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

doi:10.7498/aps.69.20191910

摘要

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$\bar \varGamma \bar L$、$\bar L\bar M$和$\bar \Gamma \bar M$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.

关键词:

表面声子谱 /
表面模 /
局域 /
极化

Abstract

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.

Keywords:

作者及机构信息

1.
西安工程大学理学院, 西安　710048

2.
西北工业大学理学院, 西安　710072

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)

Authors and contacts

1.
School of Science, Xi’an Polytechnic University, Xi’an 710048, China

2.
School of Science, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: Zhang Xiao-Jun, xiaoj_zhang@126.com

文章全文 : translate this paragraph

参考文献

[1]	Bagci S, Duman S, Mutuncu H M, Srivastava G P 2009 J. Phys. Chem. Solids 70 444 Google Scholar
[2]	Barrett C, Wang L W 2016 Comp. Phys. Commun. 200 27 Google Scholar
[3]	Campi D, Bmasconi M, Benedek G, Graham A P, Toennies J P 2017 Phys. Chem. Chem. Phys. 19 16358 Google Scholar
[4]	Hayes W W, Amjad A T, Anemone G, Manson J R 2018 Surf. Sci. 678 20 Google Scholar
[5]	Taleb A A, Anemone G, Farias D, Miranda R 2016 Carbon 99 416 Google Scholar
[6]	Anton T, Patrick K, Michael M R, Davide C, Marco B 2013 Phys. Rev. B 87 035410 Google Scholar
[7]	Minamitani E, Takagi N, Arafune R, Thomas F, Komeda T 2018 Prog. Surf. Sci. 93 131 Google Scholar
[8]	Matsushita S Y, Hu C, Kawamoto E, Kato H, Watanabe K, Suto S 2015 J. Chem. Phys. 143 214702 Google 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 086301 Google 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 11394 Google Scholar
[11]	Benedek G, Ellis J, Luo N S, Reichmuth A, Ruggerone P, Toennies J P 1993 Phys. Rev. B 48 4917 Google Scholar
[12]	杨剑瑜, 邓辉球, 胡望宇 2004 53 1946 Google Scholar Yang J Y, Deng H Q, Hu W Y 2004 Acta Phys. Sin. 53 1946 Google Scholar
[13]	Yndurain F, Jigato M P 2008 Phys. Rev. Let. 100 205501 Google 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 084020 Google 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 1648 Google Scholar
[18]	Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1661 Google Scholar
[19]	Ouyang Y F, Zhang B W, Liao S Z, Jin Z P 1996 Z Phys. B 101 161 Google Scholar
[20]	Zhang B W, Ouyang Y F, Liao S Z, Jin Z P 1999 Phys. B 262 218 Google Scholar
[21]	Hu W Y, Shu X L, Zhang B W 2002 Comp. Mater. Sci. 23 175 Google Scholar
[22]	Luo W H, Hu W Y, Su K L, Liu F S 2013 Appl. Surf. Sci. 265 375 Google 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 096301 Google Scholar
[25]	Fasolino A, Tosatti E 1987 Phys. Rev. B 35 4264 Google Scholar
[26]	Zhang X J, Chen C L 2016 Chin. Phys. B 25 016301 Google Scholar
[27]	Nelson J S, Sowa E C, Murray S D 1988 Phys. Rev. Let. 61 1977 Google Scholar
[28]	Ernst H J, Hulpke E, Toennies J P 1992 Phys. Rev. B 46 16081 Google Scholar
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施引文献

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.

下载: 全尺寸图片幻灯片

图 2 W(100)表面声子谱

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

下载: 全尺寸图片幻灯片

图 3 W(100)表面模分布

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

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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 $\bar L$ $\bar M$
S₁ S₂ S₃ S₆ S₁ S₃

MAEAM 2.63 3.08 3.33 5.03 3.44 3.91
EHA 2.77 2.98 3.46 5.31 3.27 3.99
TBM 3.21 3.34 3.81 5.06 3.46 3.93

下载: 导出CSV

map

[1]	Bagci S, Duman S, Mutuncu H M, Srivastava G P 2009 J. Phys. Chem. Solids 70 444 Google Scholar
[2]	Barrett C, Wang L W 2016 Comp. Phys. Commun. 200 27 Google Scholar
[3]	Campi D, Bmasconi M, Benedek G, Graham A P, Toennies J P 2017 Phys. Chem. Chem. Phys. 19 16358 Google Scholar
[4]	Hayes W W, Amjad A T, Anemone G, Manson J R 2018 Surf. Sci. 678 20 Google Scholar
[5]	Taleb A A, Anemone G, Farias D, Miranda R 2016 Carbon 99 416 Google Scholar
[6]	Anton T, Patrick K, Michael M R, Davide C, Marco B 2013 Phys. Rev. B 87 035410 Google Scholar
[7]	Minamitani E, Takagi N, Arafune R, Thomas F, Komeda T 2018 Prog. Surf. Sci. 93 131 Google Scholar
[8]	Matsushita S Y, Hu C, Kawamoto E, Kato H, Watanabe K, Suto S 2015 J. Chem. Phys. 143 214702 Google 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 086301 Google 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 11394 Google Scholar
[11]	Benedek G, Ellis J, Luo N S, Reichmuth A, Ruggerone P, Toennies J P 1993 Phys. Rev. B 48 4917 Google Scholar
[12]	杨剑瑜, 邓辉球, 胡望宇 2004 53 1946 Google Scholar Yang J Y, Deng H Q, Hu W Y 2004 Acta Phys. Sin. 53 1946 Google Scholar
[13]	Yndurain F, Jigato M P 2008 Phys. Rev. Let. 100 205501 Google 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 084020 Google 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 1648 Google Scholar
[18]	Allen R E, Allredge G P, Wette F W 1971 Phys. Rev. B 4 1661 Google Scholar
[19]	Ouyang Y F, Zhang B W, Liao S Z, Jin Z P 1996 Z Phys. B 101 161 Google Scholar
[20]	Zhang B W, Ouyang Y F, Liao S Z, Jin Z P 1999 Phys. B 262 218 Google Scholar
[21]	Hu W Y, Shu X L, Zhang B W 2002 Comp. Mater. Sci. 23 175 Google Scholar
[22]	Luo W H, Hu W Y, Su K L, Liu F S 2013 Appl. Surf. Sci. 265 375 Google 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 096301 Google Scholar
[25]	Fasolino A, Tosatti E 1987 Phys. Rev. B 35 4264 Google Scholar
[26]	Zhang X J, Chen C L 2016 Chin. Phys. B 25 016301 Google Scholar
[27]	Nelson J S, Sowa E C, Murray S D 1988 Phys. Rev. Let. 61 1977 Google Scholar
[28]	Ernst H J, Hulpke E, Toennies J P 1992 Phys. Rev. B 46 16081 Google Scholar
[29]	Joubert D P 1988 J. Phys. C: Solid State Phys. 21 4233 Google Scholar
[30]	Sklyadneva I Y, Rusina G G, Chulkov E V 1998 Surf. Sci. 416 17 Google Scholar
[31]	Heid R, Bohnen K P 2003 Phys. Rep. 387 151 Google Scholar

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改进分析型嵌入原子法在W(100)表面声子谱中的应用