Surface Energy of Diamond Cubic Crystals and Anisotropy Analysis Revealed by Empirical Electron Surface Models
Advances in Materials
Volume 8, Issue 2, June 2019, Pages: 61-69
Received: Apr. 2, 2019; Accepted: May 9, 2019; Published: Jun. 10, 2019
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Author
Baoqin Fu, Key Laboratory for Radiation Physics and Technology, Institute of Nuclear Science and Technology, Sichuan University, Chengdu, China
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Abstract
A detailed knowledge of structure and energy of surface contributes to the understanding of many surface phenomena. In this work, the surface energies of 48 surfaces for diamond cubic crystals, including diamond (C), silicon (Si), germanium (Ge), and tin (Sn), have been studied by using the empirical electron surface models (EESM), extended from empirical electron theory (EET). Under the first-order approximation, the calculated results are in agreement with experimental and other theoretical values. It is also found that the surface energies show a strong anisotropy. The surface energy of close-packed plane (111) is the lowest one among all index surfaces. For the low-index planes, the order of the surface energies is γ(111) < γ(110) < γ(001). And surface energy variation of the (hk0) and (hhl) planes with the change of the included angle has also been analyzed. EESM provides a good basis for the surface research, and it also can be extended to more material systems. Such extensive results from the same theoretical model should be useful to understand various surface processes for theorists and experimentalists.
Keywords
Surface Energy, Empirical Electron Theory, Dangling Bond, Valence Electron Structure, Diamond Cubic Crystals
To cite this article
Baoqin Fu, Surface Energy of Diamond Cubic Crystals and Anisotropy Analysis Revealed by Empirical Electron Surface Models, Advances in Materials. Vol. 8, No. 2, 2019, pp. 61-69. doi: 10.11648/j.am.20190802.14
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Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
H. Y. Xu, Y. B. Zhang, Y. Yuan, B. Q. Fu, A. Godfrey, G. De Temmerman, W. Liu, X. Huang, Observations of orientation dependence of surface morphology in tungsten implanted by low energy and high flux D plasma, J. Nucl. Mater. 443 (2013) 452–457.
[2]
Y. Z. Jia, W. Liu, B. Xu, G. N. Luo, C. Li, B. Q. Fu, G. De Temmerman, Nanostructures and pinholes on W surfaces exposed to high flux D plasma at high temperatures, J. Nucl. Mater. 463 (2015) 312–315.
[3]
B. Q. Fu, W. Liu, Z. L. Li, Calculation of the surface energy of bcc-metals with the empirical electron surface model, Appl. Surf. Sci. 255 (2009) 8511–8519.
[4]
B. Q. Fu, M. J. Qiu, L. Zhai, A. L. Yang, Q. Hou, Molecular dynamics studies of low-energy atomic hydrogen cumulative bombardment on tungsten surface, Nucl. Instruments Methods Phys. Res. Sect. B. (2018). doi: 10.1016/j.nimb.2018.03.027.
[5]
A. L. Yang, M. J. Qiu, J. C. Cui, Q. Hou, B. Q. Fu, Effects of temperature and surface orientation on migration behaviors of helium atoms near titanium surfaces, Nucl. Instruments Methods Phys. Res. Sect. B. (2018). doi: 10.1016/j.jnucmat.2015.06.011.
[6]
B. Q. Fu, W. S. Lai, Y. Yuan, H. Y. Xu, W. Liu, Study of interaction between low energetic hydrogen and tungsten surface by molecular dynamics simulations, Nucl. Instruments Methods Phys. Res. Sect. B. 303 (2013) 162–164.
[7]
F. R. de Boer, R. Boom, W. C. M. Matterns, A. R. Miedema, A. K. Niessen, Cohesion in Metals: Transition Metal Alloys (Cohesion and Structure), North-Holland, Amsterdam. (1988) 217.
[8]
V. K. Kumikov, K. B. Khokonov, On the measurement of surface free energy and surface tension of solid metals, J. Appl. Phys. 54 (1983) 1346–1350.
[9]
W. R. Tyson, W. A. Miller, Surface free energies of solid metals: Estimation from liquid surface tension measurements, Surf. Sci. 62 (1977) 267–276.
[10]
D. T. Read, J. W. Dally, A new method for measuring the strength and ductility of thin films, J. Mater. Res. 8 (1993) 1542.
[11]
A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, Absolute surface energies of group-IV semiconductors: Dependence on orientation and reconstruction, Phys. Rev. B. 65 (2002) 115318.
[12]
T. Hashimoto, Y. Morikawa, K. Terakura, Stability and electronic structure of Ge (1 0 5) 1 × 2: A first-principles theoretical study, Surf. Sci. 576 (2005) 61–66.
[13]
J. E. Northrup, Structure of Si (100) H: Dependence on the H chemical potential, Phys. Rev. B. 44 (1991) 1419.
[14]
K. Takahashi, C. Nara, T. Yamagishi, T. Onzawa, Calculation of surface energy and simulation of reconstruction for Si (111) 3×3, 5×5, 7×7, and 9×9 DAS structure, Appl. Surf. Sci. 151 (1999) 299–301.
[15]
T. Halicioglu, Calculation of surface energies for low index planes of diamond, Surf. Sci. 259 (1991) L714–L718.
[16]
J. M. Zhang, H. Y. Li, K. W. Xu, V. Ji, Calculation of surface energy and simulation of reconstruction for diamond cubic crystals (0 0 1) surface, Appl. Surf. Sci. 254 (2008) 4128–4133.
[17]
M. I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Phys. Rev. B. 46 (1992) 2727–2742.
[18]
C. V. Ciobanu, V. B. Shenoy, C. Z. Wang, K. M. Ho, Structure and stability of the Si (1 0 5) surface, Surf. Sci. 544 (2003) L715–L721.
[19]
F. C. Chuang, C. V. Ciobanu, C. Predescu, C. Z. Wang, K. M. Ho, Structure of Si (1 1 4) determined by global optimization methods, Surf. Sci. 578 (2005) 183–195.
[20]
B. Q. Fu, W. Liu, Z. L. Li, Calculation of the surface energy of hcp-metals with the empirical electron theory, Appl. Surf. Sci. 255 (2009) 9348–9357.
[21]
B. Q. Fu, W. Liu, Z. L. Li, Calculation of the surface energy of fcc-metals with the empirical electron surface model, Appl. Surf. Sci. 256 (2010) 6899–6907.
[22]
B. Q. Fu, W. Liu, Z. L. Li, Surface energy calculation of alkali metals with the empirical electron surface model, Mater. Chem. Phys. 123 (2010) 658–665.
[23]
R. H. Yu, The empirical electron theory of solids and molecules, Chinese Sci. Bull. 23 (1978) 217–219.
[24]
B. Q. Fu, Z. L. Li, W. Liu, Covalent electron density analysis and surface energy calculation of gold with the empirical electron surface model, Int. J. Miner. Metall. Mater. 18 (2011) 676–682.
[25]
Z. L. Li, J. Xu, B. Q. Fu, W. Liu, Influence of aluminium on the valence electron density of the interface between the bond-coat and the thermally grown oxide of thermal barrier coatings, Solid State Sci. 10 (2008) 1434–1444. doi: 10.1016/j.solidstatesciences.2008.01.030.
[26]
Z. L. Li, H. Bin Xu, S. K. Gong, Texture formation mechanism of vapor-deposited fee thin film on polycrystal or amorphous substrate, J. Phys. Chem. B. 108 (2004) 15165–15171.
[27]
C. Lin, Y. Zhao, G. Yin, Calculation of the lattice constant of solids with the use of valence electron structure parameters, Comput. Mater. Sci. 97 (2015) 86–93.
[28]
W. D. Xu, R. L. Zhang, R. H. Yu, Calculations for crystal cohesive energy of transition metal compound, Sci. China (Series A). 32 (1989) 351.
[29]
B. B. Pate, The diamond surface: atomic and electronic structure, Surf. Sci. 165 (1986) 83–142.
[30]
W. J. Huisman, J. F. Peters, S. A. de Vries, E. Vlieg, W. S. Yang, T. E. Derry, J. F. van der Veen, Structure and morphology of the as-polished diamond (111)-1× 1 surface, Surf. Sci. 387 (1997) 342–353.
[31]
Q. Jiang, H. M. Lu, M. Zhao, Modelling of surface energies of elemental crystals, J. Phys. Condens. Matter. 16 (2004) 521–530.
[32]
X. M. Huang, S. Togawa, S. I. Chung, K. Terashima, S. Kimura, Surface tension of a Si melt: influence of oxygen partial pressure, J. Cryst. Growth. 156 (1995) 52–58.
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