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

改进分析型嵌入原子法在W(100)表面声子谱中的应用

张晓军 王安祥 严祥安 陈长乐

引用本文:
Citation:

改进分析型嵌入原子法在W(100)表面声子谱中的应用

张晓军, 王安祥, 严祥安, 陈长乐

Application of the modified analytic embedded atomic method in W(100) surface phonon spectrum

Zhang Xiao-Jun, Wang An-Xiang, Yan Xiang-An, Chen Chang-Le
PDF
HTML
导出引用
  • 在表面晶格动力学理论的框架下, 采用改进分析型嵌入原子法模型模拟W(100)表面沿$\bar \varGamma \bar L$$\bar L\bar M$$\bar \Gamma \bar M$对称方向上的声子色散频谱, 并计算不同对称点处的极化矢量. 按照表面模的判定依据和标记方法绘制不同对称方向上的表面模, 并讨论表面模的分布范围和模式耦合现象. 基于计算所得的极化矢量, 构建近表面原子层的振动态分布, 分析不同对称方向上表面模的局域特征和极化方式. 以极化矢量为考察对象, 直观、形象地展示了表面模色散支之间的避免交叉现象和独立性实交叉现象.
    Based on the theory of surface lattice dynamics, the surface phonon spectrums along three symmetrical directions of $\bar \varGamma \bar L$, $\bar L\bar M$ and $\bar \varGamma \bar M$ are simulated for the W(100) surface by using the modified analytic embedded atom method. The polarization vectors at different symmetrical points are also calculated. According to the criterion and marking method of surface mode, the surface modes along different symmetrical directions are drawn, the distribution range and mode coupling of surface modes are discussed as well. The vibration frequencies of surface modes calculated by us have been compared to available experimental datum and some theoretical values correspondingly. The results display that the present results are general agreement with the referenced experimental or theoretical results. Based on the calculated polarization vector, the surface vibration states are constructed for the atomic layers in the neighboring surface. And the polarization and local features of the surface modes along different symmetrical directions are analyzed. The results show that there are some coupling phenomena between surface mode dispersion, such as avoid crossing and independence crossing. The avoid crossing is found between the surface-mode branch S1 and the surface-mode branch S2 near ${\bar \zeta _y} = 0.32$ along $\bar L\bar M$ direction. In the region, going from $\bar L$ to $\bar M$, S1 changes from y polarization to z polarization, and S2 changes from z polarization to y polarization. The independence crossings exist between surface-mode branch S1 and surface-mode branch S2 at ${\bar \zeta _x} = 0.5$ along $\bar \varGamma \bar L$ direction, and surface-mode branch S2 and surface-mode branch S3 at ${\bar \zeta _x} = 0.5$ along $\bar L\bar M$ direction, respectively. Before and after the crossings, the polarization and local features of the surface modes have not changed. Inspection of the polarization vectors, the coupling phenomena are iconically demonstrated.
      通信作者: 张晓军, xiaoj_zhang@126.com
    • 基金项目: 国际级- 基于原子相干的非线性级联效应控制光孤子传输(61405151)
      Corresponding author: Zhang Xiao-Jun, xiaoj_zhang@126.com
    [1]

    Bagci S, Duman S, Mutuncu H M, Srivastava G P 2009 J. Phys. Chem. Solids 70 444Google Scholar

    [2]

    Barrett C, Wang L W 2016 Comp. Phys. Commun. 200 27Google Scholar

    [3]

    Campi D, Bmasconi M, Benedek G, Graham A P, Toennies J P 2017 Phys. Chem. Chem. Phys. 19 16358Google Scholar

    [4]

    Hayes W W, Amjad A T, Anemone G, Manson J R 2018 Surf. Sci. 678 20Google Scholar

    [5]

    Taleb A A, Anemone G, Farias D, Miranda R 2016 Carbon 99 416Google Scholar

    [6]

    Anton T, Patrick K, Michael M R, Davide C, Marco B 2013 Phys. Rev. B 87 035410Google Scholar

    [7]

    Minamitani E, Takagi N, Arafune R, Thomas F, Komeda T 2018 Prog. Surf. Sci. 93 131Google Scholar

    [8]

    Matsushita S Y, Hu C, Kawamoto E, Kato H, Watanabe K, Suto S 2015 J. Chem. Phys. 143 214702Google Scholar

    [9]

    Hu G, Huang J Q, Wang Y N, Yang T, Dong B J, Wang J Z, Zhao B, Ali S, Zhang Z D 2018 Chin. Phys. B 27 086301Google Scholar

    [10]

    Chen Y, Tong S Y, Kim J S, Kesmodel L L, Rodach T, Bohnen K P, Ho K M 1991 Phys. Rev. B 44 11394Google Scholar

    [11]

    Benedek G, Ellis J, Luo N S, Reichmuth A, Ruggerone P, Toennies J P 1993 Phys. Rev. B 48 4917Google Scholar

    [12]

    杨剑瑜, 邓辉球, 胡望宇 2004 物理学报 53 1946Google Scholar

    Yang J Y, Deng H Q, Hu W Y 2004 Acta Phys. Sin. 53 1946Google Scholar

    [13]

    Yndurain F, Jigato M P 2008 Phys. Rev. Let. 100 205501Google Scholar

    [14]

    Łażewski J, Korecki J, Parlinski K 2007 Phys. Rev. B 75 054303

    [15]

    Benedek G, Bernasconi M, Chis V, Chulkov E, Echenique P M, Hellsing B, Toennies J P 2010 J. Phys.: Condens. Matter 22 084020Google Scholar

    [16]

    Rusina G G, Borisova S D, Chulkov EV 2016 J. Exp. Theor. Phys. 122 283

    [17]

    Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1648Google Scholar

    [18]

    Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1661Google Scholar

    [19]

    Ouyang Y F, Zhang B W, Liao S Z, Jin Z P 1996 Z Phys. B 101 161Google Scholar

    [20]

    Zhang B W, Ouyang Y F, Liao S Z, Jin Z P 1999 Phys. B 262 218Google Scholar

    [21]

    Hu W Y, Shu X L, Zhang B W 2002 Comp. Mater. Sci. 23 175Google Scholar

    [22]

    Luo W H, Hu W Y, Su K L, Liu F S 2013 Appl. Surf. Sci. 265 375Google Scholar

    [23]

    Jin H S, Pak J Y, Jong Y S 2017 Appl. Phys. A 123 257

    [24]

    Zhang X J, Chen C L, Feng F L 2013 Chin. Phys. B 22 096301Google Scholar

    [25]

    Fasolino A, Tosatti E 1987 Phys. Rev. B 35 4264Google Scholar

    [26]

    Zhang X J, Chen C L 2016 Chin. Phys. B 25 016301Google Scholar

    [27]

    Nelson J S, Sowa E C, Murray S D 1988 Phys. Rev. Let. 61 1977Google Scholar

    [28]

    Ernst H J, Hulpke E, Toennies J P 1992 Phys. Rev. B 46 16081Google Scholar

    [29]

    Joubert D P 1988 J. Phys. C: Solid State Phys. 21 4233Google Scholar

    [30]

    Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17Google Scholar

    [31]

    Heid R, Bohnen K P 2003 Phys. Rep. 387 151Google Scholar

  • 图 1  W(100)表面结构 (a)正格点阵; (b)倒格点阵

    Fig. 1.  Surface structure of W (100): (a) Crystal lattice; (b) reciprocal lattice.

    图 2  W(100)表面声子谱

    Fig. 2.  Surface phonon spectrum of W(100)

    图 3  W(100)表面模分布

    Fig. 3.  Surface mode distribution of W(100).

    图 4  S1表面模的计算结果和实验值的比较

    Fig. 4.  Comparison of calculated S1 surface mode and experimental value.

    图 5  W(100)近表面原子层沿$\bar \varGamma \bar L$对称方向的局域振动态密度 (a)第1原子层; (b)第2原子层; (c)第3原子层; (d)第4原子层

    Fig. 5.  Local vibrational state density of atomic layers in the vicinity of the W (100) surface along $\bar \varGamma \bar L$ symmetry direction: (a) First atomic layer; (b) second atomic layer; (c) third atomic layer; (d) fourth atomic layer.

    图 6  W(100)近表面原子层沿$\bar \varGamma \bar L$对称方向的极化态密度 (a)第1原子层沿x方向极化; (b)第1原子层沿y方向极化; (c)第1原子层沿z方向极化; (d)第2原子层沿x方向极化; (e)第2原子层沿y方向极化; (f)第2原子层沿z方向极化

    Fig. 6.  Polarizing state density of atomic layers in the vicinity of the W (100) surface along $\bar \varGamma \bar L$ symmetry direction: (a) x polarization for first atomic layer; (b) y polarization for first atomic layer; (c) z polarization for first atomic layer; (d) x polarization for second atomic layer; (e) y polarization for second atomic layer; (f) z polarization for second atomic layer.

    图 7  W(100)近表面原子层沿$\bar L\bar M$方向上的局域振动态密度 (a)第1原子层; (b)第2原子层; (c)第3原子层; (d)第4原子层

    Fig. 7.  Local vibrational state density of atomic layers in the vicinity of the W (100) surface along $\bar L\bar M$ symmetry direction: (a) First atomic layer; (b) second atomic layer; (c) third atomic layer; (d) fourth atomic layer.

    图 8  W(100)近表面原子层沿$\bar L\bar M$方向的极化态密度 (a)第1原子层沿x方向极化; (b)第1原子层沿y方向极化; (c)第1原子层沿z方向极化; (d)第2原子层沿x方向极化; (e)第2原子层沿y方向极化; (f)第2原子层沿z方向极化

    Fig. 8.  Polarizing state density of atomic layers in the vicinity of the W (100) surface along $\bar L\bar M$ symmetry direction: (a) x polarization for first atomic layer; (b) y polarization for first atomic layer; (c) z polarization for first atomic layer; (d) x polarization for second atomic layer; (e) y polarization for second atomic layer; (f) z polarization for second atomic layer.

    图 9  W(100)近表面原子层沿$\bar \Gamma \bar M$方向上的局域振动态密度 (a)第1原子层; (b)第2原子层

    Fig. 9.  Local vibration state density of atomic layers in the vicinity of the W (100) surface along $ \bar \Gamma \bar M $ symmetry direction: (a) First atomic layer; (b) second atomic layer.

    图 10  W(100)近表面原子层沿$\bar \varGamma \bar M$方向的极化态密度 (a)第1原子层沿x方向极化; (b)第1原子层沿y方向极化; (c)第1原子层沿z方向极化; (d)第2原子层沿x方向极化; (e)第2原子层沿y方向极化; (f)第2原子层沿z方向极化

    Fig. 10.  Polarizing state density of atomic layers in the vicinity of the W (100) surface along $\bar \varGamma \bar M$ symmetry direction: (a) x polarization for first atomic layer; (b) y polarization for first atomic layer; (c) z polarization for first atomic layer; (d) x polarization for second atomic layer; (e) y polarization for second atomic layer; (f) z polarization for second atomic layer.

    表 1  高对称点处W(100)表面模振动频率的比较 (单位: THz)

    Table 1.  Comparison of vibration frequencies of surface modes for W(100) at high symmetry points (in units of THz).

    Method$\bar L$$\bar M$
    S1S2S3S6S1S3
    MAEAM2.633.083.335.033.443.91
    EHA2.772.983.465.313.273.99
    TBM3.213.343.815.063.463.93
    下载: 导出CSV
  • [1]

    Bagci S, Duman S, Mutuncu H M, Srivastava G P 2009 J. Phys. Chem. Solids 70 444Google Scholar

    [2]

    Barrett C, Wang L W 2016 Comp. Phys. Commun. 200 27Google Scholar

    [3]

    Campi D, Bmasconi M, Benedek G, Graham A P, Toennies J P 2017 Phys. Chem. Chem. Phys. 19 16358Google Scholar

    [4]

    Hayes W W, Amjad A T, Anemone G, Manson J R 2018 Surf. Sci. 678 20Google Scholar

    [5]

    Taleb A A, Anemone G, Farias D, Miranda R 2016 Carbon 99 416Google Scholar

    [6]

    Anton T, Patrick K, Michael M R, Davide C, Marco B 2013 Phys. Rev. B 87 035410Google Scholar

    [7]

    Minamitani E, Takagi N, Arafune R, Thomas F, Komeda T 2018 Prog. Surf. Sci. 93 131Google Scholar

    [8]

    Matsushita S Y, Hu C, Kawamoto E, Kato H, Watanabe K, Suto S 2015 J. Chem. Phys. 143 214702Google Scholar

    [9]

    Hu G, Huang J Q, Wang Y N, Yang T, Dong B J, Wang J Z, Zhao B, Ali S, Zhang Z D 2018 Chin. Phys. B 27 086301Google Scholar

    [10]

    Chen Y, Tong S Y, Kim J S, Kesmodel L L, Rodach T, Bohnen K P, Ho K M 1991 Phys. Rev. B 44 11394Google Scholar

    [11]

    Benedek G, Ellis J, Luo N S, Reichmuth A, Ruggerone P, Toennies J P 1993 Phys. Rev. B 48 4917Google Scholar

    [12]

    杨剑瑜, 邓辉球, 胡望宇 2004 物理学报 53 1946Google Scholar

    Yang J Y, Deng H Q, Hu W Y 2004 Acta Phys. Sin. 53 1946Google Scholar

    [13]

    Yndurain F, Jigato M P 2008 Phys. Rev. Let. 100 205501Google Scholar

    [14]

    Łażewski J, Korecki J, Parlinski K 2007 Phys. Rev. B 75 054303

    [15]

    Benedek G, Bernasconi M, Chis V, Chulkov E, Echenique P M, Hellsing B, Toennies J P 2010 J. Phys.: Condens. Matter 22 084020Google Scholar

    [16]

    Rusina G G, Borisova S D, Chulkov EV 2016 J. Exp. Theor. Phys. 122 283

    [17]

    Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1648Google Scholar

    [18]

    Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1661Google Scholar

    [19]

    Ouyang Y F, Zhang B W, Liao S Z, Jin Z P 1996 Z Phys. B 101 161Google Scholar

    [20]

    Zhang B W, Ouyang Y F, Liao S Z, Jin Z P 1999 Phys. B 262 218Google Scholar

    [21]

    Hu W Y, Shu X L, Zhang B W 2002 Comp. Mater. Sci. 23 175Google Scholar

    [22]

    Luo W H, Hu W Y, Su K L, Liu F S 2013 Appl. Surf. Sci. 265 375Google Scholar

    [23]

    Jin H S, Pak J Y, Jong Y S 2017 Appl. Phys. A 123 257

    [24]

    Zhang X J, Chen C L, Feng F L 2013 Chin. Phys. B 22 096301Google Scholar

    [25]

    Fasolino A, Tosatti E 1987 Phys. Rev. B 35 4264Google Scholar

    [26]

    Zhang X J, Chen C L 2016 Chin. Phys. B 25 016301Google Scholar

    [27]

    Nelson J S, Sowa E C, Murray S D 1988 Phys. Rev. Let. 61 1977Google Scholar

    [28]

    Ernst H J, Hulpke E, Toennies J P 1992 Phys. Rev. B 46 16081Google Scholar

    [29]

    Joubert D P 1988 J. Phys. C: Solid State Phys. 21 4233Google Scholar

    [30]

    Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17Google Scholar

    [31]

    Heid R, Bohnen K P 2003 Phys. Rep. 387 151Google Scholar

  • [1] 韦宜政, 孙超, 朱启轩. 浅海矢量声场极化特性的深度分布规律. 物理学报, 2024, 0(0): . doi: 10.7498/aps.73.20231767
    [2] 陈昊鹏, 聂永杰, 李国倡, 魏艳慧, 胡昊, 鲁广昊, 李盛涛, 朱远惟. 聚合物分散液晶薄膜的极化特性及其对电光性能的影响. 物理学报, 2023, 72(17): 177701. doi: 10.7498/aps.72.20230664
    [3] 张东, 娄文凯, 常凯. 半导体极性界面电子结构的理论研究. 物理学报, 2019, 68(16): 167101. doi: 10.7498/aps.68.20191239
    [4] 秦黎, 李泽亚, 许静平, 张利伟, 羊亚平. 磁单负材料板附近的原子的自发辐射场分布. 物理学报, 2015, 64(1): 014206. doi: 10.7498/aps.64.014206
    [5] 孙凯, 何志群, 梁春军. 多温度阶梯退火对有机聚合物太阳能电池器件性能的影响. 物理学报, 2014, 63(4): 048801. doi: 10.7498/aps.63.048801
    [6] 屈少华, 曹万强. 球形无规键无规场模型研究弛豫铁电体极化效应. 物理学报, 2014, 63(4): 047701. doi: 10.7498/aps.63.047701
    [7] 黄旭东, 冯玉军, 唐帅. 掺镧锆锡钛酸铅陶瓷极化强度变化量对电子发射电流强度的影响. 物理学报, 2012, 61(8): 087702. doi: 10.7498/aps.61.087702
    [8] 陈龙天, 程用志, 聂彦, 龚荣洲. 人工异向介质调控电磁波极化特性的实验与仿真研究. 物理学报, 2012, 61(9): 094203. doi: 10.7498/aps.61.094203
    [9] 赵静波, 杜红亮, 屈绍波, 张红梅, 徐卓. A位等价与非等价取代对(K0.5Na0.5)NbO3陶瓷极化的影响. 物理学报, 2011, 60(10): 107701. doi: 10.7498/aps.60.107701
    [10] 尚英, 霍丙忠, 孟春宁, 袁景和. 并矢格林函数下的球形超透镜. 物理学报, 2010, 59(11): 8178-8183. doi: 10.7498/aps.59.8178
    [11] 孙贤明, 哈恒旭. 基于反射太阳光反演气溶胶光学厚度和有效半径. 物理学报, 2008, 57(9): 5565-5570. doi: 10.7498/aps.57.5565
    [12] 杨凤霞, 张端明, 邓宗伟, 姜胜林, 徐 洁, 李舒丹. 基体电导率对0-3型铁电复合材料高压极化行为及损耗的影响. 物理学报, 2008, 57(6): 3840-3845. doi: 10.7498/aps.57.3840
    [13] 顾晓玲, 郭 霞, 吴 迪, 李一博, 沈光地. 表面InGaN厚度对GaN基发光二极管特性的影响. 物理学报, 2008, 57(2): 1220-1223. doi: 10.7498/aps.57.1220
    [14] 顾晓玲, 郭 霞, 吴 迪, 徐丽华, 梁 庭, 郭 晶, 沈光地. GaN基多量子阱发光二极管的极化效应和载流子不均匀分布及其影响. 物理学报, 2007, 56(8): 4977-4982. doi: 10.7498/aps.56.4977
    [15] 朱振业, 王 彪, 郑 跃, 王 海, 李青坤, 李晨亮. 应力作用下铁电超晶格BaTiO3/SrTiO3的结构和极化的第一性原理研究. 物理学报, 2007, 56(10): 5986-5989. doi: 10.7498/aps.56.5986
    [16] 刘 洪, 蒲朝辉, 龚小刚, 王志红, 黄惠东, 李言荣, 肖定全, 朱建国. (111)取向(Pb,La)TiO3铁电薄膜中90°纳米带状畴与热释电性能的研究. 物理学报, 2006, 55(11): 6123-6128. doi: 10.7498/aps.55.6123
    [17] 徐任信, 陈 文, 周 静. 聚合物电导率对0-3型压电复合材料极化性能的影响. 物理学报, 2006, 55(8): 4292-4297. doi: 10.7498/aps.55.4292
    [18] 张春福, 郝 跃, 游海龙, 张金凤, 周小伟. 界面电偶极子对GaN/AlGaN/GaN光电探测器紫外/太阳光选择比的影响. 物理学报, 2005, 54(8): 3810-3814. doi: 10.7498/aps.54.3810
    [19] 郭冠军, 苏 林, 毕思文. 风成海面的极化辐射. 物理学报, 2005, 54(5): 2448-2452. doi: 10.7498/aps.54.2448
    [20] 杨剑瑜, 邓辉球, 胡望宇. Ag(110)表面声子谱的分析型EAM模型计算. 物理学报, 2004, 53(6): 1946-1951. doi: 10.7498/aps.53.1946
计量
  • 文章访问数:  4822
  • PDF下载量:  67
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-12-17
  • 修回日期:  2020-01-22
  • 刊出日期:  2020-04-05

/

返回文章
返回