钙钛矿结构ZrBeO<sub>3</sub>稳定性的第一性原理研究

温新竹; 彭玉颜; 刘明真

doi:10.11858/gywlxb.20190802

钙钛矿结构ZrBeO₃稳定性的第一性原理研究

doi: 10.11858/gywlxb.20190802

仰恩大学工程技术学院，福建泉州　362014

基金项目: 国家自然科学基金（11675001）；福建省科技厅引导性项目（2018H0040）；江门市基础与理论科学研究类科技计划项目（2019030101590008821）

详细信息

作者简介:
温新竹（1982－），男，副教授，主要从事材料学研究. E-mail: 64412900@qq.com

中图分类号: O521.2; TM911.4
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出版历程
- 收稿日期: 2019-07-02
- 修回日期: 2019-07-25

First-Principles Study on Structural Stability of Perovskite ZrBeO₃

Institute of Engineering and Technology, Yang-En University, Quanzhou 362014, Fujian, China

摘要

摘要: 基于密度泛函理论构建了钙钛矿结构ZrBeO₃晶体模型，计算了该晶体模型结合能，表明了该构型热力学稳定性；计算出该结构在不同压力下的弹性常数，并据此计算了ZrBeO₃的体积模量、剪切模量、杨氏模量、泊松比、B_H/G_H（体模量/剪切模量）等参数，结果表明该材料具有机械稳定性，随着等静压力增加，材料由脆性向韧性转变；计算了零压下ZrBeO₃的硬度，为34.5 GPa，表明该结构晶体应为超硬材料；计算了ZrBeO₃的声子能谱，结果表明ZrBeO₃在低温零压下热动力学不稳定，为此分析比较了不同压力下的声子能谱、不同原子轨道及化学键布居值，研究表明随着压力增加，Be原子sp杂化后形成的Be-O共价键成分增强、Zr-O键离子键成分增强，晶格动力学趋于稳定。
- ZrBeO₃ /
- 稳定性 /
- 第一性原理 /
- 晶体结构
Abstract: Based on density functional theory, a ZrBeO₃ crystal model of perovskite structure was constructed. The binding energy of the crystal model was calculated, and the thermodynamic stability of the structure was calculated. The elastic constant of the structure under different pressures was calculated, and ZrBeO₃ was calculated according to it. The bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, B_H/G_H and other parameters, the calculation results show that the material has mechanical stability, and the material changes from brittle to ductile with increasing isostatic pressure; the hardness of ZrBeO₃ under zero pressure is 34.5 GPa, which indicates that the crystal should be superhard material. The calculated phonon energy spectrum show that ZrBeO₃ is thermodynamically unstable under low temperature and zero pressure. The phonon spectrum, different atomic orbitals and chemical bond values at different pressures show that the Be-O covalent bond formed by the impurity of Be atom is enhanced and the Zr-O bond ion bond component is enhanced with the increase of pressure. The lattice dynamics tend to be stable.
- ZrBeO₃ /
- stability /
- first principles /
- crystal structure

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图 1 ZrBeO₃晶格常数a随总能E变化曲线

Figure 1. Lattice constants (a) vs. total energy (E) of ZrBeO₃

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图 2 ZrBeO₃晶体模型

Figure 2. ZrBeO₃ crystal model

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图 3 零压下的ZrBeO₃声子能谱

Figure 3. ZrBeO₃ phonon spectra at zero pressure

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图 4 不同压力下的ZrBeO₃声子能谱

Figure 4. Phonon spectra of ZrBeO₃ at different pressures

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图 5 不同压力下ZrBeO₃电子总态密度及各原子分波态密度图

Figure 5. Total density of state of ZrBeO₃ electrons and partial density of states of each atom at different pressures

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A1 ZrBeO₃的电子能带结构

A1. Electronic band structure of ZrBeO₃

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A2 ZrBeO₃的吸收谱

A2. Optical absorption spectrum of ZrBeO₃

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A3 ZrBeO₃的反射谱

A3. Optical reflectivity spectrum of ZrBeO₃

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A4 ZrBeO₃介电函数谱线

A4. Dielectric function spectrum of ZrBeO₃

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表 1 ZrBeO₃模型晶格参数

Table 1. Lattice parameters of ZrBeO₃ model

Compound	Lattice/nm	Wykoff coordinates	Volume/(10^–3 nm³)	Bond Length/nm	Bond population
ZrBeO₃ cubic	0.346 1	Zr(0.00, 0.00, 0.00)a Be(0.50, 0.50, 0.50)a O(0.50, 0.50, 0.00)a	41.447 3	Be-O 0.173 0 Zr-O 0.244 7	Be-O (3) 0.66 Zr-O (3) 0.61

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表 2 不同压力下的弹性常数、体积模量、剪切模量、杨氏模量、泊松比、B_H/G_H

Table 2. Elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, B_H/G_H under different pressures

p/GPa	C₁₁	C₁₂	C₄₄	B_H	G_H	E	$v$	B_H/G_H
0	422.45	149.33	171.48	240.37	157.55	385.86	0.232	1.53
30	582.04	212.84	222.98	335.91	206.74	514.65	0.245	1.62
50	775.37	315.82	306.78	469.01	273.25	686.43	0.256	1.72
100	1 021.29	401.25	353.07	607.94	335.17	850.86	0.267	1.81
150	1 281.55	513.85	432.03	769.75	412.76	1 049.02	0.273	1.86
200	1 515.13	614.39	500.17	914.63	479.62	1 224.67	0.277	1.91
250	1 778.26	731.79	580.32	1 080.61	556.76	1 425.47	0.280	1.94
300	2 256.08	940.80	723.01	1 379.23	696.11	1 787.60	0.284	1.98

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表 3 不同压力下原子轨道和化学键的布居值分布

Table 3. Atomic orbital and chemical bond population distribution at different pressures

p/ GPa	Atomic	s	p	d	Bond Be-O		Bond Zr-O
p/ GPa	Atomic	s	p	d	Population	Bond length/nm	Population	Bond length/nm
0	Be/Zr/O(3)	2.34/2.26/1.82	1.11/6.31/4.89	0/1.84/0	0.63	0.173 0	0.62	0.244 7
50	Be/Zr/O(3)	2.31/2.18/1.79	1.24/6.24/4.92	0/1.91/0	0.69	0.162 5	0.53	0.229 8
100	Be/Zr/O(3)	2.29/2.12/1.77	1.31/6.21/4.93	0/1.97/0	0.72	0.157 7	0.47	0.223 0
150	Be/Zr/O(3)	2.27/2.08/1.76	1.37/6.18/4.94	0/2.01/0	0.75	0.154 2	0.40	0.218 0
200	Be/Zr/O(3)	2.26/2.04/1.75	1.42/6.16/4.94	0/2.05/0	0.77	0.151 3	0.33	0.214 0

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参考文献(38)

[1]	IKEGAMI K, LU M, OHON R, et al. Nonlinear electrical properties of thin films of a light-emitting perovskite type oxide Pr_0.002(Ca_0.6Sr_0.4)_0.997TiO₃ [J]. Procedia Engineering, 2012, 36: 388–395. doi: 10.1016/j.proeng.2012.03.057
[2]	TAKASHIMA H, SHIMADA K, MIURA N, et al. Low-driving-voltage electroluminescence in perovskite films [J]. Advanced Materials, 2009, 21(36): 3699–3702. doi: 10.1002/adma.200900524
[3]	SAHA S, SINHA T P, MOOKERJEE A. Electric structure, chemical bonding, and optical properties of paraelectric BaTiO₃ [J]. Physical Review B, 2000, 62(13): 699–702.
[4]	赵国栋, 杨亚利, 任伟. 钙钛矿型氧化物非常规铁电研究进展 [J]. 物理学报, 2018, 67(15): 60–72. ZHAO G D, YANG Y L, REN W. Progress in unconventional ferroelectricity of perovskite-type oxides [J]. Acta Physica Sinica, 2018, 67(15): 60–72.
[5]	PARK S Y, KUMAR A, RABE K. Carbon fibers from polyacrylonitrile/cellulose [J]. 2016 APS Meeting, 2016, 6(17): 160–172.
[6]	FENNIE C J. Ferroelectrically induced weak ferromagnetism by design [J]. Physical Review Letters, 2008, 100(16): 167203. doi: 10.1103/PhysRevLett.100.167203
[7]	DOLAN D H, AO T. Cubic zirconia as a dynamic compression window [J]. Applied Physics Letters, 2008, 93(2): 021908. doi: 10.1063/1.2957996
[8]	RESTANI R, MARTIN M, KIVEL N, et al. Analytical investigations of irradiated inert matrix fuel [J]. Journal of Nuclear Materials, 2009, 385(2): 435–442. doi: 10.1016/j.jnucmat.2008.12.030
[9]	CONRADSON S D, DEGUELDRE C A, ESPINOSA-FALLER F J, et al. Complex behavior in quaternary zirconias for inert matrix fuel: what do these materials look like at the nanometer scale? [J]. Progress in Nuclear Energy, 2001, 38(3/4): 221–230.
[10]	WANG S J, ONG C K, XU S Y, et al. Crystalline zirconia oxide on silicon as alternative gate dielectrics [J]. Applied Physics Letters, 2001, 78(11): 1604–1606. doi: 10.1063/1.1354161
[11]	LIN Y S, PUTHENKOVILAKAM R, CHANG J P, et al. Interfacial properties of ZrO₂ on silicon [J]. Journal of Applied Physics, 2003, 93(10): 5945–5952. doi: 10.1063/1.1563844
[12]	WILK G D, WALLACE R M, ANTHONY J M. High-κ gate dielectrics: current status and materials properties considerations [J]. Journal of Applied Physics, 2001, 89(10): 5243–5275. doi: 10.1063/1.1361065
[13]	MCEVOY A. Thin SOFC electrolytes and their interfacesâ: a near-term research strategy [J]. Solid State Ionics, 2000, 132(3/4): 159–165.
[14]	BILIĆ A T, GALE J D. Ground state structure of BaZrO₃: a comparative first-principles study [J]. Physical Review B, 2009, 79(17): 174107. doi: 10.1103/PhysRevB.79.174107
[15]	ZHANG H W, FU X Y, NIU S Y, et al. Synthesis and photoluminescence properties of Eu³⁺-doped AZrO₃ (A = Ca, Sr, Ba) perovskite [J]. Journal of Alloys and Compounds, 2008, 459(1/2): 103–106.
[16]	DUBEY V, TIWARI N. Structural and optical analysis on europium doped AZrO₃ (A = Ba, Ca, Sr) phosphor for display devices application [C]//Bikaner, India. Author(s), 2016, 1728(1): 15-32.
[17]	RANDALL C A, BHALLA A S, SHROUT T R, et al. Classification and consequences of complex lead perovskite ferroelectrics with regard to B-site cation order [J]. Journal of Materials Research, 1990, 5(4): 829–834. doi: 10.1557/JMR.1990.0829
[18]	BRADHA M, HUSSAIN S, CHAKRAVARTY S, et al. Total conductivity in Sc-doped LaTiO_3+δ perovskites [J]. Ionics, 2014, 20(9): 1343–1350. doi: 10.1007/s11581-014-1216-y
[19]	GEPPERT B, GROENEVELD D, LOBODA V, et al. Finite-element simulations of a thermoelectric generator and their experimental validation [J]. Energy Harvesting and Systems, 2015, 2(1/2): 97–103.
[20]	MUHAMMAD I D, AWANG M, MAMAT O, et al. First-principles calculations of the structural, mechanical and thermodynamics properties of cubic zirconia [J]. World Journal of Nano Science and Engineering, 2014, 4(2): 97–103. doi: 10.4236/wjnse.2014.42013
[21]	BAERENDS E J. Perspective on “Self-consistent equations including exchange and correlation effects” [J]. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 2000, 103(3/4): 265–269.
[22]	SEGALL M D, LINDAN P J D, PROBERT M J, et al. First-principles simulation: ideas, illustrations and the CASTEP code [J]. Journal of Physics: Condensed Matter, 2002, 14(11): 2717–2744. doi: 10.1088/0953-8984/14/11/301
[23]	PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996, 77(18): 3865–3868. doi: 10.1103/PhysRevLett.77.3865
[24]	JIA X F, HOU Q Y, XU Z C, et al. Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle [J]. Journal of Magnetism and Magnetic Materials, 2018, 465: 128–135. doi: 10.1016/j.jmmm.2018.05.037
[25]	FISCHER T H, ALMLOF J. General methods for geometry and wave function optimization [J]. The Journal of Physical Chemistry, 1992, 96(24): 9768–9774. doi: 10.1021/j100203a036
[26]	DING Y C, CHEN M, WU W J. Phase stability, elasticity, hardness and the minimum thermal conductivity of Si₂N₂O polymorphs from first principles calculations [J]. Physica B: Condensed Matter, 2014, 449: 236–245. doi: 10.1016/j.physb.2014.05.042
[27]	GONZE X, BEUKEN J M, CARACAS R, et al. First-principles computation of material properties: the ABINIT software project [J]. Computational Materials Science, 2002, 25(3): 478–492. doi: 10.1016/S0927-0256(02)00325-7
[28]	DING J F, LI X M, CUI L L, et al. Electronic and optical properties of anion-doped c-ZrO₂ from first-principles calculations [J]. Journal of Central South University, 2014, 21(7): 2584–2589. doi: 10.1007/s11771-014-2216-9
[29]	BORN M, HUANG K, LAX M. Dynamical theory of crystal lattices [J]. American Journal of Physics, 1955, 23(7): 474.
[30]	WU Z J, HAO X F, LIU X J, et al. Structures and elastic properties of OsN₂ investigated via first-principles density functional calculations [J]. Physical Review B, 2007, 75(5): 054115. doi: 10.1103/PhysRevB.75.054115
[31]	ZHAO J J, WINEY J M, GUPTA Y M. First-principles calculations of second-and third-order elastic constants for single crystals of arbitrary symmetry [J]. Physical Review B, 2007, 75(9): 094105. doi: 10.1103/PhysRevB.75.094105
[32]	GAO F M. Theoretical model of intrinsic hardness [J]. Physical Review B, 2006, 73(13): 132104. doi: 10.1103/PhysRevB.73.132104
[33]	FAN C Z, ZENG S Y, LI L X, et al. Potential superhard osmium dinitride with fluorite and pyrite structure: first-principles calculations [J]. Physical Review B, 2006, 74(12): 125118. doi: 10.1103/PhysRevB.74.125118
[34]	丁迎春, 肖冰. 一种超硬新材料BeP₂N₄的电子结构和力学性质及本征硬度 [J]. 物理化学学报, 2011, 27(7): 1621–1632. doi: 10.3866/PKU.WHXB20110730 DING Y C, XIAO B. Electronic structure, mechanical properties and intrinsic hardness of a new superhard material BeP₂N₄ [J]. Acta Physico-Chimica Sinica, 2011, 27(7): 1621–1632. doi: 10.3866/PKU.WHXB20110730
[35]	SHARMA A D, SINHA M M. Lattice dynamics of protonic conductors AZrO₃ (A = Ba, Sr & Pb): a comparative study [J]. Advanced Materials Research, 2013, 685: 191–194. doi: 10.4028/www.scientific.net/AMR.685.191
[36]	刘哲, 李辉, 赵鹏. Ti₅Al₂C₃与Ti₂AlC、Ti₃AlC₂结构、弹性和电子性质的第一性原理对比研究 [J]. 人工晶体学报, 2019, 48(5): 834–839. doi: 10.3969/j.issn.1000-985X.2019.05.011 LIU Z, LI H, ZHAO P. A first-principles comparative study of the structure, elasticity and electronic properties of Ti₅Al₂C₃, Ti₂AlC and Ti₃AlC₂ [J]. Journal of Artificial Lenses, 2019, 48(5): 834–839. doi: 10.3969/j.issn.1000-985X.2019.05.011
[37]	LAI J, JIA X, WANG D. Thermodynamically stable whilst kinetically labile coordination bonds lead to strong and tough self-healing polymers [J]. Nature Communications, 2019, 10(1): 155–167. doi: 10.1038/s41467-018-07819-1
[38]	GULL E, PARCOLLET O, MILLIS A J. Superconductivity and the pseudogap in the two-dimensional Hubbard model [J]. Physical Review Letters, 2013, 110(21): 256–298.