International Journal of Minerals, Metallurgy and Materials
Volume 18, Number 6, Dec 2011, Page 676
DOI: 10.1007/s12613-011-0495-9
Corresponding author: Zhi-lin Li E-mail: lizl@mail.buct.edu.cn
© University of Science and Technology Beijing and Springer-Verlag Berlin Heidelberg 2011
Covalent electron density analysis and surface energy calculation of gold with
the empirical electron surface model
Bao-qin Fu
1,2)
, Zhi-lin Li
1)
, and Wei Liu
2)
1) College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China
2) Laboratory of Advanced Materials, Department of Material Science and Engineering, Tsinghua University, Beijing 100084, China
(Received: 28 November 2010; revised: 11 January 2011; accepted: 30 February 2011)
Abstract: Based on the empirical electron surface model (EESM), the covalent electron density of dangling bonds (CEDDB) was calculated
for various crystal planes of gold, and the surface energy was calculated further. Calculation results show that CEDDB has a great influence
on the surface energy of various index surfaces and the anisotropy of the surface. The calculated surface energy is in agreement with experi-
mental and other theoretical values. The calculated surface energy of the close-packed (111) surface has the lowest surface energy, which
agrees with the theoretical prediction. Also, it is found that the spatial distribution of covalent bonds has a great influence on the surface en-
ergy of various index surfaces. Therefore, CEDDB should be a suitable parameter to describe and quantify the dangling bonds and surface
energy of various crystal surfaces.
Keywords: surface energy; dangling bonds; covalent bonds; electron density; gold
[This work was financially supported by the Beijing Natural Science Foundation, China (No.2072014) and the Ph.D. Program Foundation of
the Ministry of Education of China (No.200800100006).]
1. Introduction
The interpretation of many material surface phenomena
depends on the surface structure and property. Because of its
importance in chemisorptions and catalytic processes [1-2],
the properties of gold surfaces have been extensively studied
in recent years. Film texture is of particular interest owing to
the anisotropic property variations observed in the films. For
example, the adsorption behavior of pyrazine on Au (111),
Au (100), and Au (110) electrodes is different [3]. The ani-
sotropy of the surface free energy has a large influence on
the decay rate of periodic surface profiles at temperatures
below the roughening temperature [4]. However, few ex-
perimental surface energy data can be found in literatures
[5-8] and these data include uncertainties of unknown mag-
nitude. Therefore, to determine the surface energy theoreti-
cally is very important. During the last decade the
first-principles calculations [9-16] and semi-empirical
methods [17-24] have been applied to predict the surface
energy of some metals. However, the first-principles calcu-
lation is a tough job, especially for a large scale structure.
Although the reliability of the calculation results of most
semi-empirical methods depend strongly on the selection of
the potential functions because all such methods are based
on some existing experimental results, many semi-empirical
methods are developed to simplify the calculations.
The empirical electron surface model (EESM) has been
successfully applied in the simulation of crystal surfaces
[25-28]. The starting point of EESM is the valence electron
structure (VES) calculated by the empirical electron theory
(EET)
[29-32], which was established by Yu. Because of its
simplicity, EET has been applied successfully in predicting