cho J H, Paik J, Yoon S H, Hwang K 2016 Nanomater. Nanotechno. 6 20 Google Scholar
[19]	Ye H Y, Tang Y Y, Li P F, Liao W Q, Gao J X, Hua X N, Cai H, Shi P P, You Y M, Xiong R G 2018 Science 361 151 Google Scholar
[20]	Fu D W, Cai H L, Liu Y M, Ye Q, Zhang W, Zhang Y, Chen X Y, Giovannetti G, Capone M, Li J Y, Xiong R G 2013 Science 339 425 Google Scholar
[21]	Wang H, Liu H H, Zhang Z Y, Liu Z H, Lv Z L, Li T W, Ju W W, Li H S, Cai X W, Han H 2019 npj Comput. Mater 5 17 Google Scholar
[22]	Wu H S, Wei S, Chen S W, Pan H C, Pan W P, Huang S, Tsai M, Yang P 2022 Adv. Sci. 9 2105974 Google Scholar
[23]	Choi H S, Li S N, Park I, Liew W H, Zhu Z Y, Kwon K C, Wang L, Oh I, Zheng S S, Su C L, Xu Q H, Yao K, Pan F, Loh K P 2022 Nat. Commun. 13 794 Google Scholar
[24]	Sun M J, Zheng C, Gao Y, Johnston A, Najarian A M, Wang P X, Voznyy O, Hoogland S, Sargent E H 2021 Adv. Mater. 33 2006368 Google Scholar
[25]	Kasel T W, Deng Z Y, Mroz A M, Hendon C H, Butler K T, Canepa P 2019 Chem. Sci. 10 8187 Google Scholar
[26]	Kresse, Furthmuller 1996 Phys. Rev. B 54 11169 Google Scholar
[27]	Kresse, Hafner 1994 Phys. Review. B 49 14251 Google Scholar
[28]	Kresse, Hafner 1993 Phys. Review. B 47 558 Google Scholar
[29]	Spaldin N A 2012 J. Solid State Chem. 195 2 Google Scholar
[30]	Li Z Z, Li Z H, Peng G Q, Shi C, Wang H X, Ding S Y, Wang Q, Liu Z T, Jin Z W 2023 Adv. Mater. 35 2300480 Google Scholar
[31]	King-Smith R D, Vanderbilt D 1993 Phys. Rev. B 48 4442 Google Scholar
[32]	Vanderbilt D, King-Smith R D 1993 Phys. Rev. B 47 1651 Google Scholar
[33]	Wang X M, Yan Y F 2022 arXiv: 2206.11137v1 [cond-mat. mtrl-sci]
[34]	Singh J, Kaur H, Singh G, Tripathi S K 2021 Mater. Today Energy 21 100820 Google Scholar
[35]	Al-Qaisi S, Rai D P, Haq B U, Ahmed R, Vu T V, Khuili M, Tahir S A, Alhashim H H 2021 Mater. Chem. Phys. 258 123945 Google Scholar
[36]	Kiely E, Zwane R, Fox R, Reilly A M, Guerin S 2021 CrystEngComm 23 5697 Google Scholar
[37]	Mouhat F, Coudert F 2014 Phys. Rev. B 90 224104 Google Scholar
[38]	Haid S, Bouadjemi B, Houari M, Matougui M, Lantri T, Bentata S, Aziz Z 2019 Solid State Commun. 294 29 Google Scholar
[39]	Birch F 1938 J. Appl. Phys. 9 279 Google Scholar
[40]	Kholil M I, Bhuiyan M T H 2020 Solid State Commun. 322 114053 Google Scholar
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