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Ba(Mg1/3Nb2/3)O3 (BMN)复合钙钛矿陶瓷具有高介电常数和高品质因子等介电性能, 预示了其在光学领域的应用前景. 本文采用第一性原理方法计算了BMN的电子结构, 对其本征光学性能进行分析和预测. 对固相合成六方相BMN的XRD 测试结果进行Rietveld精修(加权方差因子Rwp=6.73%, 方差因子Rp=5.05%), 在此基础上建立晶体结构模型并对其进行几何优化. 运用基于密度泛函理论(DFT)的平面波赝势方法, 对六方相BMN晶体模型的能带、态密度和光学性质进行理论计算. 结果表明BMN的能带结构为间接带隙, 禁带宽度Eg=2.728 eV. Mg-O和Ba-O以离子键结合为主, Nb-O以共价键结合为主, 费米面附近的能带主要由O-2p和Nb-4d 态电子占据, 形成了d-p轨道杂化. 修正带隙后, 计算了BMN沿[100]和[001]方向上的复介电函数、吸收系数和反射率等光学性质. 结果表明, BMN近乎光学各向同性, 在可见光区, 其本征透过率为77%T n <2.14, 并伴随一定的色散现象. 实验测试结果与理论计算结果相吻合.
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关键词:
- Ba(Mg1/3Nb2/3) O3 /
- 电子结构 /
- 光学性能 /
- 第一性原理
Transparent ceramics have been widely researched for their broad range of applications, e.g. from optical windows to laser and optoelectronic switches. However, the challenge is to obtain the optical materials with high refractive index to miniaturize optical functional elements, such as lens for optical information storage and waveguides for flat optical components. The hexagonal complex perovskite Ba(Mg1/3Nb2/3)O3(BMN) ceramic, being widely researched as a type of microwave dielectric ceramics, presents the excellent dielectric properties such as high dielectric constant and high Q value, which indicate its potential application as optical materials. In this paper, the electronic structure of BMN is calculated by using the first principle method, to analyze and predict its intrinsic optical properties. The hexagonal complex perovskite BMN ceramic is synthesized using conventional solid-state reaction at 1600 ℃ for 24 h. The structure parameters are obtained through Rietveld refinement of X-ray diffraction data. The crystal model is established, based on the Rietveld refinement result of the XRD test on synthesized BMN (with the weighted profile R-factor Rwp=6.73%, the profile R-factor Rp=5.05%), and then the crystal geometry optimized. With the optimized crystal model, the energy band structure, density of states and optical properties of BMN are calculated using the first principle method based on density functional theory (DFT) with local density approximation (LDA). Results show that BMN has an indirect band gap of 2.728 eV. There are the strong ionic interactions between Mg and O as well as Ba and O, while there is covalent interaction between Nb and O. The energy band near the Fermi level is mainly occupied by O-2p and Nb-4d electrons, which forms the d-p hybrid orbits. With real band gap correction, the optical properties of BMN are obtained from the definition of direct transition probability and the Kramers-Kronig dispersion relations along the polarization directions [100] and [001], including the complex dielectric function, absorption coefficients and reflectivity, respectively. It is shown that the optical properties of BMN are nearly isotropic. According to the Lambert-Beer's law, the intrinsic transmittance of BMN ranges from 77% to 83% in the visible region, and its refractive index is dispersive, ranging from 1.91 to 2.14. Experimental test results are consistent with the theoretical calculation results.-
Keywords:
- Ba(Mg1/3Nb2/3) O3 /
- electronic structure /
- optical property /
- first principle
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[27] Dai Y D 2009 Ph. D. Dissertation (Wuhan: Wuhan University of Technology) (in Chinese) [代亚东 2009 博士学位论文 (武汉: 武汉理工大学)]
[28] Shen J, Zhou J, Zhu J, Sun H J, Liu H X, Chen W 2011 Ferroelectrics 356 111
[29] Tauc J, Abeles F 1972 Optical Properties of Solids vol. 372 (Amsterdam, The Netherlands: North-Holland Publishers)
[30] Rinke P, Qteish A, Neugebauer J, Scheffler M 2008 Phys. Stat. Sol. 245 929
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[32] Liu X D, Jiang E Y, Li Z Q, Song Q G 2008 Appl. Phys. Lett. 92 252104
[33] Gou H, Gao F, Zhang J 2010 Comput. Mater. Sci. 49 552
[34] Singh D J 2008 Appl. Phys. Lett. 92 201908
[35] Cheng Z X, Wang X L 2008 Appl. Phys. Lett. 92 261915
[36] Cheng J, Agrawal D, Zhang Y, Roy R 2002 Mater. Lett. 56 587
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[1] Zhang B, Zhang H J, Yang Q H, Lu S Z 2010 Acta Phys. Sin. 59 1333 (in Chinese) [张斌, 张浩佳, 杨秋红, 陆神洲 2010 59 1333]
[2] Rubat du Merac M, Kleebe H J, Mller M M, Reimanis I E 2013 J. Am. Ceram. Soc. 96 3341
[3] Huang Y H, Jiang D L, Zhang J X, Lin Q L 2010 Acta Phys. Sin. 59 0300 (in Chinese) [黄毅华, 江东亮, 张景贤, 林庆玲 2010 59 0300]
[4] Lu S Z, Yang Q H 2012 Chin. Phys. B 21 047801
[5] Ruan W, Li G, Zeng J, Kamzina L S, Zeng H, Zheng L, Ding A 2012 J. Am. Ceram. Soc. 95 2103
[6] Tamura H, Sagala D A, Wakino K 1986 Jpn. J. Appl. Phys. 25 787
[7] Sagala D A, Koyasu S 1993 J. Am. Ceram. Soc. 76 2433
[8] Lu C H, Tsai C C 1996 J. Mater. Res. 11 1219
[9] Ohsato H 2012 Ceram. Int. 38 S141
[10] Kaminskii A, Tanaka N, Eichler H, Rhee H, Ueda K, Takaichi K, Shirakawa A, Tokurakawa M, Kintaka Y, Kuretake S 2007 Laser Phys. Lett. 4 819
[11] Kintaka Y, Kuretake S, Tanaka N, Kageyama K, Takagi H 2010 J. Am. Ceram. Soc. 93 1114
[12] Huang Y H, Jiang D L, Zhang J X, Lin Q L 2010 Ceram. Int. 36 1615
[13] Krell A, Hutzler T 2007 US Patent 7247589
[14] Shi Y X, Shen J, Zhou J, Xu J, Chen W, Qi Y Y, Jiao L 2015 Ceram. Int. 41 253
[15] Ching W Y, Xu Y N 1994 J. Am. Ceram. Soc. 77 404
[16] Sui P F, Dai Z H, Zhang X L, Zhao Y C 2015 Chin. Phys. Lett. 32 077101
[17] Huang D H, Yang J S, Cao Q L, Wan M J, Li Q, Sun L, Wang F H 2014 Chin. Phys. Lett. 31 037103
[18] Takahashi T 2000 Jpn. J. Appl. Phys. 39 5637
[19] Dai Y D, Zhao G H, Liu H X 2009 J. Appl. Phys. 105 034111
[20] Diao C L, Wang C H, Luo N N, Qi Z M, Shao T, Wang Y Y, Lu J, Wang Q C, Kuang X J, Fang L, Shi F, Jing X P 2014 J. Appl. Phys. 115 114103
[21] Materials Studio Release 4.0.0.02005 Accelrys Software Inc. San Diego
[22] Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condens. Matter 14 2717
[23] Lejaeghere K, Speybroeck V V, Oost G V, Cottenier S 2014 Crit. Rev. Solid State 39 1
[24] Shen X C 2002 Spectroscopy and Optical Properties of Semiconductor (Beijing: Science Press) pp76-94 (in Chinese) [沈学础 2002 半导体光谱和光学性质(北京: 科学出版社 第76–94页]
[25] Fang R C 2001 Solid State Spectroscopy(Hefei: Press of University of Science and Technology of China) pp71-75 (in Chinese) [方容川 2001 固体光谱学(合肥: 中国科学技术大学出版社) 第71–75页]
[26] Janaswamy S, Murthy G S, Dias E D, Murthy V R K 2002 Mater. Lett. 55 414
[27] Dai Y D 2009 Ph. D. Dissertation (Wuhan: Wuhan University of Technology) (in Chinese) [代亚东 2009 博士学位论文 (武汉: 武汉理工大学)]
[28] Shen J, Zhou J, Zhu J, Sun H J, Liu H X, Chen W 2011 Ferroelectrics 356 111
[29] Tauc J, Abeles F 1972 Optical Properties of Solids vol. 372 (Amsterdam, The Netherlands: North-Holland Publishers)
[30] Rinke P, Qteish A, Neugebauer J, Scheffler M 2008 Phys. Stat. Sol. 245 929
[31] Samantaray C B, Sim H, Hwang H 2005 Microelectron. J. 36 725
[32] Liu X D, Jiang E Y, Li Z Q, Song Q G 2008 Appl. Phys. Lett. 92 252104
[33] Gou H, Gao F, Zhang J 2010 Comput. Mater. Sci. 49 552
[34] Singh D J 2008 Appl. Phys. Lett. 92 201908
[35] Cheng Z X, Wang X L 2008 Appl. Phys. Lett. 92 261915
[36] Cheng J, Agrawal D, Zhang Y, Roy R 2002 Mater. Lett. 56 587
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