搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Er3+掺杂TiO2的局域结构及电子性质的第一性原理研究

陈光平 杨金妮 乔昌兵 黄陆君 虞静

引用本文:
Citation:

Er3+掺杂TiO2的局域结构及电子性质的第一性原理研究

陈光平, 杨金妮, 乔昌兵, 黄陆君, 虞静

First-principles calculations of local structure and electronic properties of Er3+-doped TiO2

Chen Guang-Ping, Yang Jin-Ni, Qiao Chang-Bing, Huang Lu-Jun, Yu Jing
PDF
HTML
导出引用
  • 三价稀土铒离子(Er3+)掺杂二氧化钛(TiO2)因其优异的光电性能, 在众多稀土掺杂发光晶体材料中脱颖而出, 具有非常广泛的应用前景. 利用CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization)结构搜索方法和第一性原理计算, 成功地预测和探究了三价铒离子掺杂二氧化钛(Er3+:TiO2)晶体的基态结构. 首次报道Er3+掺杂TiO2的最低能量结构具有$P\overline 4 m2$空间对称性. 当Er3+离子掺杂基质晶体时, Er3+离子占据Ti4+离子的位置, 并造成结构畸变, 最终使得Er3+离子的局域对称性由D2d降低为C2v. 通过电子结构计算发现Er3+掺杂TiO2的能带隙值约为2.27 eV, 这表明Er3+离子的掺杂会导致体系的带隙值降低, 但没有改变其半导体性质, 从而在光伏电池和半导体激光器等领域具有更广泛的应用. 这些发现不仅为进一步探索Er3+:TiO2晶体的性质和应用提供了数据参考, 也为探究其他稀土掺杂晶体材料提供了最新的方法.
    Trivalent rare earth erbium ion (Er3+) doped titanium oxide (TiO2) can possess a very wide range of applications due to its excellent optoelectronic properties, thus standing out among many rare-earth-doped luminescent crystals. However, the issues regarding local structure and electronic properties have not been finalized. To address these problems, the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method combined with the first-principles calculations is employed, and many converged structures of Er3+-doped TiO2 are successfully obtained. Further structural optimization is performed by using the VASP (Vienna ab initio simulation package) software package, and we report for the first time that the lowest energy structure of Er3+-doped TiO2 has the $ P\overline 4 $m2 symmetry. It can be observed that the doped Er3+ ions enter into the host crystal and occupy the positions of Ti4+ ions, resulting in structural distortion, which eventually leads the local Er3+ coordination site symmetry to reduce from D2d into C2v. We speculate that there are two reasons: 1) the difference in charge between Er3+ ions and Ti4+ ions leads to charge compensation; 2) the difference between their electron radii is obvious: the radius is 0.0881 for Er3+ ion and 0.0881 for Ti4+ ion. In addition, during the structural search, we also find many metastable structures that may exist at a special temperature or pressure, which play an important role in the studying of structural evolution. When the electronic band structure of the Er3+-doped TiO2 system is calculated, we adopt the method of local density approximation (LDA) combined with the on-site Coulomb repulsion parameter U to accurately describe the strongly correlated system. For the specific value of U, we adopt 3.5 eV and 7.6 eV to describe the strong correlation of 3d electrons of Ti4+ ions and 4f electrons of Er3+ ions, respectively. According to the calculation of electronic properties, the band gap value of Er3+ doped TiO2 is about 2.27 eV, which is lower than that of the host crystal (Eg = 2.40 eV). The results show that the reduction in the band gap is mainly caused by the f state of Er3+ ions. The doping of Er ion does reduce the band gap value, but it does not change the conductivity of the system, which have great application prospect in diode-pumped laser. These findings not only provide the data for further exploring the properties and applications of Er3+:TiO2 crystals, but also present an approach to studying other rare-earth-doped crystalline materials.
      通信作者: 陈光平, chengp205@126.com
    • 基金项目: 国家自然科学基金(批准号: 12075163, 12175129, 11775253, 12175027, 11875010)和四川文理学院科学基金(批准号: 2018SCL008Y)资助的课题.
      Corresponding author: Chen Guang-Ping, chengp205@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12075163, 12175129, 11775253, 12175027, 11875010) and the Science Foundation of Sichuan Arts and Science University, China (Grant No. 2018SCL008Y)
    [1]

    钟淑琳, 仇家豪, 罗文崴, 吴木生 2021 物理学报 70 158203Google Scholar

    Zhong S L, Qiu J H, Luo W W, Wu M S 2021 Acta Phys. Sin. 70 158203Google Scholar

    [2]

    孟勇军, 李洪, 唐建伟, 陈学文 2022 物理学报 71 027801Google Scholar

    Meng Y J, Li H, Tang J W, Chen X W 2022 Acta Phys. Sin. 71 027801Google Scholar

    [3]

    Wu B, Zhao L, Wang Y, Dong H, Yu H 2019 RSC Adv. 9 42228Google Scholar

    [4]

    Menezes L D S, Araújo C B D 2015 J. Braz. Chem. Soc. 26 2405

    [5]

    Stengl V, Bakardjieva S, Murafa N 2009 Mater. Chem. Phys. 114 217Google Scholar

    [6]

    Hassan M S, Amna T, Yang O B, Kim H C, Khil M S 2012 Ceram. Int. 38 5925Google Scholar

    [7]

    Borlaf M, Colomer M T, Moreno R, Ortiz A L 2014 J. Eur. Ceram. Soc. 34 4457Google Scholar

    [8]

    Bao R, Li R, Chen C, Wu H, Xia J, Long C, Li H 2019 J. Phys. Chem. Solid. 126 78Google Scholar

    [9]

    Li J G, Wang X H, Kamiyama H, Ishigaki T, Sekiguchi T 2006 Thin Solid Films 506 292

    [10]

    Agrios A G, Pochat P 2005 J. Appl. Electrochem. 35 655Google Scholar

    [11]

    Camps I, Borlaf M, Toudert J, Andres A D, Colomer M T, Moreno R, Serna R 2018 J. Alloys Compd. 735 2267Google Scholar

    [12]

    Talane T E 2018 M. S. Thesis (Gauteng Province: University of South Africa)

    [13]

    Pablo L I, Laeticia P, Jonathan M, Davide J, Nadia G B, Diego P, Sonia F, Chiara N, Fabrizio G, Daniel M 2017 J. Non-Cryst. Solids 460 161Google Scholar

    [14]

    Mignotte C 2004 Appl. Surf. Sci. 226 355Google Scholar

    [15]

    Talane T E, Mbule P S, Noto L L, Shingange K, Mhlongo G H, Mothudi B M, Dhlamini M S 2018 Mater. Res. Bull. 108 234Google Scholar

    [16]

    Wild J D, Meijerink A, Rath J K, van Sark W G J H M, Schropp R E I 2011 Energy Environ. Sci. 4 4835Google Scholar

    [17]

    Pablo L I, Diego P, Nadia G B, Davide J, Giovanni B, Laeticia P, Daniel M 2018 Nanomaterials 8 20Google Scholar

    [18]

    van den Hoven G N, Koper R J I M, Polman A, Dam C V, Uffelen J W M V, Smit M K 1996 Appl. Phys. Lett. 68 1886Google Scholar

    [19]

    Jia C W, Zhao J G, Duan H G, Xie E Q 2007 Mater. Lett. 61 4389Google Scholar

    [20]

    Fu C Y, Liao J S, Luo W Q, Li R F, Chen X Y 2008 Opt. Lett. 33 953Google Scholar

    [21]

    Luo W Q, Fu C Y, Li R F, Liu Y S, Zhu H M, Chen X Y 2011 Small 7 3046Google Scholar

    [22]

    Ren Z, Wu J, Wang N, Li X 2018 J. Mater. Chem. A 6 15348Google Scholar

    [23]

    Mazierski P, Mikolajczyk A, Grzybd T, Caicedo P N A, Wei Z, Kowalska E, Henry P P, Adriana Z M, Nadolna J 2020 Appl. Surf. Sci. 527 146815Google Scholar

    [24]

    Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063Google Scholar

    [25]

    Wang Y C, Lv J, Zhu L, Lu S H, Yin K T, Li Q, Wang H, Zhang L J, Ma Y M 2015 J. Phys. Condens. Matter. 27 203203Google Scholar

    [26]

    Wang H, Wang Y C, Lv J, Li Q, Zhang L J, Ma Y M 2016 Comput. Mater. Sci. 112 406Google Scholar

    [27]

    Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116Google Scholar

    [28]

    Gao B, Gao P, Lu S, Lv J, Wang Y, Ma Y 2019 Sci. Bull. 64 301Google Scholar

    [29]

    Wang Y, Miao M, Lv J, Zhu L, Yin K, Liu H, Ma Y 2012 J. Chem. Phys. 137 224108Google Scholar

    [30]

    Hafner J 2008 J. Comput. Chem. 29 2044Google Scholar

    [31]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169Google Scholar

    [32]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [33]

    Sanna S, Schmidt W G, Frauenheim T, Gerstmann U 2009 Phys. Rev. B 80 104120Google Scholar

    [34]

    Xiao Y, Ju M, Yuan H K, Yeung Y Y 2021 J. Phys. Chem. C 125 18015Google Scholar

    [35]

    Togo A, Tanaka I 2015 Scr. Mater. 108 1Google Scholar

    [36]

    Phenicie C M, Stevenson P, Welinski S, Rose B C, Asfaw A T, Cava R J, Lyon S A, de Leon N P, Thompson J D 2019 Nano Lett. 19 8928Google Scholar

    [37]

    Mills A, Hunte S L 1997 J. Photochem. Photobiol. A 108 1Google Scholar

    [38]

    Yang J, Hu Y, Jin C, Zhuge L, Wu X 2017 Thin Solid Films 637 9Google Scholar

    [39]

    Pan L, Xiao Y, Kuang X Y, Ju M 2021 Mater. Chem. Phys. 257 123824Google Scholar

    [40]

    Savin A, Nesper R, Wengert S, Fässler T F 1997 Angew. Chem. Int. Ed. Engl. 36 1808Google Scholar

    [41]

    Lu T, Chen F 2011 Acta Phys. Chim. Sin. 27 2786Google Scholar

    [42]

    Fuentealba P, Chamorro E, Santos J C 2007 Theoretical Aspects of Chemical Reactivity 19 57

  • 图 1  通过CALYPSO结构搜索法确定纯TiO2 (a)和Er3+掺杂TiO2 (b)的晶体结构

    Fig. 1.  Crystal structures of the pure TiO2 (a) and Er3+-doped TiO2 (b) by the CALYPSO structure search method.

    图 2  Er3+:TiO2晶体的亚稳态结构

    Fig. 2.  Coordination structures of the metastable for Er3+:TiO2.

    图 3  模拟的(a) TiO2和(b) Er3+掺杂TiO2的XRD图, 并与实验值进行对比

    Fig. 3.  Simulated X-ray diffraction patterns of (a) TiO2 and (b) Er3+-doped TiO2 compared with experimental data.

    图 4  计算的(a) TiO2和(b) Er3+掺杂TiO2的声子谱

    Fig. 4.  Calculated phonon spectra of the (a) TiO2 and (b) Er3+-doped TiO2.

    图 5  采用LDA方法计算的(a) TiO2和(b) Er3+掺杂TiO2的能带结构和态密度

    Fig. 5.  Band structures and the DOS of (a) TiO2 and (b) Er3+-doped TiO2, all calculated by the LDA method.

    图 6  计算得到的Er3+:TiO2电子局域函数 (a)基态结构; (b) (010)平面

    Fig. 6.  Electron localized function of the Er3+:TiO2: (a) Ground-state structure; (b) (010) plane.

    表 1  Er3+:TiO2能量最低结构中所有原子的坐标

    Table 1.  Coordinates of all atoms for the low-energy structure of Er3+:TiO2.

    AtomxyzWyckoff site
    symmetry
    O(1)0.2470.2490.2044j
    O(2)0.7530.7510.2044k
    O(3)0.2490.7530.7962g
    O(4)0.7510.2470.7968l
    O(6)0.7530.2490.2042g
    O(7)0.2500.2470.7964k
    O(8)0.7510.7530.7964j
    O(11)0.2500.0000.5452f
    O(19)0.5000.7530.0362e
    Ti(1)0.0000.2500.2514j
    Ti(2)0.0000.7500.2514k
    Ti(3)0.2500.0000.7492g
    Ti(4)0.7500.0000.7494h
    Ti(10)0.5000.0000.4951d
    Er(1)0.5000.5000.5001c
    下载: 导出CSV

    表 2  Er3+:TiO2的基态结构以及亚稳态结构的晶格参数a, b, c, 原胞体积V, 相对能量∆E

    Table 2.  Structural parameters a, b and c, unit-cell volume, relative energies for the optimized TiO2 and metastable Er3+:TiO2

    Space groupabcV3E/eV
    TiO2I41/amd7.5687.5689.515545.003
    Er3+:TiO2$ P\overline 4 $m27.6827.6829.798578.1930
    Isomer (a)$ P\overline 4 $m27.6817.6819.799578.2130.051
    Isomer (b)Cmmm13.25813.2586.0131051.7640.853
    Isomer (c)Cmmm13.26113.2616.0091051.9880.975
    下载: 导出CSV
  • [1]

    钟淑琳, 仇家豪, 罗文崴, 吴木生 2021 物理学报 70 158203Google Scholar

    Zhong S L, Qiu J H, Luo W W, Wu M S 2021 Acta Phys. Sin. 70 158203Google Scholar

    [2]

    孟勇军, 李洪, 唐建伟, 陈学文 2022 物理学报 71 027801Google Scholar

    Meng Y J, Li H, Tang J W, Chen X W 2022 Acta Phys. Sin. 71 027801Google Scholar

    [3]

    Wu B, Zhao L, Wang Y, Dong H, Yu H 2019 RSC Adv. 9 42228Google Scholar

    [4]

    Menezes L D S, Araújo C B D 2015 J. Braz. Chem. Soc. 26 2405

    [5]

    Stengl V, Bakardjieva S, Murafa N 2009 Mater. Chem. Phys. 114 217Google Scholar

    [6]

    Hassan M S, Amna T, Yang O B, Kim H C, Khil M S 2012 Ceram. Int. 38 5925Google Scholar

    [7]

    Borlaf M, Colomer M T, Moreno R, Ortiz A L 2014 J. Eur. Ceram. Soc. 34 4457Google Scholar

    [8]

    Bao R, Li R, Chen C, Wu H, Xia J, Long C, Li H 2019 J. Phys. Chem. Solid. 126 78Google Scholar

    [9]

    Li J G, Wang X H, Kamiyama H, Ishigaki T, Sekiguchi T 2006 Thin Solid Films 506 292

    [10]

    Agrios A G, Pochat P 2005 J. Appl. Electrochem. 35 655Google Scholar

    [11]

    Camps I, Borlaf M, Toudert J, Andres A D, Colomer M T, Moreno R, Serna R 2018 J. Alloys Compd. 735 2267Google Scholar

    [12]

    Talane T E 2018 M. S. Thesis (Gauteng Province: University of South Africa)

    [13]

    Pablo L I, Laeticia P, Jonathan M, Davide J, Nadia G B, Diego P, Sonia F, Chiara N, Fabrizio G, Daniel M 2017 J. Non-Cryst. Solids 460 161Google Scholar

    [14]

    Mignotte C 2004 Appl. Surf. Sci. 226 355Google Scholar

    [15]

    Talane T E, Mbule P S, Noto L L, Shingange K, Mhlongo G H, Mothudi B M, Dhlamini M S 2018 Mater. Res. Bull. 108 234Google Scholar

    [16]

    Wild J D, Meijerink A, Rath J K, van Sark W G J H M, Schropp R E I 2011 Energy Environ. Sci. 4 4835Google Scholar

    [17]

    Pablo L I, Diego P, Nadia G B, Davide J, Giovanni B, Laeticia P, Daniel M 2018 Nanomaterials 8 20Google Scholar

    [18]

    van den Hoven G N, Koper R J I M, Polman A, Dam C V, Uffelen J W M V, Smit M K 1996 Appl. Phys. Lett. 68 1886Google Scholar

    [19]

    Jia C W, Zhao J G, Duan H G, Xie E Q 2007 Mater. Lett. 61 4389Google Scholar

    [20]

    Fu C Y, Liao J S, Luo W Q, Li R F, Chen X Y 2008 Opt. Lett. 33 953Google Scholar

    [21]

    Luo W Q, Fu C Y, Li R F, Liu Y S, Zhu H M, Chen X Y 2011 Small 7 3046Google Scholar

    [22]

    Ren Z, Wu J, Wang N, Li X 2018 J. Mater. Chem. A 6 15348Google Scholar

    [23]

    Mazierski P, Mikolajczyk A, Grzybd T, Caicedo P N A, Wei Z, Kowalska E, Henry P P, Adriana Z M, Nadolna J 2020 Appl. Surf. Sci. 527 146815Google Scholar

    [24]

    Wang Y C, Lv J, Zhu L, Ma Y M 2012 Comput. Phys. Commun. 183 2063Google Scholar

    [25]

    Wang Y C, Lv J, Zhu L, Lu S H, Yin K T, Li Q, Wang H, Zhang L J, Ma Y M 2015 J. Phys. Condens. Matter. 27 203203Google Scholar

    [26]

    Wang H, Wang Y C, Lv J, Li Q, Zhang L J, Ma Y M 2016 Comput. Mater. Sci. 112 406Google Scholar

    [27]

    Wang Y C, Lv J, Zhu L, Ma Y M 2010 Phys. Rev. B 82 094116Google Scholar

    [28]

    Gao B, Gao P, Lu S, Lv J, Wang Y, Ma Y 2019 Sci. Bull. 64 301Google Scholar

    [29]

    Wang Y, Miao M, Lv J, Zhu L, Yin K, Liu H, Ma Y 2012 J. Chem. Phys. 137 224108Google Scholar

    [30]

    Hafner J 2008 J. Comput. Chem. 29 2044Google Scholar

    [31]

    Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169Google Scholar

    [32]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [33]

    Sanna S, Schmidt W G, Frauenheim T, Gerstmann U 2009 Phys. Rev. B 80 104120Google Scholar

    [34]

    Xiao Y, Ju M, Yuan H K, Yeung Y Y 2021 J. Phys. Chem. C 125 18015Google Scholar

    [35]

    Togo A, Tanaka I 2015 Scr. Mater. 108 1Google Scholar

    [36]

    Phenicie C M, Stevenson P, Welinski S, Rose B C, Asfaw A T, Cava R J, Lyon S A, de Leon N P, Thompson J D 2019 Nano Lett. 19 8928Google Scholar

    [37]

    Mills A, Hunte S L 1997 J. Photochem. Photobiol. A 108 1Google Scholar

    [38]

    Yang J, Hu Y, Jin C, Zhuge L, Wu X 2017 Thin Solid Films 637 9Google Scholar

    [39]

    Pan L, Xiao Y, Kuang X Y, Ju M 2021 Mater. Chem. Phys. 257 123824Google Scholar

    [40]

    Savin A, Nesper R, Wengert S, Fässler T F 1997 Angew. Chem. Int. Ed. Engl. 36 1808Google Scholar

    [41]

    Lu T, Chen F 2011 Acta Phys. Chim. Sin. 27 2786Google Scholar

    [42]

    Fuentealba P, Chamorro E, Santos J C 2007 Theoretical Aspects of Chemical Reactivity 19 57

  • [1] 严志, 方诚, 王芳, 许小红. 过渡金属元素掺杂对SmCo3合金结构和磁性能影响的第一性原理计算. 物理学报, 2024, 73(3): 037502. doi: 10.7498/aps.73.20231436
    [2] 周金萍, 李春梅, 姜博, 黄仁忠. Co和Ni过量影响Co2NiGa合金晶体结构及相稳定性的第一性原理研究. 物理学报, 2023, 72(15): 156301. doi: 10.7498/aps.72.20230626
    [3] 闫小童, 侯育花, 郑寿红, 黄有林, 陶小马. Ga, Ge, As掺杂对锂离子电池正极材料Li2CoSiO4的电化学特性和电子结构影响的第一性原理研究. 物理学报, 2019, 68(18): 187101. doi: 10.7498/aps.68.20190503
    [4] 叶红军, 王大威, 姜志军, 成晟, 魏晓勇. 钙钛矿结构SnTiO3铁电相变的第一性原理研究. 物理学报, 2016, 65(23): 237101. doi: 10.7498/aps.65.237101
    [5] 陈家华, 刘恩克, 李勇, 祁欣, 刘国栋, 罗鸿志, 王文洪, 吴光恒. Ga2基Heusler合金Ga2XCr(X = Mn, Fe, Co, Ni, Cu)的四方畸变、电子结构、磁性及声子谱的第一性原理计算. 物理学报, 2015, 64(7): 077104. doi: 10.7498/aps.64.077104
    [6] 焦照勇, 郭永亮, 牛毅君, 张现周. 缺陷黄铜矿结构Xga2S4 (X=Zn, Cd, Hg)晶体电子结构和光学性质的第一性原理研究. 物理学报, 2013, 62(7): 073101. doi: 10.7498/aps.62.073101
    [7] 王平, 郭立新, 杨银堂, 张志勇. 铝氮共掺杂氧化锌纳米管电子结构的第一性原理研究. 物理学报, 2013, 62(5): 056105. doi: 10.7498/aps.62.056105
    [8] 丁航晨, 施思齐, 姜平, 唐为华. BiFeO3 结构性质与相转变的第一性原理研究. 物理学报, 2010, 59(12): 8789-8793. doi: 10.7498/aps.59.8789
    [9] 张学军, 高攀, 柳清菊. 氮铁共掺锐钛矿相TiO2电子结构和光学性质的第一性原理研究. 物理学报, 2010, 59(7): 4930-4938. doi: 10.7498/aps.59.4930
    [10] 李沛娟, 周薇薇, 唐元昊, 张华, 施思齐. CeO2的电子结构,光学和晶格动力学性质:第一性原理研究. 物理学报, 2010, 59(5): 3426-3431. doi: 10.7498/aps.59.3426
    [11] 吴红丽, 赵新青, 宫声凯. Nb掺杂影响NiTi金属间化合物电子结构的第一性原理计算. 物理学报, 2010, 59(1): 515-520. doi: 10.7498/aps.59.515
    [12] 谭兴毅, 金克新, 陈长乐, 周超超. YFe2B2电子结构的第一性原理计算. 物理学报, 2010, 59(5): 3414-3417. doi: 10.7498/aps.59.3414
    [13] 胡方, 明星, 范厚刚, 陈岗, 王春忠, 魏英进, 黄祖飞. 梯形化合物NaV2O4F电子结构的第一性原理研究. 物理学报, 2009, 58(2): 1173-1178. doi: 10.7498/aps.58.1173
    [14] 宋庆功, 王延峰, 宋庆龙, 康建海, 褚 勇. 插层化合物Ag1/4TiSe2电子结构的第一性原理研究. 物理学报, 2008, 57(12): 7827-7832. doi: 10.7498/aps.57.7827
    [15] 明 星, 范厚刚, 胡 方, 王春忠, 孟 醒, 黄祖飞, 陈 岗. 自旋-Peierls化合物GeCuO3电子结构的第一性原理研究. 物理学报, 2008, 57(4): 2368-2373. doi: 10.7498/aps.57.2368
    [16] 吴红丽, 赵新青, 宫声凯. Nb掺杂对TiO2/NiTi界面电子结构影响的第一性原理计算. 物理学报, 2008, 57(12): 7794-7799. doi: 10.7498/aps.57.7794
    [17] 宋庆功, 姜恩永, 裴海林, 康建海, 郭 英. 插层化合物LixTiS2中Li离子-空位二维有序结构稳定性的第一性原理研究. 物理学报, 2007, 56(8): 4817-4822. doi: 10.7498/aps.56.4817
    [18] 马松华, 方建平, 任清褒. (2+1)维非对称 Nizhnik-Novikov-Veselov系统的新映射解及其局域结构. 物理学报, 2007, 56(12): 6784-6790. doi: 10.7498/aps.56.6784
    [19] 魏 群, 杨子元, 王参军, 许启明. Al2O3:V3+晶体局域结构及其自旋哈密顿参量研究. 物理学报, 2007, 56(4): 2393-2398. doi: 10.7498/aps.56.2393
    [20] 闫文胜, 王文楼, 吴敏昌, 韦世强. 同步辐射XAFS研究高比能LiMn2O4材料的局域结构. 物理学报, 2002, 51(10): 2302-2307. doi: 10.7498/aps.51.2302
计量
  • 文章访问数:  3530
  • PDF下载量:  108
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-09-22
  • 修回日期:  2022-11-14
  • 上网日期:  2022-12-02
  • 刊出日期:  2022-12-24

/

返回文章
返回