First principles study of structure and property of Nb<sup>5+</sup>-doped SrTiO<sub>3</sub>

Gong Ling-Yun; Zhang Ping; Chen qian; Lou Zhi-Hao; Xu Jie; Gao Feng

doi:10.7498/aps.70.20211241

Abstract

The modification of SrTiO₃ materials by doping Nb⁵⁺ ions in B-site is studied through using the first-principles method to calculate the electronic structure, optical properties, mechanical properties and thermal properties at different Nb⁵⁺ doping concentrations. The calculation results show that as the doping content of Nb⁵⁺ increases, the lattice parameters increase. After being doped with Nb⁵⁺, SrTiO₃ changes from an indirect band gap compound into a direct band gap compound. Doping Nb⁵⁺ can reduce the reflection coefficient, absorption coefficient, and energy loss of SrTiO₃material, which can be used to modify its optical properties. Additionally, the brittleness of SrTiO₃material is improved through doping Nb⁵⁺. As the doping content of Nb⁵⁺increases, the elastic modulus of the material hardly changes, the shear modulus and Young's modulus decrease, the Poisson's ratio increases, and the Debye temperature decreases, and both the lattice thermal conductivity and the theoretical minimum lattice thermal conductivity decrease as well.

Keywords:

Authors and contacts

1.
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China
2.
School of Chemistry and Chemical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Corresponding author: Gao Feng, gaofeng@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51672219) and International Cooperation Project of Key R&D Plan of Shaanxi Province, China(Grant No. 2020KW-032)

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References

[1]	Huang W, Nechache R, Li S, Chaker M, Rosei F 2016 Am. Ceram. Soc. 99 226 Google Scholar
[2]	李守委 2015 硕士学位论文 (哈尔滨: 哈尔滨工业大学) Li S W 2015 M. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)
[3]	Jing P P, Lan W, Su Q, Xie E Q 2015 Beilstein J. Nanotechnol. 6 1281 Google Scholar
[4]	Zhang T F, Tang X G, Xiang Q, Jiang Y P 2018 J. Alloys Compd. 730 516 Google Scholar
[5]	Blennow P, Hagen A, HansenK K, Wallenberg L R, Mogensen M 2008 Solid State Ion. 179 2047 Google Scholar
[6]	Gerblinger J, Meixner H 1991 Sens. Actuators B Chem. 4 99 Google Scholar
[7]	Ham Y S, Koh J H 2009 Ferroelectrics 382 85 Google Scholar
[8]	Nakano Y, Ichinose N 1990 J. Mater. Res. 5 2910 Google Scholar
[9]	Iwashina K, Kudo A 2011 J. Am. Chem. Soc. 133 13272 Google Scholar
[10]	Rheinheimer W, Bäurer M, Handwerker C A, Blendell J E, Hoffmann M J 2015 Acta Mater. 95 111 Google Scholar
[11]	王欣 2017 硕士学位论文 (西安: 西安理工大学) Wang X 2017 M. S. Thesis (Xi'an: Xi'an University of Technology) (in Chinese)
[12]	常亮亮 2014 材料开发与应用 29 89 Chang L L 2014 Development and Application of Materials 29 89
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[14]	Tomio T, Miki H, Tabata H, Kawai T, Kawai S 1994 J. Appl. Phys. 76 5886 Google Scholar
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[16]	Benrekia A R, Benkhettou N, Nassour A, Driz M, Sahnoun M, Lebèguec S 2012 Phys. Rev., B Condens. Matter 407 2632 Google Scholar
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[19]	Guo X G, Chen X S, Lu W 2003 Solid State Commun. 126 441 Google Scholar
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[21]	Nishiyama J, Kanehara K, Takeda H, Tsurumi T, Hoshina T 2019 J. Ceram. Soc. Japan 127 357 Google Scholar
[22]	Guo X G, Chen X, Sun Y L, Sun L Z, Zhou X H, Lu W 2003 Phys. Lett. A 317 501 Google Scholar
[23]	Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B:Condens. Matter 49 16223 Google Scholar
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图 1 晶胞结构　(a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃

Figure 1. Cell structure: (a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃.

DownLoad: Full-Size Img PowerPoint

图 2 能带结构图　(a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃

Figure 2. Band structure: (a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃.

DownLoad: Full-Size Img PowerPoint

图 3 态密度图　(a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃

Figure 3. Density of states: (a) SrTiO₃; (b) SrTi_0.875Nb_0.125O₃; (c) SrTi_0.75Nb_0.25O₃.

DownLoad: Full-Size Img PowerPoint

图 4 SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃的光学性质　(a) 介电常数实部与虚部; (b)折射系数与消光系数

Figure 4. Optical properties of SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃: (a) Real and imaginary part of the dielectric function; (b) refraction coefficient and extinction coefficient.

DownLoad: Full-Size Img PowerPoint

图 5 SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃的吸收系数与 (a)能量和 (b)波长的关系图

Figure 5. Relationship between absorption coefficients of SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃ and (a) energy; (b) wavelength.

DownLoad: Full-Size Img PowerPoint

图 6 SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃的光学性质　(a)反射系数; (b)能量损失谱

Figure 6. Optical properties of SrTiO₃, SrTi_0.875Nb_0.125O₃ and SrTi_0.75Nb_0.25O₃ (a) Reflection coefficient; (b) energy loss spectrum.

DownLoad: Full-Size Img PowerPoint

图 7 SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃的热导率　(a) κ_slack; (b) κ_min

Figure 7. Thermal conductivity of SrTiO₃, SrTi_0.875Nb_0.125O₃, SrTi_0.75Nb_0.25O₃: (a) κ_slack; (b) κ_min.

DownLoad: Full-Size Img PowerPoint

表 1 SrTi_1–xNb_xO₃晶胞参数(a = b = c, 单位: nm)

Table 1. Cell parameters of SrTi_1–xNb_xO₃ (a = b = c, unit: nm).

	GGA(380 V)	Experimental results	Error (380 eV)/%
SrTiO₃	0.3939	0.3905 (PDF 84-0444)	0.87
SrTi_0.875Nb_0.125O₃	0.3957	0.3950^[14]	0.18
SrTi_0.75Nb_0.25O₃	0.3972	0.3980^[14]	–0.20

DownLoad: CSV

表 2 SrTi_1–xNb_xO₃弹性刚度张量 (单位: GPa)

Table 2. Elastic constants (Unit: GPa) of SrTi_1–xNb_xO₃.

	SrTiO₃ (Caculation)^[16]	SrTiO₃ (Experiment)^[32]	SrTiO₃	SrTi_0.875Nb_0.125O₃	SrTi_0.75Nb_0.25O₃
C₁₁	318.6	317.0	311.1	299.1	306.3
C₁₂	99.3	102.5	97.2	105.9	122.9
C₄₄	109.8	123.5	109.4	99.4	79.3

DownLoad: CSV

表 3 SrTi_1–xNb_xO₃力学性能参数

Table 3. Mechanical property parameters of SrTi_1–xNb_xO₃.

Parameters	Symbel	SrTiO₃	SrTi_0.875Nb_0.125O₃	SrTi_0.75Nb_0.25O₃
Bulk elastic modulus/GPa	B	168.8	169.7	166.0
Shear modulus/GPa	G	108.3	100.8	78.3
G/B	/	0.64	0.59	0.47
Young's modulus/GPa	E	267.7	252.4	202.9
Poisson's ratio/(m·s^–1)	σ	0.236	0.252	0.296

DownLoad: CSV

表 4 SrTi_1–xNb_xO₃的声速和德拜温度

Table 4. Calculated sound velocity and Debye temperature of SrTi_1–xNb_xO₃.

Parameters	Symbel	SrTiO₃	SrTi_0.875Nb_0.125O₃	SrTi_0.75Nb_0.25O₃
Compression wave velocity/(m·s^–1)	v_p	7916.5	7745.6	7241.4
Shear wave velocity/(m·s^–1)	v_s	4655.3	4460.2	3897.8
Average wave velocity/(m·s^–1)	v_m	4876.2	4694.3	4351.6
Debye temperature/K	Θ_D	630.7	603.9	557.7

DownLoad: CSV

map

[1]	Huang W, Nechache R, Li S, Chaker M, Rosei F 2016 Am. Ceram. Soc. 99 226 Google Scholar
[2]	李守委 2015 硕士学位论文 (哈尔滨: 哈尔滨工业大学) Li S W 2015 M. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)
[3]	Jing P P, Lan W, Su Q, Xie E Q 2015 Beilstein J. Nanotechnol. 6 1281 Google Scholar
[4]	Zhang T F, Tang X G, Xiang Q, Jiang Y P 2018 J. Alloys Compd. 730 516 Google Scholar
[5]	Blennow P, Hagen A, HansenK K, Wallenberg L R, Mogensen M 2008 Solid State Ion. 179 2047 Google Scholar
[6]	Gerblinger J, Meixner H 1991 Sens. Actuators B Chem. 4 99 Google Scholar
[7]	Ham Y S, Koh J H 2009 Ferroelectrics 382 85 Google Scholar
[8]	Nakano Y, Ichinose N 1990 J. Mater. Res. 5 2910 Google Scholar
[9]	Iwashina K, Kudo A 2011 J. Am. Chem. Soc. 133 13272 Google Scholar
[10]	Rheinheimer W, Bäurer M, Handwerker C A, Blendell J E, Hoffmann M J 2015 Acta Mater. 95 111 Google Scholar
[11]	王欣 2017 硕士学位论文 (西安: 西安理工大学) Wang X 2017 M. S. Thesis (Xi'an: Xi'an University of Technology) (in Chinese)
[12]	常亮亮 2014 材料开发与应用 29 89 Chang L L 2014 Development and Application of Materials 29 89
[13]	Ohta S, Ohta H, Koumoto K 2006 J. Ceram. Soc. Japan 114 102 Google Scholar
[14]	Tomio T, Miki H, Tabata H, Kawai T, Kawai S 1994 J. Appl. Phys. 76 5886 Google Scholar
[15]	Bakhshi H, Sarraf M R, Yourdkhania A, AbdelNabi A A, Mozharivskyj Y 2020 Ceram. Int. 46 3224 Google Scholar
[16]	Benrekia A R, Benkhettou N, Nassour A, Driz M, Sahnoun M, Lebèguec S 2012 Phys. Rev., B Condens. Matter 407 2632 Google Scholar
[17]	Ghebouli B, Ghebouli M A, Chihi T, Fatmi M, Boucetta S, Reffas M 2009 Solid State Commun. 149 2244 Google Scholar
[18]	贠江妮 2010 博士学位论文 (西安: 西北大学) Yun J N 2010 Ph. D. Dissertation (Xi'an: Northwest University) (in Chinese)
[19]	Guo X G, Chen X S, Lu W 2003 Solid State Commun. 126 441 Google Scholar
[20]	Eglitis R I, Kotomin E A 2010 Phys. B:Condens. Matter 405 3164 Google Scholar
[21]	Nishiyama J, Kanehara K, Takeda H, Tsurumi T, Hoshina T 2019 J. Ceram. Soc. Japan 127 357 Google Scholar
[22]	Guo X G, Chen X, Sun Y L, Sun L Z, Zhou X H, Lu W 2003 Phys. Lett. A 317 501 Google Scholar
[23]	Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B:Condens. Matter 49 16223 Google Scholar
[24]	Kohn W, Sham L J 1965 Phys. Rev. A 140 A1133 Google Scholar
[25]	Benthem K V, Elsässer C, French R H 2001 J. Appl. Phys. 90 6156 Google Scholar
[26]	陈敏强, 李廷鱼, 王开鹰, 胡杰, 李朋伟, 胡文秀, 李刚 2017 固体电子学研究与进展 37 316 Chen M Q, Li Y Y, Wang K Y, Hu J, Li P W, Hu W X, Li G 2017 Res. Prog. Solid State Electron. 37 316
[27]	Chen Q, Gao F, Xu J, Cao S Y, Guo Y T, Cheng G H 2019 Ceram. Int. 45 9967 Google Scholar
[28]	Kato H, Kudo A 2002 J. Phys. Chem. B 106 5029 Google Scholar
[29]	侯清玉, 吕致远, 赵春旺 2015 64 017201 Google Scholar Hou Q Y, Lv Z Y, Zhao C W 2015 Acta Phys. Sin. 64 017201 Google Scholar
[30]	Kumar A, Dho J 2013 Curr. Appl. Phys. 13 768 Google Scholar
[31]	刘娜娜, 宋仁伯, 孙翰英, 杜大伟 2008 57 7145 Google Scholar Liu N N, Song R B, Sun H Y, Du D W 2008 Acta Phys. Sin. 57 7145 Google Scholar
[32]	Piskunov S, Heifets E, Eglitis R I, Borstel G 2004 Comput. Mater. Sci. 29 165
[33]	项建英, 黄继华, 陈树海, 梁文建, 赵兴科, 张华 2012 航空材料学报 32 1 Google Scholar Xiang J Y, Huang J H, Chen H S, Liang W J, Zhao X K, Zhang H 2012 J Aeron. Mater. 32 1 Google Scholar
[34]	Pugh S F 1954 Philos. Mag. 45 823 Google Scholar
[35]	Xiang H M, Feng Z H, Li Z P, Zhou Y C 2017 J. Eur. Ceram. Soc. 37 2491
[36]	Wan C L, Pan W, Xu Q, Qin Y X, Wang J D, Qu Z X, Fang M H 2006 Phys. Rev. B 74 144
[37]	Slack G A 1973 J. Phys. Chem. Solids. 34 321 Google Scholar
[38]	Clarke D R 2003 Surf. Coat. Technol. 163-164 67
[39]	Zhang B Y, Wang J, Zou T, Zhang S, Yaer X B, Ding N, Liu C Y, Miao L, Li Y, Wu Y 2015 J. Mater. Chem. C 3 11406 Google Scholar
[40]	Okhay O, Zlotnik S, Xie W, Orlinski K, Gallo M J, Otero G, Fernandes A, Pawlak D, Weidenkaff A, Tkach A 2019 Carbon 143 215 Google Scholar
[41]	Wang K, Wang J, Li Y, Zou T, Wang X H, Li J B, Cao Z, Shi W J, Year X 2018 Chin. Phys. B 27 121
[42]	Liu D, Zhang Y, Kang H, Li J L, Chen Z N, Wang T M 2018 J. Eur. Ceram. Soc. 38 807 Google Scholar

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First principles study of structure and property of Nb⁵⁺-doped SrTiO₃

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First principles study of structure and property of Nb5+-doped SrTiO3

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Corresponding author: Gao Feng, gaofeng@nwpu.edu.cn

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First principles study of structure and property of Nb⁵⁺-doped SrTiO₃