无机材料学报 ›› 2016, Vol. 31 ›› Issue (2): 171-179.DOI: 10.15541/jim20150338
邵栋元, 程南璞, 陈晶晶, 李 孝, 陈志谦, 李春梅, 惠 群
收稿日期:
2015-07-14
修回日期:
2015-10-19
出版日期:
2016-02-20
网络出版日期:
2016-01-15
作者简介:
邵栋元(1988–), 男, 硕士研究生. E-mail: sdy1988719@swu.edu.cn
基金资助:
SHAO Dong-Yuan, CHENG Nan-Pu, CHEN Jing-Jing, LI Xiao, CHEN Zhi-Qian, LI Chun-Mei, HUI Qun
Received:
2015-07-14
Revised:
2015-10-19
Published:
2016-02-20
Online:
2016-01-15
About author:
SHAO Dong-Yuan. E-mail: sdy1988719@swu.edu.cn
Supported by:
摘要:
本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO3和LiTaO3的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。 电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)-O键呈现强共价键作用, 并且Nb-O(Ta-O)键长小于Li-O键长。LiNbO3和LiTaO3晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在xy平面呈现六重对称性, 在xz和yz平面各向异性程度强于xy平面, 沿[001]、晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO3晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO3晶体。
中图分类号:
邵栋元, 程南璞, 陈晶晶, 李 孝, 陈志谦, 李春梅, 惠 群. LiNbO3和LiTaO3晶体电子结构、平面声波和光折射特性[J]. 无机材料学报, 2016, 31(2): 171-179.
SHAO Dong-Yuan, CHENG Nan-Pu, CHEN Jing-Jing, LI Xiao, CHEN Zhi-Qian, LI Chun-Mei, HUI Qun. Electronic Structure, Plane Acoustic Velocity and Refractive Property of LiNbO3 and LiTaO3[J]. Journal of Inorganic Materials, 2016, 31(2): 171-179.
Material | Method | (a=b)/nm | c/nm | ρ/(g·cm-3) | V/nm3 |
---|---|---|---|---|---|
LiNbO3 | Exp | 0.51483 | 1.3863 | 0.131821[ | |
LDA | 0.52332 | 1.4131 | 4.395 | 0.33514 | |
GGA | 0.52447 | 1.4222 | 4.251 | 0.33999 | |
PBEsol | 0.51531 | 1.3837 | 4.630 | 0.31821[ | |
LiTaO3 | Exp | 0.5147 | 1.3766 | 0.31585[ | |
GGA | 0.5104 | 1.3546 | 7.434 | 0.32610 | |
LDA | 5.050 | 13.386 | 7.433 | 0.29578 | |
LDA | 5.129 | 13.938 | 7.400 | 0.31763[ |
表1 晶格参数(a, c)、密度ρ和体积V
Table 1 Lattice constants (a, c), density ρ and volume V
Material | Method | (a=b)/nm | c/nm | ρ/(g·cm-3) | V/nm3 |
---|---|---|---|---|---|
LiNbO3 | Exp | 0.51483 | 1.3863 | 0.131821[ | |
LDA | 0.52332 | 1.4131 | 4.395 | 0.33514 | |
GGA | 0.52447 | 1.4222 | 4.251 | 0.33999 | |
PBEsol | 0.51531 | 1.3837 | 4.630 | 0.31821[ | |
LiTaO3 | Exp | 0.5147 | 1.3766 | 0.31585[ | |
GGA | 0.5104 | 1.3546 | 7.434 | 0.32610 | |
LDA | 5.050 | 13.386 | 7.433 | 0.29578 | |
LDA | 5.129 | 13.938 | 7.400 | 0.31763[ |
Material | Atom | s | p | d | Total | Charge | Bond | L1/nm | P1 | L2/nm | P2 |
---|---|---|---|---|---|---|---|---|---|---|---|
LiNbO3 | Li | -0.17 | 0 | 0 | -0.17 | 1.17 | O—Nb | 0.1971 | 0.79 | 0.2184 | 0.37 |
O | 1.87 | 4.87 | 0 | 6.75 | -0.75 | O—Li | 0.2084 | -0.06 | 0.2289 | 0.01 | |
Nb | 0.36 | 0.38 | 3.20 | 3.93 | 1.07 | O—O | 0.2869 | ||||
LiTaO3 | Li | 0.22 | 0 | 0 | -0.22 | 1.22 | O—Ta | 0.1852 | 0.82 | 0.2047 | 0.45 |
O | 1.84 | 4.99 | 0 | 6.83 | -0.83 | O—Li | 0.2093 | -0.08 | 0.2230 | 0.01 | |
Ta | 0.38 | 0.41 | 2.94 | 3.73 | 1.27 | O—O | 0.2669 |
表2 LiNbO3和LiTaO3原子轨道电子占据数、各原子静电荷、键长(L1, L2)和电子云重叠布居(P1, P2)
Table 2 Atomic orbital populations, atomic charges, bond lengths (L1, L2), and band populations (P1, P2) of LiNbO3 and LiTaO3
Material | Atom | s | p | d | Total | Charge | Bond | L1/nm | P1 | L2/nm | P2 |
---|---|---|---|---|---|---|---|---|---|---|---|
LiNbO3 | Li | -0.17 | 0 | 0 | -0.17 | 1.17 | O—Nb | 0.1971 | 0.79 | 0.2184 | 0.37 |
O | 1.87 | 4.87 | 0 | 6.75 | -0.75 | O—Li | 0.2084 | -0.06 | 0.2289 | 0.01 | |
Nb | 0.36 | 0.38 | 3.20 | 3.93 | 1.07 | O—O | 0.2869 | ||||
LiTaO3 | Li | 0.22 | 0 | 0 | -0.22 | 1.22 | O—Ta | 0.1852 | 0.82 | 0.2047 | 0.45 |
O | 1.84 | 4.99 | 0 | 6.83 | -0.83 | O—Li | 0.2093 | -0.08 | 0.2230 | 0.01 | |
Ta | 0.38 | 0.41 | 2.94 | 3.73 | 1.27 | O—O | 0.2669 |
Material | Method | C11/GPa | C12/GPa | C13/GPa | C14/GPa | C33/GPa | C44/GPa | C66/GPa |
---|---|---|---|---|---|---|---|---|
LiNbO3 | LDA | 191.7 | 61.8 | 71.7 | 4.6 | 205.1 | 57.7 | 64.9 |
GGA | 160.11 | 9.37 | 19.36 | -12.04 | 161.77 | 63.50 | 75.37 | |
Other work | 203.0 | 53.0 | 75.0 | 9 | 245.0 | 60 | 75[ | |
196.9 | 54.8 | 66.4 | 0 | 225.4 | 58.8[ | |||
LiTaO3 | GGA | 193.6 | 44.1 | 58.9 | 21.7 | 292.1 | 39.3 | 74.7 |
LDA | 235.7 | 64.1 | 97.6 | 11.6 | 256.1 | 60.7 | 85.8 | |
Other work | 233.3 | 47.0 | 80.0 | -11.0 | 275.0 | 94.0[ | ||
235.2 | 63.8 | 87.7 | 0 | 264.1 | 102.1[ |
表3 LiNbO3和LiTaO3晶体弹性常数Cij
Table 3 Elastic constants Cij of LiNbO3 and LiTaO3
Material | Method | C11/GPa | C12/GPa | C13/GPa | C14/GPa | C33/GPa | C44/GPa | C66/GPa |
---|---|---|---|---|---|---|---|---|
LiNbO3 | LDA | 191.7 | 61.8 | 71.7 | 4.6 | 205.1 | 57.7 | 64.9 |
GGA | 160.11 | 9.37 | 19.36 | -12.04 | 161.77 | 63.50 | 75.37 | |
Other work | 203.0 | 53.0 | 75.0 | 9 | 245.0 | 60 | 75[ | |
196.9 | 54.8 | 66.4 | 0 | 225.4 | 58.8[ | |||
LiTaO3 | GGA | 193.6 | 44.1 | 58.9 | 21.7 | 292.1 | 39.3 | 74.7 |
LDA | 235.7 | 64.1 | 97.6 | 11.6 | 256.1 | 60.7 | 85.8 | |
Other work | 233.3 | 47.0 | 80.0 | -11.0 | 275.0 | 94.0[ | ||
235.2 | 63.8 | 87.7 | 0 | 264.1 | 102.1[ |
图5 LiNbO3晶体平面声波三维图(a, b横波模型, c纵波模型)与平面投影图(d~f) (红线和蓝线表示横波, 绿线表示纵波)(LDA)
Fig. 5 The 3-D planar acoustic velocities, in which a and b are transverse wave models, and c longitudinal model, and the plane projected pictures of LiNbO3 with red and blue lines indicating transverse wave velocities, and the green line indicating longitudinal wave velocity (LDA)
图6 LiTaO3晶体平面声波三维图(a, b横波模型, c纵波模型)与平面投影图(d~f) (红线和蓝线表示横波, 绿线表示纵波) (LDA)
Fig. 6 The 3-D plane acoustic velocities, in which a and b are transverse wave models, and c longitudinal model, and the planar projected picture of LiTaO3 crystal with red and blue lines indicating transverse wave velocities, and the green line indicating longitudinal wave velocity (LDA)
Materal | Method | Index | ε(0) | n | ε(∞) |
---|---|---|---|---|---|
LiNbO3 | GGA | 11 | 43.6779 | 2.5401 | 6.4557 |
33 | 30.6094 | 2.4925 | 6.2126 | ||
LDA | 11 | 43.6779 | 2.5587 | 6.5467 | |
33 | 30.6094 | 2.5408 | 6.4980 | ||
Other Work[ | 11 | 50.42 | 2.58 | 6.68 | |
33 | 34.16 | 2.57 | 6.58 | ||
11 | 41.50 | 2.29 | 5.00 | ||
33 | 26.00 | 2.20 | 4.60 | ||
LiTaO3 | GGA | 11 | 47.0227 | 2.1751 | 4.7311 |
33 | 31.9626 | 2.2199 | 4.8637 | ||
LDA | 11 | 34.1709 | 2.2054 | 4.9278 | |
33 | 34.8047 | 2.2236 | 4.9446 |
表5 静态介电常数ε (0)、静态折射率n和光学介电 常数ε(∞)
Table 5 Calculated static dielectric constants ε (0), static refractive indices n and optical permittivity ε (∞)
Materal | Method | Index | ε(0) | n | ε(∞) |
---|---|---|---|---|---|
LiNbO3 | GGA | 11 | 43.6779 | 2.5401 | 6.4557 |
33 | 30.6094 | 2.4925 | 6.2126 | ||
LDA | 11 | 43.6779 | 2.5587 | 6.5467 | |
33 | 30.6094 | 2.5408 | 6.4980 | ||
Other Work[ | 11 | 50.42 | 2.58 | 6.68 | |
33 | 34.16 | 2.57 | 6.58 | ||
11 | 41.50 | 2.29 | 5.00 | ||
33 | 26.00 | 2.20 | 4.60 | ||
LiTaO3 | GGA | 11 | 47.0227 | 2.1751 | 4.7311 |
33 | 31.9626 | 2.2199 | 4.8637 | ||
LDA | 11 | 34.1709 | 2.2054 | 4.9278 | |
33 | 34.8047 | 2.2236 | 4.9446 |
[1] | CHEN WEI-JUN, LU KE-QING, HUI JUAN-LI, et al.Study onnonlinear surface waves along the boundary of LiNbO3 crystals.Acta Physica Sinica, 2015, 64(1): 014204. |
[2] | BUSACCA A C, STIVALA S, CURCIO L, et al.Soft protonxchanged channel waveguides in congruent lithium tantalite for frequency doubling.Optics Express, 2010, 18(25): 25967-25972. |
[3] | KUSHIBIKI J, TAKANAGA I, ARAKAWA M, et al.Accurate measurements of the acoustical physical constants of LiNbO3 and LiTaO3 single crystals.IEEE Transactions on Ultrasonics ferroelectrics and Frequency Control, 1999, 46(5): 1315-1323. |
[4] | ABD-ALLA A N, ASKAR N A. Calculation of bulk acoustic wave propagation velocities in trigonal piezoelectric smart materials.Applied Mathematics & Information Sciences, 2014, 8(4): 1625-1632. |
[5] | LIU MEI-NAN, XUE DONG-FENG, LI KE-YAN.Soft-chemistry synthesis of LiNbO3 crystallites. Journal of Alloys and Compounds, 2008, 449(1): 28-31. |
[6] | GONG XIN-XIN, FANG MING, FEI GUAN-TAO, et al.LiTaO3 microbubes: thelayered structure and the increased Curie temperature. Royal Society of Chemistry, 2015, 5: 31615-31621. |
[7] | YANG JIN, LONG JIAN-PING, YANG LI-JUN.First-principles investigations of the physical properties of lithium niobate and lithium tantalite.Physica B, 2013, 425(12): 12-16. |
[8] | TOYOURA K, OHTA M, NAKAMURA A, et al.First-principles study on phase transition and ferroelectricity in lithium niobate and tantalate. Journal of Applied Physics, 2015, 118(6): 64103. |
[9] | LI JIN, ZHOU XIAN-MING, ZHU WEN-JIN, et al.Ashock- induced phase transformation in a LiTaO3 crystal.Journal of Applied Physics, 2007, 102(8): 083503. |
[10] | SANG DAN-DAN, WANG QING-LIN, HAN CHONG, et al.Electronic and optical properties of lithium niobate under high pressure: A first-principles study. Chinese Physics B, 2015, 24(7): 077104. |
[11] | LIU YUE, ZHU HAO-NAN, PEI ZI-DONG, et al.Molecular dynamic simulations of surface morphology and pulsed laser deposition growth of lithium niobate thin films on silicon substrate.Chinese Physics B, 2015, 24(5):056802. |
[12] | NAKAMURA K, HIGUCHI S, OHNUMA T.First-principles in vestigation of pressure-induced phase transition in LiNbO3.Journal of Applied Physics, 2012, 111(3):033522. |
[13] | MUKAIDE T, YAGI T, MIYAJIMA N, et al.High pressure and high temperature phase transformations in LiNbO3. Journal of Applied Physics, 2003, 93(7): 3852-3858. |
[14] | WANG FAN-HOU, YANG JUN-SHENG, HUANG DUO-HUI, et al.Study on magnetic and optical properties of Mn-deped LiNbO3 by using the first principles.Acta Physica Sinica, 2015, 64(9): 097102. |
[15] | REICHENBACH P, KAMPFE T, THIESSEN A, et al.Multiphton photoluminescence contrast in switched Mg: LiNbO3 and Mg:LiTaO3 single crystals.Applied Physics Letters, 2014, 105(12): 122906. |
[16] | ZHAO BAI-QIANG, ZHANG YUN, QIU XIAO-YAN, et al.First-principles study of the electronic structures and absorptionspectrum of Fe: Mg: LiNbO3 crystals.Acta Physica Sinica, 2015, 64(12): 124210. |
[17] | MAMOUN S, MERAD A E, GUILBERT L.Energy band gap and optical properties of lithium niobate from ab initio calculations.Computational Materials Science, 2013, 79: 125-131. |
[18] | SHAO DONG-YUAN, CHENG NAN-PU, CHEN ZHI-QIAN, et al.First-principles studies electronic structures and optical properties of LiNbO3 under high pressure.Journal of Atomic and Molecular Physics, 2014, 31(6): 6-13. |
[19] | RIMEIKA R, SEREIKA A, ČIPLYS D.Acoustoelectric effects in reflection of leaky acoustic waves from LiTaO3 crystal surface coated with metal film.Applied Physics Letters, 2011, 98(5): 052909. |
[20] | ANISIMKIN V I.Anisotropy of the acoustic plate modes in ST-Quartz and 128 degrees Y-LiNbO3.IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2014, 61(1): 120-132. |
[21] | ALSHITS V I, LOTHE J.Acoustic axes in trigonal crystals.Wave Motion, 2006, 43(3): 177-192. |
[22] | ČIPLYS D, RIMEIKA R.Measurements of electromechanical coupling coefficient for surface acoustic waves in proton exchanged lithium niobate.Ultragarsas, 1999, 3(33): 14-20. |
[23] | TAKANAGA I, KUSHIBIKI J.A method of determining acoustical physical constants for piezoelectric materials by line-focus-beam acoustic microscopy.IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2002, 49(7): 893-904. |
[24] | OHGAKI M, TANAKA K, MARUMO F.Anharmonic thermal vibration in a crystal of lithium(I) tantalum(V) trioxide, LiTaO3.Mineralogical Journal, 1989, 14(8): 373-382. |
[25] | HOHENBERG P, KOHN W.Inhomogeneous electron gas.Physical Review B, 1964, 136(3B): 864-871. |
[26] | CEPERLEY D M, ALDER B J.Ground state of the electrongas by a stochastic method.Physical Review Letters, 1980, 45(7): 566-569. |
[27] | PERDEW J P, BURKE K, ERNZERHOF M.Generalized gradient approximation made simple.Physical Review Letters, 1996, 77(18): 3865-3868. |
[28] | VANDERBILT D.Soft self-consistent pseudopotentials in a generalized eigenvalue formalism.Physical Review B, 1990, 41(11): 7892-7895. |
[29] | MONKHORST H J, PACK J D.Special points for Brillouin-zone integrations.Physical Review B, 1976, 13(12): 5188-5192. |
[30] | BROYDEN C G.The convergence of a class of double-rank minimization algorithms 1. General Considerations.Ima Journal of Applied Mathematics, 1970, 6(1): 76-90. |
[31] | FLETCHER R.A new approach to variable metric algorithms.Computer Journal, 1970, 13(3): 317-322. |
[32] | GOLDFARB D.A family of variable-metric methods derived by variational means.Mathematics of Computation, 1970, 24(109): 23-26. |
[33] | SHANNO D F.Conditioning of quasi-newton methods for function minimization.Mathematics of Computation, 1970, 24(4): 647-656. |
[34] | OZISIK H, COLAKOGLU K, OZISIK H B, et al.Structural, elastic, and lattice dynamical properties of Germanium diiodide (GeI2).Computational Materials Science, 2010, 50(2): 349-355. |
[35] | 陈纲, 廖理几. 晶体物理学基础. 北京: 科学出版社, 1992(2): 238-276. |
[1] | 张守超, 陈洪雨, 刘洪飞, 杨羽, 李欣, 刘德峰. 6H-SiC中子辐照肿胀高温回复及光学特性研究[J]. 无机材料学报, 2023, 38(6): 678-686. |
[2] | 杨颖康, 邵怡晴, 李柏良, 吕志伟, 王路路, 王亮君, 曹逊, 吴宇宁, 黄荣, 杨长. Cl掺杂对CuI薄膜发光性能增强研究[J]. 无机材料学报, 2023, 38(6): 687-692. |
[3] | 文志勤, 黄彬荣, 卢涛仪, 邹正光. 压力对PbTiO3结构和热物性质影响的第一性原理研究[J]. 无机材料学报, 2022, 37(7): 787-794. |
[4] | 孙铭, 邵溥真, 孙凯, 黄建华, 张强, 修子扬, 肖海英, 武高辉. RGO/Al复合材料界面性质第一性原理研究[J]. 无机材料学报, 2022, 37(6): 651-659. |
[5] | 肖美霞, 李苗苗, 宋二红, 宋海洋, 李钊, 毕佳颖. 表面端基卤化Ti3C2 MXene应用于锂离子电池高容量电极材料的研究[J]. 无机材料学报, 2022, 37(6): 660-668. |
[6] | 袁罡, 马新国, 贺华, 邓水全, 段汪洋, 程正旺, 邹维. 平面应变对二维单层MoSi2N4能带结构和光电性质的影响[J]. 无机材料学报, 2022, 37(5): 527-533. |
[7] | 冯清影, 刘东, 张莹, 冯浩, 李强. 太阳能驱动的两步热化学循环二氧化碳裂解反应活性材料的热力学与第一性原理评价[J]. 无机材料学报, 2022, 37(2): 223-229. |
[8] | 张弦, 张策, 姜文君, 冯德强, 姚伟. 四元BiMnVO5的合成、电子结构与可见光催化性能研究[J]. 无机材料学报, 2022, 37(1): 58-64. |
[9] | 彭军辉, TIKHONOV Evgenii. 空位对Hf-Ta-C体系的结构、力学性质及电子性质影响的第一性原理研究[J]. 无机材料学报, 2022, 37(1): 51-57. |
[10] | 张晓君, 李佳乐, 邱吴劼, 杨淼森, 刘建军. 钠离子电池正极材料P2-Nax[Mg0.33Mn0.67]O2的电化学活性研究[J]. 无机材料学报, 2021, 36(6): 623-628. |
[11] | 向晖, 全慧, 胡艺媛, 赵炜骞, 徐波, 殷江. 类石墨烯单层结构ZnO和GaN的压电特性对比研究[J]. 无机材料学报, 2021, 36(5): 492-496. |
[12] | 闫宇星, 汪帆, 张珏璇, 李付绍. 空位缺陷对ZnNb2O6光电特性影响的第一性原理研究[J]. 无机材料学报, 2021, 36(3): 269-276. |
[13] | 赵林艳, 刘阳思, 席晓丽, 马立文, 聂祚仁. 基于第一性原理计算的纳米氧化钨研究进展[J]. 无机材料学报, 2021, 36(11): 1125-1136. |
[14] | 赵宇鹏,贺勇,张敏,史俊杰. 新型二维Zr2CO2/InS异质结可见光催化产氢性能的第一性原理研究[J]. 无机材料学报, 2020, 35(9): 993-998. |
[15] | 孙顶, 丁彦妍, 孔令炜, 张玉红, 郭秀娟, 魏立明, 张力, 张立新. Mg掺杂Cu2ZnSnS4的第一性原理研究[J]. 无机材料学报, 2020, 35(11): 1290-1294. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||